Automatic spectral dye matrix adjustment to reduce spectral crosstalk for multiple QPCR assays

Abstract

A method for reducing spectral crosstalk in multiplex assays is provided. The method includes receiving filtered signal data from multiple fluorometry and an initial dye matrix including calibrated spectral dye data. The method further includes generating an updated dye matrix based on the initial dye matrix and the estimated crosstalk replacement value, and then adjusting the updated dye matrix to meet a calculated optimization value. The calculated optimization value is calculated based at least on the estimated crosstalk substitution value and the filtered signal data. The calculated optimization value may be further calculated based on each adjustment of the updated dye matrix and a cross-correlation between dyes used in the assay. The method further includes generating an improved dye matrix based on the adjusted updated dye matrix, and then generating spectral adjustment data based on the improved dye matrix.

Description

Cross-reference to related applications

[0001] This application claims the benefit of priority to U.S. Provisional Patent Application No. 63 / 511,569, filed June 30, 2023, the contents of which are incorporated herein by reference in their entirety. Background Technology

[0002] This disclosure relates to bioanalysis (such as polymerase chain reaction (PCR)) and bioanalytical devices (such as instruments for PCR), particularly to reducing spectral crosstalk in multiplex assays, and to computer systems and computer software for methods of reducing spectral crosstalk in multiplex assays.

[0003] The demand for rapid and high-volume testing of different viral strains, diagnostics for co-infections with different organisms, or investigations of large-scale microbial combinations is increasing. Therefore, there is a need for qPCR testing instruments with higher throughput and lower cost per sample. This necessitates more advanced qPCR dye multiplexing. However, in multiplexing scenarios, dye spectra tend to overlap, leading to an increased tendency for spectral crosstalk. Therefore, it is important to reduce or eliminate this tendency for spectral crosstalk.

[0004] Therefore, there is an increasing need for an algorithmic tool to help achieve lower detection limits in multiple assays. Summary of the Invention

[0005] In one exemplary embodiment, a method for reducing spectral crosstalk in multiplex assays is provided. The method includes receiving filtered signal data from multiplex fluorescence assays and an initial dye matrix including calibrated spectral dye data. The method further includes generating an updated dye matrix based on the initial dye matrix and an estimated crosstalk substitution value, and then adjusting the updated dye matrix to meet a calculated optimized value. The calculated optimized value is calculated at least based on the estimated crosstalk substitution value and the filtered signal data. The calculated optimized value may be further calculated based on each adjustment of the updated dye matrix and the cross-correlation between the dyes used in the assays. The method further includes generating an improved dye matrix based on the adjusted updated dye matrix, and then generating spectral adjustment data based on the improved dye matrix.

[0006] In another exemplary embodiment, a system for reducing spectral crosstalk in multiplex assays is provided. The system includes: a detector configured to receive filtered signal data from multiplex fluorescence assays; and a memory configured to store an initial dye matrix including calibrated spectral dye data. The system further includes a processor configured to generate an updated dye matrix based on the initial dye matrix and an estimated crosstalk substitution value, and to adjust the updated dye matrix to meet a calculated optimized value. The calculated optimized value is calculated based on the estimated crosstalk substitution value and the filtered signal data. The calculated optimized value can be further calculated based on each adjustment of the updated dye matrix and the cross-correlation between the dyes used in the assay. The processor is further configured to generate an improved dye matrix based on the adjusted updated dye matrix, and then generate spectral adjustment data based on the improved dye matrix.

[0007] In yet another exemplary embodiment, a computer-readable medium encoded with computer-readable instructions is provided. When executed by a computer's processor, the computer-readable instructions cause the computer to implement a method for reducing spectral crosstalk in multiplex measurements. The method includes receiving filtered signal data from multiplex fluorescence measurements and an initial dye matrix including calibrated spectral dye data. The method further includes generating an updated dye matrix based on the initial dye matrix and an estimated crosstalk substitution value, and then adjusting the updated dye matrix to meet a calculated optimized value. The calculated optimized value is calculated at least based on the estimated crosstalk substitution value and the filtered signal data. The calculated optimized value may be further calculated based on each adjustment of the updated dye matrix and the cross-correlation between the dyes used in the measurements. The method further includes generating an improved dye matrix based on the adjusted updated dye matrix, and then generating spectral adjustment data based on the improved dye matrix. Attached Figure Description

[0008] Figure 1 illustrates a flowchart of a method for reducing spectral crosstalk in multiple measurements according to various embodiments described herein.

[0009] Figure 2 is a block diagram illustrating a PCR instrument on which the implementation scheme of the content taught in this invention can be carried out.

[0010] Figure 3 depicts an exemplary optical system for imaging according to the embodiments described herein.

[0011] Figure 4 illustrates exemplary computing systems used to implement the various implementation schemes described herein.

[0012] Figure 5 illustrates exemplary distributed network systems according to various embodiments described herein.

[0013] Figure 6 illustrates an example of spectral sampling of fluorescence signals.

[0014] Figure 7 illustrates the normalized dye matrix according to the various implementation schemes described herein.

[0015] Figure 8 illustrates a block diagram of the spectral crosstalk reduction workflow according to the various implementation schemes described herein.

[0016] Figure 9 illustrates the spectral crosstalk reduction workflow according to the various implementation schemes described herein.

[0017] Figure 10 illustrates the signal discontinuity workflow according to the various implementation schemes described herein.

[0018] Figure 11 illustrates examples of signal discontinuities according to the various implementation schemes described herein.

[0019] Figure 12A Examples of signal discontinuity detection according to the various implementation schemes described herein are illustrated up to page 12F.

[0020] Figure 13 illustrates the adjusted signal based on signal discontinuity according to the various implementation schemes described herein.

[0021] Figure 14A Examples of spectral crosstalk reduction according to the various implementations described herein are illustrated in 14D.

[0022] Figure 15A Figure 15D illustrates another example of spectral crosstalk reduction according to the various implementations described herein.

[0023] Figure 16 illustrates the optimized workflow for reducing spectral crosstalk according to the various implementation schemes described herein.

[0024] Figure 17 illustrates a more detailed portion of the optimized workflow for reducing spectral crosstalk according to the various implementation schemes described herein.

[0025] Figure 18 illustrates another part of the optimized workflow for reducing spectral crosstalk according to the various implementation schemes described herein. Detailed Implementation

[0026] To provide a more thorough understanding of the invention, the following description sets forth many specific details, such as particular configurations, parameters, examples, etc. However, it should be understood that such description is not intended to be a limitation on the scope of the invention, but rather to provide a better description of exemplary embodiments.

[0027] Current qPCR (quantitative polymerase chain reaction) instruments are complex systems requiring skilled users. qPCR instruments require calibrated spectral dye matrices (“DMs”) to convert raw spectral filtered data into multi-component dye data (“raw data”). These calibrated spectral dye matrices represent our best estimate of the spectrum for each dye. The dye matrix is ​​obtained by arranging the spectrum of each dye along the rows of the dye matrix and normalizing each spectrum to have a maximum value of 1. The need for dye matrix (DM) recalibration may potentially stem from: Time drift from optical changes in the light source or instrument Spectral changes due to changes in ambient temperature and / or instrument movement Determine the changes in chemistry over time / Determine the changes in batches Possible calibration changes / drifts during qPCR runs Using custom dyes

[0028] According to various embodiments of the teachings of the present invention, an algorithm can be used to minimize spectral crosstalk by performing dye matrix optimization (DMO) on the dye matrix used for spectral deconvolution. DMO is performed using machine learning techniques, such as constrained multi-objective nonlinear optimization, to iteratively adjust the initial dye matrix, thereby minimizing the cross-correlation and / or crosstalk between dye amplification curves generated by the adjusted dye matrix. Absolute cross-correlation is the absolute value of the off-diagonal terms in the multi-component dye cross-correlation matrix. It is noteworthy that spectral crosstalk occurs during deconvolution due to errors in the dye matrix (DM) relative to the true DM (DM0). If no errors exist in the dye matrix, no spectral crosstalk will occur. Reducing the error in the DM relative to the true DM (DM0) during optimization results in a reduction in crosstalk.

