Method and system for analysing sample fluorophore by generalized least square spectroscopy

Abstract

Aspects of the present disclosure include methods for spectrally resolving light from fluorophores in a sample. A method according to certain embodiments includes detecting light from a sample including a plurality of fluorophores having overlapping fluorescence spectra using a light detection system, and spectrally parsing the light from each fluorophore in the sample using a generalized least square algorithm. In some embodiments, a method includes estimating abundance of one or more fluorophores in a sample (e.g., on a particle). In certain examples, a method includes identifying particles in a sample based on the abundance of each fluorophore and sorting the particles. A method according to some embodiments includes spectrally parsing light from each fluorophore by calculating a spectral demixing matrix for a fluorescence spectrum for each fluorophore. Systems and integrated circuit devices (e.g., field programmable gate arrays) for practicing the subject methods are also provided.

Description

[0001] Cross - reference to related applications

[0002] This application claims the benefit of the filing date of U.S. Provisional Patent Application No. 63 / 622,370, filed on January 18, 2024, under 35 U.S.C.§119 (e), the disclosure of which is hereby incorporated by reference in its entirety. Technical field

[0003] This application relates to methods and systems for spectral analysis of fluorophores in a sample by generalized least squares. Background art

[0004] Flow - type particle sorting systems, such as sorting flow cytometers, are used to sort particles in a fluid sample based on at least one measured characteristic of the particles. In a flow - type particle sorting system, particles (e.g., molecules, analyte - conjugated beads, or single cells) in a fluid suspension pass through a detection region in a flow, where a sensor detects the particles contained in the flow of the type to be sorted. When the sensor detects a particle of the type to be sorted, it triggers a sorting mechanism that selectively separates the particles of interest.

[0005] Particle sensing is typically performed by passing the flow through a detection region where the particles are exposed to illumination light from one or more lasers, and the light - scattering and fluorescence characteristics of the particles are measured. The particles or their components can be labeled with fluorescent dyes for easy detection, and different particles or components can be labeled with spectrally - distinct fluorescent dyes so that multiple different particles or components can be detected simultaneously. Detection is performed using one or more photoelectric sensors to facilitate independent measurement of the fluorescence of each different fluorescent dye.

[0006] To sort the particles in a sample, a droplet - charging mechanism charges the droplets of the flow containing the type of particle to be sorted at the break - point of the flow. The droplets pass through an electrostatic field and are deflected into one or more collection containers based on the polarity and magnitude of the charge on the droplets. Uncharged droplets are not deflected by the electrostatic field. Summary of the invention

[0007] Aspects of the present disclosure include methods for spectrally resolving light from fluorophores in a sample. Methods according to certain embodiments include: detecting light from a sample of multiple fluorophores having overlapping fluorescence spectra using a light detection system, and spectrally resolving the light from each fluorophore in the sample using a generalized least squares algorithm. In some embodiments, the method includes estimating the abundance of one or more fluorophores in the sample (e.g., on a particle). In certain instances, the method includes identifying particles in the sample and sorting the particles based on the abundance of each fluorophore. Methods according to some embodiments include spectrally resolving the light from each fluorophore by calculating a spectral unmixing matrix for the fluorescence spectrum of each fluorophore. Systems and integrated circuit devices (e.g., field programmable gate arrays) for practicing the subject methods are also provided.

[0008] In some embodiments, the sample of interest includes multiple fluorophores, wherein the fluorescence spectrum of each fluorophore overlaps with the fluorescence spectrum of at least one other fluorophore in the sample. In certain instances, the fluorescence spectrum of each fluorophore overlaps with the fluorescence spectrum of at least one other fluorophore in the sample by 10 nm or more, such as 25 nm or more and including 50 nm or more. In some instances, the fluorescence spectrum of one or more fluorophores in the sample overlaps with the fluorescence spectra of two different fluorophores in the sample, such as 10 nm or more, such as 25 nm or more and including 50 nm or more. In other embodiments, the sample of interest includes multiple fluorophores having non-overlapping fluorescence spectra. In these embodiments, the fluorescence spectrum of each fluorophore is adjacent to at least one other fluorophore within a range of 10 nm or less, such as 9 nm or less, such as 8 nm or less, such as 7 nm or less, such as 6 nm or less, such as 5 nm or less, such as 4 nm or less, such as 3 nm or less, such as 2 nm or less and including 1 nm or less.

[0009] In some embodiments, light from the sample is detected by a light detection system in one or more photodetector channels, such as in multiple photodetection channels. In some instances, the light is detected using multiple photodetectors. In some instances, data signals are generated in each photodetector channel in response to the detected light. In some embodiments, real-time spectral resolution of each fluorophore is performed. In some instances, the method includes using an integrated circuit (such as a field programmable gate array (FPGA)) to spectrally resolve the light in real time.

[0010] In some embodiments, the data signal covariance is determined in each photodetector channel. In some instances, the data signal covariance within each photodetector channel includes one or more of an inherent sample variability component and a measurement variability component. In some instances, the data signal covariance includes the electronic noise in each photodetector channel. In some instances, the data signal covariance includes the shot noise in each photodetector channel. In some instances, the data signal covariance varies linearly with the generated data signal. In some instances, the data signal covariance varies quadratically with the generated data signal. In some instances, the data signal covariance is related to two or more of the plurality of photodetector channels. In some instances, the data signal covariance is calculated according to:

[0011] ,

[0012] where:

[0013] is the measured detector signal;

[0014] is the baseline noise component;

[0015] is the Poisson noise component;

[0016] is the Poisson noise coefficient;

[0017] is the quadratic noise component; and

[0018] is the quadratic noise coefficient.

[0019] In some embodiments, the data signal covariance is calculated using a covariance matrix. In some instances, the covariance matrix contains non-zero diagonal values. In certain instances, the covariance is calculated using the covariance matrix according to:

[0020] ,

[0021] where, represents generating a diagonal matrix from the column vector x, and represents the covariance between a and b.

[0022] In some instances, the generalized least squares problem is calculated by multiplying the inverse of the calculated covariance matrix. In some instances, the method includes estimating the data signal covariance based on the fluorescence intensity of two or more photodetectors of the optical detection system. In some instances, the method includes estimating the data signal covariance based on the fluorescence intensity of each in the optical detection channels. In some embodiments, the generalized least squares problem is calculated according to:

[0023] ,

[0024] wherein:

[0025] is a weight matrix;

[0026] is a covariance matrix;

[0027] X is a spectral matrix (overflow matrix);

[0028] y is the detector value measured by a plurality of photodetectors of the light detection system for each cell;

[0029] f is the true fluorophore abundance for each cell; and

[0030] is the estimated (unmixed) fluorophore abundance for each cell.

[0031] In some instances, the method further includes generating a prior estimated covariance matrix. In certain instances, the generalized least squares problem is applied in real time (e.g., using an integrated circuit such as a field programmable gate array). In some instances, a prior noise model is used to estimate each event covariance (e.g., calculating each event covariance matrix in real time). In some instances, the prior noise model uses only the data collected for each specific event. In some instances, the covariance matrix includes an estimate of the entire collected data set. In some instances, the covariance matrix is generated by an iterative optimization method that empirically tunes the covariance matrix to minimize the variance of the unmixed data.

[0032] In some embodiments, the data signal covariance is determined by an estimate of an iterative optimization of the covariance matrix that minimizes the variance of the unmixed data signal. In certain instances, the generalized least squares problem is characterized by a Cholesky decomposition of the covariance matrix. In certain instances, the generalized least squares problem is characterized by calculating the Cholesky decomposition of the covariance matrix and solving a triangular system according to the following to generate a transformed input for the ordinary least squares algorithm:

[0033] Solving to generate , which is the decorrelated and whitened version of the data vector y.

[0034] Solving Generating , which is the corresponding transformed version of the spectral matrix X.

[0035] Transformed system Solve by ordinary least squares, for example, by solving the so-called normal equations .

[0036] In some examples, the method includes finding the least squares solution of a generalized least squares problem. In some examples, the least squares solution of the generalized least squares problem is found by one or more of matrix factorization, matrix factorization, QR factorization, Cholesky factorization, singular value decomposition, LDL factorization, and pre-permutation and post-permutation. In some examples, the method includes finding the least squares solution of the generalized least squares problem by solving the so-called normal equations by Cholesky factorization or LDL factorization, for example, according to the following by Cholesky factorization or LDL factorization:

[0037] ,

[0038] where:

[0039] y is the detector value measured by a plurality of photodetectors of the light detection system of each cell; X is the overflow; and

[0040] G is .

[0041] In some examples, the method includes finding the least squares solution of the generalized least squares problem by Cholesky factorization or LDL factorization according to the following:

[0042] ,

[0043] ,

[0044] , LDL factorization,

[0045] where , lower triangular matrix solution,

[0046] where , diagonal matrix solution,

[0047] , solve , upper triangular matrix solution.

[0048] In some embodiments, the method includes finding the least squares solution of the generalized least squares problem by matrix factorization.

[0049] In some embodiments, the method includes obtaining a least squares solution to the generalized least squares problem by matrix factorization. In some instances, the method includes obtaining a least squares solution to the generalized least squares problem by QR factorization. In some instances, the generalized least squares problem is calculated according to the following using the transformed and (calculated by Cholesky factorization of the covariance matrix above) to calculate the generalized least squares problem:

[0050] , the normal equation of the transformed GLS problem;

[0051] , the QR factorization of the transformed X;

[0052] , permutation;

[0053] , the expanded transpose of QR;

[0054] , which can be eliminated due to orthogonality,

[0055] , triangular solution .

[0056] In some embodiments, the method includes obtaining a least squares solution to the generalized least squares problem by singular value decomposition. In some instances, the singular value decomposition is the product of matrices, where U and V are orthogonal matrices, is a diagonal matrix containing singular values. In some instances, the generalized least squares problem is calculated according to the following using singular value decomposition:

[0057]

[0058]

[0059] ,

[0060] where U and V are orthogonal matrices, and is a diagonal matrix containing singular values. In certain embodiments, the method includes obtaining a least squares solution to the generalized least squares problem by LDL decomposition. In certain embodiments, the method includes solving the least squares solution of the generalized least squares problem by pre-permutation and post-permutation.

[0061] Systems for practicing the subject methods are also provided. Systems according to some embodiments include a light source configured to illuminate a sample including a plurality of fluorophores having overlapping fluorescence spectra; a light detection system including a plurality of photodetectors; and a processor having a memory operably coupled to the processor, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to perform spectral analysis of the light of each fluorophore in the sample using a generalized least squares problem. In some instances, the system is configured to detect light in one or more photodetector channels via the light detection system, such as in a plurality of photodetector channels. In some instances, the system includes a plurality of photodetectors. In some instances, the photodetectors include one or more photomultiplier tubes. In some instances, the light detection system includes a photodetector array. In some instances, the photodetector array includes a charge-coupled device.

[0062] In some embodiments, the memory includes instructions stored thereon that, when executed by the processor, cause the processor to determine the data signal covariance within each photodetector channel. In some instances, the data signal covariance within each photodetector channel includes an inherent sample variability component and a measurement variability component. In some instances, the data signal covariance includes the electronic noise in each photodetector channel. In some instances, the data signal covariance includes the shot noise in each photodetector channel. In some instances, the data signal covariance varies linearly with the generated data signal. In some instances, the data signal covariance varies quadratically with the generated data signal. In some instances, the data signal covariance is related to two or more of the plurality of photodetector channels. In some instances, the memory includes instructions for calculating the data signal covariance according to:

[0063] ,

[0064] where:

[0065] is the measured detector signal;

[0066] is the baseline noise component;

[0067] is the Poisson noise component;

[0068] is the Poisson noise coefficient;

[0069] is the quadratic noise component; and

[0070] is the quadratic noise coefficient.

[0071] In some instances, the memory includes instructions for calculating the covariance of data signals using a covariance matrix. In some instances, the covariance matrix includes non-zero diagonal values. In some instances, the memory includes instructions for calculating covariance using the covariance matrix as follows:

[0072] ,

[0073] where, represents the diagonal matrix generated by the column vector x, and represents the covariance between a and b.

[0074] In some instances, the memory includes instructions for calculating a generalized least squares problem by multiplying the inverse of the calculated covariance matrix. In some instances, the memory includes instructions for estimating the covariance of data signals based on the fluorescence intensities of two or more photodetectors of an optical detection system. In some instances, the memory includes instructions for estimating the covariance of data signals based on the fluorescence intensity of each in the optical detection channels. In some embodiments, the memory includes instructions for calculating a generalized least squares problem as follows:

[0075] ,

[0076] where:

[0077] is the weight matrix;

[0078] is the covariance matrix;

[0079] X is the spectral matrix (overflow matrix);

[0080] y is the detector value measured by multiple photodetectors of the optical detection system for each cell;

[0081] f is the true fluorophore abundance for each cell; and

[0082] is the estimated (unmixed) fluorophore abundance for each cell.

[0083] In some instances, the memory includes instructions for priori estimating the covariance matrix. In certain instances, the memory includes instructions for applying the generalized least squares problem in real time (e.g., using an integrated circuit such as a field programmable gate array). In some instances, a priori noise models are used to estimate the covariance of each event (e.g., calculating the covariance matrix of each event in real time). In some instances, the a priori noise model only uses the data collected for each specific event. In some instances, the covariance matrix includes an estimate of the entire collected data set.

[0084] In some instances, the memory includes instructions to determine the data signal covariance by using an iterative optimization of a covariance matrix that minimizes the variance of the demixed data signals. In certain instances, the memory includes instructions to compute a generalized least squares problem by Cholesky factorization of the covariance matrix. In certain instances, the generalized least squares problem is characterized by computing the Cholesky factorization of the covariance matrix and solving a triangular system according to the following to generate a transformed input for an ordinary least squares algorithm:

[0085] Solve to generate , which is the decorrelated and whitened version of the data vector y.

[0086] Solve Generate , which is the corresponding transformed version of the spectral matrix X.

[0087] The transformed system is solved by ordinary least squares, for example by solving the so-called normal equations .

[0088] In some embodiments, the memory includes instructions to find the least squares solution of a generalized least squares problem. In some instances, the memory includes instructions to find the least squares solution of a generalized least squares problem by one or more of matrix factorization, matrix factorization, QR factorization, Cholesky factorization, singular value factorization, LDL factorization, and pre-permutation and post-permutation. In some instances, the memory includes instructions to find the least squares solution of a generalized least squares problem by solving the so-called normal equations by Cholesky factorization or LDL factorization, for example according to the following by Cholesky factorization or LDL factorization:

[0089] ,

[0090] where:

[0091] y is the detector value measured by a plurality of photodetectors of a light detection system for each cell; X is the overflow; and

[0092] G is .

[0093] In some instances, the memory includes instructions to find the least squares solution of the generalized least squares problem by Cholesky factorization or LDL factorization according to the following:

[0094] ,

[0095] ,

[0096] , LDL decomposition,

[0097] where , lower triangular matrix solution,

[0098] where , diagonal matrix solution,

[0099] , solving , upper triangular matrix solution.

[0100] In some embodiments, the memory includes instructions for obtaining a least squares solution to a generalized least squares problem by matrix factorization.

[0101] In some instances, the memory includes instructions for obtaining a least squares solution to a generalized least squares problem by matrix factorization. In some instances, the memory includes instructions for obtaining a least squares solution to a generalized least squares problem by QR factorization. In some instances, the memory includes instructions for using QR factorization according to the following using the transformed and (calculated by Cholesky decomposition of the covariance matrix described above) to calculate a generalized least squares problem:

[0102] , normal equations of the transformed GLS problem;

[0103] , QR factorization of the transformed X;

[0104] , permutation;

[0105] , expanded transpose of QR;

[0106] , Since orthogonality can be eliminated,

[0107] , triangular solution .

[0108] In some embodiments, the memory includes instructions for obtaining a least squares solution to a generalized least squares problem by singular value decomposition. In some instances, the singular value decomposition is the product matrix, where U and V are orthogonal matrices, is a diagonal matrix containing singular values. In some instances, the memory includes instructions for using singular value decomposition to calculate a generalized least squares problem according to the following:

[0109]

[0110]

[0111] ,

[0112] where U and V are orthogonal matrices, and is a diagonal matrix containing the singular values. In some embodiments, the memory includes instructions for obtaining the least squares solution of the generalized least squares problem by LDL decomposition. In certain embodiments, the memory includes instructions for minimizing the least squares solution of the generalized least squares problem by pre-permutation and post-permutation.

[0113] In some embodiments, the system includes a processor having a memory operatively coupled to the processor, where the memory includes instructions stored thereon that, when executed by the processor, cause the processor to estimate the abundance of one or more fluorophores in a sample based on a calculated spectral unmixing matrix. In certain instances, the memory includes instructions for estimating the abundance of one or more fluorophores on particles in a sample. In some embodiments, the memory includes instructions for identifying particles in a sample based on the estimated abundance of each fluorophore on the particles. In certain instances, the memory includes instructions for sorting the identified particles in a sample.

[0114] An integrated circuit device is also provided that is programmed to perform spectral analysis of light from multiple fluorophores in a sample using a generalized least squares problem. In an embodiment, the integrated circuit device can be a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), or a complex programmable logic device (CPLD), or some other integrated circuit device.

[0115] In some embodiments, the integrated circuit device is programmed to determine the data signal covariance in each photodetector channel. In some instances, the data signal covariance within each photodetector channel includes an inherent sample variability component and a measurement variability component. In some instances, the data signal covariance includes the electronic noise within each photodetector channel. In some instances, the data signal covariance includes the shot noise within each photodetector channel. In some instances, the data signal covariance varies linearly with the generated data signal. In some instances, the data signal covariance varies quadratically with the generated data signal. In some instances, the data signal covariance is related to two or more of the multiple photodetector channels. In some instances, the integrated circuit device is programmed to calculate the data signal covariance according to:

[0116] ,

[0117] Wherein:

[0118] is the measured detector signal;

[0119] is the baseline noise component;

[0120] is the Poisson noise component;

[0121] is the Poisson noise coefficient;

[0122] is the quadratic noise component; and

[0123] is the quadratic noise coefficient.

[0124] In some instances, the integrated circuit device is programmed to calculate the data signal covariance using a covariance matrix. In some instances, the covariance matrix contains non-zero diagonal values. In certain instances, the integrated circuit device is programmed to calculate the covariance according to the following using the covariance matrix:

[0125] ,

[0126] Wherein, represents generating a diagonal matrix from the column vector x, and represents the covariance between a and b.

[0127] In some instances, the integrated circuit device is programmed to calculate the solution of the generalized least squares problem by multiplying the inverse of the calculated covariance matrix. In some instances, the method includes estimating the data signal covariance based on the fluorescence intensities of two or more photodetectors of an optical detection system. In some instances, the method includes estimating the data signal covariance based on the fluorescence intensity of each in an optical detection channel. In some embodiments, the integrated circuit device is programmed to calculate the generalized least squares problem according to the following:

[0128] ,

[0129] Wherein:

[0130] is the weight matrix;

[0131] is the covariance matrix;

[0132] X is the spectral matrix (overflow matrix);

[0133] y is the detector values measured by multiple photodetectors of the optical detection system for each cell;

[0134] f is the true fluorophore abundance for each cell; and

[0135] is the estimated (unmixed) fluorophore abundance for each cell.

[0136] In some instances, the integrated circuit device is programmed to estimate a prior covariance matrix. In certain instances, the integrated circuit device is programmed to apply a generalized least squares algorithm in real time (e.g., using an integrated circuit such as a field programmable gate array). In some instances, a prior noise model is used to estimate each event covariance (e.g., computing each event covariance matrix in real time). In some instances, the prior noise model uses only the data collected for each specific event. In some instances, the covariance matrix includes an estimate of the entire collected data set. In some instances, the covariance matrix is generated by an iterative optimization method that empirically tunes the covariance matrix to minimize the variance of the unmixed data.

[0137] In some embodiments, the integrated circuit device is programmed to determine the data signal covariance by an iterative optimization estimate of the covariance matrix that minimizes the variance of the unmixed data signal. In certain instances, the integrated circuit device is programmed to compute a generalized least squares problem by Cholesky factorization of the covariance matrix. In certain instances, the generalized least squares problem is characterized by computing the Cholesky factorization of the covariance matrix and solving a triangular system as follows to generate a transformed input for an ordinary least squares algorithm:

[0138] Solve to generate , which is the decorrelated and whitened version of the data vector y.

[0139] Solve to generate , which is the corresponding transformed version of the spectral matrix X.

[0140] The transformed system is solved by ordinary least squares, e.g., by solving the so-called normal equations .

[0141] In some instances, an integrated circuit device is programmed to find a least squares solution to a generalized least squares problem. In some instances, the integrated circuit device is programmed to find a least squares solution to the generalized least squares problem by one or more of matrix decomposition, matrix factorization, QR factorization, Cholesky factorization, singular value decomposition, LDL factorization, and pre-permutation and post-permutation. In some instances, the integrated circuit device is programmed to find a least squares solution to the generalized least squares problem by solving the so-called normal equations through Cholesky factorization or LDL factorization, for example, according to the following through Cholesky factorization or LDL factorization:

[0142] ,

[0143] where:

[0144] y is the detector value measured by a plurality of photodetectors of the light detection system of each cell; X is the overflow; and

[0145] G is .

[0146] In some instances, the integrated circuit device is programmed to find a least squares solution to the generalized least squares problem according to the following through Cholesky factorization or LDL factorization:

[0147] ,

[0148] ,

[0149] , LDL factorization,

[0150] where , lower triangular matrix solution,

[0151] where , diagonal matrix solution,

[0152] , solve , upper triangular matrix solution.

[0153] In some embodiments, the integrated circuit device is programmed to find a least squares solution to the generalized least squares problem by matrix decomposition. In some embodiments, the integrated circuit device is programmed to find a least squares solution to the generalized least squares problem by matrix factorization. In some instances, the integrated circuit device is programmed to minimize the least squares solution of the generalized least squares problem by QR factorization. In some instances, the integrated circuit device is programmed to use the transformed and (Calculated through the Cholesky decomposition of the above covariance matrix) to calculate the generalized least squares problem:

[0154] , the normal equation of the transformed GLS problem;

[0155] , the QR decomposition of the transformed X;

[0156] , permutation;

[0157] , the expanded transpose of QR;

[0158] , Since orthogonality can be eliminated,

[0159] , triangular solution .

[0160] In some embodiments, the integrated circuit device is programmed to minimize the least squares solution of the generalized least squares problem by singular value decomposition. In some instances, the singular value decomposition is the product of matrices, where U and V are orthogonal matrices, is a diagonal matrix containing singular values. In some instances, the integrated circuit device is programmed to calculate the generalized least squares problem using singular value decomposition as follows:

[0161]

[0162]

[0163] ,

[0164] where U and V are orthogonal matrices, and is a diagonal matrix containing singular values. In certain embodiments, the integrated circuit device is programmed to find the least squares solution of the generalized least squares problem by LDL decomposition. In certain embodiments, the integrated circuit device is programmed to find the least squares solution of the generalized least squares problem by pre-permutation and post-permutation.

[0165] In some embodiments, the integrated circuit device is programmed to estimate the abundance of one or more fluorophores in a sample based on the calculated spectral unmixing matrix. In certain instances, the integrated circuit device is programmed to estimate the abundance of one or more fluorophores on particles in a sample. In some embodiments, the integrated circuit device is programmed to identify particles in the sample based on the estimated abundance of each fluorophore on the particles. In certain instances, the integrated circuit device is programmed to sort the identified particles in the sample. BRIEF DESCRIPTION OF THE DRAWINGS

[0166] The present invention may best be understood from the following detailed description when read in conjunction with the accompanying drawings. The drawings include the following figures:

[0167] Figure 1A A flowchart is described for spectral resolution of light using a generalized least squares problem according to certain embodiments.

[0168] Figure 1B The raw measurement variance of particles in an optically irradiated sample is described according to certain embodiments.

[0169] Figure 1C Determining the quadratic noise coefficient in the measurement covariance is described according to certain embodiments.

[0170] Figure 1D Estimation of the unmixing distribution in the absence (i.e., zero) covariance is described.

[0171] Figure 1E Including a non-zero quadratic covariance term in the noise model results in an accurate prediction of the unmixing distribution is described.

[0172] Figure 2A Comparison of correlation and anti-correlation in quadratic noise is described according to certain embodiments.