[0029] Typically, algorithms and identification of qPCR crosstalk are challenging because each dye amplification curve usually contains only 40 to 45 data points. The various implementation schemes described in this paper utilize the idea that the cross-correlation between actual dye signals is minimally affected by small changes in the dye matrix, while crosstalk is strongly influenced by these small changes.

[0030] Therefore, the dye matrix that minimizes cross-correlation approaches the true DM (DM0), thereby minimizing DM error and reducing spectral crosstalk. Thus, the algorithm of the embodiment of the present invention optimizes / improves the dye matrix (DM) by minimizing multiple objectives, which consist of a weighted combination of the absolute cross-correlation between the multi-component dye amplification curves and the absolute values ​​of possible crosstalk between the dye traces as multiple objectives.

[0031] Using the algorithms of embodiments taught in this invention to reduce spectral crosstalk increases our ability to increase throughput by allowing for higher multiplex analyses. Spectral crosstalk (often considered as induced pull-up / pull-down in filtered signal data) is caused by the use of an incorrect dye matrix when deconvolving spectral filtered data to produce dye data during multicomponent processing (spectral deconvolution). Furthermore, at a given qPCR Ct threshold, spectral crosstalk reduction generally leads to a reduction in false positives and false negatives. It is not necessary to raise the Ct threshold to extremely high values ​​to avoid all potential spectral crosstalk. Therefore, by combining spectral crosstalk correction with a low to moderate Ct threshold, the overall limit of detection (LOD) is improved without increasing false positives. Pure dye calibration background

[0032] Currently, the method to prevent spectral errors in extracting dye signals from raw filtered data is to perform pure dye calibration. A pure dye calibration plate consists of a plate loaded with dye attached to oligonucleotides and sealed with a plate seal. Attaching the dye to the oligonucleotides allows these dyes to dissolve in solution and match the spectral characteristics of the actual dye-labeled probes, as the DNA attached to the dye can affect the dye's spectral characteristics. Since different DNA nucleotide bases attached to the dye can slightly alter the dye's spectral characteristics, pure dye calibration solutions use degenerate oligonucleotides. This means there is a mixture of different bases at some positions of the oligonucleotides, resulting in a calibration solution with a series of different oligonucleotide sequences attached to the dye. Because the calibration solution contains a mixture of oligonucleotide sequences that give an average spectral performance (when the actual assay only has one sequence attached to the dye), the pure dye calibration mixture will never precisely match the spectral characteristics of any given assay. Furthermore, if the buffer in the pure dye calibration solution is mismatched with the buffer in the actual reaction, the spectral characteristics may also change. In some cases, we fill only a subgroup of wells in the plate with any one dye and model the spectral performance across the entire plate by interpolating and extrapolating the spectrum of each well in the plate from that subgroup of wells.

[0033] Therefore, in order to perform pure dye calibration, all other calibrations in the system must be applied. This includes background subtraction with a plate containing only buffer solution, so that we know that any signal we measure will not be affected by the background. It also includes uniformity calibration to compensate for signal variations between holes using a uniform plate. It also includes a "color balance" correction, which multiplies a correction factor by each filter combination so that the relative signal level of each filter combination is consistent across different instruments.

[0034] After applying these calibrations, the system measures the signal level in each filter combination for each well. These signals are then divided by the maximum signal across all filter combinations to obtain the dye spectrum for that well, normalized to a maximum value of 1.

[0035] Pure dye calibration can be error-prone and complex. Therefore, alternative methods are needed to reduce spectral crosstalk.

[0036] Figure 1 illustrates a flowchart of a method for reducing spectral crosstalk in multiplex measurements according to various embodiments described herein. The method includes receiving filtered signal data from multiplex fluorescence measurements in step 102. The method further includes receiving an initial dye matrix in step 104, wherein the initial dye matrix includes calibrated spectral dye data, and generating an updated dye matrix based on the initial dye matrix and an estimated crosstalk substitution value in step 106. The method further includes adjusting the updated dye matrix in step 108 to satisfy a calculated optimized value. The calculated optimized value is calculated based on the estimated crosstalk substitution value and the filtered signal data. The adjustment step may be an iterative process of iteratively calculating the calculated optimized value. The optimized value may be further calculated based on each adjustment of the updated dye matrix and the cross-correlation between the dyes used in the measurements. In some embodiments, multiple calculated optimized values ​​are satisfied before adjustment is stopped. Each optimized value may be calculated based on each fluorescent dye used in the measurements. The method further includes, in step 110, generating an improved dye matrix based on the adjusted and updated dye matrix, and in step 112, generating spectral adjustment data based on the adjusted and updated dye matrix.

[0037] Those skilled in the art will recognize that, where appropriate, hardware, software, firmware, or combinations thereof can be used to implement the operation of various embodiments. For example, some processing can be performed using a processor or other digital circuitry under the control of software, firmware, or hardwired logic. (The term "logic" herein refers to fixed hardware, programmable logic, and / or suitable combinations thereof, as will be recognized by those skilled in the art, for implementing the described functions.) Software and firmware can be stored on a computer-readable medium. Other processing can be implemented using analog circuitry, as is known to those skilled in the art. Furthermore, memory or other storage devices and communication components may be employed in embodiments of the invention. PCR instrument

[0038] As mentioned above, instruments that can be used according to various embodiments are (but are not limited to) polymerase chain reaction (PCR) instruments. Figure 2 is a block diagram illustrating a PCR instrument 200 on which embodiments of the teachings of this invention can be implemented. The PCR instrument 200 may include a heating cap 210 placed over a plurality of samples 212 contained in a substrate (not shown). In various embodiments, the substrate may be a glass or plastic slide having a plurality of sample areas with a cap between the sample areas and the heating cap 210. Some examples of the substrate may include (but are not limited to) multiwell plates, such as standard microtiter 96-well plates, 384-well plates, or microcards, or substantially flat supports, such as glass or plastic slides. In various embodiments of the substrate, reaction sites may include depressions, notches, ridges, and combinations thereof patterned in a regular or irregular array on the surface of the substrate. Various embodiments of the PCR instrument include a sample block 214, elements 216 for heating and cooling, a heat exchanger 218, a control system 220, and a user interface 222. Various embodiments of the hot block assembly according to the teachings of the present invention include components 214 to 218 of the PCR instrument 200 of FIG. 2.

[0039] The real-time PCR instrument 200 has an optical system 224. In Figure 2, the optical system 224 may include an illumination source (not shown) that emits electromagnetic energy, an optical sensor, detector, or imager (not shown) for receiving electromagnetic energy from the sample 212 in the substrate, and optics for directing electromagnetic energy from each DNA sample to the imager. For the PCR instrument 200 and the real-time PCR instrument 200 in Figure 2, a control system 220 can be used to control the functions of the detection system, heating cap, and hot block assembly. The control system 220 can be accessed by the end user through the user interface 222 of the PCR instrument 200 and the real-time PCR instrument 200 in Figure 2. Furthermore, as depicted in Figure 4, a computer system 400 can be used to provide control over the functions of the PCR instrument 200 in Figure 2 and the user interface functions. Additionally, the computer system 400 in Figure 4 can provide data processing, display, and report preparation functions. All such instrument control functions can be localized to the PCR instrument. Alternatively, the computer system 400 of Figure 4 can provide remote control over some or all of the control, analysis, and reporting functions, for example, as a server system, which will be discussed in more detail later. Optical systems for imaging

[0040] Figure 3 depicts an exemplary optical system 300 for imaging according to an embodiment described herein. It should be understood that optical system 300 is an exemplary optical system, and those skilled in the art will recognize that other optical systems can be used to capture images of an object of interest. According to various embodiments, the object of interest may be a sample holder, such as a calibration plate, as described herein. For example, an optical sensor 302 included in a camera 304 can image the object of interest 310. The optical sensor 302 may be a CCD sensor, and the camera 304 may be a CCD camera. Furthermore, the optical sensor includes a camera lens 306.