[0173] Figure 2B Comparison of spectral unmixing using a generalized least squares problem with unmixing using ordinary least squares and weighted least squares is described according to certain embodiments.

[0174] Figure 3A An image-enabled particle sorter is described according to certain embodiments. Figure 3B Image-enabled particle sorting data processing is described according to certain embodiments.

[0175] Figure 4A A functional block diagram of a particle analysis system is described according to certain embodiments. Figure 4B A flow cytometer is described according to certain embodiments.

[0176] Figure 5 A functional block diagram of an example of a particle analyzer control system is described according to certain embodiments.

[0177] Figure 6A Disclosed is a schematic diagram of a particle sorting system according to certain embodiments.

[0178] Figure 6B Disclosed is a schematic diagram of a particle sorting system according to certain embodiments.

[0179] Figure 7 Disclosed is a block diagram of a computing system according to certain embodiments. DETAILED DESCRIPTION

[0180] Aspects of the present disclosure include methods for spectrally resolving light from fluorophores in a sample. Methods according to certain embodiments include: detecting light from a sample comprising a plurality of fluorophores having overlapping fluorescence spectra using an optical detection system, and spectrally resolving the light from each fluorophore in the sample using a generalized least squares problem. In some embodiments, the method includes estimating the abundance of one or more fluorophores in the sample (e.g., on particles). In certain instances, the method includes identifying particles in the sample and sorting the particles based on the abundance of each fluorophore. Methods according to some embodiments include spectrally resolving the light from each fluorophore by calculating a spectral unmixing matrix for the fluorescence spectrum of each fluorophore. Systems and integrated circuit devices (e.g., field programmable gate arrays) for practicing the subject methods are also provided.

[0181] Before describing the present invention in more detail, it is to be understood that the invention is not limited to the particular embodiments described, as these may of course vary. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting, since the scope of the present invention will be limited only by the appended claims.

[0182] Where a range of values is provided, it is understood that, unless the context clearly dictates otherwise, each intervening value, to the tenth of the unit of the lower limit, between the upper and lower limits of that range and any other stated value or intervening value in that stated range is encompassed within the invention. The upper and lower limits of these smaller ranges may independently be included in the smaller ranges and are also encompassed within the invention, subject to any specifically excluded limitation in the stated range. Where the stated range includes one or both of the limits, ranges excluding either one or both of those included limits are also included in the invention.

[0183] This document presents certain ranges, with the term "about" preceding the numerical values. The term "about" is used herein to provide literal support for the exact number that follows it, as well as for numbers that are close to or approximate the number that follows it. In determining whether a number is close to or approximate to a specifically recited number, an unrecited number that is close or approximate may be a number that provides substantial equivalence to the specifically recited number in the context in which it occurs.

[0184] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. Although any methods and materials similar or equivalent to those described herein can also be used in the practice or testing of the present invention, representative illustrative methods and materials are now described.

[0185] All publications and patents cited in this specification are incorporated herein by reference as if each individual publication or patent was specifically and individually indicated to be incorporated by reference in its entirety, and are incorporated by reference to disclose and describe the methods and / or materials associated with the cited publications. Any reference to a publication is to its disclosure prior to the filing date of the application, and should not be construed as an admission that the present invention is not entitled to antedate such publication by virtue of an earlier invention. Additionally, the provided publication dates may differ from the actual publication dates and may need to be independently verified.

[0186] It should be noted that, unless the context clearly indicates otherwise, the singular forms "a", "an", "the", etc. used herein and in the appended claims include plural referents. It should also be noted that the claims can be drafted to exclude any optional elements. Thus, this statement is intended to serve as a basis for the use of exclusive terms such as "solely", "only", etc. when referring to claim elements or using "negative" limitations.

[0187] As will be apparent to those skilled in the art upon reading this disclosure, each individual embodiment described and illustrated herein has discrete components and features that can be readily separated from or combined with the features of any one of several other embodiments without departing from the scope or spirit of the invention. Any recited method can be performed in the order of the recited events or in any other logically possible order.

[0188] Although the apparatus and method have been or will be described for purposes of grammatical fluency and functional explanation, it should be clearly understood that the claims should never be construed as necessarily limited by the recitation of "means" or "step" unless expressly provided for in 35 U.S.C. § 112, but rather should be given the full scope of the meaning and equivalents of the definition provided by the claims under the doctrine of judicial equivalents, and if the claims are expressly provided for in 35 U.S.C. § 112, they should be given their full statutory equivalents under 35 U.S.C. § 112.

[0189] As described above, the present disclosure provides a method for spectroscopically resolving fluorophores in a sample by a generalized least squares algorithm. In further describing embodiments of the present disclosure, a method for spectroscopically resolving fluorophores in a sample is first described in more detail, the method including estimating the abundance of each fluorophore in the sample (e.g., on particles in the sample) and identifying and sorting the particles based on the estimated abundance of each fluorophore. Second, a system and an integrated circuit device programmed to practice the subject method using the generalized least squares algorithm are described.

[0190] Method for spectroscopically resolving light from fluorophores having overlapping fluorescence spectra in a sample using a generalized least squares algorithm

[0191] Aspects of the present disclosure include a method for spectroscopically resolving light from fluorophores in a sample (including light having overlapping fluorescence spectra). In an embodiment, the light from each fluorophore is resolved (e.g., unmixed) using a generalized least squares algorithm. In some instances, the generalized least squares algorithm is used to spectroscopically unmix the light from the fluorophores to model the covariance caused by measurement variations in a particle analyzer (such as a flow cytometer). In certain embodiments, the generalized least squares algorithm provides a lower variance of the unmixed data than that obtained by spectroscopically resolving the light from the fluorophores using an ordinary least squares algorithm or a weighted least squares algorithm. In some instances, the spectroscopic unmixing is more accurate than the weighted least squares algorithm when the measurement noise is related to the photodetector in the light detection system. In some embodiments, the methods described herein provide measurement data from the sample, illustrating the heteroscedasticity and non-zero covariance in the measured data. In some instances, the generalized least squares algorithm described herein uses the inverse of the estimated covariance matrix for each event as a weight matrix, which whitens and decorrelates the data, thereby ensuring the optimality (minimum variance) of the least squares solution. In certain instances, the subject method estimates the covariance caused only by measurement variability and is not affected by the inherent sample variability. Figure 1AA flowchart is described for spectroscopically resolving light using a generalized least squares algorithm according to certain embodiments. As discussed in more detail below, a data signal is generated from light detected by particles irradiated in a flowing stream (101), and the covariance between photodetectors is determined on a per-event basis (i.e., the measurement variance is calculated for each particle) (102). Using the calculated measurement covariance, the data signal is spectroscopically resolved using a generalized least squares algorithm to which the calculated measurement covariance is applied (103).

[0192] As used herein, the term "spectroscopic resolution" refers in its conventional sense to spectroscopically differentiating each fluorophore in a sample by assigning or attributing overlapping light wavelengths to each contributing fluorophore. In embodiments, the overlapping fluorescence spectral components attributed to each fluorophore are determined by solving a generalized least squares problem. In certain instances, the generalized least squares algorithm (described in more detail below) includes calculating a spectral unmixing matrix. In some embodiments, the sample of interest has multiple fluorophores, where the fluorescence spectrum of each fluorophore overlaps the fluorescence spectrum of at least one other fluorophore in the sample. In some instances, the fluorescence spectrum of each fluorophore overlaps the fluorescence spectrum of at least one other fluorophore in the sample by 5 nm or more, such as by 10 nm or more, such as by 25 nm or more and including by 50 nm or more. In certain instances, the fluorescence spectrum of one or more fluorophores in the sample overlaps the fluorescence spectrum of two or more different fluorophores in the sample, such as each overlap in the fluorescence spectrum is 5 nm or more, such as 10 nm or more, such as 25 nm or more and including 50 nm or more. In other embodiments, the sample of interest includes multiple fluorophores having non-overlapping fluorescence spectra. In these embodiments, within a range of 10 nm or less, such as 9 nm or less, such as 8 nm or less, such as 7 nm or less, such as 6 nm or less, such as 5 nm or less, such as 4 nm or less, such as 3 nm or less, such as 2 nm or less and including 1 nm or less, the fluorescence spectrum of each fluorophore is adjacent to at least one other fluorophore.

[0193] In practicing the subject method, a sample is illuminated with a light source and light from the sample is detected with a light detection system having one or more photodetectors. In some instances, the light detection system includes a plurality of photodetectors. In some embodiments, the sample is a biological sample. The term "biological sample" is used in its conventional sense and refers to a subset of a whole organism, plant, fungus, or animal tissue, cell, or component, which whole organism may be found in, in certain instances, blood, mucus, lymph fluid, synovial fluid, cerebrospinal fluid, saliva, bronchoalveolar lavage fluid, amniotic fluid, amniotic cord blood, urine, vaginal fluid, and semen. Thus, a "biological sample" refers to a subset of a natural organism or its tissue, as well as a homogenate, lysate, or extract prepared from a subset of an organism or its tissue, the subset of an organism or its tissue including, but not limited to, for example, plasma, serum, spinal fluid, lymph fluid, skin biopsies, respiratory, gastrointestinal, cardiovascular, and urogenital tracts, tears, saliva, milk, blood cells, tumors, organs. A biological sample can be any type of biological tissue, including healthy and diseased tissue (e.g., cancerous tissue, malignant tissue, necrotic tissue, etc.). In certain embodiments, the biological sample is a liquid sample, such as blood or a derivative thereof, such as plasma, tears, urine, semen, etc., where in some instances, the sample is a blood sample, including whole blood, such as blood obtained by venipuncture or fingerstick (the blood may or may not be combined with any reagents such as preservatives, anticoagulants, etc. prior to testing).

[0194] In certain embodiments, the source of the sample is a "mammal" or "mammalian animal", where these terms are used broadly to describe organisms within the class Mammalia, including the order Carnivora (e.g., dogs and cats), the order Rodentia (e.g., mice, guinea pigs, and rats), and the order Primates (e.g., humans, chimpanzees, and monkeys). In some instances, the subject is a human. The method can be applied to samples obtained from human subjects of both genders and at any stage of development (i.e., neonate, infant, child, adolescent, adult), where in certain embodiments, the human subject is a child, adolescent, or adult. While the present invention can be applied to samples from human subjects, it should be understood that the method can also be performed on samples from other animal subjects (i.e., "non-human subjects") (e.g., but not limited to birds, mice, rats, dogs, cats, livestock, and horses).

[0195] In practicing the subject method, a sample is irradiated with light from a light source (e.g., in the flow stream of a flow cytometer). In some embodiments, the light source is a broadband light source that emits light having a wide wavelength range, such as spanning 50 nm or greater, such as 100 nm or greater, such as 150 nm or greater, such as 200 nm or greater, such as 250 nm or greater, such as 300 nm or greater, such as 350 nm or greater, such as 400 nm or greater and including spanning 500 nm or greater. For example, a suitable broadband light source emits light having a wavelength of 200 nm to 1500 nm. Another example of a suitable broadband light source includes a light source that emits light having a wavelength of 400 nm to 1000 nm. In cases where the method includes irradiation with a broadband light source, broadband light source scenarios of interest may include, but are not limited to, halogen lamps, deuterium arc lamps, xenon arc lamps, stable fiber-coupled broadband light sources, broadband LEDs having a continuous spectrum, superluminescent diodes, semiconductor light-emitting diodes, broadband LED white light sources, multi-LED integrated white light sources, and other broadband light sources or any combination thereof.

[0196] In other embodiments, the method includes irradiation with a narrowband light source that emits a specific wavelength or a narrow wavelength range, such as a light source that emits light in a narrow wavelength range such as 50 nm or less, such as 40 nm or less, such as 30 nm or less, such as 25 nm or less, such as 20 nm or less, such as 15 nm or less, such as 10 nm or less, such as 5 nm or less, such as 2 nm or less and including a light source that emits light of a specific wavelength (i.e., monochromatic light). In cases where the method includes irradiation with a narrowband light source, narrowband light source scenarios of interest may include, but are not limited to, narrow wavelength LEDs, laser diodes, or broadband light sources coupled to one or more optical bandpass filters, diffraction gratings, monochromators, or any combination thereof.

[0197] In some embodiments, the method includes irradiating a sample with one or more lasers. As discussed above, the type and number of lasers will vary depending on the sample and the desired light to be collected. The lasers may be gas lasers such as helium-neon lasers, argon lasers, krypton lasers, xenon lasers, nitrogen lasers, CO2 lasers, CO lasers, argon-fluoride (ArF) excimer lasers, krypton-fluoride (KrF) excimer lasers, xenon-chloride (XeCl) excimer lasers or xenon-fluoride (XeF) excimer lasers or combinations thereof. In other instances, the method includes irradiating a flowing stream with a dye laser such as a stilbene laser, a coumarin laser or a rhodamine laser. In other instances, the method includes irradiating a flowing stream with a metal-vapor laser such as a helium-cadmium (HeCd) laser, a helium-mercury (HeHg) laser, a helium-selenium (HeSe) laser, a helium-silver (HeAg) laser, a strontium laser, a neon-copper (NeCu) laser, a copper laser or a gold laser or combinations thereof. In yet other instances, the method includes irradiating a flowing stream with a solid-state laser such as a ruby laser, a Nd:YAG laser, a NdCrYAG laser, an Er:YAG laser, a Nd:YLF laser, a Nd:YVO4 laser, a Nd:YCa4O(BO3)3 laser, a Nd:YCOB laser, a titanium-sapphire laser, a thulium YAG laser, a ytterbium YAG laser, a Yb2O3 laser or a cerium-doped laser or combinations thereof.

[0198] The sample may be irradiated with one or more of the above light sources, such as two or more light sources, such as three or more light sources, such as four or more light sources, such as five or more light sources and including ten or more light sources. The light sources may include any combination type of light sources. For example, in some embodiments, the method includes irradiating a sample in a flowing stream with a laser array (e.g., an array having one or more gas lasers, one or more dye lasers and one or more solid-state lasers).

[0199] The sample can be irradiated with wavelengths in the range of 200 nm to 1500 nm, such as 250 nm to 1250 nm, such as 300 nm to 1000 nm, such as 350 nm to 900 nm and including 400 nm to 800 nm. For example, in the case where the light source is a broadband light source, the sample can be irradiated with wavelengths of 200 nm to 900 nm. In other examples, in the case where the light source includes a plurality of narrowband light sources, the sample can be irradiated with specific wavelengths within the range of 200 nm to 900 nm. For example, the light source can be a plurality of narrowband LEDs (1 nm to 25 nm), each LED independently emitting light with a wavelength range of 200 nm to 900 nm. In other embodiments, the narrowband light source includes one or more lasers (such as a laser array) and irradiates the sample with specific wavelengths in the range of 200 nm to 700 nm, for example, irradiates the sample with a laser array having gas lasers, excimer lasers, dye lasers, metal vapor lasers, and solid-state lasers as described above.

[0200] In the case of using more than one light source, the light source or a combination thereof can be used to irradiate the sample simultaneously or sequentially. For example, the sample can be irradiated simultaneously with each of the light sources. In other embodiments, the flowing stream can be irradiated sequentially with each of the light sources. In the case of irradiating the sample sequentially with more than one light source, the irradiation time of each light source on the sample can independently be 0.001 microseconds or more, such as 0.01 microseconds or more, such as 0.1 microseconds or more, such as 1 microseconds or more, such as 5 microseconds or more, such as 10 microseconds or more, such as 30 microseconds or more and including 60 microseconds or more. For example, the method can include irradiating the sample with a light source (such as a laser) for a duration of 0.001 microseconds to 100 microseconds, such as 0.01 microseconds to 75 microseconds, such as 0.1 microseconds to 50 microseconds, such as 1 microseconds to 25 microseconds and including 5 microseconds to 10 microseconds. In embodiments where the sample is irradiated sequentially with two or more light sources, the duration of irradiation of the sample by each light source can be the same or different.

[0201] The time period between each light source irradiation can also vary as needed and is independently separated by a delay of 0.001 microseconds or more, such as 0.01 microseconds or more, such as 0.1 microseconds or more, such as 1 microsecond or more, such as 5 microseconds or more, such as 10 microseconds or more, such as 15 microseconds or more, such as 30 microseconds or more and including 60 microseconds or more. For example, the time period between each light source irradiation can be from 0.001 microseconds to 60 microseconds, such as from 0.01 microseconds to 50 microseconds, such as from 0.1 microseconds to 35 microseconds, such as from 1 microsecond to 25 microseconds and including from 5 microseconds to 10 microseconds. In some embodiments, the time period between each light source irradiation is 10 microseconds. In embodiments where the sample is irradiated sequentially by more than two (i.e., 3 or more) light sources, the delay between each light source irradiation can be the same or different.

[0202] The sample can be irradiated continuously or at discrete intervals. In some instances, the method includes continuously irradiating the sample in the sample with a light source. In other instances, the sample is irradiated with a light source at discrete intervals, such as every 0.001 milliseconds, every 0.01 milliseconds, every 0.1 milliseconds, every 1 millisecond, every 10 milliseconds, every 100 milliseconds and including every 1000 milliseconds, or other intervals.

[0203] Depending on the light source, the sample can be irradiated at a distance, the distance being, for example, 0.01 mm or more, such as 0.05 mm or more, such as 0.1 mm or more, such as 0.5 mm or more, such as 1 mm or more, such as 2.5 mm or more, such as 5 mm or more, such as 10 mm or more, such as 15 mm or more, such as 25 mm or more and including 50 mm or more. Additionally, the angle or irradiation can also vary, ranging from 10° to 90°, such as from 15° to 85°, such as from 20 to 80°, such as from 25° to 75° and including from 30° to 60°, such as at a 90° angle.

[0204] In some embodiments, the method includes irradiating a sample with two or more frequency-shifted light beams. As described above, a beam generator assembly having a laser and an acousto-optic device for frequency-shifting the laser can be used. In these embodiments, the method includes irradiating the acousto-optic device with the laser. Depending on the desired wavelength of the light generated in the output laser beam (e.g., for irradiating a sample in a flowing stream), the laser can have a specific wavelength that varies from 200 nm to 1500 nm, such as from 250 nm to 1250 nm, such as from 300 nm to 1000 nm, such as from 350 nm to 900 nm and including from 400 nm to 800 nm. The acousto-optic device can be irradiated with one or more lasers, such as two or more lasers, such as three or more lasers, such as four or more lasers, such as five or more lasers and including ten or more lasers. The lasers can include any combination of laser types. For example, in some embodiments, the method includes irradiating the acousto-optic device with a laser array, such as an array having one or more gas lasers, one or more dye lasers, and one or more solid-state lasers.

[0205] In cases where more than one laser is used, the acousto-optic device can be irradiated with the lasers simultaneously, sequentially, or a combination thereof. For example, the acousto-optic device can be irradiated simultaneously with each of the lasers. In other embodiments, the acousto-optic device is irradiated sequentially with each laser. When more than one laser is used to irradiate the acousto-optic device sequentially, the time for each laser to irradiate the acousto-optic device can independently be 0.001 microseconds or more, such as 0.01 microseconds or more, such as 0.1 microseconds or more, such as 1 microseconds or more, such as 5 microseconds or more, such as 10 microseconds or more, such as 30 microseconds or more and including 60 microseconds or more. For example, the method can include irradiating the acousto-optic device with the laser for a duration of 0.001 microseconds to 100 microseconds, such as 0.01 microseconds to 75 microseconds, such as 0.1 microseconds to 50 microseconds, such as 1 microseconds to 25 microseconds and including 5 microseconds to 10 microseconds. In embodiments where two or more lasers irradiate the acousto-optic device sequentially, the duration for which the acousto-optic device is irradiated by each laser can be the same or different.

[0206] The time period between each laser irradiation can also vary as needed and is independently separated by a delay of 0.001 microseconds or more, such as 0.01 microseconds or more, such as 0.1 microseconds or more, such as 1 microsecond or more, such as 5 microseconds or more, such as 10 microseconds or more, such as 15 microseconds or more, such as 30 microseconds or more and includes 60 microseconds or more. For example, the time period between each light source irradiation can be from 0.001 microseconds to 60 microseconds, such as from 0.01 microseconds to 50 microseconds, such as from 0.1 microseconds to 35 microseconds, such as from 1 microsecond to 25 microseconds and includes from 5 microseconds to 10 microseconds. In certain embodiments, the time period between each laser irradiation is 10 microseconds. In embodiments where the acousto-optic device is irradiated sequentially by more than two (i.e., 3 or more) lasers, the delay between each laser irradiation can be the same or different.

[0207] The acousto-optic device can be irradiated continuously or at discrete intervals. In some instances, the method includes continuously irradiating the acousto-optic device with a laser. In other instances, the acousto-optic device is irradiated with a laser at discrete intervals, such as every 0.001 milliseconds, every 0.01 milliseconds, every 0.1 milliseconds, every 1 millisecond, every 10 milliseconds, every 100 milliseconds and includes every 1000 milliseconds, or some other interval.

[0208] Depending on the laser, the acousto-optic device can be irradiated at a distance, which is for example 0.01 mm or more, such as 0.05 mm or more, such as 0.1 mm or more, such as 0.5 mm or more, such as 1 mm or more, such as 2.5 mm or more, such as 5 mm or more, such as 10 mm or more, such as 15 mm or more, such as 25 mm or more and includes 50 mm or more. Additionally, the angle or irradiation can also vary, ranging from 10° to 90°, such as from 15° to 85°, such as from 20° to 80°, such as from 25° to 75° and includes from 30° to 60°, such as at a 90° angle.

[0209] In an embodiment, the method includes applying a radio frequency drive signal to the acousto-optic device to generate an angularly deflected laser beam. Two or more radio frequency drive signals can be applied to the acousto-optic device to generate an output laser beam having a desired number of angularly deflected laser beams, such as 3 or more radio frequency drive signals, such as 4 or more radio frequency drive signals, such as 5 or more radio frequency drive signals, such as 6 or more radio frequency drive signals, such as 7 or more radio frequency drive signals, such as 8 or more radio frequency drive signals, such as 9 or more radio frequency drive signals, such as 10 or more radio frequency drive signals, such as 15 or more radio frequency drive signals, such as 25 or more radio frequency drive signals, such as 50 or more radio frequency drive signals and includes 100 or more radio frequency drive signals.

[0210] The angularly deflected laser beams generated by the radio frequency drive signals each have an intensity based on the amplitude of the applied radio frequency drive signal. In some embodiments, the method includes applying a radio frequency drive signal having an amplitude sufficient to produce an angularly deflected laser beam having a desired intensity. In some instances, each applied radio frequency drive signal independently has an amplitude of from about 0.001 V to about 500 V, such as from about 0.005 V to about 400 V, such as from about 0.01 V to about 300 V, such as from about 0.05 V to about 200 V, such as from about 0.1 V to about 100 V, such as from about 0.5 V to about 75 V, such as from about 1 V to 50 V, such as from about 2 V to 40 V, such as from 3 V to about 30 V and including from about 5 V to about 25 V. In some embodiments, each applied radio frequency drive signal has a frequency of from about 0.001 MHz to about 500 MHz, such as from about 0.005 MHz to about 400 MHz, such as from about 0.01 MHz to about 300 MHz, such as from about 0.05 MHz to about 200 MHz, such as from about 0.1 MHz to about 100 MHz, such as from about 0.5 MHz to about 90 MHz, such as from about 1 MHz to about 75 MHz, such as from about 2 MHz to about 70 MHz, such as from about 3 MHz to about 65 MHz, such as from about 4 MHz to about 60 MHz and including from about 5 MHz to about 50 MHz.

[0211] In these embodiments, the angularly deflected laser beams in the output laser beam are spatially separated. Depending on the applied radio frequency drive signal and the desired irradiation profile of the output laser beam, the angularly deflected laser beams can be separated by 0.001 µm or more, such as 0.005 µm or more, such as 0.01 µm or more, such as 0.05 µm or more, such as 0.1 µm or more, such as 0.5 µm or more, such as 1 µm or more, such as 5 µm or more, such as 10 µm or more, such as 100 µm or more, such as 500 µm or more, such as 1000 µm or more and including 5000 µm or more. In some embodiments, the angularly deflected laser beams overlap, for example, with adjacent angularly deflected laser beams along the horizontal axis of the output laser beam. The overlap between adjacent angularly deflected laser beams (such as the overlap of the beam spots) can be an overlap of 0.001 µm or more, such as 0.005 µm or more, such as 0.01 µm or more, such as 0.05 µm or more, such as 0.1 µm or more, such as 0.5 µm or more, such as 1 µm or more, such as 5 µm or more, such as 10 µm or more and including 100 µm or more.