[0041] Depending on the object of interest, depending on the implementation, emission filter 308 can be selected to image object 310. In other implementations, emission filter 308 can be changed to image fluorescence emission emitted from object 301.

[0042] Optical system 300 can image object 310 of interest using reflective light source 312. Light from light source 312 is filtered by aspherical surface 314, focuser / divergent 316, and excitation filter 318 before being reflected to object 310 by beam splitter 320. Optical system 300 may also include field lens 322. Depending on the object of interest, emission filter 318 may be selected to image object 310 according to various embodiments.

[0043] The following description of various embodiments of the teachings of this invention has been presented for illustrative and descriptive purposes. It is not exhaustive and does not limit the teachings of this invention to the precise forms disclosed. Modifications and changes are possible in light of the above teachings, or modifications and changes can be obtained from the practice of the teachings of this invention. Furthermore, the described embodiments include software, but the teachings of this invention can be implemented as a combination of hardware and software or solely in hardware. The teachings of this invention can be implemented using both object-oriented and non-object-oriented programming systems. Computing System

[0044] Figure 4 is a block diagram illustrating a computer system 400 that can be used to implement processing functions according to various embodiments. Experimental instruments can be connected to the exemplary computing system 400. The computing system 400 can be locally connected to the instruments according to various embodiments. In other embodiments, the computing system 400 can act as a server via an Internet connection, controlling the functions of the instruments, generating results based on data obtained by the instruments, or analyzing and processing the data obtained by the instruments. The computing system 400 may include one or more processors, such as processor 404. Processor 404 can be implemented using general-purpose or special-purpose processing engines, such as, for example, microprocessors, controllers, or other control logic. In this example, processor 404 is connected to bus 402 or other communication media.

[0045] Furthermore, it should be understood that the computing system 400 of Figure 4 can be embodied in any of several forms, such as rack-mounted computers, mainframes, supercomputers, servers, clients, desktop computers, laptop computers, tablet computers, handheld computing devices (e.g., PDAs, cellular phones, smartphones, PDAs, etc.), cluster grids, netbooks, embedded systems, or any other type of dedicated or general-purpose computing device that may be required or suitable for a given application or environment. Additionally, the computing system 400 may include a conventional network system comprising a client / server environment and one or more database servers, or integrated with a LIS / LIMS infrastructure. Various conventional network systems, including local area networks (LANs) or wide area networks (WANs), and including wireless and / or wired components, are known in the art. Furthermore, client / server environments, database servers, and networks are well documented in the art. According to the various embodiments described herein, the computing system 400 can be configured to connect to one or more servers in a distributed network. The computing system 400 can receive information or updates from the distributed network. The computing system 400 can also transmit information to be stored within a distributed network, which can be accessed by other clients connected to the distributed network.

[0046] The computing system 400 may include a bus 402 or other communication mechanism for conveying information, and a processor 404 coupled to the bus 402 for processing information.

[0047] The computing system 400 also includes a memory 406, which may be random access memory (RAM) or other dynamic memory, coupled to the bus 402 to store instructions to be executed by the processor 404. The memory 406 may also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor 404. The computing system 400 further includes a read-only memory (ROM) 408 or other static storage device coupled to the bus 402 to store static information and instructions for the processor 404.

[0048] The computing system 400 may also include a storage device 410, such as a hard disk, optical disk, or solid-state drive (SSD), which is provided and coupled to a bus 402 for storing information and instructions. The storage device 410 may include a media drive and a removable storage interface. The media drive may include a drive or other mechanism for supporting fixed or removable storage media, such as a hard disk drive, floppy disk drive, magnetic tape drive, optical disk drive, CD or DVD drive (R or RW), flash drive, or other removable or fixed media drive. As illustrated in these examples, the storage media may include a computer-readable storage medium in which specific computer software, instructions, or data are stored.

[0049] In an alternative implementation, storage device 410 may include other similar tools for allowing computer programs or other instructions or data to be loaded into computing system 400. Such tools may include, for example, removable storage units and interfaces (such as program cassettes and cassette interfaces), removable memory (e.g., flash memory or other removable memory modules) and memory slots, as well as other removable storage units and interfaces that allow software and data to be transferred from storage device 410 to computing system 400.

[0050] The computing system 400 may also include a communication interface 418. The communication interface 418 can be used to allow software and data to be transferred between the computing system 400 and external devices. Examples of the communication interface 418 may include a modem, a network interface (such as an Ethernet or other NIC card), a communication port (such as a USB port, an RS-232C serial port), a PCMCIA slot and card, Bluetooth, etc. Software and data transferred via the communication interface 418 may be in the form of electronic, electromagnetic, optical, or other signals that can be received by the communication interface 418. These signals may be transmitted and received via a channel (such as a wireless medium, wire or cable, optical fiber, or other communication medium) through the communication interface 418. Some examples of channels include telephone lines, cellular telephone links, RF links, network interfaces, local area networks or wide area networks, and other communication channels.

[0051] The computing system 400 can be coupled to a display 412 (such as a cathode ray tube (CRT) or liquid crystal display (LCD)) via a bus 402 for displaying information to a computer user. An input device 414, including alphanumeric and other keys, is coupled to the bus 402 for conveying information and command selections to the processor 404, for example. The input device can also be a display configured with touchscreen input capabilities, such as an LCD display. Another type of user input device is a cursor control 416, such as a mouse, trackball, or arrow keys, for conveying directional information and command selections to the processor 404 and for controlling cursor movement on the display 412. This input device typically has two degrees of freedom on two axes (a first axis (e.g., x) and a second axis (e.g., y)), allowing the device to specify a position in a plane. The computing system 400 provides data processing and provides a confidence level for such data. In accordance with certain implementations of the embodiments taught in this invention, computing system 400 provides data processing and confidence values ​​in response to processor 404 executing one or more sequences of one or more instructions contained in memory 406. Such instructions may be read into memory 406 from another computer-readable medium, such as storage device 410. Execution of the sequence of instructions contained in memory 406 causes processor 404 to perform the process states described herein. Alternatively, hard-wired circuitry may be used in place of or in combination with software instructions to implement embodiments taught in this invention. Therefore, implementation of the embodiments taught in this invention is not limited to any particular combination of hardware circuitry and software.

[0052] As used herein, the terms “computer-readable medium” and “computer program product” generally refer to any medium relating to providing processor 404 with one or more sequences or instructions for execution. Such instructions, generally referred to as “computer program code” (which may be grouped in the form of a computer program or other groupings), when executed, enable computing system 400 to perform the features or functions of embodiments of the present invention. These and other forms of non-transitory computer-readable media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, solid-state drives, optical disks, or magnetic disks, such as storage device 410. Volatile media include dynamic memory, such as memory 406. Transmission media include coaxial cables, copper wires, and optical fibers, including wires containing bus 402.

[0053] Common forms of computer-readable media include, for example, floppy disks, floppy disks, hard disks, magnetic tapes or any other magnetic media, CD-ROMs, any other optical media, punched cards, paper tapes, any other physical media with a perforated pattern, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chips or cassettes, carrier waves as described below, or any other media from which a computer may read.

[0054] Various forms of computer-readable media may involve loading one or more sequences of one or more instructions to processor 404 for execution. For example, instructions may first be loaded onto a disk of a remote computer. The remote computer may load the instructions into its dynamic memory and transmit the instructions over a telephone line using a modem. A modem local to computing system 400 may receive data over the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to bus 402 may receive the data carried in the infrared signal and place the data on bus 402. Bus 402 loads the data to memory 406, from which processor 404 retrieves and executes the instructions. Instructions received by memory 406 may optionally be stored on storage device 410 before or after execution by processor 404.