[0212] In some instances, a flowing stream is illuminated with beams of multiple frequency-shifted light, and cells in the flowing stream are imaged by fluorescence imaging using frequency-tagged emission (FIRE) to generate a frequency-encoded image, as described, for example, in Diebold et al., Nature Photonics Vol. 7(10) 806-810 (2013) and U.S. Patent Nos. 9,423,353, 9,784,661, 9,983,132, 10,006,852, 10,078,045, 10,036,699, 10,222,316, 10,288,546, 10,324,019, 10,408,758, 10,451,538, 10,620,111 and U.S. Patent Publication Nos. 2017 / 0133857, 2017 / 0328826, 2017 / 0350803, 2018 / 0275042, 2019 / 0376895 and 2019 / 0376894, the disclosures of which are incorporated herein by reference.

[0213] As described above, in some embodiments, light from the illuminated sample is delivered to a light detection system described in more detail below and can be measured by a plurality of photodetectors. In some embodiments, the method includes measuring light collected in a wavelength range (e.g., 200 nm to 1000 nm). For example, the method can include collecting a spectrum of light in one or more wavelength ranges from 200 nm to 1000 nm. In still other embodiments, the method includes measuring the collected light at one or more specific wavelengths. For example, the collected light can be measured at 450 nm, 518 nm, 519 nm, 561 nm, 578 nm, 605 nm, 607 nm, 625 nm, 650 nm, 660 nm, 667 nm, 670 nm, 668 nm, 695 nm, 710 nm, 723 nm, 780 nm, 785 nm, 647 nm, 617 nm, and any combination thereof. In certain embodiments, the method includes measuring the wavelength of light corresponding to the fluorescence peak wavelength of a fluorophore. In some embodiments, the method includes measuring the collected light across the entire fluorescence spectrum of each fluorophore in the sample.

[0214] The collected light can be measured continuously or at discrete intervals. In certain instances, the method includes continuously measuring the light. In other instances, the light can be measured at discrete intervals, such as every 0.001 milliseconds, every 0.01 milliseconds, every 0.1 milliseconds, every 1 millisecond, every 10 milliseconds, every 100 milliseconds, and including every 1000 milliseconds, or some other interval.

[0215] The measurement of the collected light can be performed one or more times during the subject method, such as two or more times, such as three or more times, such as five or more times and including ten or more times. In certain embodiments, the light propagation is measured two or more times and the data is averaged in certain instances.

[0216] The light from the sample can be measured at one or more wavelengths, such as at five or more different wavelengths, such as at ten or more different wavelengths, such as at twenty-five or more different wavelengths, such as at fifty or more different wavelengths, such as at one hundred or more different wavelengths, such as at two hundred or more different wavelengths, such as at three hundred or more different wavelengths and including at four hundred or more different wavelengths for the collected light.

[0217] In an embodiment, the method includes spectral resolution of the light from each fluorophore in the sample using a generalized least squares algorithm. In some embodiments, the overlap between each different fluorophore is determined and the contribution of each fluorophore to the overlapping fluorescence is calculated. In some embodiments, spectral resolution of the light using a generalized least squares algorithm includes calculating a spectral unmixing matrix of the fluorescence spectra of each of a plurality of fluorophores having overlapping fluorescence in the sample detected by the light detection system. For example, spectral resolution of the light according to the methods described herein can include the Moore-Penrose inverse or pseudoinverse of a spectral matrix. As described in more detail below, spectral resolution of the light from each fluorophore in the sample using a generalized least squares algorithm (e.g., calculating a spectral unmixing matrix for each fluorophore) can be used to estimate the abundance of each fluorophore in the sample. In certain embodiments, the abundance of each fluorophore associated with a target particle can be determined. The abundance of each fluorophore associated with a target particle can be used to identify and classify the particle. In some instances, the identified or classified particles can be used to sort the target particles (e.g., cells) in the sample. In certain embodiments, the fluorophores in the sample are spectrally resolved, such as by calculating spectral unmixing, such that the sorting is fast enough to sort the particles in real time after detection by the light detection system.

[0218] In some embodiments, the method includes determining the data signal covariance in one or more photodetector channels. In certain instances, the data signal covariance is determined in each photodetector channel. As used herein, the term "data signal covariance" refers in its ordinary sense to the differential measurement of each photodetector channel. For example, different measurements in embodiments (from particle to particle, from detector to detector) will have different noise levels due to both: a constant noise source independent of the signal (e.g., baseline electronic noise from amplifiers and analog-to-digital converters, and baseline shot noise from a constant light source such as ambient lighting or scattered laser light), and, a signal-dependent noise source that varies linearly with the signal (e.g., shot noise due to photon measurements following Poisson statistics) or varies quadratically with the signal (e.g., multiplicative noise due to random fluctuations in fluid and illumination intensity as particles flow through the system). Figure 1B Describes the raw measurement variance of particles in an optically illuminated sample according to certain embodiments, which raw measurement variance is a quadratic function of intensity. The variance is the baseline noise , Poisson noise and quadratic covariance (CV) noise function, i.e., . Figure 1C Describes determining the quadratic noise coefficient (CV term) in the measurement covariance, where the quadratic noise coefficient (CV term) can be inferred by fitting a curve of variance versus median intensity, i.e., . In some instances, the quadratic noise coefficient is inferred by fitting a curve of variance versus the median intensity of the light detected within each photodetector channel. In certain instances, the quadratic covariance coefficient for each detector is inferred from the raw measurement data using the linear Poisson coefficient and the baseline noise of each detector. Figure 1D Describes the estimation of the unmixing distribution in the absence (i.e., zero) covariance. As Figure 1D shown, the quadratic term containing zero covariance will overestimate the unmixing distribution. In Figure 1D , the X-axis represents the predicted distribution (variance) assuming zero covariance, and the Y-axis represents the measured distribution. In the left subplot of Figure 1D , each point corresponds to a different fluorophore whose expression gives rise to the distribution (measured on a sample of CD4+ cells specifically expressing that fluorophore). The comparison between the measured distribution and the simulation based on the no-covariance model shows an overestimation of this distribution. According to Figure 1D 's right subplot, the model-based simulation overestimates the distribution without correlated noise. According to Figure 1E , including a non-zero quadratic covariance term in the noise model enables accurate prediction of the unmixing distribution.

[0219] In some embodiments, the subject method accounts for non-zero covariance in measurements made by different photodetector channels. In some instances, the spectral resolution of light using a generalized least squares algorithm is weighted by the inverse of the variance between photodetector channels. In some instances, measurements in different photodetector channels are decorrelated by multiplying by the inverse of the measurement covariance matrix (as described below). In some instances, the data signal covariance within each photodetector channel includes one or more of an inherent sample variability component and a measurement variability component. In some instances, the data signal covariance includes electronic noise in each photodetector channel. In some instances, the data signal covariance includes shot noise in each photodetector channel. In some instances, the data signal covariance varies linearly with the generated data signal. In some instances, the data signal covariance varies quadratically with the generated data signal. In some instances, the data signal covariance is correlated with two or more of the plurality of photodetector channels. In some instances, the data signal covariance is calculated according to:

[0220] ,

[0221] where:

[0222] is the measured detector signal;

[0223] is the baseline noise component;

[0224] is the Poisson noise component;

[0225] is the Poisson noise coefficient;

[0226] is the quadratic noise component; and

[0227] is the quadratic noise coefficient.

[0228] In some embodiments, the data signal covariance is calculated using a covariance matrix. In some instances, the covariance matrix contains non-zero diagonal values. In certain instances, the covariance is calculated using the covariance matrix according to:

[0229] ,

[0230] where, represents generating a diagonal matrix from the column vector x, and represents the covariance between a and b.

[0231] In some instances, the solution to the generalized least squares problem is calculated by multiplying by the inverse of the calculated covariance matrix. In some instances, the method includes estimating the data signal covariance based on the fluorescence intensities of two or more photodetectors of the optical detection system. In some instances, the method includes estimating the data signal covariance based on the fluorescence intensity of each in the optical detection channels. In some embodiments, the generalized least squares problem is calculated as follows:

[0232] ,

[0233] where:

[0234] is the weight matrix;

[0235] is the covariance matrix;

[0236] X is the spectral matrix (overflow matrix);

[0237] y is the detector value measured by multiple photodetectors of the optical detection system for each cell;

[0238] f is the true fluorophore abundance for each cell; and

[0239] is the estimated (unmixed) fluorophore abundance for each cell.

[0240] In some instances, the method further includes generating a prior estimated covariance matrix. In certain instances, the generalized least squares algorithm is applied in real time (e.g., using an integrated circuit such as a field programmable gate array). In some instances, a prior noise model is used to estimate each event covariance (e.g., calculating each event covariance matrix in real time). In some instances, the prior noise model uses only the data collected for each specific event. In some instances, the covariance matrix includes an estimate of the entire collected data set. In some instances, the covariance matrix is generated by an iterative optimization method that empirically tunes the covariance matrix to minimize the variance of the unmixed data.

[0241] In some embodiments, the data signal covariance is determined by an iterative optimization estimate of the covariance matrix that minimizes the variance of the unmixed data signal. In certain instances, the solution of the generalized least squares problem is characterized by a Cholesky decomposition of the covariance matrix. In certain instances, the solution of the generalized least squares problem is characterized by calculating the Cholesky decomposition of the covariance matrix and solving the triangular system according to the following to generate a transformed input for the ordinary least squares algorithm:

[0242] Solve to generate , i.e., the decorrelated and whitened version of the data vector y.

[0243] Solve Generate , i.e., the corresponding transformed version of the spectral matrix X.

[0244] Transformed system is solved by ordinary least squares, e.g., by solving the so-called normal equations .

[0245] Figure 2A Describes the comparison of correlation and anti-correlation in secondary noise according to certain embodiments, where the correlation and anti-correlation in secondary noise due to non-uniform illumination and fluid fluctuations are shown. For positive correlation, detectors on the same laser line will tend to brighten or dim together, and if the lasers are aligned relative to each other, the trajectories of the particles will tend to pass through the bright or dim regions on all laser lines together, resulting in correlation across laser lines. For negative correlation, if the lasers are not perfectly aligned with each other, according to the particle trajectories, detectors on some lasers may dim while detectors on other lasers brighten. In some instances, the random fluctuations of the measurement signals caused by system perturbations may be correlated across multiple detectors. Figure 2A Describes the flow stream in a flow cytometer flow cell, where an illumination laser beam with a Gaussian beam intensity distribution is aligned such that the illumination laser beam is brightest at the center of the core flow and dimmer at the edges. Although a single particle generally follows a straight trajectory in the core flow (i.e., in the axial direction of the cylindrical core flow), its radial position is essentially random after entering the core flow. In a well-aligned flow cytometer, a particle passing through the center of the core flow will be irradiated to a greater extent by all lasers, while the same particle passing near the outer edge through the core flow will pass through the low-intensity regions of each beam. This will result in a dimmed recorded signal for the second particle compared to the first particle on all detectors; in other words, although the fluctuations themselves are random, they are "in the same direction" for all measurement channels. Imperfect alignment and differences in the collection efficiency of different wavelengths mean that such fluctuations will not be perfectly correlated between detectors. In some instances, these fluctuations are negatively correlated (i.e., some detectors receive brighter signals while other detectors receive dimmer signals). In some instances, the structure of the secondary noise is correlated (i.e., a covariance matrix with non-zero diagonal elements).

[0246] Figure 2BDescribes a comparison of spectral unmixing using a generalized least squares problem with unmixing using ordinary least squares and weighted least squares, where examples of unmixing using the generalized least squares method are shown in the presence of non-zero noise covariance in a simulated panel. As Figure 2B shown in the examples in, the simulation results indicate that for spectral measurements of an optical detection system with multiple photodetectors, in the presence of correlated, heteroscedastic measurement noise, the generalized least squares provides a significant improvement (lower unmixing data variance) over both ordinary least squares and weighted least squares.

[0247] In some instances, the method includes finding the least squares solution to a generalized least squares problem. In some instances, the least squares solution to the generalized least squares problem is found by one or more of matrix factorization, matrix factorization, QR factorization, Cholesky factorization, singular value decomposition, LDL factorization, and pre-permutation and post-permutation. In some instances, the method includes finding the least squares solution to the generalized least squares problem by solving the so-called normal equations by Cholesky factorization or LDL factorization, for example according to the following by Cholesky factorization or LDL factorization:

[0248] ,

[0249] where y is the detector value measured by multiple photodetectors of the optical detection system for each cell; X is the spectral spillover; and

[0250] G is .

[0251] In some instances, the method includes finding the least squares solution to the generalized least squares problem by Cholesky factorization or LDL factorization according to the following:

[0252] ,

[0253] ,

[0254] , LDL factorization,

[0255] where , lower triangular matrix solution,

[0256] where , diagonal matrix solution,

[0257] , solve , upper triangular matrix solution.

[0258] In some embodiments, the method includes obtaining a least squares solution to a generalized least squares problem by matrix factorization.

[0259] In some embodiments, the method includes obtaining a least squares solution to a generalized least squares problem by matrix factorization. In some instances, the method includes obtaining a least squares solution to a generalized least squares problem by QR factorization. In some instances, the following is used to calculate the generalized least squares problem using QR factorization with a transformed and (calculated by Cholesky factorization of the covariance matrix above) to calculate the generalized least squares problem:

[0260] , the normal equations of the transformed GLS problem,

[0261] , the QR factorization of the transformed X,

[0262] , permutation,

[0263] , the expanded transpose of QR,

[0264] , which can be eliminated due to orthogonality,

[0265] , triangular solution .

[0266] In some embodiments, the method includes obtaining a least squares solution to a generalized least squares problem by singular value decomposition. In some instances, the singular value decomposition is the product of matrices, where U and V are orthogonal matrices, is a diagonal matrix containing singular values. In some instances, the following is used to calculate the generalized least squares problem using singular value decomposition:

[0267]

[0268]

[0269] ,

[0270] where U and V are orthogonal matrices, and is a diagonal matrix containing singular values. In certain embodiments, the method includes obtaining a least squares solution to a generalized least squares problem by LDL decomposition. In certain embodiments, the method includes minimizing the least squares solution to a generalized least squares problem by pre-permutation and post-permutation.

[0271] In some embodiments, the method includes estimating the covariance caused only by measurement variability in the absence of the influence of inherent sample variability. In certain embodiments, an analytical covariance model is used to predict the measurement covariance of one or more particles (e.g., each particle in a sample) as a function of the intensity distribution of that particle across all photodetectors. In some instances, the measurement covariance includes one or more parameters, such as: (1) the baseline noise of each photodetector; (2) the linear Poisson coefficient (photoelectron scaling factor) of each photodetector; (3) the quadratic CV coefficient of each photodetector (which can be directly estimated from the raw data in some instances); and (4) the quadratic CV correlation coefficient that describes the degree of quadratic noise correlation between each pair of photodetectors. In some instances, the baseline noise and the linear Poisson coefficient of each photodetector are determined during instrument calibration. In some instances, the quadratic CV coefficient of each photodetector can be estimated from the measured raw data. In certain instances, the quadratic CV correlation is determined through a model fitting process using a specific class of measurement calibration data (e.g., cells or particles stained with individual fluorophores and subsequently spectrally unmixed).

[0272] In certain embodiments, in other homogeneous populations of particles, the inherent variability of a single spectral signal source (e.g., a single fluorophore) is correlated with all photodetectors that receive signals from that fluorophore. In some instances, this can lead to high covariance in the raw data space. In certain instances, when the sample is spectrally unmixed, all of the inherent variations in fluorophore expression are included in the variance of the unmixed signal of each fluorophore. In certain instances, any other dimension (fluorophore) present in the unmixing matrix will have zero variance due to the single source fluorophore.

[0273] In some instances, the measurement noise has non-zero covariance and is at least partially uncorrelated, and the covariant noise sources can cause variances in the unmixed dimensions that do not correspond to the expressed fluorophores. In some instances, the method includes measuring the unmixed variance of the non-expressed fluorophore channels in the measured data to determine the true data unmixed variance. In certain instances, the method includes applying a noise model that includes constants, linear terms, and quadratic coefficients, where the quadratic noise correlation coefficient is pre-estimated and the correlation coefficient is adjusted (e.g., through a range of values) until the unmixed variance estimated by the model for the median intensity level of the true data sample matches the measured unmixed variance. In some instances, the noise model is defined and used to calculate the generalized least squares problem on an event-by-event basis.

[0274] In some embodiments, the method includes calculating the abundance of one or more fluorophores in a sample based on spectrally resolved light from each fluorophore. In certain instances, the abundance of fluorophores associated with a target particle (e.g., chemically associated (i.e., covalently associated, ionically associated) or physically associated) is calculated based on spectrally resolved light from each fluorophore associated with the particle. For example, in one example, the relative abundance of each fluorophore associated with a target particle is calculated based on spectrally resolved light from each fluorophore. In another example, the absolute abundance of each fluorophore associated with a target particle is calculated based on spectrally resolved light from each fluorophore. In certain embodiments, particles may be identified or classified based on the relative abundance of each fluorophore determined to be associated with the particle. In these embodiments, particles may be identified or classified by any convenient scheme, such as by: comparing the relative or absolute abundance of each fluorophore associated with the particle to a control sample of particles having known characteristics; or by performing spectral analysis or other analysis on a population of particles (e.g., cells) for which the relative or absolute abundance of associated fluorophores has been calculated.

[0275] In certain embodiments, the method includes sorting one or more of the particles (e.g., cells) in a sample based on the estimated abundance of fluorophores associated with the particles. As used herein, the term "sorting" refers in its conventional sense to separating the components of a sample (e.g., droplets containing cells, droplets containing non - cell particles such as biological macromolecules), and in some instances, delivering the separated components to one or more sample collection containers. For example, the method may include sorting 2 or more components of a sample, such as 3 or more components, such as 4 or more components, such as 5 or more components, such as 10 or more components, such as 15 or more components and including sorting 25 or more components of a sample.

[0276] When sorting particles based on the abundance of fluorophores associated with the particles, the method includes, for example, using a computer for data acquisition, analysis, and recording, where multiple data channels record data from each detector, and the detector is used to obtain the overlapping spectra of multiple fluorophores associated with the particle. In these embodiments, the analysis includes spectrally resolving the light from multiple fluorophores having overlapping spectra associated with the particle (e.g., by calculating a spectral unmixing matrix), and identifying the particle based on the estimated abundance of each fluorophore associated with the particle. The analysis may be transmitted to a sorting system that is configured to generate a set of digital parameters based on the particle classification.

[0277] In some embodiments, a method for sorting sample components includes sorting particles (e.g., cells in a biological sample) using a particle sorting module having deflection plates, such as the system described in U.S. Patent Publication No. 2017 / 0299493, filed Mar. 28, 2017, the disclosure of which is incorporated herein by reference. In certain embodiments, cells of a sample are sorted using a sorting decision module having a plurality of sorting decision units, such as the sorting decision units described in U.S. Provisional Patent Application No. 62 / 803,264, filed Feb. 8, 2019, the disclosure of which is incorporated herein by reference.

[0278] A system for spectral resolution of light from fluorophores having overlapping fluorescence spectra in a sample using a generalized least squares algorithm

[0279] As described above, aspects of the present disclosure include a system for spectral resolution of light from fluorophores having overlapping fluorescence spectra in a sample. As used herein, the term "spectral resolution" is used in its conventional sense to refer to spectrally distinguishing each fluorophore in a sample by assigning or attributing overlapping light wavelengths to each contributing fluorophore. In an embodiment, a spectral unmixing matrix is calculated to determine the overlapping fluorescence spectral components attributed to each fluorophore. In an embodiment, the subject system is used to characterize a sample having a plurality of fluorophores, wherein the fluorescence spectrum of each fluorophore overlaps the fluorescence spectrum of at least one other fluorophore in the sample. In some instances, the fluorescence spectrum of each fluorophore overlaps the fluorescence spectrum of at least one other fluorophore in the sample by 5 nm or more, such as by 10 nm or more, such as by 25 nm or more and including 50 nm or more. In certain instances, the fluorescence spectrum of one or more fluorophores in the sample overlaps the fluorescence spectrum of two or more different fluorophores in the sample, such as each overlap in the fluorescence spectrum being 5 nm or more, such as 10 nm or more, such as 25 nm or more and including 50 nm or more.

[0280] In an embodiment, the system includes a light source configured to illuminate a sample having a plurality of fluorophores, wherein the fluorescence spectrum of each fluorophore overlaps with the fluorescence spectrum of at least one other fluorophore in the sample. In an embodiment, the light source can be any suitable broadband or narrowband light source. Depending on the components in the sample (e.g., cells, beads, non-cellular particles, etc.), the light source can be configured to emit light having wavelengths that vary in the range of 200 nm to 1500 nm, such as 250 nm to 1250 nm, such as 300 nm to 1000 nm, such as 350 nm to 900 nm and including 400 nm to 800 nm. For example, the light source can include a broadband light source that emits light having wavelengths of 200 nm to 900 nm. In other instances, the light source includes a narrowband light source that emits wavelengths in the range of 200 nm to 900 nm. For example, the light source can be a narrowband LED (1 nm to 25 nm) that emits light having wavelengths in the range of 200 nm to 900 nm.

[0281] In certain embodiments, the light source is a laser. In some instances, the subject system includes gas lasers such as helium-neon lasers, argon lasers, krypton lasers, xenon lasers, nitrogen lasers, CO2 lasers, CO lasers, argon-fluoride (ArF) excimer lasers, krypton-fluoride (KrF) excimer lasers, xenon-chloride (XeCl) excimer lasers or xenon-fluoride (XeF) excimer lasers or combinations thereof. In other instances, the subject system includes dye lasers such as stilbene lasers, coumarin lasers or rhodamine lasers. In other instances, lasers of interest include metal vapor lasers such as helium-cadmium (HeCd) lasers, helium-mercury (HeHg) lasers, helium-selenium (HeSe) lasers, helium-silver (HeAg) lasers, strontium lasers, neon-copper (NeCu) lasers, copper lasers or gold lasers and combinations thereof. In other instances, the subject system includes solid-state lasers such as ruby lasers, Nd:YAG lasers, NdCrYAG lasers, Er:YAG lasers, Nd:YLF lasers, Nd: YVO4 lasers, Nd: YCa4O(BO3)3 lasers, Nd:YCOB lasers, titanium sapphire lasers, thulium YAG lasers, ytterbium YAG lasers, Yb2O3 lasers or cerium-doped lasers and combinations thereof.

[0282] In other embodiments, the light source is a non-laser light source, such as a lamp, including but not limited to halogen lamps, deuterium arc lamps, xenon arc lamps, light-emitting diodes, such as broadband LEDs with a continuous spectrum, superluminescent diodes, semiconductor light-emitting diodes, broadband LED white light sources, multi-LED integrations. In some instances, the non-laser light source is a stable fiber-coupled broadband light source, a white light source, and other light sources or any combination thereof.

[0283] The light source can be at any suitable distance from the sample (e.g., the flowing stream in a flow cytometer), such as a distance of 0.001 mm or more from the flowing stream, such as 0.005 mm or more, such as 0.01 mm or more, such as 0.05 mm or more, such as 0.1 mm or more, such as 0.5 mm or more, such as 1 mm or more, such as 5 mm or more, such as 10 mm or more, such as 25 mm or more and including a distance of 100 mm or more. Additionally, the light source irradiates the sample at any suitable angle (e.g., relative to the vertical axis of the flowing stream), such as an angle in the range of 10° to 90°, such as 15° to 85°, such as 20° to 80°, such as 25° to 75° and including 30° to 60°, such as a 90° angle.

[0284] The light source can be configured to irradiate the sample continuously or at discrete intervals. In some instances, the system includes a light source configured to continuously irradiate the sample, such as a continuous-wave laser that continuously irradiates the flowing stream at the interrogation point in a flow cytometer. In other instances, the system of interest includes a light source configured to irradiate the sample at discrete intervals, such as every 0.001 milliseconds, every 0.01 milliseconds, every 0.1 milliseconds, every 1 millisecond, every 10 milliseconds, every 100 milliseconds and including every 1000 milliseconds, or some other interval. In cases where the light source is configured to irradiate the sample at discrete intervals, the system can include one or more additional components to provide intermittent irradiation of the sample with the light source. For example, the subject system in these embodiments can include one or more laser beam choppers, manually or computer-controlled beam stoppers, for blocking and exposing the sample to the light source.