[0055] It should be understood that, for clarity, the above description has referenced various functional units and processors to illustrate embodiments of the invention. However, it will be apparent that any suitable functional distribution among different functional units, processors, or domains can be used without departing from the invention. For example, illustrated functions that would be performed by separate processors or controllers may be performed by the same processor or controller. Therefore, references to specific functional units should be considered merely as references to the appropriate components used to provide said functions, and not as indications of a strict logical or physical structure or organization. Distributed systems

[0056] Some components of a typical Internet network configuration 500 are shown in Figure 5, where multiple client machines 502, possibly located in remote local offices, are shown connected to a gateway / hub / tunnel server, etc. 510, itself connected to the Internet 508 via an Internet Service Provider (ISP) connection 510. Other possible clients 512 are also shown connected to the Internet 508 similarly via an ISP connection 514. These units communicate, for example, with a possible central lab or office via an ISP connection 516 connected to a gateway / tunnel server 518, which in turn connects to various enterprise application servers 522, which may be connected to the various local clients 530 via another hub / router 526. Any of these servers 522 can act as a development server for analyzing potential content management and delivering design solutions as described in the present invention, as described more fully below. Overview of Spectral Matrix

[0057] As an introduction, we will first establish the mathematical foundation of spectral deconvolution and explain why the error of the dye matrix relative to the real dye matrix leads to spectral crosstalk.

[0058] The concept of spectral deconvolution can be described by a simple example using three dyes with different fluorescence spectral properties and four filters measured in separate spectral bandwidths during a single scan:

[0059] Here Indicated by filter number or id Individual filter fluorescence measurements were performed at the corresponding relative spectral bandwidths. Indicates that it is made of dye Fluorescence generated under the same number of scans. In the matrix notation: in This represents the transpose of the dye matrix.

[0060] Filtered signal data, also known as filtered data, refers to the temporal and spectral sampling of fluorescence caused by different dyes present within the multiplex qPCR reaction sites. Arrays of different filters are used to generate filtered signal data, or filtered data. Each filter detects fluorescence within a different narrow band of the spectrum (Figure 6), and therefore the filter array allows sampling of total fluorescence generated by different dyes and wells at specific time points or cycles within the qPCR process. Figure 6 illustrates an example of spectral sampling of fluorescence signals.

[0061] The filtered signal data is then defined as a two-dimensional data array consisting of spectral separation measurements (identified by filter number or ID) collected at specific time points defined by the cycle sequence in the qPCR experiment.

[0062] Figure 6 shows an example of spectral sampling of fluorescence within the reaction site (continuous line 602) at fixed time points or cycles during a qPCR process. In this example, an array of 10 spectral distributed filters was used to measure fluorescence induced by several dyes within the reaction site.

[0063] Dye matrix data refers to a two-dimensional array of values ​​that correlate the fluorescence of an individual dye with spectral measurements obtained from individual filters in a filter array used in multiplex qPCR experiments.

[0064] The example can be rewritten using more compact matrix notation as follows: Here, f is the column vector of the currently scanned filtered data. DM T It is the transpose of the dye matrix. And d is a column vector containing the deconvolutioned dye data that we want to obtain.

[0065] This is more typically written in mathematically equivalent transpose form: in, f T It is a row vector [f1 f2 f3 f4], representing the filtered data in the current scan, d T It is a row vector [d1d2 d3], representing the corresponding dye data under the current scan, and DM is a spectral dye matrix. The number of rows equals the number of normalized dye calibration spectra represented, and the number of columns equals the number of spectral bins used to represent the normalized spectra of each dye.

[0066] Figure 7 illustrates examples of normalized dye matrices according to various embodiments described herein. Figure 7 shows the relationship between the normalized dye matrix (DM) values ​​of a dye system with four dyes (FAM, VIC, ABY, and JUN) measured using 10 filters and the filter number. The dye matrix is ​​typically normalized to a maximum value of 1 for each dye.

[0067] Table 1 below illustrates the normalized dye matrix values ​​associated with the example in Figure 7. It shows the relationship between the normalized dye matrix (DM) values ​​of a dye system with four dyes (FAM, VIC, ABY, and JUN) measured using 10 filters and the filter numbers. Table 1

[0068] Using direct linear algebra to invert Equation 2, we obtain an equation describing the spectral deconvolution of the filtered signal data to generate dye data on each scan, as shown below: Where pinv(DM) is the pseudo-inverse of the dye matrix DM.

[0069] The pseudo-inverse is the "best-fit" linear least-squares matrix inverse of the dye matrix DM when the number of rows >= the number of columns. This spectral deconvolution is true in every scan. The spectral deconvolution equation can be generalized as: Where D is the dye data matrix (size numScans x numDyes), where the dye data is obtained by scanning down each row, and F is the filter data matrix (size numScans x numFilters), where the filter data is obtained by scanning down each row.

[0070] As described in Equations 3 and 4, if the dye matrix is ​​calibrated, optimized, or improved to have minimal or no error, spectral deconvolution will not produce spectral errors or crosstalk. However, spectral crosstalk occurs when the estimated value of the dye matrix used during spectral deconvolution is incorrect. Therefore, the closer we adjust the dye matrix to the true dye matrix, the less spectral crosstalk we will experience. The dye matrix can be iteratively updated to approximate the true dye matrix. Mathematically, this can be stated as the closer our currently updated dye matrix is ​​to the true dye matrix, the closer the spectral crosstalk matrix (C) becomes to the identity matrix. The resulting adjusted and updated dye matrix is ​​an improved dye matrix used to deconvolve the filtered signal data to reduce spectral crosstalk.

[0071] Note that if we rewrite the real dye matrix as DM0 and write the real dye data without any crosstalk as D0, then we can write Equation 4 as: Where D0 is the actual dye data matrix or calibrated spectral dye data without any error (size numScans x numDyes), where the dye data is for each row in each downward scan, F is the filtered data matrix (size numScans x numFilters), where the filter data is for each row in each downward scan, and DM0 is the actual dye matrix.

[0072] If we base it on the initial dye matrix DM Reconceptualizing Equation 4 with initial dye data D that may have crosstalk, without loss of generality, we can define the initial dye matrix as... As mentioned earlier, DM is the initial dye matrix, DM0 is the actual dye matrix, and DM... e This refers to the error in the initial dye matrix. For a good / reasonable initial dye matrix, DM e The maximum value in should be less than the actual dye matrix DM. o The maximum value in (by definition, it is one (unity), since the dye matrix is ​​normalized to have a maximum value of one).

[0073] We can also define the initial dye data generated by deconvolution as... Where D e This is spectral crosstalk error. Therefore, equation 4 can be rewritten as:

[0074] With a slight rearrangement and using equation 4a, we obtain the spectral crosstalk error (D). e ) is given as Therefore, this led us to observe the dye matrix DM e The error in the equation, when its elements become zero, we obtain:

[0075] Equations 7 and 8 assure us that by reducing the dye matrix error (DM) e The optimization process of updating the initial dye matrix (DM) to be closer to zero and closer to the true dye matrix (DM0) will result in a reduction of spectral crosstalk, thereby adjusting the updated DM to the improved dye matrix.

[0076] Also note that, without losing mathematical generality, we can also use the actual dye matrix (DM0) and error matrix (C)e The improved dye matrix is ​​defined by the product of () and (). DM ≡C e * DM0 (5c)

[0077] Error matrix C e It has a size of numDyes x numDyes and is typically a diagonally dominated matrix. That is, since DM is expected to be a close approximation of DM0, the largest elements will tend to be on the diagonal and closer to one. Off-diagonal elements will have absolute values ​​less than 1.