[0285] In some embodiments, the light source is a laser. Lasers of interest may include pulsed lasers or continuous wave lasers. For example, the laser can be a gas laser, such as a helium-neon laser, an argon laser, a krypton laser, a xenon laser, a nitrogen laser, a CO2 laser, a CO laser, an argon-fluoride (ArF) excimer laser, a krypton-fluoride (KrF) excimer laser, a xenon-chloride (XeCl) excimer laser or a xenon-fluoride (XeF) excimer laser or a combination thereof; a dye laser, such as a stilbene laser, a coumarin or a rhodamine laser; a metal vapor laser, such as a helium-cadmium (HeCd) laser, a helium-mercury (HeHg) laser, a helium-selenium (HeSe) laser, a helium-silver (HeAg) laser, a strontium laser, a neon-copper (NeCu) laser, a copper laser or a gold laser and combinations thereof; a solid-state laser, such as a ruby laser, a Nd:YAG laser, a NdCrYAG laser, an Er:YAG laser, a Nd:YLF laser, a Nd: YVO4 laser, a Nd: YCa4O(BO3)3 laser, a Nd:YCOB laser, a titanium sapphire laser, a thulium YAG laser, a ytterbium YAG laser, a Yb2O3 laser or a cerium-doped laser and combinations thereof; a semiconductor diode laser, an optically pumped semiconductor laser (OPSL) or a second harmonic generation or third harmonic generation implementation of any of the above lasers.

[0286] In some embodiments, the light source is a beam generator configured to generate two or more frequency-shifted light beams. In some instances, the beam generator includes a laser and a radio frequency (RF) generator configured to apply an RF drive signal to an acousto-optic device to generate two or more angularly deflected laser beams. In these embodiments, the laser can be a pulsed laser or a continuous wave laser. For example, the laser in the beam generator of interest can be a gas laser such as a helium-neon laser, an argon laser, a krypton laser, a xenon laser, a nitrogen laser, a CO2 laser, a CO laser, an argon-fluoride (ArF) excimer laser, a krypton-fluoride (KrF) excimer laser, a xenon-chloride (XeCl) excimer laser, or a xenon-fluoride (XeF) excimer laser or a combination thereof; a dye laser such as a stilbene laser, a coumarin laser, or a rhodamine laser; a metal-vapor laser such as a helium-cadmium (HeCd) laser, a helium-mercury (HeHg) laser, a helium-selenium (HeSe) laser, a helium-silver (HeAg) laser, a strontium laser, a neon-copper (NeCu) laser, a copper laser, or a gold laser and combinations thereof; a solid-state laser such as a ruby laser, a Nd:YAG laser, a NdCrYAG laser, an Er:YAG laser, a Nd:YLF laser, a Nd:YVO4 laser, a Nd:YCa4O(BO3)3 laser, a Nd:YCOB laser, a titanium-sapphire laser, a thulium YAG laser, a ytterbium YAG laser, a Yb2O3 laser, or a cerium-doped laser and combinations thereof.

[0287] The acousto-optic device can be any convenient acousto-optic scheme configured to frequency-shift laser light using an applied acoustic wave. In some embodiments, the acousto-optic device is an acousto-optic deflector. The acousto-optic device in the subject system is configured to generate angularly deflected laser beams based on the light from the laser and the applied RF drive signal. The RF drive signal can be applied to the acousto-optic device with any suitable RF drive signal source, such as a direct digital synthesizer (DDS), an arbitrary waveform generator (AWG), or an electrical pulse generator.

[0288] In an embodiment, the controller is configured to apply a radio frequency drive signal to the acousto-optic device to generate a desired number of angularly deflected laser beams in the output laser beam, e.g., configured to apply 3 or more radio frequency drive signals, e.g., 4 or more radio frequency drive signals, e.g., 5 or more radio frequency drive signals, e.g., 6 or more radio frequency drive signals, e.g., 7 or more radio frequency drive signals, e.g., 8 or more radio frequency drive signals, e.g., 9 or more radio frequency drive signals, e.g., 10 or more radio frequency drive signals, e.g., 15 or more radio frequency drive signals, e.g., 25 or more radio frequency drive signals, e.g., 50 or more radio frequency drive signals and including being configured to apply 100 or more radio frequency drive signals.

[0289] In some instances, to generate an intensity distribution of the angularly deflected laser beams in the output laser beam, the controller is configured to apply a radio frequency drive signal having an amplitude of, e.g., from about 0.001 V to about 500 V, e.g., from about 0.005 V to about 400 V, e.g., from about 0.01 V to about 300 V, e.g., from about 0.05 V to about 200 V, e.g., from about 0.1 V to about 100 V, e.g., from about 0.5 V to about 75 V, e.g., from about 1 V to 50 V, e.g., from about 2 V to about 40 V, e.g., from 3 V to about 30 V and including from about 5 V to about 25 V. In some embodiments, each applied radio frequency drive signal has a frequency of from about 0.001 MHz to about 500 MHz, e.g., from about 0.005 MHz to about 400 MHz, e.g., from about 0.01 MHz to about 300 MHz, e.g., from about 0.05 MHz to about 200 MHz, e.g., from about 0.1 MHz to about 100 MHz, e.g., from about 0.5 MHz to about 90 MHz, e.g., from about 1 MHz to about 75 MHz, e.g., from about 2 MHz to about 70 MHz, e.g., from about 3 MHz to about 65 MHz, e.g., from about 4 MHz to about 60 MHz and including from about 5 MHz to about 50 MHz.

[0290] In some embodiments, the controller has a processor, and a memory is operably coupled to the processor such that the memory includes instructions stored thereon that, when executed by the processor, cause the processor to produce an output laser beam having an angularly deflected laser beam with a desired intensity profile. For example, the memory may include instructions for producing two or more angularly deflected laser beams having the same intensity, such as three or more, such as four or more, such as five or more, such as ten or more, such as twenty-five or more, such as fifty or more, and including that the memory may include instructions for producing one hundred or more angularly deflected laser beams having the same intensity. In other embodiments, the memory may include instructions for producing two or more angularly deflected laser beams having different intensities, such as three or more, such as four or more, such as five or more, such as ten or more, such as twenty-five or more, such as fifty or more, and including that the memory may include instructions for producing one hundred or more angularly deflected laser beams having different intensities.

[0291] In some embodiments, the controller has a processor, and a memory is operably coupled to the processor such that the memory includes instructions stored thereon that, when executed by the processor, cause the processor to produce an output laser beam having an intensity that increases from the edge to the center of the output laser beam along a horizontal axis. In these instances, the intensity of the angularly deflected laser beam at the center of the output beam can be from 0.1% to about 99% of the intensity of the angularly deflected laser beam at the edge of the output laser beam along the horizontal axis, such as from 0.5% to about 95%, such as from 1% to about 90%, such as from about 2% to about 85%, such as from about 3% to about 80%, such as from about 4% to about 75%, such as from about 5% to about 70%, such as from about 6% to about 65%, such as from about 7% to about 60%, such as from about 8% to about 55%, and includes from about 10% to about 50% of the intensity of the angularly deflected laser beam at the edge of the output laser beam along the horizontal axis. In other embodiments, the controller has a processor, and a memory is operably coupled to the processor such that the memory includes instructions stored thereon that, when executed by the processor, cause the processor to produce an output laser beam having an intensity that increases from the edge to the center of the output laser beam along a horizontal axis. In these instances, the intensity of the angularly deflected laser beam at the edge of the output laser beam can be from 0.1% to about 99% of the intensity of the angularly deflected laser beam at the center of the output laser beam along the horizontal axis, such as from 0.5% to about 95%, such as from 1% to about 90%, such as from about 2% to about 85%, such as from about 3% to about 80%, such as from about 4% to about 75%, such as from about 5% to about 70%, such as from about 6% to about 65%, such as from about 7% to about 60%, such as from about 8% to about 55%, and includes from about 10% to about 50% of the intensity of the angularly deflected laser beam at the center of the output laser beam along the horizontal axis. In still other embodiments, the controller has a processor, and a memory is operably coupled to the processor such that the memory includes instructions stored thereon that, when executed by the processor, cause the processor to produce an output laser beam having a Gaussian intensity distribution along the horizontal axis. In yet other embodiments, the controller has a processor, and a memory is operably coupled to the processor such that the memory includes instructions stored thereon that, when executed by the processor, cause the processor to produce an output laser beam having a top-hat intensity distribution along the horizontal axis.

[0292] In an embodiment, the beam generator of interest can be configured to produce angularly deflected laser beams that are spatially separated in an output laser beam. Depending on the applied radio frequency drive signal and the desired illumination profile of the output laser beam, the angularly deflected laser beams can be separated by 0.001 µm or more, such as 0.005 µm or more, such as 0.01 µm or more, such as 0.05 µm or more, such as 0.1 µm or more, such as 0.5 µm or more, such as 1 µm or more, such as 5 µm or more, such as 10 µm or more, such as 100 µm or more, such as 500 µm or more, such as 1000 µm or more and including 5000 µm or more. In some embodiments, the system is configured to produce overlapping angularly deflected laser beams in the output laser beam, such as overlapping with adjacent angularly deflected laser beams along the horizontal axis of the output laser beam. The overlap between adjacent angularly deflected laser beams (such as the overlap of the beam spots) can be an overlap of 0.001 µm or more, such as an overlap of 0.005 µm or more, such as an overlap of 0.01 µm or more, such as an overlap of 0.05 µm or more, such as an overlap of 0.1 µm or more, such as an overlap of 0.5 µm or more, such as an overlap of 1 µm or more, such as an overlap of 5 µm or more, such as an overlap of 10 µm or more and including an overlap of 100 µm or more.

[0293] In certain instances, a beam generator configured to generate two or more frequency-shifted light beams includes a laser excitation module as described in U.S. Patent Nos. 9,423,353, 9,784,661, 9,983,132, 10,006,852, 10,078,045, 10,036,699, 10,222,316, 10,288,546, 10,324,019, 10,408,758, 10,451,538, 10,620,111 and U.S. Patent Publication Nos. 2017 / 0133857, 2017 / 0328826, 2017 / 0350803, 2018 / 0275042, 2019 / 0376895 and 2019 / 0376894, the disclosures of which are incorporated herein by reference.

[0294] In an embodiment, the system includes a light detection system having a plurality of photodetectors. The photodetectors of interest may include, but are not limited to, optical sensors such as active pixel sensors (APS), avalanche photodiodes, image sensors, charge-coupled devices (CCD), intensified charge-coupled devices (ICCD), light-emitting diodes, photon counters, bolometers, pyroelectric detectors, photoresistors, photovoltaic cells, photodiodes, photomultiplier tubes, phototransistors, quantum dot photoconductors or photodiodes and combinations thereof, and other photodetectors. In certain embodiments, the light from the sample is detected using a charge-coupled device (CCD), a semiconductor charge-coupled device (CCD), an active pixel sensor (APS), a complementary metal-oxide-semiconductor (CMOS) image sensor, or an N-type metal-oxide-semiconductor (NMOS) image sensor.

[0295] In some embodiments, the light detection system of interest includes a plurality of photodetectors. In certain instances, the light detection system includes a plurality of solid-state detectors such as photodiodes. In certain instances, the light detection system includes an array of photodetectors such as an array of photodiodes. In these embodiments, the array of photodetectors may include 4 or more photodetectors, such as 10 or more photodetectors, such as 25 or more photodetectors, such as 50 or more photodetectors, such as 100 or more photodetectors, such as 250 or more photodetectors, such as 500 or more photodetectors, such as 750 or more photodetectors and includes 1000 or more photodetectors. For example, the detector may be an array of photodiodes having 4 or more photodiodes, such as 10 or more photodiodes, such as 25 or more photodiodes, such as 50 or more photodiodes, such as 100 or more photodiodes, such as 250 or more photodiodes, such as 500 or more photodiodes, such as 750 or more photodiodes and includes 1000 or more photodiodes.

[0296] The photodetector can be arranged in any geometric configuration as needed, and the arrangements of interest include, but are not limited to, a square configuration, a rectangular configuration, a trapezoidal configuration, a triangular configuration, a hexagonal configuration, a heptagonal configuration, an octagonal configuration, a nonagonal configuration, a decagonal configuration, a dodecagonal configuration, a circular configuration, an elliptical configuration, and an irregular pattern configuration. The photodetectors in the photodetector array can be oriented at an angle of 10° to 180° relative to other photodetectors (e.g., referenced in the X-Z plane), such as 15° to 170°, such as 20° to 160°, such as 25° to 150°, such as 30° to 120°, and including 45° to 90°. The photodetector array can be of any suitable shape and can be a linear shape, such as a square, a rectangle, a trapezoid, a triangle, a hexagon, etc., a curved shape, such as a circle, an ellipse, and an irregular shape, such as a parabolic bottom coupled to the top of a plane. In some embodiments, the photodetector array has a rectangular active surface.

[0297] Each photodetector (e.g., a photodiode) in the array can have an active surface with a width ranging from 5 µm to 250 µm, such as 10 µm to 225 µm, such as 15 µm to 200 µm, such as 20 µm to 175 µm, such as 25 µm to 150 µm, such as 30 µm to 125 µm, and including 50 µm to 100 µm, and a length ranging from 5 µm to 250 µm, such as 10 µm to 225 µm, such as 15 µm to 200 µm, such as 20 µm to 175 µm, such as 25 µm to 150 µm, such as 30 µm to 125 µm, and including 50 µm to 100 µm, where the surface area of each photodetector (e.g., a photodiode) in the array is from 25 to µm 2 to 10000 µm 2 such as 50 µm 2 to 9000 µm 2 such as 75 µm 2 to 8000 µm 2 such as 100 µm 2 to 7000 µm 2 such as 150 µm 2 to 6000 µm 2 and including 200 µm 2 to 5000 µm 2 .

[0298] The size of the photodetector array can vary according to the amount and intensity of light, the number of photodetectors, and the desired sensitivity, and the photodetector array can have a length in the range of 0.01 mm to 100 mm, such as 0.05 mm to 90 mm, such as 0.1 mm to 80 mm, such as 0.5 mm to 70 mm, such as 1 mm to 60 mm, such as 2 mm to 50 mm, such as 3 mm to 40 mm, such as 4 mm to 30 mm and including 5 mm to 25 mm. The width of the photodetector array can also vary within the following range, which is 0.01 mm to 100 mm, such as 0.05 mm to 90 mm, such as 0.1 mm to 80 mm, such as 0.5 mm to 70 mm, such as 1 mm to 60 mm, such as 2 mm to 50 mm, such as 3 mm to 40 mm, such as 4 mm to 30 mm and including 5 mm to 25 mm. Thus, the active surface of the photodetector array can range from 0.1 mm 2 to 10000 mm 2 such as 0.5 mm 2 to 5000 mm 2 such as 1 mm 2 to 1000 mm 2 such as 5 mm 2 to 500 mm 2 and including 10 mm 2 to 100 mm 2 .

[0299] The photodetectors of interest are configured to measure light of one or more wavelengths collected, such as 2 or more wavelengths, such as 5 or more different wavelengths, such as 10 or more different wavelengths, such as 25 or more different wavelengths, such as 50 or more different wavelengths, such as 100 or more different wavelengths, such as 200 or more different wavelengths, such as 300 or more different wavelengths and including measuring light emitted by a sample in a flowing stream at 400 or more different wavelengths.

[0300] In some embodiments, the photodetector is configured to measure light collected within a wavelength range (e.g., 200 nm to 1000 nm). In certain embodiments, the photodetector of interest is configured to collect the spectrum of light within a wavelength range. For example, the system can include one or more detectors configured to collect the spectrum of light within one or more wavelength ranges from 200 nm to 1000 nm. In still other embodiments, the detector of interest is configured to measure light of one or more specific wavelengths from a sample in a flowing stream. For example, the system can include one or more detectors configured to measure one or more of the light at 450 nm, 518 nm, 519 nm, 561 nm, 578 nm, 605 nm, 607 nm, 625 nm, 650 nm, 660 nm, 667 nm, 670 nm, 668 nm, 695 nm, 710 nm, 723 nm, 780 nm, 785 nm, 647 nm, 617 nm, and any combination thereof. In certain embodiments, the photodetector can be configured to be paired with a specific fluorophore (e.g., a fluorophore used with a sample in a fluorescence assay). In some embodiments, the photodetector is configured to measure the light collected in the entire fluorescence spectrum of each fluorophore in the sample.

[0301] The light detection system is configured to measure light continuously or at discrete intervals. In some instances, the light detector of interest is configured to continuously measure the collected light. In other instances, the light detection system is configured to take measurements at discrete intervals, such as measuring light every 0.001 milliseconds, every 0.01 milliseconds, every 0.1 milliseconds, every 1 millisecond, every 10 milliseconds, every 100 milliseconds, and including measuring light every 1000 milliseconds or some other interval.

[0302] In an embodiment, the system is configured to analyze light from an illuminated sample and perform spectral decomposition of the light from each fluorophore in the sample using a generalized least squares algorithm. In some embodiments, the system includes a memory having instructions stored thereon for determining the overlap between each different fluorophore in the sample and calculating the contribution of each fluorophore to the overlapping fluorescence. In certain embodiments, the system is configured to calculate a spectral unmixing matrix of the fluorescence spectra of multiple fluorophores having overlapping fluorescence in the sample detected by a light detection system. As described in more detail below, the system can also be configured to estimate the abundance of each fluorophore in the sample. In certain embodiments, the abundance of each fluorophore associated with a target particle can be determined. The system can be configured to identify and classify target particles based on the abundance of each fluorophore associated with the target particle. In some instances, the system is configured to sort the identified or classified particles. In these embodiments, the system can include a computer control system, wherein the system further includes one or more computers for fully or partially automating the system for practicing the methods described herein.

[0303] In some embodiments, the system includes a computer having a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is loaded onto the computer, it includes instructions to: illuminate a flow cell having a sample in a flowing stream with a light source and detect light from the flow cell with a light detection system having a plurality of photodetectors, perform spectral decomposition of the light emitted from each fluorophore in the sample using a generalized least squares algorithm, estimate the abundance of each fluorophore; and sort particles in the sample based on the estimated fluorophore abundances.

[0304] In some embodiments, the memory includes instructions stored thereon that, when executed by a processor, cause the processor to determine the data signal covariance within each photodetector channel. In some instances, the data signal covariance within each photodetector channel includes an inherent sample variability component and a measurement variability component. In some instances, the data signal covariance includes the electronic noise in each photodetector channel. In some instances, the data signal covariance includes the shot noise in each photodetector channel. In some instances, the data signal covariance varies linearly with the generated data signal. In some instances, the data signal covariance varies quadratically with the generated data signal. In some instances, the data signal covariance is correlated between two or more of the plurality of photodetector channels. In some instances, the memory includes instructions for calculating the data signal covariance according to:

[0305] ,

[0306] where:

[0307] is the measured detector signal;

[0308] is the baseline noise component;

[0309] is the Poisson noise component;

[0310] is the Poisson noise coefficient;

[0311] is the quadratic noise component; and

[0312] is the quadratic noise coefficient.

[0313] In some instances, the memory includes instructions for calculating the covariance of data signals using a covariance matrix. In some instances, the covariance matrix contains non-zero diagonal values. In some instances, the memory includes instructions for calculating the covariance using the covariance matrix as follows:

[0314] ,

[0315] where, represents generating a diagonal matrix from the column vector x, and represents the covariance between a and b.

[0316] In some instances, the memory includes instructions for calculating a generalized least squares problem by multiplying the inverse of the calculated covariance matrix. In some instances, the memory includes instructions for estimating the covariance of data signals based on the fluorescence intensities of two or more photodetectors of an optical detection system. In some instances, the memory includes instructions for estimating the covariance of data signals based on the fluorescence intensity of each in an optical detection channel. In some embodiments, the memory includes instructions for calculating a generalized least squares problem as follows:

[0317] ,

[0318] where:

[0319] is the weight matrix;

[0320] is the covariance matrix;

[0321] X is the spectral matrix (overflow matrix);

[0322] y is the detector values measured by multiple photodetectors of the optical detection system for each cell;

[0323] f is the true fluorophore abundance for each cell; and

[0324] The estimated (unmixed) fluorophore abundances for each cell.

[0325] In some instances, the memory includes instructions for a prior estimate covariance matrix. In certain instances, the memory includes instructions for real-time application of the generalized least squares problem (e.g., using an integrated circuit such as a field programmable gate array). In some instances, a prior noise model is used to estimate each event covariance (e.g., calculating each event covariance matrix in real-time). In some instances, the prior noise model only uses data collected for each specific event. In some instances, the covariance matrix includes an estimate for the entire collected data set.

[0326] In some instances, the memory includes instructions for determining the data signal covariance by estimation through iterative optimization of a covariance matrix that minimizes the variance of the unmixed data signal. In certain instances, the memory includes instructions for calculating the generalized least squares problem through Cholesky decomposition of the covariance matrix. In certain instances, the generalized least squares problem is characterized by calculating the Cholesky decomposition of the covariance matrix and solving a triangular system according to the following to generate a transformed input for an ordinary least squares algorithm:

[0327] Solve to generate , which is the decorrelated and whitened version of the data vector y.

[0328] Solve to generate , which is the corresponding transformed version of the spectral matrix X.

[0329] The transformed system is solved by ordinary least squares, e.g., by solving the so-called normal equations .

[0330] In some embodiments, the memory includes instructions for finding the least squares solution of the generalized least squares problem. In some instances, the memory includes instructions for finding the least squares solution of the generalized least squares problem through one or more of matrix decomposition, matrix factorization, QR factorization, Cholesky decomposition, singular value decomposition, LDL decomposition, and pre-permutation and post-permutation. In some instances, the memory includes instructions for finding the least squares solution of the generalized least squares problem by solving the so-called normal equations through Cholesky decomposition or LDL decomposition, e.g., according to the following through Cholesky decomposition or LDL decomposition:

[0331] ,

[0332] where y is the detector value measured by a plurality of photodetectors of the optical detection system for each cell; X is the overflow; and

[0333] G is 。

[0334] In some examples, the memory includes instructions for solving the least squares solution of the generalized least squares problem by Cholesky decomposition or LDL decomposition according to the following:

[0335] ,

[0336] ,

[0337] ,LDL decomposition,

[0338] where ,lower triangular matrix solution,

[0339] where ,diagonal matrix solution,

[0340] ,solve ,upper triangular matrix solution.

[0341] In some embodiments, the memory includes instructions for solving the least squares solution of the generalized least squares problem by matrix factorization.

[0342] In some examples, the memory includes instructions for solving the least squares solution of the generalized least squares problem by matrix factorization. In some examples, the memory includes instructions for solving the least squares solution of the generalized least squares problem by QR factorization. In some examples, the memory includes instructions for using the transformed and (calculated by Cholesky decomposition of the covariance matrix above) to calculate the generalized least squares problem according to the following:

[0343] ,normal equations of the transformed GLS problem,

[0344] ,QR decomposition of the transformed X,

[0345] ,permutation,

[0346] ,expanded transpose of QR,

[0347] , Since orthogonality can be eliminated,

[0348] , triangular solution .

[0349] In some embodiments, the memory includes instructions for obtaining a least squares solution of a generalized least squares problem by singular value decomposition. In some instances, the singular value decomposition is a product of matrices, where U and V are orthogonal matrices, is a diagonal matrix containing singular values. In some instances, the singular value decomposition is a product of matrices, where U and V are orthogonal matrices, and is a diagonal matrix containing singular values. In some instances, the memory includes instructions for calculating a generalized least squares problem using singular value decomposition as follows:

[0350]

[0351]

[0352] ,

[0353] where U and V are orthogonal matrices, and is a diagonal matrix containing singular values.

[0354] In some embodiments, the memory includes instructions for obtaining a least squares solution of a generalized least squares problem by LDL decomposition. In certain embodiments, the memory includes instructions for minimizing the least squares solution of a generalized least squares problem by pre-permutation and post-permutation.

[0355] In certain embodiments, the subject system includes a field programmable gate array, and a spectral unmixing algorithm is calculated in real time for each cell on the field programmable gate array.