[0078] Therefore, equation 6 becomes: D = D0 + D e = F * pinv(C e *DM0). (6a)

[0079] Please note the spectral deconvolution result (F * pinv(C)). e *DM0)) becomes, after following the rules for inverting matrix multiplication, that... F * pinv(C -DM0) = F * pinv(DM0) * pinv(C e ). According to the definition in equation 4a, we get: D = F * pinv(C *DM0) = D0* pinv(C e ). Or to put it more simply: D = D0* pinv(C e (9)

[0080] We can define the observed multi-component dye data (D) based on the actual dye data (D0) and the crosstalk matrix: D = D0 * C. (10)

[0081] For a crosstalk matrix, the diagonal elements are all close to one, and the absolute values ​​of the off-diagonal elements are usually much smaller than one. They can be positive or negative. Therefore, according to the rules of matrix multiplication, the elements C of the crosstalk matrix... 23 , which are the second row and third column of the crosstalk matrix C, representing the spectral crosstalk from dye 2 to dye 3. And typically, the elements C of the crosstalk matrix... ij , which is the i-th row and j-th column of the crosstalk matrix C, representing the spectral crosstalk from dye i to dye j.

[0082] Comparing equations 9 and 10, it is clear that the crosstalk matrix is ​​given by the following equation: C = pinv(C e (11)

[0083] According to the original definition in equation 5c DM ≡ C e *DM0 (5c) therefore, DM0 = pinv(C e ) * DM (12)

[0084] Alternatively, using Equation 11, we obtain: DM0 = C * DM (13)

[0085] Equation 13 implies that if we have a good estimate of the crosstalk C, we can adjust the updated dye matrix by updating Equation 13 using the dye matrix to give a good estimate of the true dye matrix (DM0). This leads to an iterative optimization method at the i-th iteration, as follows: DM i+1 = C i * DM i。 (14)

[0086] Here, based on the estimated crosstalk Ci and dye matrix DMi at the i-th iteration, we obtain the updated dye matrix DMi+1 for the next (i+1)-th iteration.

[0087] Please note that we can rewrite equation 5a as: DM0 ≡DM - DM e (5a')

[0088] Therefore, equations 5a', 13 and 14 represent three alternative ways to optimize the dye matrix.

[0089] In an embodiment of the invention, using Equation 5a', we can use an optimization process to adjust the elements of the initial dye matrix, limited by the extent to which these elements can deviate from the initial dye matrix, to meet optimization criteria. As described in the summary, a novel set of preferred optimization criteria is to minimize multiple objectives, which consist of a weighted combination of the absolute cross-correlation between the multicomponent dye amplification curves and the absolute values ​​of possible crosstalk between the dye traces as multiple objectives.

[0090] Please note that in this implementation, we are attempting to find estimates of all values ​​in the true dye matrix (DM0). The size of the dye matrix is ​​numDyes x numFilters. Here, numDyes is the number of dyes, and numFilters is the number of filters. Therefore, for the case where numDyes is 5 and numFilters is 12, this means we are trying to find 60 (i.e., 5 x 12) values.

[0091] In another implementation, using Equation 13, we can use an optimization process to fine-tune the elements of the estimated crosstalk matrix (C), subject to constraints on the off-diagonal elements of C to satisfy the aforementioned optimization criteria. Note that in this implementation, we attempt to find estimates of all values ​​in the crosstalk matrix (C). The crosstalk matrix has a size of numDyes x numDyes. An advantage of this approach is that, given numDyes x numDyes, the number of elements in C is typically much smaller than the number of elements in the estimated true dye matrix DM0, given by numDyes x numFilters.

[0092] Therefore, the number of values ​​to be optimized is smaller. This is because numFilters is typically >> numDyes. Therefore, the second preferred implementation should be faster than the first preferred implementation because the number of variables to be optimized is much smaller; and the optimization speed tends to be at least the cube of the number of variables to be optimized.

[0093] However, in the first preferred embodiment, the constraints (bounds) that need to be set around the values ​​of the dye matrix can be directly represented by the values ​​of the dye matrix. Therefore, the optimization is more robust. In the second embodiment, even if we solve for the values ​​of the crosstalk matrix, we must still utilize Equation 13. DM0 = C * DM (13) The estimated true dye matrix (DM0) is obtained from the crosstalk estimate (C) and the initial dye matrix (DM) used to begin the optimization process. Therefore, we cannot restrict the values ​​of the dye matrix. They need to be placed indirectly on the dye matrix through bounds on the crosstalk matrix.

[0094] However, we can impose constraints on the crosstalk matrix by utilizing the observation that crosstalk tends to be greater among dyes that are spectral neighbors when it occurs. That is, all other things being equal, dyes whose peaks are closer to each other spectrally tend to have a greater probability of crosstalk. Conversely, dyes that are farther apart spectrally tend to have a smaller probability of crosstalk. In other words, the spectral distance between dyes is approximately inversely proportional to the probability of crosstalk between them. That is, dyes that are spectrally close to each other should have a wider constraint on their crosstalk probability during optimization, which is reflected in the corresponding off-diagonal values ​​of the optimized crosstalk matrix (C). Conversely, dyes that are spectrally far apart should have a tighter constraint on their crosstalk probability during optimization, which is reflected in the corresponding off-diagonal values ​​of the optimized crosstalk matrix (C).

[0095] In mathematics, the concept of spectral distance can be defined based on the spectral overlap between dyes. Spectral overlap is given as: in This is the spectral overlap matrix of the dyes. For the example dye matrices shown in Table 1, the corresponding spectral overlap matrices are shown in Table 2 below. Note that in Table 1, the peaks of dyes FAM, VIC, ABY, and JUN are in filters 1, 3, 5, and 7, respectively. Therefore, for example, FAM is spectrally furthest from JUN.

[0096] Therefore, for example, we see in Table 2 that the spectral overlap between FAM and JUN is 0.004. This is smaller than the overlap between FAM and VIC (0.408) and between FAM and ABY (0.043). This reflects the fact that JUN is spectrally furthest from FAM relative to the other dyes. Similar spectral distance relationships can be inferred from the dye spectral overlap matrix shown in Table 2 below. Table 2

[0097] By dividing each row by its maximum value, the dye spectral overlap matrix can be normalized to have a maximum value of 1 along each row. This yields the normalized dye spectral overlap matrix, S. NO Table 3 below shows the normalized dye spectral overlap matrix values ​​obtained from Table 2. It is correlated with the examples in Figure 7 and Table 1. This normalized dye spectral overlap matrix, S... NO This inverse relationship between spectral distance and the off-diagonal term of normalized dye spectral overlap is shown very clearly. For example, FAM is the furthest from JUN in the spectrum. Table 3

[0098] As we see in Table 3, for example, the normalized spectral overlap between FAM and JUN is 0.003. This is less than the normalized overlap between FAM and VIC (0.350) and between FAM and ABY (0.043). Note that the normalized spectral overlap of adjacent dyes in this group of dyes (FAM, VIC, ABY, JUN) is 0.350 for FAM-VIC, 0.257 for VIV-FAM, 0.422 for VIC-ABY, 0.452 for ABY-VIC, 0.412 for ABY-JUN, and 0.499 for JUN-ABY. Therefore, the normalized spectral overlap of adjacent dyes in this group of dyes is approximately 0.4.