[0356] In some embodiments, the system includes a computer having a computer-readable storage medium storing a computer program, wherein when the computer program is loaded onto the computer, it further includes instructions for calculating the abundance of one or more fluorophores in a sample based on spectrally resolved light from each fluorophore. In certain instances, the abundance of fluorophores associated (e.g., chemically associated (i.e., covalently associated, ionically associated) or physically associated) with a target particle is calculated based on spectrally resolved light from each fluorophore associated with the particle. For example, in one example, the relative abundance of each fluorophore associated with a target particle is calculated based on spectrally resolved light from each fluorophore. In another example, the absolute abundance of each fluorophore associated with a target particle is calculated based on spectrally resolved light from each fluorophore.

[0357] In some embodiments, the system is configured to identify or classify particles based on determining the relative abundance of each fluorophore associated with the particle. In these embodiments, the subject system can be configured to identify or classify particles by any convenient scheme, such as by: comparing the relative or absolute abundance of each fluorophore associated with the particle to a control sample of particles having known characteristics; or by performing spectral or other assay analysis on a population of particles (e.g., cells) for which the relative or absolute abundance of associated fluorophores has been calculated.

[0358] The system according to some embodiments can include a display and an operator input device. The operator input device can be, for example, a keyboard, a mouse, etc. The processing module includes a processor that can access a memory storing instructions for performing the steps of the subject method. The processing module can include an operating system, a graphical user interface (GUI) controller, a system memory, a memory storage device, and an input-output controller, a cache memory, a data backup unit, and many other devices. The processor can be a commercially available processor or one of other processors that are already available or will be available. The processor executes the operating system, and the operating system interfaces with the firmware and hardware in a well-known manner and facilitates the processor to coordinate and execute the functions of various computer programs, which can be written in various programming languages known in the art, such as Java, Perl, C++, other high-level or low-level languages, and combinations thereof. The operating system typically cooperates with the processor to coordinate and execute the functions of other components of the computer. The operating system also provides scheduling, input-output control, file and data management, memory management, communication control, and related services according to known techniques. The processor can be any suitable analog or digital system. In some embodiments, the processor includes analog electronics providing feedback control (e.g., negative feedback control).

[0359] The system memory can be any one of a variety of known or future memory storage devices. Examples include any common random access memory (RAM), magnetic media such as a resident hard disk or tape, optical media such as a read / write optical disk, flash memory devices, or other memory storage devices. The memory storage device can be any one of a variety of known or future devices, including an optical disk drive, a tape drive, a removable hard disk drive, or a floppy disk drive. This type of memory storage device typically reads from and / or writes to a program storage medium (not shown) (such as an optical disk, a tape, a removable hard disk, or a floppy disk, respectively). Any one of these program storage media, or other media that are now in use or may be developed in the future, can be considered a computer program product. It should be understood that these program storage media typically store computer software programs and / or data. The computer software program (also known as computer control logic) is typically stored in the system memory and / or in a program storage device used in conjunction with the memory storage device.

[0360] In some embodiments, a computer program product is described that includes a computer-usable medium having control logic (computer software program, including program code) stored therein. The control logic, when executed by a processor or computer, causes the processor to perform the functions described herein. In other embodiments, some functions are implemented primarily in hardware using, for example, a hardware state machine. Implementing a hardware state machine to perform the functions described herein will be apparent to those skilled in the relevant art.

[0361] The memory can be any suitable device capable of storing and retrieving data by the processor, such as a magnetic, optical, or solid-state storage device (including a disk or optical disk or tape or RAM, or any other suitable fixed or portable device). The processor can include a general-purpose digital microprocessor that is appropriately programmed from a computer-readable medium carrying the necessary program code. The programming can be provided remotely to the processor via a communication channel, or pre-stored in a computer program product (such as a memory or some other portable or fixed computer-readable storage medium) using any one of those devices connected to the memory. For example, a disk or optical disk can carry the programming and be readable by a disk writer / reader. The system of the present invention also includes programming, such as in the form of a computer program product, an algorithm for practicing the above-described method. The programming according to the present invention can be recorded on a computer-readable medium (such as any medium that can be directly read and accessed by a computer). Such media include, but are not limited to: magnetic storage media (such as floppy disks, hard disk storage media, and tapes); optical storage media (such as CD-ROMs); electrical storage media (such as RAM and ROM); portable flash drives; and hybrids of these categories (such as magnetic / optical storage media).

[0362] The processor can also access a communication channel to communicate with a user at a remote location. A remote location means that the user is not in direct contact with the system and relays input information from an external device (such as a computer connected to a wide area network (WAN), telephone network, satellite network, or any other suitable communication channel, including a mobile phone (i.e., a smartphone)) to the input manager.

[0363] In some embodiments, a system according to the present disclosure can be configured to include a communication interface. In some embodiments, the communication interface includes a receiver and / or a transmitter for communicating with a network and / or another device. The communication interface can be configured for wired or wireless communication, including but not limited to radio frequency (RF) communication (e.g., radio frequency identification (RFID)), Zigbee communication protocol, Wi-Fi, infrared, wireless universal serial bus (USB), ultra-wideband (UWB), Bluetooth communication protocols, and cellular communication (e.g., code division multiple access (CDMA) or global system for mobile communications (GSM)).

[0364] In one embodiment, the communication interface is configured to include one or more communication ports, such as physical ports or interfaces (e.g., USB ports, RS-232 ports, or any other suitable electrical connection ports), to allow data communication between the subject system and other external devices, such as computer terminals (e.g., in a doctor's office or hospital environment) configured for similar complementary data communication.

[0365] In one embodiment, the communication interface is configured for infrared communication, Bluetooth communication, or any other suitable wireless communication protocol to enable the subject system to communicate with other devices, such as computer terminals and / or networks, communication-enabled mobile phones, personal digital assistants, or any other communication device that a user can use in combination.

[0366] In one embodiment, the communication interface is configured to provide a connection for data transmission using the Internet protocol (IP) via a cellular telephone network, short message service (SMS), a wireless connection to a personal computer (PC) on a local area network (LAN) connected to the Internet, or a Wi-Fi connection to the Internet at a Wi-Fi hotspot.

[0367] In one embodiment, the subject system is configured to communicate via the communication interface (e.g., using protocols such as 802.11 or Bluetooth Wirelessly communicate with the server device using a general standard of the RF protocol or the IrDA infrared protocol). The server device can be another portable device, such as a smart phone, a personal digital assistant (PDA), or a laptop computer; or a larger device, such as a desktop computer, a device, etc. In some embodiments, the server device has a display, such as a liquid crystal display (LCD), and an input device, such as a button, a keyboard, a mouse, or a touch screen.

[0368] In some embodiments, the communication interface is configured to automatically or semi-automatically transfer data stored in the subject system (e.g., stored in the optional data storage unit) to a network or a server device using one or more of the above communication protocols and / or mechanisms.

[0369] The output controller can include a controller for any of a variety of known display devices for presenting information to a user, whether human or machine, local or remote. If one of the display devices provides visual information, the information can generally be logically and / or physically organized as an array of image elements. The graphical user interface (GUI) controller can include any of a variety of known or future software programs for providing a graphical input and output interface between the system and the user and for processing user input. The functional elements of the computer can communicate with each other via the system bus. In alternative embodiments, some of these communications can be implemented using a network or other type of remote communication. According to known techniques, the output manager can also provide information generated by the processing module to a user at a remote location, for example, via the Internet, a telephone, or a satellite network. The presentation of data by the output manager can be implemented according to various known techniques. As some examples, the data can include SQL, HTML, or XML documents, emails, or other files or other forms of data. The data can include Internet URL addresses such that the user can retrieve additional SQL, HTML, XML, or other documents or data from a remote source. One or more platforms present in the subject system can be any type of computer platform known or to be developed in the future, although they will generally be of the category of computers (commonly referred to as servers). However, they can also be mainframe computers, workstations, or other computer types. They can be connected by any known or future type of cable or other communication system, including wireless systems, whether networked or otherwise. They may be co-located or may also be physically separated. Depending on the type and / or brand of the computer platform selected, various operating systems can be employed on any computer platform. Suitable operating systems include Windows 10, Windows NT , Windows XP, Windows 7, Windows 8, iOS, Sun Solaris, Linux, OS / 400, Compaq Tru64 Unix, SGI IRIX, Siemens Reliant Unix, Ubuntu, Zorin OS, etc.

[0370] In some embodiments, the subject system includes one or more optical conditioning components for conditioning light, such as light that is incident on a sample (e.g., from a laser) or light that is collected from a sample (e.g., scattered, fluorescent). For example, optical conditioning can be increasing the size of the light, focusing the light, or collimating the light. In some embodiments, the optical conditioning is a magnification scheme to increase the size of the light (e.g., beam spot), such as increasing the size by 5% or more, such as 10% or more, such as 25% or more, such as 50% or more and including 75% or more. In other embodiments, the optical conditioning includes focusing the light to decrease the size of the light, such as decreasing by 5% or more, such as 10% or more, such as 25% or more, such as 50% or more and including decreasing the size of the beam spot by 75% or more. In certain embodiments, the optical conditioning includes collimating the light. The term "collimate" is used in its conventional sense to refer to conditioning the collinearity of light propagation or reducing the divergence of light from a common propagation axis. In some embodiments, collimating includes narrowing the spatial cross-section of the beam (e.g., reducing the beam profile of a laser).

[0371] In some embodiments, the optical conditioning component is a focusing lens having a magnification ratio of 0.1 to 0.95, such as a magnification ratio of 0.2 to 0.9, such as a magnification ratio of 0.3 to 0.85, such as a magnification ratio of 0.35 to 0.8, such as a magnification ratio of 0.5 to 0.75 and including a magnification ratio of 0.55 to 0.7, such as a magnification ratio of 0.6. For example, in certain instances, the focusing lens is a double achromatic de-magnifying lens having a magnification ratio of about 0.6. The focal length of the focusing lens can be 5 mm to 20 mm, such as 6 mm to 19 mm, such as 7 mm to 18 mm, such as 8 mm to 17 mm, such as 9 mm to 16 and including a focal length of 10 mm to 15 mm. In certain embodiments, the focusing lens has a focal length of about 13 mm.

[0372] In other embodiments, the optical adjustment component is a collimator. The collimator can be any convenient collimation scheme, such as one or more mirrors or aspherical lenses or a combination thereof. For example, the collimator is a single collimating lens in some instances. In other instances, the collimator is a collimating mirror. In still other instances, the collimator includes two lenses. In yet other instances, the collimator includes a mirror and a lens. When the collimator includes one or more lenses, the focal length of the collimating lens can be from 5 mm to 40 mm, such as from 6 mm to 37.5 mm, such as from 7 mm to 35 mm, such as from 8 mm to 32.5 mm, such as from 9 mm to 30 mm, such as from 10 mm to 27.5 mm, such as from 12.5 mm to 25 mm and including a focal length in the range of 15 mm to 20 mm.

[0373] In some embodiments, the subject system includes a flow cell nozzle having a nozzle orifice configured to enable a flowing stream to flow through the flow cell nozzle. The subject flow cell nozzle has an orifice for propagating a fluid sample to a sample interrogation region, wherein in some embodiments, the flow cell nozzle includes a proximal cylindrical portion defining a longitudinal axis and a distal frustoconical portion terminating in a flat surface and having a nozzle orifice transverse to the longitudinal axis. The length of such proximal cylindrical portion (measured along the longitudinal axis) can be from 1 mm to 15 mm, such as from 1.5 mm to 12.5 mm, such as from 2 mm to 10 mm, such as from 3 mm to 9 mm and including from 4 mm to 8 mm. The length of such distal frustoconical portion (measured along the longitudinal axis) can also be from 1 mm to 10 mm, such as from 2 mm to 9 mm, such as from 3 mm to 8 mm and including from 4 mm to 7 mm. In some embodiments, the diameter of the flow cell nozzle chamber can be from 1 mm to 10 mm, such as from 2 mm to 9 mm, such as from 3 mm to 8 mm and including from 4 mm to 7 mm.

[0374] In certain instances, the nozzle chamber does not include a cylindrical portion and the entire flow cell nozzle chamber is frustoconical. In these embodiments, the length of the frustoconical nozzle chamber (measured along the longitudinal axis transverse to the nozzle orifice) can be in the range of 1 mm to 15 mm, such as from 1.5 mm to 12.5 mm, such as from 2 mm to 10 mm, such as from 3 mm to 9 mm and including from 4 mm to 8 mm. The diameter of the proximal portion of the frustoconical nozzle chamber can be in the range of 1 mm to 10 mm, such as from 2 mm to 9 mm, such as from 3 mm to 8 mm and including from 4 mm to 7 mm.

[0375] In an embodiment, the sample flow stream exits through an orifice at the distal end of the flow cell nozzle. Depending on the desired characteristics of the flow stream, the flow cell nozzle orifice can be any suitable shape, where cross-sectional shapes of interest include, but are not limited to: linear cross-sectional shapes (such as square, rectangular, trapezoidal, triangular, hexagonal, etc.), curved cross-sectional shapes (such as circular, elliptical), and irregular shapes (such as a parabolic bottom portion coupled to a flat top portion). In certain embodiments, the flow cell nozzle of interest has a circular orifice. The size of the nozzle orifice can vary and, in some embodiments, ranges from 1 μm to 20000 μm, such as 2 μm to 17500 μm, such as 5 μm to 15000 μm, such as 10 μm to 12500 μm, such as 15 μm to 10000 μm, such as 25 μm to 7500 μm, such as 50 μm to 5000 μm, such as 75 μm to 1000 μm, such as 100 μm to 750 μm and includes 150 μm to 500 μm. In certain embodiments, the nozzle orifice is 100 μm.

[0376] In some embodiments, the flow cell nozzle includes a sample injection port configured to provide a sample to the flow cell nozzle. In an embodiment, the sample injection system is configured to provide a suitable sample flow to the flow cell nozzle chamber. Depending on the characteristics of the desired flow stream, the rate at which the sample is delivered to the flow stream nozzle chamber by the sample injection port can be 1 μL / second or more, such as 2 μL / second or more, such as 3 μL / second or more, such as 5 μL / second or more, such as 10 μL / second or more, such as 15 μL / second or more, such as 25 μL / second or more, such as 50 μL / second or more, such as 100 μL / second or more, such as 150 μL / second or more, such as 200 μL / second or more, such as 250 μL / second or more, such as 300 μL / second and more, such as 350 μL / second or more, such as 400 μL / second or more, such as 450 μL / second or more and includes 500 μL / second or more. For example, the sample flow rate can be in the range of 1 μL / second to about 500 μL / second, such as 2 μL / second to about 450 μL / second, such as 3 μL / second to about 400 μL / second, such as 4 μL / second to about 350 μL / second, such as 5 μL / second to about 300 μL / second, such as 6 μL / second to about 250 μL / second, such as 7 μL / second to about 200 μL / second, such as 8 μL / second to about 150 μL / second, such as 9 μL / second to about 125 μL / second and includes 10 μL / second to about 100 μL / second.

[0377] The sample injection port can be an orifice positioned in the wall of the nozzle chamber or can be a catheter positioned at the proximal end of the nozzle chamber. When the sample injection port is an orifice positioned in the wall of the nozzle chamber, the orifice of the sample injection port can be of any suitable shape, where the cross-sectional shapes of interest include but are not limited to: linear cross-sectional shapes (such as square, rectangle, trapezoid, triangle, hexagon, etc.), curved cross-sectional shapes (such as circle, ellipse, etc.), and irregular shapes (such as a parabolic bottom portion coupled to a flat top portion). In some embodiments, the sample injection port has a circular orifice. The size of the orifice of the sample injection port can vary according to the shape, and in some instances, it has an opening of 0.1 mm to 5.0 mm, such as 0.2 mm to 3.0 mm, such as 0.5 mm to 2.5 mm, such as 0.75 mm to 2.25 mm, such as 1 mm to 2 mm and includes an opening of 1.25 mm to 1.75 mm, such as an opening of 1.5 mm.

[0378] In some instances, the sample injection port is a catheter positioned at the proximal end of the flow cell nozzle chamber. For example, the sample injection port can be a catheter positioned such that the orifice of the sample injection port is aligned with the flow cell nozzle orifice. When the sample injection port is a catheter positioned to be aligned with the flow cell nozzle orifice, the cross-sectional shape of the sample injection tube can be of any suitable shape, where the cross-sectional shapes of interest include but are not limited to: linear cross-sectional shapes (such as square, rectangle, trapezoid, triangle, hexagon, etc.), curved cross-sectional shapes (such as circle, ellipse), and irregular shapes (such as a parabolic bottom portion coupled to a flat top portion). The orifice of the catheter can vary according to the shape, and in some instances, the orifice of the catheter has an opening of 0.1 mm to 5.0 mm, such as 0.2 mm to 3.0 mm, such as 0.5 mm to 2.5 mm, such as 0.75 mm to 2.25 mm, such as 1 mm to 2 mm and includes an opening of 1.25 mm to 1.75 mm, such as an opening of 1.5 mm. The shape of the tip of the sample injection port can be the same as or different from the cross-sectional shape of the sample injection tube. For example, the orifice of the sample injection port can include an angled tip with an angle of inclination of 1° to 10°, such as 2° to 9°, such as 3° to 8°, such as 4° to 7° and includes an inclination angle of 5°.

[0379] In some embodiments, the flow cell nozzle further includes a sheath fluid injection port configured to provide sheath fluid to the flow cell nozzle. In an embodiment, the sheath fluid injection system is configured to provide a sheath fluid flow to the flow cell nozzle chamber, e.g., to combine with the sample to create a stratified flow of sheath fluid that flows around the sample flow stream. Depending on the characteristics of the desired flow stream, the velocity of the sheath fluid delivery to the flow cell nozzle chamber can be 25 μL / second or more, e.g., 50 μL / second or more, e.g., 75 μL / second or more, e.g., 100 μL / second or more, e.g., 250 μL / second or more, e.g., 500 μL / second or more, e.g., 750 μL / second or more, e.g., 1000 μL / second or more and including 2500 μL / second or more. For example, the sheath fluid flow rate may be in the range of 1 μL / second to about 500 μL / second, e.g., 2 μL / second to about 450 μL / second, e.g., 3 μL / second to about 400 μL / second, e.g., 4 μL / second to about 350 μL / second, e.g., 5 μL / second to about 300 μL / second, e.g., 6 μL / second to about 250 μL / second, e.g., 7 μL / second to about 200 μL / second, e.g., 8 μL / second to about 150 μL / second, e.g., 9 μL / second to about 125 μL / second and including 10 μL / second to about 100 μL / second.

[0380] In some embodiments, the sheath fluid injection port is an orifice located in the wall of the nozzle chamber. The orifice of the sheath fluid injection port can be any suitable shape, where cross-sectional shapes of interest include, but are not limited to: linear cross-sectional shapes (e.g., square, rectangle, trapezoid, triangle, hexagon, etc.), curved cross-sectional shapes (e.g., circle, ellipse), and irregular shapes (e.g., a parabolic bottom portion coupled to a flat top portion). The size of the orifice of the sample injection port can vary depending on the shape and, in certain instances, has an opening of 0.1 mm to 5.0 mm, e.g., 0.2 mm to 3.0 mm, e.g., 0.5 mm to 2.5 mm, e.g., 0.75 mm to 2.25 mm, e.g., 1 mm to 2 mm and including 1.25 mm to 1.75 mm, e.g., 1.5 mm.

[0381] In some instances, the subject system includes a sample interrogation region that is in fluid communication with an orifice of a flow cell nozzle. In these instances, a sample flow stream issues from the orifice at the distal end of the flow cell nozzle, and particles in the flow stream can be illuminated by a light source in the sample interrogation region. The size of the interrogation region can vary depending on the characteristics of the flow nozzle (e.g., the size of the nozzle orifice and the size of the sample injection port). In an embodiment, the interrogation region can have a width of 0.01 mm or greater, such as 0.05 mm or greater, such as 0.1 mm or greater, such as 0.5 mm or greater, such as 1 mm or greater, such as 2 mm or greater, such as 3 mm or greater, such as 5 mm or greater and including 10 mm or greater. In some instances the length of the interrogation region varies in the range of 0.01 mm or greater, such as 0.1 mm or greater, such as 0.5 mm or greater, such as 1 mm or greater, such as 1.5 mm or greater, such as 2 mm or greater, such as 3 mm or greater, such as 5 mm or greater, such as 10 mm or greater, such as 15 mm or greater, such as 20 mm or greater, such as 25 mm or greater and including 50 mm or greater.

[0382] The interrogation region can be configured to facilitate illumination of a planar cross-section of the emission flow stream or can be configured to facilitate illumination of a diffusion field of a predetermined length (e.g., using a diffusive laser or lamp). In some embodiments, the interrogation region includes a transparent window that facilitates illumination of a predetermined length of the emission flow stream, such as 1 mm or longer, such as 2 mm or longer, such as 3 mm or longer, such as 4 mm or longer, such as 5 mm or longer and including 10 mm or longer. Depending on the light source used to illuminate the emission flow stream (described below), the interrogation region can be configured to allow light of 100 nm to 1500 nm to pass through, such as 150 nm to 1400 nm, such as 200 nm to 1300 nm, such as 250 nm to 1200 nm, such as 300 nm to 1100 nm, such as 350 nm to 1000 nm, such as 400 nm to 900 nm and including 500 nm to 800 nm.Accordingly, the interrogation region can be formed from any transparent material through which the desired wavelength range passes, including but not limited to optical glass, borosilicate glass, Pyrex glass, ultraviolet quartz, infrared quartz, sapphire, and plastics such as polycarbonate, polyvinyl chloride (PVC), polyurethane, polyether, polyamide, polyimide, or copolymers of these thermoplastics such as PETG (ethylene glycol modified polyethylene terephthalate), where the polyesters of interest can include but are not limited to poly(alkylene terephthalates) such as poly(ethylene terephthalate) (PET), bottle grade PET (a copolymer made from monoethylene glycol, terephthalic acid, and other comonomers such as isophthalic acid, cyclohexanedimethanol, etc.), poly(butylene terephthalate) (PBT), and poly(hexamethylene terephthalate); poly(alkylene adipates) such as poly(ethylene adipate), poly(1,4-butylene adipate), and poly(hexamethylene adipate); poly(octylene adipates) such as poly(ethylene octylene adipate); poly(alkylene sebacates), such as poly(ethylene sebacate); poly(ε-caprolactone) and poly(β-propiolactone); poly(isophthalic acid alkylene esters), such as poly(ethylene isophthalate); poly(2,6-naphthalenedicarboxylic acid alkylene esters), such as poly(ethylene 2,6-naphthalenedicarboxylate); poly(sulfonyl-4,4'-dibenzoic acid alkylene esters), such as poly(ethylene sulfonyl-4,4'-dibenzoate); poly(p-phenylene alkylene dicarboxylates), such as poly(ethylene p-phenylene dicarboxylate); poly(trans-1,4-cyclohexane diyl alkylene dicarboxylates), such as poly(ethylene trans-1,4-cyclohexane dicarboxylate); poly(1,4-cyclohexane-dimethylene alkylene dicarboxylates), such as poly(ethylene 1,4-cyclohexane-dimethylene dicarboxylate); poly([2.2.2]-bicyclooctane-1,4-dimethylene alkylene dicarboxylates), such as poly([2.2.2]-bicyclooctane-1,4-dimethylene ethylene dicarboxylate); lactic acid polymers and copolymers, such as (S)-polylactide, (R,S)-polylactide, poly(tetramethyl glycolide), and poly(lactide-co-glycolide); and polycarbonates of bisphenol A, 3,3'-dimethyl bisphenol A, 3,3',5,5'-tetrachloro bisphenol A, 3,3',5,5'-tetramethyl bisphenol A; polyamides such as poly(p-phenylene terephthalamide); polyesters such as polyethylene terephthalate, such as Mylar™ polyethylene terephthalate; etc. In some embodiments, the subject system includes a test tube positioned within the sample interrogation region.In an embodiment, the test tube can allow light with a wavelength ranging from 100 nm to 1500 nm to pass through, such as 150 nm to 1400 nm, such as 200 nm to 1300 nm, such as 250 nm to 1200 nm, such as 300 nm to 1100 nm, such as 350 nm to 1000 nm, such as 400 nm to 900 nm and including 500 nm to 800 nm.

[0383] In certain embodiments, a light detection system having a plurality of photodetectors as described above is part of or located within a particle analyzer (such as a particle sorter). In certain embodiments, the subject system is a flow cytometry system that includes an amplifier assembly and a photodiode as part of the light detection system for detecting light emitted by a sample in a flowing stream. Suitable flow cytometry systems can include, but are not limited to, those described in the following documents: Ormerod (ed.), Flow Cytometry: A Practical Approach, Oxford Univ. Press (1997); Jaroszeski et al. (eds.), Flow Cytometry Protocols, Methods in Molecular Biology No. 91, Humana Press (1997); Practical Flow Cytometry, 3rd Edition, Wiley-Liss (1995); Virgo et al. (2012) Ann Clin Biochem. Jan;49(pt 1):17 - 28; Linden et al., Semin Throm Hemost. October 2004; 30(5):502 - 11; Alison et al. J Pathol, December 2010; 222(4):335 - 344; and Herbig et al. (2007) Crit Rev Ther Drug Carrier Syst. 24(3):203 - 255; the disclosures of which are incorporated herein by reference. In certain instances, the flow cytometry system of interest includes BD Biosciences FACSCanto TM Flow cytometer, BD Biosciences FACSCanto TM II Flow cytometer, BD Accuri TM Flow cytometer, BD Accuri TM C6 Plus Flow cytometer, BD Biosciences FACSCelesta TMFlow cytometer, BD Biosciences FACSLyric TM Flow cytometer, BD Biosciences FACSVerse TM Flow cytometer, BD Biosciences FACSymphony TM Flow cytometer, BD Biosciences LSRFortessa TM Flow cytometer, BD Biosciences LSRFortessa TM X-20 Flow cytometer, BD Biosciences FACSPresto TM Flow cytometer, BD Biosciences FACSVia TM Flow cytometer and BD Biosciences FACSCalibur TM Cell sorter, BD Biosciences FACSCount TM Cell sorter, BD Biosciences FACSLyric TM Cell sorter, BD Biosciences Via TM Cell sorter, BD Biosciences Influx™ Cell Sorter, BD Biosciences Jazz™ Cell Sorter, BD Biosciences Aria™ Cell Sorter, BD Biosciences FACSAria™ II Cell Sorter, BD Biosciences FACSAria™ III Cell Sorter, BD Biosciences FACSAria™ Fusion Cell Sorter and BD Biosciences FACSMelody™ Cell Sorter, BD Biosciences FACSymphony TM S6 cell sorter, etc.

[0384] In some embodiments, the subject system is a flow cytometry system, such as the flow cytometry systems described in U.S. Patent Nos. 10,663,476, 10,620,111, 10,613,017, 10,605,713, 10,585,031, 10,578,542, 10,578,469, 10,481,074, 10,302,545, 10,145,793, 10,113,967, 10,006,852, 9,952,076, 9,933,341, 9,726,527, 9,453,789, 9,200,334, 9,097,640, 9,095,494, 9,092,034, 8,975,595, 8,753,573, 8,233,146, 8,140,300, 7,544,326, 7,201,875, 7,129,505, 6,821,740, 6,813,017, 6,809,804, 6,372,506, 5,700,692, 5,643,796, 5,627,040, 5,620,842, 5,602,039, 4,987,086, 4,498,766, the entire disclosures of which are incorporated herein by reference.

[0385] In some embodiments, the subject system is a particle sorting system configured to sort particles with a closed particle sorting module, such as those described in U.S. Patent Publication No. 2017 / 0299493, the disclosure of which is incorporated herein by reference. In certain embodiments, a sorting decision module having a plurality of sorting decision units is used to sort particles (e.g., cells) of a sample, such as those described in U.S. Patent Publication No. 2020 / 0256781, the disclosure of which is incorporated herein by reference. In some embodiments, the subject system includes a particle sorting module having deflection plates, such as the particle sorting module described in U.S. Patent Publication No. 2017 / 0299493 filed on Mar. 28, 2017, the disclosure of which is incorporated herein by reference.

[0386] In some instances, the flow cytometry system of the present invention is configured to image particles in a flowing stream by fluorescence imaging using fluorescence imaging with radiofrequency tags emission (FIRE), such as the flow cytometry systems described in Diebold et al. in Nature Photonics Vol. 7(10); 806 - 810 (2013) and U.S. Patent Nos. 9,423, 9,983,132, 10,006,852, 10,078,045, 10,036,699, 10,222,316, 10,288,546, 10,324,019, 10,408,758, 10,451,538, 10,620,111 and U.S. Patent Publication Nos. 2017 / 0133857, 2017 / 0328826, 2017 / 0350803, 2018 / 0275042, 2019 / 0376895 and 2019 / 0376894, the disclosures of which are incorporated herein by reference.

[0387] In some embodiments, the subject system is configured to sort one or more of the particles (e.g., cells) of a sample identified based on the estimated abundance of fluorophores associated with the particles as described above. The term "sort" refers in its conventional sense to separating the components of a sample (e.g., cells, non - cellular particles such as biological macromolecules), and in some instances, delivering the separated components to one or more sample collection containers. For example, the subject system can be configured to sort a sample having 2 or more components, such as 3 or more components, such as 4 or more components, such as 5 or more components, such as 10 or more components, such as 15 or more components and including sorting a sample having 25 or more components. One or more of the sample components can be separated from the sample and delivered to a sample collection container, such as 2 or more sample components, such as 3 or more sample components, such as 4 or more sample components, such as 5 or more sample components, such as 10 or more sample components and including separating and delivering 15 or more sample components from the sample to a sample collection container.

[0388] In some embodiments, the particle sorting system of interest is configured to sort particles using an enclosed particle sorting module, such as those described in U.S. Patent Publication No. 2017 / 0299493, filed Mar. 28, 2017, the disclosure of which is incorporated herein by reference. In certain embodiments, a sorting decision module having a plurality of sorting decision units is used to sort particles (e.g., cells) of a sample, such as those described in U.S. Patent Publication No. 2020 / 0256781, the disclosure of which is incorporated herein by reference. In some embodiments, the subject system includes a particle sorting module having deflection plates, as described in U.S. Patent Publication No. 2017 / 0299493, filed Mar. 28, 2017, the disclosure of which is incorporated herein by reference.

[0389] In certain embodiments, the system is a fluorescence imaging of a radiofrequency tag emission enabled image particle sorter as depicted Figure 3A The particle sorter 300 includes an optical illumination assembly 300a that includes a light source 301 (e.g., a 488 nm laser) that produces an output beam 301a of light, which output beam is split into beam 302a and beam 302b by a beam splitter 302. Beam 302a propagates through an acousto-optic device (e.g., an acousto-optic deflector, AOD) 303 to produce an output beam 303a having one or more angularly deflected beams. In some instances, the output beam 303a produced by the acousto-optic device 303 includes a local oscillator beam and a plurality of radiofrequency comb beams. Beam 302b propagates through an acousto-optic device (e.g., an acousto-optic deflector, AOD) 304 to produce an output beam 304a having one or more angularly deflected beams. In some instances, the output beam 304a produced by the acousto-optic device 304 includes a local oscillator beam and additional radiofrequency comb beams. The output beam 303a and the output beam 304a, respectively produced by the acousto-optic devices 303 and 304, are combined with a beam splitter 305 to produce an output beam 305a, which output beam is transmitted through an optical element 306 (e.g., an objective lens) to illuminate particles in a flow cell 307. In certain embodiments, the acousto-optic device 303 (AOD) splits a single laser beam into an array of small beams, each having a different optical frequency and angle. A second AOD 304 adjusts the optical frequency of a reference beam and then overlaps it with the beam array of the beam combiner 305. In certain embodiments, the optical illumination system having a light source and acousto-optic devices may also include those described in Schraivogel et al. (“High-Speed Fluorescence-Enabled Image Cell Sorting” Science (2022), 375(6578): 315-320) and U.S. Patent Publication No. 2021 / 0404943, the disclosures of which are incorporated herein by reference.

[0390] The output beam 305a irradiates sample particles 308 propagating through a flow cell 307 (e.g., having a sheath fluid 309) at an illumination region 310. As shown in the illumination region 310, multiple beams (e.g., angularly deflected radio-frequency shifted beams, depicted as passing through points in the illumination region 310) overlap with a reference local oscillator beam (depicted as a shaded line passing through the illumination region 310). Due to their different optical frequencies, the overlapping beams exhibit a beating behavior, which causes each small beam to carry a sinusoidal modulation at a different frequency f 1-n at which the sinusoidal modulation is carried.

[0391] Light from the irradiated sample is transmitted to a light detection system 300b, which includes a plurality of photodetectors. The light detection system 300b includes a forward scatter light photodetector 311 for generating a forward scatter image 311a and a side scatter light photodetector 312 for generating a side scatter image 312a. The light detection system 300b also includes a bright field photodetector 313 for generating a light loss image 313a. In some embodiments, the forward scatter detector 311 and the side scatter detector 312 are photodiodes (e.g., avalanche photodiodes, APDs). In certain instances, the bright field photodetector 313 is a photomultiplier tube (PMT). Fluorescence of the irradiated sample is detected with fluorescence photodetectors 314 - 317. In certain instances, the photodetectors 314 - 317 are photomultiplier tubes. Light from the irradiated sample is directed to the side scatter detection channel 312 and the fluorescence detection channels 314 - 317 through a beam splitter 320. The light detection system 300b includes bandpass optical components 321, 322, 323, and 324 (e.g., dichroic mirrors) for propagating light of a predetermined wavelength to the photodetectors 314 - 317. In certain instances, the optical component 321 is a 534 nm / 40 nm bandpass. In certain instances, the optical component 322 is a 586nm / 42 nm bandpass. In certain instances, the optical component 323 is a 700 nm / 54 nm bandpass. In certain instances, the optical component 324 is a 783 nm / 56 nm bandpass. The first number represents the center of the spectral band. The second number provides the range of the spectral band. Thus, a 510 / 20 filter extends 10 nm on each side of the spectral band center, or from 500 nm to 520 nm.

[0392] The data signals generated in response to the light detected in the scattered light detection channels 311 and 312, bright field light detection channel 313, and fluorescence detection channels 314 - 317 by processors 350 and 351 are subjected to real-time digital processing. Based on the data signals generated in processors 350 and 351, images 311a - 317a can be generated in each light detection channel. Sorting of the enabled images is performed in response to a sorting signal generated in sorting trigger 352. Sorting assembly 300c includes a deflection plate 331 for deflecting particles into sample container 332 or waste stream 333. In some instances, sorting assembly 300c is configured to sort particles using a closed particle sorting module, such as those described in U.S. Patent Publication No. 2017 / 0299493, filed on March 28, 2017, the disclosure of which is incorporated herein by reference. In certain embodiments, sorting assembly 300c includes a sorting decision module having a plurality of sorting decision units, such as those described in U.S. Patent Publication No. 2020 / 0256781, the disclosure of which is incorporated herein by reference.

[0393] Figure 3B Image-enabled particle sorting data processing according to certain embodiments is described. In some instances, image-enabled particle sorting data processing is a low-latency data processing pipeline. Each photodetector generates pulses that encode an image (waveform) using high-frequency modulation. Fourier analysis reconstructs the image based on the modulated pulses. An image processing pipeline generates a set of image features (image analysis) that are combined with features derived from the pulse processing pipeline (event packets). Then, real-time sorting classification electronics classify particles based on the image features and generate sorting decisions for selectively charging droplets.

[0394] In some embodiments, the system is a particle analyzer, wherein particle analysis system 401 ( Figure 4A ) can be used to analyze and characterize particles by physically sorting the particles into collection containers or without physically sorting the particles into collection containers. Figure 4A A functional block diagram of a particle analysis system for computational sample analysis and particle characterization is shown. In some embodiments, particle analysis system 401 is a flow system. As Figure 4A shown, particle analysis system 401 can be configured to perform all or part of the methods described herein. Particle analysis system 401 includes a fluid system 402. Fluid system 402 can include or be coupled to a sample tube 405 and a moving fluid column within the sample tube, wherein particles 403 (e.g., cells) of the sample move along a common sample path 409.

[0395] The particle analysis system 401 includes a detection system 404 configured to collect signals from each particle as each particle passes through one or more detection stations along a common sample path. The detection station 408 generally refers to the monitoring area 407 of the common sampling path. In some embodiments, the detection can include detecting light or one or more other characteristics of the particle 403 as the particle 403 passes through the monitoring area 407. Figure 4A FIG. shows a detection station 408 and a monitoring area 407. Some embodiments of the particle analysis system 401 can include multiple detection stations. In addition, some detection stations can monitor more than one area.

[0396] Each signal is assigned a signal value to form a data point for each particle. As described above, this data can be referred to as event data. The data point can be a multi-dimensional data point that includes values of the corresponding attributes measured for the particle. The detection system 404 is configured to collect successive said data points in a first time interval.

[0397] The particle analysis system 401 can also include a control system 306. The control system 406 can include one or more processors, amplitude control circuitry, and / or frequency control circuitry. The illustrated control system can be operatively associated with the fluid system 402. The control system can be configured to generate a calculated signal frequency for at least a portion of the first time interval based on a Poisson distribution and the number of data points collected by the detection system 404 in the first time interval. The control system 406 can further be configured to generate an experimental signal frequency based on the number of data points in a portion of the first time interval. The control system 406 can also compare the experimental signal frequency with the calculated signal frequency or a predetermined signal frequency.

[0398] Figure 4B FIG. shows a system 400 for flow cytometry according to an illustrative embodiment of the present invention. The system 400 includes a flow cytometer 410, a controller / processor 490, and a memory 495. The flow cytometer 410 includes one or more excitation lasers 415a-415c, a focusing lens 420, a flow cell 425, a forward scatter detector 430, a side scatter detector 435, a fluorescence collection lens 440, one or more beam splitters 445a-445g, one or more bandpass filters 450a-350e, one or more long pass (“LP”) filters 455a-455b, and one or more fluorescence detectors 460a-460f.

[0399] The excitation lasers 115a to 115c emit light in the form of laser beams. In Figure 4BIn the example system, the wavelengths of the laser beams emitted from the excitation lasers 415a - 415c are 488 nm, 633 nm, and 325 nm, respectively. The laser beams are first directed through one or more of the beam splitters 445a and 445b. Beam splitter 445a transmits light at 488 nm and reflects light at 633 nm. Beam splitter 445b transmits UV light (light with wavelengths from 10 nm to 400 nm) and reflects light at 488 nm and 633 nm.

[0400] Then, the laser beams are directed to the focusing lens 420, which focuses the laser beams onto a portion of the flow stream in the flow chamber 425 where the particles of the sample are located. The flow chamber is part of a fluidic system that directs the particles in the flow (usually one at a time) to the focused laser beam for interrogation. In a benchtop cytometer, the flow chamber can include a flow cell, or in an air - flow cytometer, the flow chamber can include a nozzle tip.

[0401] Light from one or more of the laser beams interacts with the particles in the sample through diffraction, refraction, reflection, scattering, and absorption, and is re - emitted at various different wavelengths depending on the properties of the particles (such as their size, internal structure, and the presence of one or more fluorescent molecules attached to, within, or naturally occurring on the particles). The fluorescence emission, as well as the diffracted, refracted, reflected, and scattered light, can be routed through one or more of the beam splitters 445a - 445g, band - pass filters 450a - 450e, long - pass filters 455a - 455b, and the fluorescence collection lens 340 to one or more of the forward scatter detector 430, side scatter detector 435, and one or more fluorescence detectors 460a - 460f.

[0402] The fluorescence collection lens 440 collects the light emitted due to the interaction of the particles with the laser beam and routes the light towards one or more beam splitters and filters. Band - pass filters, such as band - pass filters 450a - 450e, allow a narrow range of wavelengths to pass through the filter. For example, band - pass filter 450a is a 510 / 20 filter. The first number represents the center of the spectral band. The second number provides the range of the spectral band. Thus, the 510 / 20 filter extends 10 nm on each side of the center of the spectral band, or from 500 nm to 520 nm. Short - pass filters transmit light with wavelengths equal to or shorter than a specific wavelength. Long - pass filters, such as long - pass filters 455a - 455b, transmit light with wavelengths equal to or longer than a specific light wavelength. For example, long - pass filter 455b, which is a 670 nm long - pass filter, transmits light equal to or longer than 670 nm. Filters are typically selected to optimize the specificity of the detector for a particular fluorescent dye. The filters can be configured such that the spectral band of the light transmitted to the detector is close to the emission peak of the fluorescent dye.

[0403] The beam splitter directs light of different wavelengths in different directions. The characteristics of the beam splitter can lie in filter characteristics, such as short-pass and long-pass. For example, the beam splitter 445g is a 620 SP beam splitter, which means that the beam splitter 445g transmits light with a wavelength of 620 nm or shorter and reflects light with a wavelength longer than 620 nm in a different direction. In one embodiment, the beam splitters 445a - 445g can include optical mirrors, such as dichroic mirrors.

[0404] The forward scatter detector 430 is positioned slightly axially offset from the direct beam passing through the flow cell and is configured to detect diffracted light, i.e., the excitation light that mainly passes through or propagates around the particles in the forward direction. The intensity of the light detected by the forward scatter detector depends on the overall size of the particles. The forward scatter detector can include a photodiode. The side scatter detector 435 is configured to detect light refracted and reflected from the surface and internal structure of the particles and tends to increase as the complexity of the particle structure increases. Fluorescent emission from fluorescent molecules associated with the particles can be detected by one or more fluorescence detectors 460a - 460f. The side scatter detector 435 and the fluorescence detectors can include photomultiplier tubes. The signals detected at the forward scatter detector 430, the side scatter detector 435, and the fluorescence detectors can be converted by the detectors into electrical signals (voltages). This data can provide information about the sample.

[0405] Those skilled in the art will recognize that the flow cytometer according to the embodiments of the present invention is not limited to Figure 4B the depicted flow cytometer, but can include any flow cytometer known in the art. For example, the flow cytometer can have any number of lasers, beam splitters, filters, and detectors at various wavelengths and with various different configurations.

[0406] In operation, the operation of the cytometer is controlled by a controller / processor 490, and measurement data from the detector can be stored in a memory 495 and processed by the controller / processor 490. Although not explicitly shown, the controller / processor 490 is coupled to the detector to receive output signals from the detector, and may also be coupled to the electrical and electromechanical components of the flow cytometer 410 to control lasers, fluid flow parameters, etc. Input / output (I / O) capabilities 497 may also be provided in the system. The memory 495, the controller / processor 490, and the I / O 497 may all be fully provided as an integrated part of the flow cytometer 410. In such an embodiment, the display may also form part of the I / O capabilities 497 for presenting experimental data to the user of the cytometer 410. Alternatively, some or all of the memory 495, the controller / processor 490, and the I / O capabilities may be part of one or more external devices (e.g., a general-purpose computer). In some embodiments, some or all of the memory 495 and the controller / processor 490 are capable of communicating wirelessly or wired with the flow cytometer 410. The controller / processor 490 together with the memory 495 and the I / O 497 can be configured to perform various functions related to the preparation and analysis of flow cytometry experiments.

[0407] Figure 4BThe system shown includes six different detectors that detect fluorescence in six different wavelength bands (which may be referred to herein as the "filter window" of a given detector), the six different wavelength bands being defined by the configuration of filters and / or beam splitters in the beam path from flow cell 425 to each detector. Different fluorescent molecules used in flow cytometry experiments will emit light in their own characteristic wavelength bands. The particular fluorescent tags used in an experiment and their associated fluorescence emission bands can be selected to be generally consistent with the filter windows of the detectors. However, as more detectors are provided and more labels are used, a perfect correspondence between the filter windows and the fluorescence emission spectra is not possible. Generally speaking, while the peak of the emission spectrum of a particular fluorescent molecule may lie within the filter window of a particular detector, some of the emission spectrum of that label will also overlap with the filter windows of one or more other detectors. This can be referred to as spillover. I / O 497 can be configured to receive data regarding a flow cytometry experiment that has a set of fluorescent tags and multiple cell populations with multiple labels, each cell population having a subset of the multiple labels. I / O 497 can also be configured to receive biological data that assigns one or more labels to one or more cell populations, marker density data, emission spectrum data, data that assigns labels to one or more markers, and cytometer configuration data. Flow cytometry experiment data (such as label spectral characteristics and cytometer configuration data) can also be stored in memory 495. Controller / processor 490 can be configured to estimate one or more assignments of labels to markers.

[0408] Figure 5 A functional block diagram showing an example of a particle analyzer control system (such as analysis controller 500) for analyzing and displaying biological events is shown. Analysis controller 500 can be configured to implement various processes for controlling the graphical display of biological events.

[0409] Particle analyzer or sorting system 502 can be configured to acquire biological event data. For example, a flow cytometer can generate flow cytometry event data. Particle analyzer 502 can be configured to provide biological event data to analysis controller 500. A data communication channel can be included between particle analyzer or sorting system 502 and analysis controller 500. Biological event data can be provided to analysis controller 500 via the data communication channel.

[0410] The analysis controller 500 can be configured to receive biological event data from a particle analyzer or sorting system 502. The biological event data received from the particle analyzer or sorting system 502 can include flow cytometry event data. The analysis controller 500 can be configured to provide a graphical display including a first plot of the biological event data to a display device 506. The analysis controller 500 can also be configured to present a region of interest as a gate, for example, overlaid on the first plot and surrounding a population of biological event data shown by the display device 506. In some embodiments, the gate can be a logical combination of one or more graphical regions of interest plotted on a single-parameter histogram or a bivariate plot. In some embodiments, the display can be used to display particle parameters or saturated detector data.

[0411] The analysis controller 500 can also be configured to display biological event data within the gate on the display device 506 in a different manner than other events in the biological event data outside the gate. For example, the analysis controller 500 can be configured to present the color of the biological event data contained within the gate as different from the color of the biological events outside the gate. The display device 506 can be implemented as a monitor, a tablet, a smartphone, or other electronic device configured to present a graphical interface.

[0412] The analysis controller 500 can be configured to receive a gate selection signal identifying the gate from a first input device. For example, the first input device can be implemented as a mouse 510. The mouse 510 can initiate a gate selection signal to the analysis controller 500 to identify the gate to be displayed on the display device 506 or manipulated via the display device 506 (e.g., by clicking on or within the desired gate when the cursor is located at the desired gate). In some implementations, the first device can be implemented as a keyboard 508 or other means for providing an input signal to the analysis controller 500, such as a touchscreen, a stylus, an optical detector, or a voice recognition system. Some input devices can include multiple input functions. In such implementations, each input function can be considered an input device. For example, as Figure 5 shown, the mouse 510 can include a right mouse button and a left mouse button, and each of the right mouse button and the left mouse button can generate a trigger event.

[0413] The trigger event can cause the analysis controller 500 to change the way the data is displayed, which portions of the data are actually displayed on the display device 506, and / or can cause the analysis controller 500 to provide input for further processing, such as selecting a population of interest for particle sorting.

[0414] In some embodiments, the analysis controller 500 can be configured to detect when the mouse 510 initiates a gate selection. The analysis controller 500 can also be configured to automatically modify the plot visualization to facilitate the gating process. The modification can be based on a particular distribution of the biological event data received by the analysis controller 500.

[0415] The analysis controller 500 can be connected to a storage device 504. The storage device 504 can be configured to receive and store biological event data from the analysis controller 500. The storage device 504 can also be configured to receive and store flow cytometry event data from the analysis controller 500. The storage device 504 can also be configured to allow the analysis controller 500 to retrieve biological event data, such as flow cytometry event data.

[0416] The display device 506 can be configured to receive display data from the analysis controller 500. The display data can include a plot of biological event data and gates that outline portions of the plot. The display device 506 can also be configured to change the presented information based on inputs received from the analysis controller 500 in combination with inputs from the particle analyzer 502, the storage device 504, the keyboard 508, and / or the mouse 510.

[0417] In some implementations, the analysis controller 500 can generate a user interface to receive example events for sorting. For example, the user interface can include controls for receiving example events or example images. The example events or images or example gates can be provided before collecting the event data of the sample or based on an initial set of events of a portion of the sample in the sample.

[0418] Figure 6A is a schematic diagram of a particle sorting system 600 (e.g., a particle analyzer or sorting system 502) according to an embodiment presented herein. In some embodiments, the particle sorting system 600 is a cell sorter system. As Figure 6A shown, a droplet formation transducer 602 (e.g., a piezoelectric oscillator) is coupled to a fluid conduit 601, and the fluid conduit 601 can be coupled to, can include, or can be a nozzle 603. Within the fluid conduit 601, a sheath fluid 604 hydrodynamically focuses a sample fluid 606 that includes particles 609 into a moving fluid column 608 (e.g., a stream). Within the moving fluid column 608, the particles 609 (e.g., cells) are arranged in a single file to pass through a monitoring region 611 (e.g., where the laser intersects the stream) irradiated by an irradiation source 612 (e.g., a laser). The vibration of the droplet formation transducer 602 causes the moving fluid column 608 to break into a plurality of droplets 610, and some of the plurality of droplets 610 contain particles 609.