[0099] Since we have observed that, all other things being equal, spectrally adjacent dyes tend to have a greater likelihood of crosstalk, while spectrally distant dyes have a much smaller likelihood of crosstalk, we can approximate the upper bound of the off-diagonal elements of the crosstalk matrix as follows: Where c 上界 It is a parameter that sets an approximate upper bound on the off-diagonal elements of the crosstalk matrix allowed during optimization, c 最小界 It is a parameter that sets the upper bound of the expected minimum absolute value, c 最大界 It is a parameter that sets the upper bound of the expected maximum absolute value. S is a parameter representing the average crosstalk factor of adjacent dyes (approximately 0.4 for this dye group). NO It is the previously defined normalized spectral overlap, and I is the identity matrix that is 1 on the diagonal and 0 elsewhere. 最小界 It is usually set to a small value ~< 0.005 (~< 0.5%). 最大界 Typically ~< 0.15 (~< 15%), but can be set larger or smaller depending on the dye set and qPCR instrument. (S) NO - I) means that the terms on the diagonal are zero, reflecting that the crosstalk of the dye itself is zero. The upper bound on the diagonal elements is given by the following formula: c 上界 ≈ c 最小界 + I, (16b) Similarly, we can approximate the lower bound on the off-diagonal elements of the crosstalk matrix as: in This is a parameter that sets an approximate lower bound on the off-diagonal elements of the crosstalk matrix allowed during optimization. The lower bound on the diagonal elements is given by the following equation: Therefore, in this embodiment according to the teachings of the present invention (the explicit definition and parameterized values ​​of the upper and lower bounds of the element values ​​in the crosstalk matrix), we now have a suitable definition for the constrained nonlinear optimization of the elements of the crosstalk matrix to produce an estimate of the crosstalk matrix (C). The estimate of the true dye matrix (DM0) is then directly derived from Equation 13: DM0 = C * DM (13) In another implementation, using Equation 14, we independently estimate the crosstalk matrix (C) at each iteration of the optimization. i The method begins with the elements of qPCR. This is typically difficult to achieve in qPCR because we usually only have 40 to 45 cycles to work, and the amplification in each dye is guaranteed to begin in distinct, well-separated, and characteristic cycling ranges. If the amplification in each dye used for assay is expected to begin in distinct, well-separated, and characteristic cycling ranges, a crosstalk matrix (C0) may be generated at each optimized iteration. i This method provides reasonable estimates of the elements of C. It has the advantage of involving only matrix multiplication of small matrices. Explicit optimization of the elements of C is not required. Therefore, this alternative implementation will be much faster than the preferred implementation. However, its applicability is limited to more specific cases where the crosstalk matrix can be estimated. Also note that by applying Equation 14, multiplying both sides by pinv(DM), and then rearranging, the following occurs: C = DM0 * pinv(DM) (17) This means that if at the end of our dye matrix optimization, we produce an improved dye matrix (DM) 经改善 ), so that: DM 经改善 -> DM0 We can then estimate the spectral crosstalk generated by the initial dye matrix (DM) as follows: C est =DM 经改善 * pinv(DM) (18) This is a useful result because measuring spectral crosstalk in qPCR is often difficult to do accurately. It can be used for various types of quality control related to optimization processes and / or assay development processes. Overall System Figure 8 illustrates a block diagram 800 of a spectral crosstalk reduction workflow according to the various embodiments described herein. System 804 is configured to reduce spectral crosstalk and can also operate in conjunction with another system 802. System 802 may provide a user interface or additional analytical functions for qPCR data. System 804 receives inputs of filtered signal data (which is a multiplex fluorescence signal), calibration spectral dye matrix data, and optimized values. System 804 includes a signal discontinuity detection component 806 and a dye matrix optimization component 808. The signal discontinuity component 806 is configured to detect and correct sudden drops or increases in the filtered signal data. Such sudden discontinuities can produce erroneous cross-correlation, which can lead to incorrect "crosstalk" identification and reduction. These sudden signal discontinuities are limited to occurring simultaneously in each filtered time data sequence within two points (qPCR cycles) of time data acquisition. If a signal discontinuity causes the measured signal trend to suddenly decrease at its point of occurrence, it is marked as a "declining" signal discontinuity. Otherwise, if a sudden change causes the measured signal trend to increase at its point of occurrence, it is marked as an "increasing" signal discontinuity. The goal of the dye matrix optimization component 808 is to minimize the "crosstalk" effect observed in multiplex qPCR assays, where signals from several dyes are acquired simultaneously. Crosstalk refers to the effect where a measured increase in the signal corresponding to one dye causes a corresponding increase or decrease in the signal of another dye. Figure 9 illustrates a more detailed spectral crosstalk reduction workflow 900 according to the various implementation schemes described herein. Similar to Figure 8, system 904 is configured to reduce spectral crosstalk and can also operate in conjunction with another system 902. System 902 can provide a user interface or additional analytical functions for qPCR data. System 904 receives inputs of filtered signal data (which is a multiplex fluorescence signal), calibrated spectral dye matrix data, and optimized values. According to the various embodiments described herein, the output of system 904 depends on the data type received from external system 902. As illustrated in the diagram in Figure 9, at decision 908, if only filtered signal data is received and no calibrated spectral dye matrix data is provided, system 904 activates signal discontinuity detection unit 906 and adjusts the filtered signal data based on the detected discontinuity. If, at decision 908, it is determined that calibrated spectral dye matrix data is also provided, then system 904 further runs dye matrix optimization component 910 to correct for any crosstalk effects (if any). At decision 912, if there is a problem preventing the algorithm from running, the original input data is returned unchanged. The following sections describe the signal discontinuity detection component 906 and the dye matrix optimization component 910 in more detail. Signal discontinuity bit components Figure 10 illustrates the signal discontinuity detection process of the signal discontinuity detection unit 1000 according to various embodiments described herein. The input to the signal discontinuity detection unit 1000 is single-well filtered signal data. Signal discontinuity detection is performed in the signal discontinuity detection unit 1002. If no signal discontinuity is detected at decision 1008, the filtered signal data sequence remains unchanged. If a signal discontinuity is detected at decision 1008, the location of the signal discontinuity is estimated in the signal discontinuity location estimation unit 1004. Once the location of the signal discontinuity is calculated, the effect of the signal discontinuity on the filtered signal data sequence is eliminated in the signal discontinuity correction unit 1006. Based on decision 1010, this process is then repeated to detect additional signal discontinuities. In one example, the signal discontinuity detection component 1000 limits the number of signal discontinuities to be detected and corrected to an internally set limit of 5, since a large number of signal discontinuities may be associated with noise measurement data, which would be unreliable and unable to be analyzed further. Signal discontinuity detection unit 1002 detects signal discontinuities through a characteristic waveform obtained by processing the filtered data sequence and combining the results in several steps. Figure 11 illustrates examples of signal discontinuities in filtered signal data according to various embodiments described herein. Curve 1100 of the filtered signal data 1100 shows a distinct abrupt change (dashed line) occurring in all filtered signal data sequences at the same cyclic measurement point. This characteristic abrupt change is associated with the presence of signal discontinuities at the reaction site. Figures 12A to 12F illustrate examples of signal discontinuity detection according to various embodiments described herein. After processing steps S1-S6, waveforms are generated for detecting signal discontinuities. The steps S1-S6 corresponding to Figures 12A to 12F are described below: Figure 12A illustrates step S1, which is the uncorrected filtered data. The uncorrected filtered signal data shows abrupt changes in all filtered signal data sequences at the same cyclic measurement point. The dashed filtered signal data in Figure 11 illustrates an example where such abrupt changes are evident. Figure 12B illustrates step S2. S2 = diff(abs(S1)). A cyclic difference operation is performed on the absolute value of each filtered signal data sequence. In other words: for i = 2…M, S2… F1 (i) = S2 F1 (C i ) – S2 F1 (C i -1), where M is the total number of measurement cycle points. Differential operations highlight abrupt changes. Based on the sign of the change, if the change is positive, the signal discontinuity is "upward," and if the change is negative, the signal discontinuity is "downward." Figure 12C illustrates step S3. S2 = abs(S2). Once the discontinuity type of the "up" and "down" signals is identified, the absolute values ​​of the differential filtered signal data in S2 are obtained. Figure 12D illustrates step S4. S4 = Normed(S3). Then, within a reasonable cyclic range, the sum of the data sequences from S3 is normalized relative to the median obtained from the initial time measurement, within which the initial conditions of all filters being measured for all filtered signal data measurement sequences (e.g., cycle 7) can be assumed, plus the value of the initial reference cycle for each corresponding data sequence in S3. This step normalizes for variations caused by signal discontinuities on each filtered signal data sequence. Figure 12E illustrates step S5. S5 = Sum(S4). The data sequences from S4 are summed together to obtain a single data sequence that reflects the normalized cumulative effect of the signal discontinuities in all filtered signal data sequences. Figure 12F illustrates step S6. S6 = diff(S5). Finally, a difference operation is performed on the data sequence from S5 to produce a sequence with characteristic "up and down" behavior of data points around the locations of signal discontinuities in the original filtered signal data sequence. Based on the above steps, if a characteristic "up and down" behavior is found within the continuous data points in the relevant data sequence S6, the signal discontinuity component detects the signal discontinuity in the associated filtered signal dataset. 