[0419] In operation, a detection station 614 (e.g., an event detector) identifies when a particle of interest (or a cell of interest) passes through a monitoring region 611. The detection station 614 feeds a timing circuit 628, which in turn feeds a flash charging circuit 630. At a droplet break point notified by a timing droplet delay (Δt), a flash charge can be applied to the moving fluid column 608 such that droplets of interest carry a charge. Droplets of interest can include one or more particles or cells to be sorted. Then, the charged droplets can be sorted by activating deflection plates (not shown) to deflect the droplets into vessels such as collection tubes or porous or microwell sample plates, where the wells or microwells can be associated with droplets of particular interest. As Figure 6A shown, the droplets can be collected in a discharge container 638.

[0420] A detection system 616 (e.g., a droplet boundary detector) is used to automatically determine the phase of a droplet drive signal when a particle of interest passes through the monitoring region 611. An exemplary droplet boundary detector is described in U.S. Patent No. 7,679,039, the entire contents of which are incorporated herein by reference. The detection system 616 allows the instrument to accurately calculate the position of each detected particle in a droplet. The detection system 616 can feed into an amplitude signal 620 and / or a phase signal 618, which in turn feed (via an amplifier 622) into an amplitude control circuit 626 and / or a frequency control circuit 624. The amplitude control circuit 626 and / or the frequency control circuit 624 in turn control a droplet formation transducer 602. The amplitude control circuit 626 and / or the frequency control circuit 624 can be included in a control system.

[0421] In some implementations, sorting electronics (e.g., the detection system 616, the detection station 614, and a processor 640) can be coupled to a memory configured to store detected events and sorting decisions based on the detected events. The sorting decision can be included in the event data of a particle. In some embodiments, the detection system 616 and the detection station 614 can be implemented as a single detection unit or communicatively coupled such that event measurements can be collected by one of the detection system 616 or the detection station 614 and provided to the non-collecting element.

[0422] Figure 6B is a schematic diagram of a particle sorting system according to one embodiment presented herein. Figure 6B The particle sorting system 600 shown includes deflection plates 652 and 654. Charge can be applied via a stream-charging wire in a barb. This produces a stream of droplets 610 containing particles 609 for analysis. The particles can be irradiated with one or more light sources (e.g., lasers) to produce light scattering and fluorescence information. For example, by sorting electronics or other detection systems (Figure 6B (not shown in the figure) to analyze the information of the particles. The deflection plates 652 and 654 can be independently controlled to attract or repel the charged droplets to direct the droplets towards the target collection container (e.g., one of 672, 674, 676, or 678). As Figure 6B shown, the deflection plates 652 and 654 can be controlled to direct the particles along the first path 662 towards the container 674 or along the second path 668 towards the container 678. If the particles are not the particles of interest (e.g., do not exhibit scattering or irradiation information within a specific sorting range), the deflection plates can allow the particles to continue to travel along the flow path 664. Such uncharged droplets can enter the waste liquid container via, for example, the aspirator 670.

[0423] can include sorting electronics to initiate the collection of measurement results, receive the fluorescence signals of the particles, and determine how to adjust the deflection plates to sort the particles. Figure 6B An example implementation of the illustrated embodiment includes the BD FACSAria™ series of flow cytometers commercially available from Becton, Dickinson and Company (Franklin Lakes, NJ).

[0424] Integrated circuit device

[0425] Aspects of the present disclosure also include integrated circuit devices programmed to use the generalized least squares problem described in the methods detailed above for the spectrally resolved light from each fluorophore in a sample. In some embodiments, the integrated circuit devices of interest include field programmable gate arrays (FPGAs). In other embodiments, the integrated circuit devices include application specific integrated circuits (ASICs). In still other embodiments, the integrated circuit devices include complex programmable logic devices (CPLDs). In some embodiments, the subject integrated circuit devices are programmed to determine the overlap between each different fluorophore in the sample and calculate the contribution of each fluorophore to the overlapping fluorescence. In certain embodiments, the integrated circuit is programmed to calculate a spectral unmixing matrix for the fluorescence spectra of multiple fluorophores with overlapping fluorescence in a sample detected by a light detection system having multiple photodetectors. In certain embodiments, the integrated circuit devices according to certain embodiments are programmed to calculate a spectral unmixing matrix for the fluorescence spectra of multiple fluorophores for each cell in the sample. As described in more detail below, the integrated circuit devices can be programmed to estimate the abundance of each fluorophore in the sample. In certain embodiments, the abundance of each fluorophore associated with the target particles can be determined. The integrated circuit can be programmed to identify and classify the target particles based on the abundance of each fluorophore associated with the target particles. In some instances, the integrated circuit is configured to sort the identified or classified particles.

[0426] In some embodiments, the integrated circuit device is programmed to determine the data signal covariance in each photodetector channel. In some instances, the data signal covariance within each photodetector channel includes an inherent sample variability component and a measurement variability component. In some instances, the data signal covariance includes the electronic noise within each photodetector channel. In some instances, the data signal covariance includes the shot noise within each photodetector channel. In some instances, the data signal covariance varies linearly with the generated data signal. In some instances, the data signal covariance varies quadratically with the generated data signal. In some instances, the data signal covariance is correlated between two or more of the plurality of photodetector channels. In some instances, the integrated circuit device is programmed to calculate the data signal covariance according to:

[0427] ,

[0428] where:

[0429] is the measured detector signal;

[0430] is the baseline noise component;

[0431] is the Poisson noise component;

[0432] is the Poisson noise coefficient;

[0433] is the quadratic noise component; and

[0434] is the quadratic noise coefficient.

[0435] In some instances, the integrated circuit device is programmed to calculate the data signal covariance using a covariance matrix. In some instances, the covariance matrix contains non-zero diagonal values. In certain instances, the integrated circuit device is programmed to calculate the covariance using the covariance matrix according to:

[0436] ,

[0437] where, represents generating a diagonal matrix from the column vector x, and represents the covariance between a and b.

[0438] In some instances, an integrated circuit device is programmed to compute a solution to a generalized least squares problem by multiplying the inverse of a computed covariance matrix. In some instances, a method includes estimating a data signal covariance based on fluorescence intensities of two or more photodetectors of a light detection system. In some instances, a method includes estimating a data signal covariance based on fluorescence intensities of each of the light detection channels. In some embodiments, an integrated circuit device is programmed to compute a generalized least squares problem according to:

[0439] ,

[0440] where:

[0441] is a weight matrix;

[0442] is a covariance matrix;

[0443] X is a spectral matrix (overflow matrix);

[0444] y is a detector value measured by a plurality of photodetectors of a light detection system for each cell;

[0445] f is the true fluorophore abundance for each cell; and

[0446] is the estimated (unmixed) fluorophore abundance for each cell.

[0447] In some instances, an integrated circuit device is programmed to estimate a prior covariance matrix. In certain instances, an integrated circuit device is programmed to apply a generalized least squares algorithm in real time (e.g., using an integrated circuit such as a field programmable gate array). In some instances, a prior noise model is used to estimate each event covariance (e.g., computing each event covariance matrix in real time). In some instances, the prior noise model uses only data collected for each specific event. In some instances, the covariance matrix includes an estimate for the entire collected data set. In some instances, the covariance matrix is generated by an iterative optimization method that empirically tunes the covariance matrix to minimize the variance of the unmixed data.

[0448] In some embodiments, an integrated circuit device is programmed to determine a data signal covariance by an estimate through iterative optimization of a covariance matrix that minimizes the variance of the unmixed data signal. In certain instances, an integrated circuit device is programmed to compute a generalized least squares problem by Cholesky decomposition of the covariance matrix. In certain instances, the generalized least squares problem is characterized by computing a Cholesky decomposition of the covariance matrix and solving a triangular system according to the following to generate a transformed input for an ordinary least squares algorithm:

[0449] Solve to generate , i.e., the decorrelated and whitened version of the data vector y.

[0450] Solve Generate , i.e., the corresponding transformed version of the spectral matrix X.

[0451] Transformed system is solved by ordinary least squares, for example by solving the so-called normal equations .

[0452] In some instances, the integrated circuit device is programmed to find the least squares solution of a generalized least squares problem. In some instances, the integrated circuit device is programmed to find the least squares solution of a generalized least squares problem by one or more of matrix factorization, matrix factorization, QR factorization, Cholesky factorization, singular value factorization, LDL factorization, and pre-permutation and post-permutation. In some instances, the integrated circuit device is programmed to find the least squares solution of a generalized least squares problem by solving the so-called normal equations by Cholesky factorization or LDL factorization, for example according to the following by Cholesky factorization or LDL factorization:

[0453] ,

[0454] where: y is the detector value measured by a plurality of photodetectors of the light detection system of each cell; X is the overflow; and

[0455] G is .

[0456] In some instances, the integrated circuit device is programmed to find the least squares solution of the generalized least squares problem by Cholesky factorization or LDL factorization according to the following:

[0457] ,

[0458] ,

[0459] , LDL factorization,

[0460] where , lower triangular matrix solution,

[0461] where , diagonal matrix solution,

[0462] , Solve , upper triangular matrix solution.

[0463] In some embodiments, the integrated circuit device is programmed to find the least squares solution of the generalized least squares problem by matrix factorization. In some embodiments, the integrated circuit device is programmed to find the least squares solution of the generalized least squares problem by matrix decomposition. In some instances, the integrated circuit device is programmed to minimize the least squares solution of the generalized least squares problem by QR factorization. In some instances, the integrated circuit device is programmed to use QR factorization according to the following using the transformed and (calculated by Cholesky decomposition of the covariance matrix described above) to calculate the generalized least squares problem:

[0464] , the normal equation of the transformed GLS problem,

[0465] , the QR factorization of the transformed X,

[0466] , permutation,

[0467] , the expanded transpose of QR,

[0468] , Since orthogonality can be eliminated,

[0469] , the triangular solution of.

[0470] In some embodiments, the integrated circuit device is programmed to minimize the least squares solution of the generalized least squares problem by singular value decomposition. In some instances, the singular value decomposition is the product matrix, where U and V are orthogonal matrices, is a diagonal matrix containing singular values. In some instances, the integrated circuit device is programmed to calculate the generalized least squares problem using singular value decomposition according to the following:

[0471]

[0472]

[0473] ,

[0474] where U and V are orthogonal matrices, and is a diagonal matrix containing A diagonal matrix of the singular values. In some embodiments, the integrated circuit device is programmed to find the least squares solution of the generalized least squares problem by LDL decomposition. In some embodiments, the integrated circuit device is programmed to find the least squares solution of the generalized least squares problem by pre-permutation and post-permutation.

[0475] In some embodiments, the integrated circuit device is programmed to estimate the abundance of one or more fluorophores in a sample based on the calculated spectral unmixing matrix. In certain instances, the integrated circuit device is programmed to estimate the abundance of one or more fluorophores on a particle in a sample. In some embodiments, the integrated circuit device is programmed to identify particles in the sample based on the estimated abundance of each fluorophore on the particle. In certain instances, the integrated circuit device is programmed to sort the identified particles in the sample.

[0476] In some embodiments, the integrated circuit of interest is programmed to calculate the abundance of one or more fluorophores in a sample based on the spectrally resolved light from each fluorophore. In certain instances, the abundance of fluorophores associated with a target particle (e.g., chemically associated (i.e., covalently associated, ionically associated) or physically associated) is calculated based on the spectrally resolved light from each fluorophore associated with the particle. For example, in one example, the integrated circuit is programmed to calculate the relative abundance of each fluorophore associated with a target particle based on the spectrally resolved light from each fluorophore. In another example, the integrated circuit is programmed to calculate the absolute abundance of each fluorophore associated with a target particle based on the spectrally resolved light from each fluorophore.

[0477] In certain embodiments, the integrated circuit is programmed to identify or classify particles based on determining the relative abundance of each fluorophore associated with the particle. In these embodiments, the integrated circuit can be programmed to identify or classify particles by any convenient scheme, such as by: comparing the relative or absolute abundance of each fluorophore associated with the particle to a control sample of particles with known properties; or by performing spectral analysis or other analysis on a population of particles (e.g., cells) for which the relative or absolute abundance of the associated fluorophores has been calculated.

[0478] Kit

[0479] Aspects of the present disclosure also include toolkits, where the toolkit includes one or more of the integrated circuits described herein. In some embodiments, the toolkit also includes programming for the subject system, for example, in the form of a computer-readable medium (e.g., flash drive, USB storage, optical disk, DVD, Blu-ray disk, etc.) or instructions for downloading programming from an Internet web protocol or cloud server. The toolkit also includes instructions for practicing the subject methods. These instructions can exist in a variety of forms in the subject toolkit, and one or more of these forms can be present in the tool. One form in which these instructions may exist is as printed information on a suitable medium or substrate, e.g., one or more sheets of paper with printed information, in the package of the tool, inserted in the package, or the like. Another form of these instructions is a computer-readable medium, such as a floppy disk, optical disk, portable flash drive, etc., on which the information has been recorded. However, another form of these instructions may be a website address through which information of a deleted site can be accessed via the Internet.

[0480] Utility

[0481] The subject systems, methods, and computer systems can be used in a variety of applications that require the analysis and sorting of particle components in a sample in a fluid medium, such as a biological sample. In some embodiments, the systems and methods described herein can be used for flow cytometry characterization of biological samples labeled with fluorescent tags. In other embodiments, the systems and methods are used for spectroscopy of emitted light. Additionally, the subject systems and methods are used to increase the obtainable signal of light collected from a sample (e.g., in a flowing stream). In certain instances, the present disclosure is used to enhance the measurement of light collected from a sample irradiated in a flowing stream in a flow cytometer. Embodiments of the present disclosure can be used in scenarios that require a flow cytometer with improved cell sorting accuracy, enhanced particle collection, particle charging efficiency, more accurate particle charging, and enhanced particle deflection during cell sorting.

[0482] Embodiments of the present disclosure can also be used in applications where cells prepared from a biological sample are desired for research, laboratory testing, or for treatment. In some embodiments, the subject methods and devices can facilitate obtaining individual cells prepared from a target fluid or tissue biological sample. For example, the subject methods and systems assist in obtaining cells from a fluid or tissue sample for use as a research or diagnostic sample for diseases such as cancer. Similarly, the methods and systems of the present invention can facilitate obtaining cells for treatment from a fluid or tissue sample. Compared with traditional flow cytometry systems, the methods and devices of the present disclosure allow for the separation and collection of cells from biological samples (e.g., organs, tissues, tissue fragments, liquids) with higher efficiency and at lower cost.

[0483] Experiment

[0484] The following presents a description of spectral unmixing and covariance modeling according to certain embodiments of the present disclosure. The scope of the present disclosure is not intended to be limited to the exemplary embodiments shown and described below.

[0485] 1 Definitions and Terms

[0486] 1.1 Variable

[0487] m: The number of detectors;

[0488] n: The number of fluorophores;

[0489] y: The vector of measured intensities for each detector ;

[0490] f: The vector of fluorophore abundances (unmixing); ;

[0491] X: The spectral spillover matrix ;

[0492] : The k-th column of X (i.e., the SOV corresponding to fluorophore k);

[0493] : The pseudo-inverse of the spillover matrix (unmixing matrix) ;

[0494] : The k-th row of (i.e., the unmixing coefficient corresponding to fluorophore k);

[0495] : The noise (error) vector for each detector ;

[0496] W: The weight matrix for WLS (diagonal);

[0497] G: The weight matrix for GLS.

[0498] GLS

[0499] We use a linear mixing model to describe the measurement signal in a flow cytometer:

[0500] ,

[0501] where y is the vector of measured detector values, X is the spectral ("spillover") matrix that describes how the signal maps from the fluorophores to the detectors, f is the vector of fluorophore abundances, is the noise vector representing the zero-mean random error for each observation (detector). We know y and X and want to find f.

[0502] In spectral unmixing, our goal is to estimate the fluorophore abundance f given the observed signal y and the spectral matrix x. The family of least-squares solutions treats this as an optimization problem, where the best estimate of f (denoted as ) is the f that minimizes some objective function that quantifies the Euclidean distance between the observed values of y and the predicted values computed by the linear mixing model. In the case of ordinary least squares (OLS), this difference is defined as the 2-norm between the measured and predicted values of the dependent variable:

[0503] .

[0504] For this problem, there are many mathematically equivalent solutions that make different trade-offs in terms of computational complexity and numerical stability. A common approach is to solve the so-called "normal equations":

[0505] .

[0506] The Gauss-Markov theorem states that if the following assumptions are satisfied, then the OLS solution is the best linear unbiased estimator (BLUE): 1. The error vector ϵ has zero mean, 2. The errors are homoscedastic (i.e., all detectors have the same variance), and 3. The errors between detectors are uncorrelated (i.e., the detector covariance matrix is diagonal).

[0507] In fluorescence measurements by flow cytometry, the measured data satisfy the first requirement (mainly due to the use of baseline recovery in signal processing), but may not satisfy the second and third requirements. Weighted least squares (WLS) allows us to perform optimal unmixing in the presence of heteroscedasticity, while generalized least squares (GLS) allows us to perform optimal unmixing in the presence of heteroscedasticity and correlated noise (non-zero detector covariance). Both WLS and GLS can be considered as transformations that modify the data to satisfy the three assumptions of the Gauss-Markov theorem so that OLS can be applied to the transformed problem.

[0508] Generalized least squares takes a form similar to the WLS problem, but instead of using a diagonal weight matrix, it uses the inverse of the full covariance matrix of the original detector signals. This allows for the consideration of non-zero detector covariance caused by correlated noise sources.

[0509] ,

[0510] where . This solution takes the same general approach as WLS, but now uses a more complex non-diagonal weight matrix G:

[0511] .

[0512] Note that this whitens and decorrelates the noise and reformulates the GLS problem as an OLS problem. We can go even further and prewhiten X and y with , , and to get back to the original OLS problem with respect to the transformation matrix .

[0513] This can be solved using the following matrix factorization approach. Cholesky factorization (technically, LDL factorization is a special case of Cholesky) allows us to express as , where L is unit lower triangular (meaning it has ones on the diagonal) and D is diagonal. Let and , we can rewrite the WLS problem as and proceed as follows:

[0514] Transform the LHS, ,

[0515] Transform the RHS, ,

[0516] Normal equations, ,

[0517] Cholesky factorization, ,

[0518] Lower triangular solution, for ,

[0519] Diagonal solution, for ,

[0520] Upper triangular solution, for .

[0521] The final equation will give us the GLS solution. Note that we used two intermediate vectors z and u to reduce the problem to a fully triangular and diagonal solution.

[0522] Note that the technique involves computing . To avoid this, we can do the following:

[0523] Cholesky factorization, ,

[0524] Lower triangular solution, for ,

[0525] Lower triangular solution For ,

[0526] solution transformation system For .

[0527] Here, the lower triangular solution is used to form the transformed and (whitening and decorrelation), and the transformed OLS problem can now be solved by any method.

[0528] Noise model

[0529] Define

[0530] : Variance-covariance matrix of the original detector intensity;

[0531] : Variance-covariance matrix of the original detector intensity without biological distribution (biological "point sources");

[0532] : Original / detector-space variance of detector i;

[0533] : Variance-covariance matrix of the unmixed fluorophore abundances;

[0534] : Unmixed / marker-space variance of fluorophore k.

[0535] Baseline noise:

[0536] : Matrix of baseline variances (constant with intensity, diagonal / uncorrelated);

[0537] B: Vector of detector baseline variances of .

[0538] Poisson noise:

[0539] : Matrix of Poisson / photoelectron variances (linear with intensity, diagonal / uncorrelated);

[0540] Q: Vector of photoelectron scale factors per channel statistics .

[0541] CV noise:

[0542] : Multiplicative measurement / system variance matrix (Quadratic and intensity related);

[0543] CV: Vector of CV for each channel ;

[0544] Corr: Detector CV noise correlation matrix ;

[0545] : Correlation coefficient between channel i and channel j.

[0546] Biological (intrinsic) distribution:

[0547] : Matrix of raw variance / covariance caused by underlying biological distribution ;

[0548] : True variance of the basal expression of fluorescence k.

[0549] Single Detector Noise Model

[0550] The variance of flow cytometry intensity signals is described by the following noise model (shown here for a single detector i):

[0551] 。

[0552] This expression contains constant, linear, and quadratic terms:

[0553] 1. Independent of intensity, usually called baseline noise or background noise,

[0554] 2. Linear in intensity, usually called Poisson noise or photoelectron noise (the coefficient here is just the conversion factor for detector i from the measurement unit to statistical photoelectrons SPE), and

[0555] 3. Quadratic in intensity, where describes the time-varying source of measurement variance, such as fluid / laser fluctuations.

[0556] The baseline error and Poisson error between detectors are uncorrelated, but for The same assumptions cannot be made. Since the detectors are grouped by laser, all detectors on the same laser sample at the same time point, which means that to some extent, the time-correlated errors between detectors on the same laser will be correlated. In addition, other random variations in the fluid (which affects the particle position) or the laser intensity / position may be correlated or anti-correlated between lasers, and chromatic aberration effects in the acquisition optics may result in imperfect correlation between different detectors on the same laser.

[0557] Thus (in the case where the operator diag(z) converts the column vector z into a diagonal matrix):

[0558] 。

[0559] Detector Covariance in the Absence of Biological Distribution

[0560] The total raw variance-covariance matrix in the absence of biodistribution is given by the following expression:

[0561] 。

[0562] Notwithstanding the appended claims, the present disclosure is also defined by the following clauses:

[0563] 1. A method, comprising:

[0564] detecting light from a sample comprising a plurality of fluorophores having overlapping fluorescence spectra by a light detection system;

[0565] performing spectral analysis on the light from each fluorophore in the sample using a generalized least squares algorithm.

[0566] 2. The method according to clause 1, wherein the light detection system detects light within a plurality of photodetector channels.

[0567] 3. The method according to any one of clauses 1 to 2, wherein the light detection system comprises a plurality of photodetectors.

[0568] 4. The method according to any one of clauses 2 to 3, wherein the method comprises generating a data signal within each photodetector channel in response to the detected light.

[0569] 5. The method according to clause 4, wherein the method comprises determining the data signal covariance in each photodetector channel.

[0570] 6. The method according to clause 5, wherein the data signal covariance in each photodetector channel comprises:

[0571] an inherent sample variability component; and

[0572] Measure the variability component.

[0573] 7. The method according to any one of clauses 5 to 6, wherein the data signal covariance includes electronic noise within each photodetector channel.

[0574] 8. The method according to any one of clauses 5 to 6, wherein the data signal covariance includes shot noise within each photodetector channel.

[0575] 9. The method according to any one of clauses 5 to 8, wherein the data signal covariance varies linearly with the generated data signal.

[0576] 10. The method according to any one of clauses 5 to 8, wherein the data signal covariance varies quadratically with the generated data signal.

[0577] 11. The method according to any one of clauses 5 to 10, wherein the data signal covariance is related to two or more of the plurality of photodetector channels.

[0578] 12. The method according to any one of clauses 5 to 11, wherein the data signal covariance is calculated according to the following:

[0579] ,

[0580] where:

[0581] is the measured detector signal;

[0582] is the baseline noise component;

[0583] is the Poisson noise component;

[0584] is the Poisson noise component;

[0585] is the quadratic noise component; and

[0586] is the quadratic noise coefficient.

[0587] 13. The method according to any one of clauses 5 to 12, wherein the method includes using a covariance matrix to calculate the data signal covariance.

[0588] 14. The method according to clause 13, wherein the covariance matrix includes non-zero diagonal values.

[0589] 15. The method according to any one of clauses 12 to 13, wherein the covariance is calculated using a covariance matrix as follows:

[0590] ,

[0591] wherein, represents generating a diagonal matrix from the column vector x, and represents the covariance between a and b.

[0592] 16. The method according to any one of clauses 13 to 15, wherein the generalized least squares algorithm includes solving the generalized least squares problem by multiplying the inverse of the calculated covariance matrix.

[0593] 17. The method according to any one of clauses 5 to 16, wherein the method includes estimating the data signal covariance based on the fluorescence intensities of two or more photodetectors of the optical detection system.

[0594] 18. The method according to clause 17, wherein the method includes estimating the data signal covariance based on the fluorescence intensity of each of the optical detection channels.

[0595] 19. The method according to any one of clauses 1 to 18, wherein solving the generalized least squares problem includes calculating according to the following:

[0596] ,

[0597] where:

[0598] is the weight matrix;

[0599] is the covariance matrix;

[0600] X is the spectral matrix (overflow matrix);

[0601] y is the detector value measured by multiple photodetectors of the optical detection system for each cell;

[0602] f is the true fluorophore abundance for each cell; and

[0603] is the estimated (unmixed) fluorophore abundance for each cell.

[0604] 20. The method according to any one of clauses 1 to 19, wherein the method further includes generating a prior estimated covariance matrix.

[0605] 21. The method according to any one of clauses 13 to 20, wherein the data signal covariance is determined by an estimate obtained through iterative optimization of a covariance matrix that minimizes the variance of the unmixing data signal.

[0606] 22. The method according to any one of clauses 13 to 20, wherein solving the generalized least squares problem includes Cholesky decomposition of the covariance matrix.

[0607] 23. The method according to any one of clauses 1 to 22, wherein the method includes finding a least squares solution to the generalized least squares problem.

[0608] 24. The method according to any one of clauses 1 to 23, wherein the method includes minimizing the least squares solution of the generalized least squares problem by one or more of matrix decomposition, matrix factorization, QR factorization, Cholesky decomposition, singular value decomposition, LDL decomposition, and pre - permutation and post - permutation.

[0609] 25. The method according to clause 24, wherein the method includes finding the least squares solution of the generalized least squares problem by Cholesky decomposition or LDL decomposition.

[0610] 26. The method according to clause 25, wherein the method includes minimizing the least squares solution of the generalized least squares problem by Cholesky decomposition as follows:

[0611] ,

[0612] where:

[0613] y is the detector value measured by a plurality of photodetectors of the optical detection system for each cell;

[0614] X is the overflow; and

[0615] G is .

[0616] 27. The method according to any one of clauses 25 to 26, wherein the method includes finding the least squares solution of the generalized least squares problem by Cholesky decomposition or LDL decomposition as follows:

[0617] ,

[0618] ,

[0619] , LDL decomposition,

[0620] where , lower triangular matrix solution,

[0621] where , diagonal matrix solution,

[0622] , solve , upper triangular matrix solution.

[0623] 28. The method according to clause 23, wherein the method includes obtaining a least squares solution of the generalized least squares problem by matrix factorization.

[0624] 29. The method according to clause 23, wherein the method includes obtaining a least squares solution of the generalized least squares problem by matrix factorization.

[0625] 30. The method according to clause 23, wherein the method includes obtaining a least squares solution of the generalized least squares problem by QR factorization.

[0626] 31. The method according to clause 30, wherein the generalized least squares problem is calculated according to the following using the transformed and to calculate the generalized least squares problem:

[0627] , normal equation of the transformed GLS problem;

[0628] , QR decomposition of the transformed X;

[0629] , permutation;

[0630] , expanded transpose of QR;

[0631] , since orthogonality can be eliminated,

[0632] , triangular solution .

[0633] 32. The method according to clause 23, wherein the method includes obtaining a least squares solution of the generalized least squares problem by singular value decomposition.

[0634] 33. The method according to clause 32, wherein the generalized least squares problem is calculated according to the following using singular value decomposition:

[0635]

[0636]

[0637] ,

[0638] where U and V are orthogonal matrices, and is a diagonal matrix containing the singular values.

[0639] 34. The method according to clause 23, wherein the method includes obtaining a least-squares solution to the generalized least-squares problem by LDL decomposition.

[0640] 35. The method according to clause 23, wherein the method includes obtaining the least-squares solution to the generalized least-squares problem by pre-permutation and post-permutation.

[0641] 36. The method according to any one of clauses 1 to 35, wherein the method includes real-time spectral analysis of light from each fluorophore.

[0642] 37. The method according to clause 36, wherein real-time spectral analysis of light from each fluorophore is performed using an integrated circuit.

[0643] 38. The method according to clause 37, wherein the integrated circuit includes a field programmable gate array (FPGA).

[0644] 39. The method according to any one of clauses 1 to 38, wherein the fluorescence spectrum of each fluorophore overlaps with the fluorescence spectrum of at least one other fluorophore in the sample.

[0645] 40. The method according to clause 39, wherein the fluorescence spectrum of each fluorophore overlaps with the fluorescence spectrum of at least one other fluorophore in the sample by 10 nm or more.

[0646] 41. The method according to clause 39, wherein the fluorescence spectrum of each fluorophore overlaps with the fluorescence spectrum of at least one other fluorophore in the sample by 25 nm or more.

[0647] 42. The method according to clause 39, wherein the fluorescence spectrum of at least one fluorophore in the sample overlaps with the fluorescence spectra of two different fluorophores in the sample.

[0648] 43. The method according to clause 42, wherein the fluorescence spectrum of at least one fluorophore in the sample overlaps with the fluorescence spectra of two different fluorophores in the sample by 10 nm or more.

[0649] 44. The method according to clause 42, wherein the fluorescence spectrum of at least one fluorophore in the sample overlaps with the fluorescence spectra of two different fluorophores in the sample by 25 nm or more.

[0650] 45. The method according to any one of clauses 1 to 44 further comprises irradiating a sample with a light source.

[0651] 46. The method according to clause 45, wherein the light source comprises a laser.

[0652] 47. The method according to clause 46, wherein the light source comprises a plurality of lasers.

[0653] 48. A system comprising:

[0654] A light source configured to irradiate a sample comprising a plurality of fluorophores having overlapping fluorescence spectra;

[0655] A light detection system comprising a plurality of photodetectors; and

[0656] A processor comprising a memory operably coupled to the processor, wherein the memory comprises instructions stored thereon that, when executed by the processor, cause the processor to perform spectral analysis of light from each fluorophore in the sample using a generalized least squares algorithm.

[0657] 49. The system according to clause 48, wherein the system is configured to detect light within a plurality of photodetector channels by the light detection system.

[0658] 50. The system according to any one of clauses 48 to 49, wherein the light detection system comprises a plurality of photodetectors.

[0659] 51. The system according to clause 50, wherein the photodetector comprises one or more photomultiplier tubes.

[0660] 52. The system according to any one of clauses 48 to 51, wherein the light detection system comprises a photodetector array.

[0661] 53. The system according to clause 52, wherein the photodetector array comprises photodiodes.

[0662] 54. The system according to clause 53, wherein the photodetector array comprises a charge coupled device.

[0663] 55. The system according to any one of clauses 48 to 54, wherein the memory comprises instructions stored thereon that, when executed by the processor, cause the processor to determine the data signal covariance in each photodetector channel.

[0664] 56. The system according to clause 55, wherein the data signal covariance in each photodetector channel includes:

[0665] An inherent sample variability component; and

[0666] A measurement variability component.

[0667] 57. The system according to any one of clauses 55 to 56, wherein the data signal covariance includes electronic noise within each photodetector channel.

[0668] 58. The system according to any one of clauses 55 to 56, wherein the data signal covariance includes shot noise within each photodetector channel.

[0669] 59. The system according to any one of clauses 55 to 58, wherein the data signal covariance varies linearly with the generated data signal.

[0670] 60. The system according to any one of clauses 55 to 58, wherein the data signal covariance varies quadratically with the generated data signal.

[0671] 61. The system according to any one of clauses 55 to 60, wherein the data signal covariance is related to two or more of the plurality of photodetector channels.

[0672] 62. The system according to any one of clauses 48 to 61, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to calculate the covariance according to the following:

[0673] ,

[0674] where:

[0675] is the measured detector signal;

[0676] is the baseline noise component;

[0677] is the Poisson noise component;

[0678] is the Poisson noise coefficient;

[0679] is the quadratic noise component; and

[0680] is the quadratic noise coefficient.

[0681] 63. The system according to any one of clauses 48 to 62, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to calculate the data signal covariance using a covariance matrix.

[0682] 64. The system according to clause 63, wherein the covariance matrix includes non-zero diagonal values.

[0683] 65. The system according to any one of clauses 63 to 64, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to calculate the covariance using the covariance matrix as follows:

[0684] ,

[0685] wherein, represents generating a diagonal matrix from the column vector x, and represents the covariance between a and b.

[0686] 66. The system according to any one of clauses 63 to 65, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to calculate the generalized least squares problem by multiplying the data signal by the inverse of the calculated covariance matrix.

[0687] 67. The system according to any one of clauses 55 to 66, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to estimate the data signal covariance based on the fluorescence intensities of two or more photodetectors of the optical detection system.

[0688] 68. The system according to any one of clauses 55 to 66, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to estimate the data signal covariance based on the fluorescence intensity of each in the optical detection channels.

[0689] 69. The system according to any one of clauses 48 to 68, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to calculate the generalized least squares problem as follows:

[0690] ,

[0691] wherein:

[0692] is the weight matrix;

[0693] is the covariance matrix;

[0694] X is the spectral matrix (overflow matrix);

[0695] y is the detector values measured by a plurality of photodetectors of the light detection system for each cell;

[0696] f is the true fluorophore abundance for each cell; and

[0697] is the estimated (unmixed) fluorophore abundance for each cell.

[0698] 70. The system according to any one of clauses 48 to 69, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to generate a covariance matrix of a priori estimates.

[0699] 71. The system according to any one of clauses 48 to 70, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to determine a data signal covariance by an iterative optimization estimate of a covariance matrix that minimizes the variance of the unmixed data signal.

[0700] 72. The system according to any one of clauses 48 to 71, wherein the generalized least squares problem includes a Cholesky decomposition of a covariance matrix.

[0701] 73. The system according to any one of clauses 48 to 72, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to find a least squares solution to the generalized least squares problem.

[0702] 74. The system according to any one of clauses 48 to 73, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to find a least squares solution to the generalized least squares problem by one or more of matrix decomposition, matrix factorization, QR factorization, Cholesky decomposition, singular value decomposition, LDL decomposition, and pre-permutation and post-permutation.

[0703] 75. The system according to clause 74, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to find a least squares solution to the generalized least squares problem by Cholesky decomposition.

[0704] 76. The system according to clause 75, wherein the memory includes instructions stored thereon, which, when executed by the processor, cause the processor to obtain the least squares solution of the generalized least squares problem by Cholesky decomposition as follows:

[0705] ,

[0706] where:

[0707] y is the detector value measured by the plurality of photodetectors of the optical detection system for each cell;

[0708] X is the overflow; and

[0709] G is .

[0710] 77. The system according to any one of clauses 75 to 76, wherein the memory includes instructions stored thereon, which, when executed by the processor, cause the processor to obtain the least squares solution of the generalized least squares problem by Cholesky decomposition or LDL decomposition as follows:

[0711] ,

[0712] ,

[0713] , LDL decomposition,

[0714] where , lower triangular matrix solution,

[0715] where , diagonal matrix solution,

[0716] , solve , upper triangular matrix solution.

[0717] 78. The system according to clause 74, wherein the memory includes instructions stored thereon, which, when executed by the processor, cause the processor to obtain the least squares solution of the generalized least squares problem by matrix decomposition.

[0718] 79. The system according to clause 74, wherein the memory includes instructions stored thereon, which, when executed by the processor, cause the processor to obtain the least squares solution of the generalized least squares problem by matrix factorization.

[0719] 80. The system according to clause 74, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to find the least squares solution of the generalized least squares problem by QR factorization.

[0720] 81. The system according to clause 80, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to use the following transformed and using QR factorization to calculate the generalized least squares problem:

[0721] , the normal equation of the transformed GLS problem;

[0722] , the QR decomposition of the transformed X;

[0723] , permutation;

[0724] , the expanded transpose of QR;

[0725] , which can be eliminated due to orthogonality,

[0726] , triangular solution .

[0727] 82. The system according to clause 74, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to find the least squares solution of the generalized least squares problem by singular value decomposition.

[0728] 83. The system according to clause 82, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to find the least squares solution of the generalized least squares problem by singular value decomposition as follows:

[0729]

[0730]

[0731] ,

[0732] where U and V are orthogonal matrices, and is a diagonal matrix containing the singular values.

[0733] 84. The system according to clause 74, wherein the memory includes instructions stored thereon, which when executed by the processor, cause the processor to find the least-squares solution of the generalized least-squares problem by LDL decomposition.

[0734] 85. The system according to clause 74, wherein the memory includes instructions stored thereon, which when executed by the processor, cause the processor to find the least-squares solution of the generalized least-squares problem by pre-permutation and post-permutation.

[0735] 86. The system according to any one of clauses 48 to 85, wherein the system is configured to spectrally analyze the light from each fluorophore in real time.

[0736] 87. The system according to any one of clauses 48 to 86, wherein the system further includes an integrated circuit.

[0737] 88. The system according to clause 87, wherein the integrated circuit includes a field-programmable gate array (FPGA).

[0738] 89. The system according to any one of clauses 48 to 88, wherein the light source includes a laser.

[0739] 90. The system according to clause 89, wherein the light source includes a plurality of lasers.

[0740] 91. An integrated circuit programmed to spectrally analyze the light from each fluorophore in a sample using a generalized least-squares problem, the sample including a plurality of fluorophores having overlapping fluorescence spectra.

[0741] 92. The integrated circuit according to clause 91, wherein the integrated circuit is a field-programmable gate array (FPGA).

[0742] 93. The integrated circuit according to clause 91, wherein the integrated circuit is an application-specific integrated circuit (ASIC).

[0743] 94. The integrated circuit according to clause 91, wherein the integrated circuit is a complex programmable logic device (CPLD).

[0744] 95. The integrated circuit according to any one of clauses 91 to 94, wherein the integrated circuit is programmed to determine the data signal covariance in each photodetector channel of a light detection system.

[0745] 96. The integrated circuit according to clause 95, wherein the data signal covariance in each photodetector channel includes:

[0746] Intrinsic sample variability component; and

[0747] Measurement variability component.

[0748] 97. The integrated circuit according to any one of clauses 95 to 96, wherein the data signal covariance includes electronic noise within each photodetector channel.

[0749] 98. The integrated circuit according to any one of clauses 95 to 96, wherein the data signal covariance includes shot noise within each photodetector channel.

[0750] 99. The integrated circuit according to any one of clauses 95 to 98, wherein the data signal covariance varies linearly with the generated data signal.

[0751] 100. The integrated circuit according to any one of clauses 95 to 98, wherein the data signal covariance varies quadratically with the generated data signal.

[0752] 101. The integrated circuit according to any one of clauses 95 to 98, wherein the data signal covariance is related to two or more of the plurality of photodetector channels.

[0753] 102. The integrated circuit according to any one of clauses 95 to 101, wherein the integrated circuit is programmed to calculate the covariance according to the following:

[0754] ,

[0755] wherein:

[0756] is the measured detector signal;

[0757] is the baseline noise component;

[0758] is the Poisson noise component;

[0759] is the Poisson noise coefficient;

[0760] is the quadratic noise component; and

[0761] is the quadratic noise coefficient.

[0762] 103. The integrated circuit according to any one of clauses 95 to 102, wherein the integrated circuit is programmed to calculate the data signal covariance using a covariance matrix.

[0763] 104. The integrated circuit according to clause 103, wherein the covariance matrix includes non-zero diagonal values.

[0764] 105. The integrated circuit according to any one of clauses 103 to 104, wherein the integrated circuit is programmed to calculate the covariance using the covariance matrix as follows:

[0765] ,

[0766] wherein, represents generating a diagonal matrix from the column vector x, and represents the covariance between a and b.

[0767] 106. The integrated circuit according to any one of clauses 103 to 105, wherein the integrated circuit is programmed to calculate the generalized least squares problem by multiplying the data signal by the inverse of the calculated covariance matrix.

[0768] 107. The integrated circuit according to any one of clauses 91 to 106, wherein the integrated circuit is programmed to estimate the data signal covariance based on the fluorescence intensities of two or more photodetectors of the optical detection system.

[0769] 108. The integrated circuit according to any one of clauses 91 to 106, wherein the integrated circuit is programmed to estimate the data signal covariance based on the fluorescence intensity of each optical detection channel of the optical detection system.

[0770] 109. The integrated circuit according to any one of clauses 91 to 108, wherein the integrated circuit is programmed to calculate the generalized least squares problem as follows:

[0771] ,

[0772] where:

[0773] is the weight matrix;

[0774] is the covariance matrix;

[0775] X is the spectral matrix (overflow matrix);

[0776] y is the detector value measured by multiple photodetectors of the optical detection system for each cell;

[0777] f is the true fluorophore abundance for each cell; and

[0778] is the estimated (unmixed) fluorophore abundance for each cell.

[0779] 110. An integrated circuit according to any one of clauses 91 to 109, wherein the integrated circuit is programmed to generate a prior estimated covariance matrix.

[0780] 111. An integrated circuit according to any one of clauses 91 to 110, wherein the integrated circuit is programmed to determine a data signal covariance by estimating in the following manner: iterative optimization of a covariance matrix that minimizes the variance of the unmixed data signal.

[0781] 112. An integrated circuit according to any one of clauses 91 to 111, wherein the generalized least squares problem includes a Cholesky decomposition of a covariance matrix.

[0782] 113. An integrated circuit according to any one of clauses 91 to 112, wherein the integrated circuit is programmed to find a least squares solution to the generalized least squares problem.

[0783] 114. An integrated circuit according to any one of clauses 91 to 113, wherein the integrated circuit is programmed to find a least squares solution to the generalized least squares problem by one or more of matrix decomposition, matrix factorization, QR factorization, Cholesky decomposition, singular value decomposition, LDL decomposition, and pre-permutation and post-permutation.

[0784] 115. The integrated circuit according to clause 114, wherein the integrated circuit is programmed to find a least squares solution to the generalized least squares problem by Cholesky decomposition or LDL decomposition.

[0785] 116. The integrated circuit according to clause 115, wherein the integrated circuit is programmed to find a least squares solution to the generalized least squares problem by Cholesky decomposition as follows:

[0786] ,

[0787] where:

[0788] y is the detector value measured by a plurality of photodetectors of the optical detection system for each cell;

[0789] X is the overflow; and

[0790] G is .

[0791] 117. The integrated circuit according to any one of clauses 115 to 116, wherein the integrated circuit is programmed to find a least squares solution to the generalized least squares problem by Cholesky decomposition or LDL decomposition as follows:

[0792] ,

[0793] ,

[0794] , LDL decomposition,

[0795] wherein , lower triangular matrix solution,

[0796] wherein , diagonal matrix solution,

[0797] , solve , upper triangular matrix solution.

[0798] 118. The integrated circuit according to clause 114, wherein the integrated circuit is programmed to find the least-squares solution of the generalized least-squares problem by matrix factorization.

[0799] 119. The integrated circuit according to clause 114, wherein the integrated circuit is programmed to find the least-squares solution of the generalized least-squares problem by matrix factorization.

[0800] 120. The integrated circuit according to clause 114, wherein the integrated circuit is programmed to find the least-squares solution of the generalized least-squares problem by QR factorization.

[0801] 121. The integrated circuit according to clause 120, wherein the integrated circuit is programmed to calculate the generalized least-squares problem according to the following using the transformed and by using QR factorization:

[0802] , normal equation of the transformed GLS problem;

[0803] , QR decomposition of the transformed X;

[0804] , permutation;

[0805] , expanded transpose of QR;

[0806] , which can be eliminated due to orthogonality,

[0807] , triangular solution .

[0808] 122. The integrated circuit according to clause 114, wherein the integrated circuit is programmed to obtain a least squares solution of the generalized least squares problem by singular value decomposition.

[0809] 123. The integrated circuit according to clause 122, wherein the integrated circuit is programmed to obtain a least squares solution of the generalized least squares problem by singular value decomposition as follows:

[0810]

[0811]

[0812] ,

[0813] wherein U and V are orthogonal matrices, and is a diagonal matrix containing singular values.

[0814] 124. The integrated circuit according to clause 114, wherein the integrated circuit is programmed to obtain a least squares solution of the generalized least squares problem by LDL decomposition.

[0815] 125. The integrated circuit according to clause 114, wherein the integrated circuit is programmed to obtain a least squares solution of the generalized least squares problem by pre-permutation and post-permutation.

[0816] 126. The integrated circuit according to any one of clauses 91 to 125, wherein the integrated circuit is programmed to spectrally analyze light from each fluorophore in real time.

[0817] Although the above invention has been described in some detail by way of illustration and example for the purpose of clear understanding, it will be apparent to those of ordinary skill in the art that certain changes and modifications can be made thereto without departing from the spirit or scope of the appended claims according to the teachings of the present invention.

[0818] Accordingly, only the principles of the present invention have been described above. It should be understood that although not explicitly described or shown herein, those skilled in the art will be able to design various arrangements that embody the principles of the present invention and are included within the spirit and scope of the present invention. In addition, all of the examples and conditional language recited herein are principally intended to assist the reader in understanding the principles of the present invention and the concepts contributed by the inventor to further the art and are to be construed as not being limited to these specifically recited examples and conditions. Moreover, all statements herein reciting principles, aspects, and embodiments of the present invention as well as specific examples thereof are intended to cover both structural and functional equivalents thereof. Additionally, such equivalents are intended to include both currently known equivalents and equivalents developed in the future (i.e., any elements developed, regardless of structure, that perform the same function). Furthermore, nothing disclosed herein is intended for dedication to the public, whether or not it is explicitly recited in the claims.

[0819] Accordingly, the scope of the present invention is not limited to the exemplary embodiments shown and described herein. Rather, the scope and spirit of the present invention are embodied by the appended claims. In the claims, 35 U.S.C.§112(f) or 35 U.S.C.§112(6) is expressly defined as being invoked for a limitation in a claim only when the exact phrase "means for" or the exact phrase "step for" is recited at the beginning of such limitation in the claim; if such exact phrase is not used in the limitation of the claim, then 35 U.S.C.§112(f) or 35 U.S.C.§112(6) is not invoked.

Claims

1. A method, comprising: Detecting light from a sample comprising a plurality of fluorophores having overlapping fluorescence spectra using a light detection system; Performing spectral analysis on the light from each fluorophore in the sample using a generalized least squares algorithm.

2. The method according to claim 1, wherein, Detecting light in a plurality of photodetector channels by the light detection system.

3. The method according to any one of claims 1 to 2, wherein, The light detection system includes a plurality of photodetectors.

4. The method according to any one of claims 2 to 3, wherein The method includes generating a data signal in each of the photodetector channels in response to the detected light.

5. The method according to claim 4, wherein, The method includes determining the data signal covariance in each photodetector channel.

6. The method according to claim 5, wherein, The data signal covariance in each photodetector channel includes: An inherent sample variability component; and A measurement variability component.

7. The method according to any one of claims 5 to 6, wherein The data signal covariance is associated with two or more of the plurality of photodetector channels.

8. The method according to any one of claims 5 to 7, wherein, The method includes using a covariance matrix to calculate the data signal covariance.

9. The method according to claim 8, wherein, The covariance matrix includes non-zero diagonal values.

10. The method according to any one of claims 5 to 9, wherein, The method includes estimating the data signal covariance based on the fluorescence intensities of two or more photodetectors of the light detection system.

11. The method according to any one of claims 1 to 10, wherein The method includes finding the least squares solution of a generalized least squares problem.

12. The method according to any one of claims 1 to 11, wherein, The method includes minimizing the least squares solution of the generalized least squares problem by one or more of matrix decomposition, matrix factorization, QR factorization, Cholesky factorization, singular value decomposition, LDL decomposition, and pre-permutation and post-permutation.

13. The method according to any one of claims 1 to 12, wherein, The method includes performing real-time spectral analysis on the light from each fluorophore.

14. A system, comprising: A light source configured to irradiate a sample comprising a plurality of fluorophores having overlapping fluorescence spectra; A light detection system including a plurality of photodetectors; And A processor including a memory operably coupled to the processor, wherein the memory includes instructions stored thereon that, when executed by the processor, cause the processor to perform spectral analysis on the light from each fluorophore in the sample using a generalized least squares algorithm.

15. An integrated circuit programmed to perform spectral analysis on the light from each fluorophore in a sample, the sample comprising a plurality of fluorophores having overlapping fluorescence spectra, using a generalized least squares problem.

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