5.1.2 Signal Discontinuity Location Estimation Referring back to Figure 10, if a signal discontinuity is detected, the signal discontinuity location estimation unit 1004 estimates the cycle in which the signal discontinuity occurs based on the location of the maximum value of the sequence signal obtained in step S5. Next, the signal discontinuity correction unit 1006 corrects the impact of the signal discontinuity on the filtered signal data curve. Figure 13 illustrates the adjusted signal based on signal discontinuities according to various embodiments described herein. First, before estimating the location of the signal discontinuity, a third-order polynomial curve 1302 is fitted to each filtered signal data curve 1300 using five measurement points. Next, a fixed measurement value 1304 at the location of the signal discontinuity is estimated by extrapolation using polynomial fitting. Then, a correction value (offset) 1306 is estimated using the found value, which is added to all measurements after the location of the signal discontinuity to generate adjusted filtered signal data 1308. The third-order polynomial fitting allows for better correction if an exponential or transition phase exists. Dye Matrix Optimization Component The purpose of the dye matrix optimization component in various embodiments of the present invention is to minimize crosstalk effects between dye signals associated with a corresponding set of targets in multiple determinations. Crosstalk refers to the induced positive or negative amplification of the dye / target signal caused by the amplification of another dye signal. When crosstalk is present, it can be assumed that the amplification of one dye signal is positively or negatively correlated to some extent with the amplification of another dye signal. Figures 14A to 14D illustrate examples of spectral crosstalk reduction according to various embodiments described herein. In this example, cross-correlation is used as an optimization value. The examples in Figures 14A to 14D show a 5-dye group system with dyes ABY, FAM, VIC, JUN, and AF647. Table 1402 in Figure 14A shows the cross-correlation matrix of the signal-dye data (amplitude curves) before dye matrix optimization. Referring to Figure 14C, curve 1404 shows the amplitude curves of the dyes in the PCR cycle before dye matrix optimization, which illustrates the crosstalk generated between the unexcited dyes. Since the two excited dyes are VIC and JUN, the correlated elements of the cross-correlation matrix are the rows corresponding to VIC and JUN. The other rows do not carry much information due to the low signal levels. Note that the absolute values ​​of the elements corresponding to ABY, FAM, and AF647 in these rows are high (>0.79), indicating pull-up crosstalk (positive cross-correlation) and pull-down crosstalk (negative cross-correlation). Table 1408 in Figure 14B shows the cross-correlation matrix of the signal dye data (amplitude curves) after dye matrix optimization. Referring to Figure 14D, curve 1406 shows the dye amplitude curves during the PCR cycle after dye matrix optimization. As mentioned earlier, since the two stimulated dyes are VIC and JUN, the correlated elements of the cross-correlation matrix are the rows corresponding to VIC and JUN. Note that the absolute values ​​of the elements corresponding to ABY, FAM, and AF647 in this row are much lower (<0.49), indicating a significant reduction in both pull-up crosstalk (positive cross-correlation) and pull-down crosstalk (negative cross-correlation). The reduction in crosstalk is reflected in the solid lines of curves 1404 and 1406. Figures 15A to 15D illustrate another example of spectral crosstalk reduction according to the various embodiments described herein. In this example, cross-correlation is used as an optimization value. This example shows a 5-dye group system with dyes ABY, FAM, VIC, JUN, and AF647. In Figure 15A, Table 1502 shows the cross-correlation matrix of the signal data (amplitude curves) before dye matrix optimization. Referring to Figure 15C, the plot of dye amplitudes during the PCR cycle before dye matrix optimization is shown in curve 1504, which shows significant crosstalk between VIC and FAM dyes. Since the stimulated dyes are FAM and JUN, the relevant elements of the cross-correlation matrix are those corresponding to the rows for FAM and JUN. The other rows do not carry much information due to the low signal levels. Note that the absolute values ​​of the elements corresponding to ABY, VIC, and AF647 in this row are high (>0.83), indicating pull-up crosstalk (positive cross-correlation) and pull-down crosstalk (negative cross-correlation). Referring to Figure 15B, Table 1508 shows the cross-correlation matrix of the signal data (amplitude curves) after dye matrix optimization. Referring to Figure 15D, the curves of dye amplitudes in the PCR cycle after dye matrix optimization are shown in curve 1506, which shows the reduction of FAM to VIC crosstalk. As previously mentioned, since the stimulated dyes are FAM and JUN, the correlated elements of the cross-correlation matrix are the rows corresponding to FAM and JUN. Note that the absolute values ​​of the elements corresponding to ABY, VIC, JUN, and AF647 in this row are much lower (< 0.27), indicating a significant reduction in both pull-up crosstalk (positive cross-correlation) and pull-down crosstalk (negative cross-correlation). This reduction in crosstalk is reflected in the solid lines in 1504 and 1506. As previously mentioned, when crosstalk is present, the amplification of one dye signal will be positively or negatively correlated with the amplification of another dye signal. Therefore, the dye matrix optimization component evaluates the crosstalk effect by focusing on the off-diagonal elements of the cross-correlation matrix among all dye signals, since the off-diagonal elements of the cross-correlation matrix (as shown in Figures 14A to 14D and Figures 15A to 15D) reflect the correlation between different dye signal pairs. In multiplex qPCR assays, where the amplification of several targets / dyes is tested, the dye signal is estimated based on a set of discrete measurements of the combined spectral characteristics of the dyes (filtered or raw data) and a system of equations relating each dye (multi-component data) to a defined dye matrix. Crosstalk is an additional overlapping effect of the spectral measurements or filtered signal data. Therefore, the crosstalk effect is considered through the system of equations or the dye matrix and can be corrected so that the resulting estimated dye signal reflects only the corresponding amplification trend. In the dye matrix optimization component, the crosstalk effect is modeled within the definition of the dye matrix. Based on the above assumptions, the crosstalk reduction method implemented by the dye matrix optimization unit updates the dye matrix through an iterative optimization method, minimizing the off-diagonal elements of the resulting cross-correlation matrix among all dyes. The cross-correlation matrix is ​​also weighted by the corresponding dye signal intensities. In other words, and at a high level, the dye matrix optimization unit works by having the dye matrix pass through an optimizer that modifies the dye matrix values ​​so that it minimizes the off-diagonal elements when performing modified cross-correlation on all multi-component data. Optimization process Figures 16, 17, and 18 illustrate the general optimization process and how it applies to dye matrix optimization. Figure 16 illustrates an optimized workflow 1600 for reducing spectral crosstalk according to the various implementation schemes described herein. The initial settings 1602 of the dye matrix optimization component define the input data and parameters required for the optimization method. The input data consists of signal discontinuity adjustment data and an initial dye matrix (if no signal discontinuity is detected). An initial loop point is included in the input parameters; all filtered signal data will be considered from this point. This parameter is used to avoid including often noisy measurements in early qPCR cycles. Other parameters control the operation of the optimization value calculator 1604, such as the maximum number of iterations and the optimization target value. The dye matrix optimization component further utilizes a constrained "DogLeg" solver ("CoDoSol") 1606. minimize Figure 17 illustrates the multi-objective constrained optimization of the CoDoSol component 1700 for reducing spectral crosstalk according to various embodiments described herein. The constrained "DogLeg" solver (CoDoSol) is a multi-objective constrained optimization method for solving nonlinear systems / problems. The CoDoSol component 1700 can be parameterized to minimize a single optimization objective. This is the standard way we usually think about optimization problems. It can also be parameterized to minimize several objectives coupled simultaneously. This is a more complex form of multi-objective optimization. The objectives of the CoDoSol component 1700 are typically set for each dye and are described in Equations 19 and 20 below. These are weighted squares of the off-diagonal cross-correlation elements of the multi-component dye data for each inactive dye. Off-diagonal elements involving two reactive dyes are not included. In one implementation, the variable that CoDoSol component 1700 changes is an element of the dye matrix. In this implementation, the variable that CoDoSol component 1700 is adjusting is an element of the dye matrix that begins with an initial dye matrix derived from the filtered signal data. In another implementation, the variable changed by CoDoSol component 1700 is an estimated crosstalk element. In this implementation, the Jacobian matrix is ​​calculated. Mathematically, the Jacobian matrix is ​​defined as the gradient of one or more objective variables with respect to small changes in the optimized variable. The inverse of this Jacobian matrix gives the suggested direction in which the optimizer needs to change the optimized variable so that the optimization moves in the direction of the minimum. This follows the conceptual principles of the Newton-Raphson optimization method. The step size in the suggested direction is determined by the internal optimization parameters. In this implementation, the optimizer is adjusting the elements of a crosstalk matrix starting from the initial dye matrix. At the i-th optimization iteration, a small update to Equation 13 is used to obtain the updated dye matrix. DM0, i = C j * DM, (13a) Where DM0, i is the updated dye matrix at the i-th iteration, and It is an estimate of the spectral crosstalk that the initial dye matrix DM will produce. During optimization in Optimization Calculator 1706, numerous small variations of the dye matrix are applied. These variations are used to deconvolve the filtered signal data to produce multi-component dye data, which is then used to generate a cross-correlation matrix. Optimization Calculator 1706 uses these variations to return the associated optimized values ​​for each objective. The CoDoSol optimizer aggregates these objective values ​​to form a Jacobian matrix. The inverse of this Jacobian matrix points to the direction of the lowest gradient of the currently updated dye matrix. This is the direction in which the updated dye matrix is ​​updated to produce a reduction in the objective value. The reduction in the objective value is associated with a reduction in crosstalk. Then, the multi-component data is recalculated using this data and fed back to the baseline. In decision 1704, this process is repeated until the minimum step size along the gradient is hit, or until the maximum number of iterations is reached. The adjusted and updated spectral-adjusted data matrix is ​​returned. Figure 18 illustrates an optimization value calculator component 1800 for reducing spectral crosstalk according to various embodiments described herein. The optimization value calculator component 1800 includes a deconvolution component 1804, a baseline adjustment component 1806, and a weighted cross-correlation component 1808. Deconvolution The optimization calculator component 1800 operates at a single-well level. Input 1802 includes signal discontinuity adjustment data, an initial dye matrix including a calibrated spectral dye matrix, and parameters. These parameters include a minimum loop to begin the optimization process and DyeFractThresh, the latter being a parameter that determines the upper bound of the range of fractions inactive dyes that should be treated more aggressively. In the deconvolution component 1804, the adjusted filtered signal data based on the detected signal discontinuities is mapped to specific dye matrix data by multiplying the filtered data by the inverse of the dye matrix (or a pseudo-inverse if the number of filters differs from the number of dyes). The dye dataset is also referred to as a multi-component dataset. Baseline adjustment The baseline adjustment step smooths and adjusts the initial dye matrix data to reduce measurement noise and generate a flat baseline dye signal consistent across all dye levels. The baseline adjustment step can be performed using known baseline algorithms. Weighted cross-correlation The cross-correlation between the two dye signal curves produces a square matrix, where the off-diagonal elements have absolute values ​​close to zero if the two dye signals are uncorrelated. If the two dye signals are correlated, for example due to crosstalk, the off-diagonal elements have absolute values ​​closer to 1. To emphasize the region of measurement amplification, the cross-correlation is weighted by the measured values ​​of the dye signals. For signals with crosstalk, the off-diagonal elements are non-zero and therefore become the minimization target of the overall crosstalk reduction methods of the various embodiments described herein. For example, the weighted cross-correlation target for each dye is given by the following: Where optTarget[dye] is the optimization objective for each dye to be minimized, dye1 and dye2 are the off-diagonal rows and columns of the correlation matrix such that dye1 ≠ dye2, W(dye1, dye2) is the weight associated with the dye pair represented by row dye1 and column dye2, corrAddConst is a constant that has a value of 0.0 or 2.25 in the exemplary form, but is typically between 0 and 0.5, and corrMultiplierConst = (1.0 - corrAddConst), and powPos is typically set to 2 but can be a value in the typical range of 0.125 to 8. The dyes to be minimized, represented by the dyes, are selected for each inactive dye. The weight of each dye pair (W(dye1, dye2)) is given by the following formula: Where cumAbsSumEmphasizeNegs[dye2] is the cumulative absolute sum of the baseline curve values ​​of dye2, performed in a manner emphasizing negative values, and cumNormedPositiveSum[dye1] is the cumulative normalized sum of the positive values ​​of the baseline curve of dye1. According to the various embodiments described herein, both values ​​are considered as estimated crosstalk substitution values. Furthermore, powMultiple is typically 1, but can be parameterized to values ​​from 0.125 to 4, and isPossibleCrosstalkInfo[dye1][dye2] typically has a value of 0 or 1, but can have values ​​between 0 and 1. isPossibleCrosstalkInfo[dye1][dye2] is typically calculated by applying a threshold to the normalized dye spectral overlap matrix S. NOThe value of 0 or 1 obtained from dye 1 and dye 2 is such that the result is 0 when the value of the spectral overlap matrix of the dye 1-dye2 pair is below a threshold (e.g., 0.1). Alternatively, it can be the dye spectral overlap matrix value of the dye 1-dye2 pair itself. Our optimization method provides a very rich set of optimization strategies, focusing on the calculated optimal values. 1) It can make optTarget a single target independent of the dye. 2) It can make optTarget a target that tracks multiple dyes. 3) It can make optTarget a target that tracks multiple targets for each reactive dye. 4) optTarget can be made into multiple targets that track each dye pair. 5) It can make optTarget a multiple target that tracks each pair of reactive dyes. Our optimization method also provides several feasible strategies for how to weight the calculated optimization values. 1) The weights can be set to constants (e.g., 1 without loss of generality). This results in an optimization objective based on the unweighted powers of the elements of the correlation matrix (powPos). powPos is typically set to 2, but can be a value in the typical range of 0.125 to 8. This will focus the optimizer solely on reducing / minimizing the cross-correlation between the dye curves. This results in minimizing the optimization / objective value based solely on the unweighted minimization of the off-diagonal elements of the cross-correlation matrix. 2) The weighting can be set based on the relative intensity of the reactive (excited) dye signal. Note that in the discussion of Figures 9 and 10, it is observed that only the cross-correlation of reactive dyes relative to inactive (unexcited) dyes contains direct information that we should optimize. The cross-correlation of inactive dyes relative to other inactive dyes contains indirect information about crosstalk that is essentially driven by reactive dyes. 3) The weighting can be set based on the intensity of the apparent crosstalk signal in the inactive dye. The intensity of the apparent crosstalk signal in the inactive dye is measured by the variables cumAbsSumEmphasizeNegs[dye2] (which is the cumulative absolute sum of the baseline curve values ​​of dye2 in an emphasis-on-negative manner) and cumNormedPositiveSum[dye1] (which is the cumulative normalized sum of the positive values ​​of the baseline curve of dye1). The constants corrAddConst and corrMultiplierConst (equal to (1.0 - corrAddConst)) adjust the relative importance of setting the target to a single weighted term relative to the product of cross-correlation and the weighted terms. Therefore, setting corrAddConst to 1 is equivalent to setting the target to be based solely on the intensity of the apparent crosstalk signal in the inactive dye. Conversely, setting corrAddConst to 0 is equivalent to setting the target to the product of the cross-correlation and the weighted terms based solely on the intensity of the apparent crosstalk signal in the inactive dye. Example The following numbered examples are implementation examples: 1. A method for reducing spectral crosstalk in multiplex measurements, the method comprising: Receive filtered signal data from multiplex fluorescence measurements; Receive an initial dye matrix, wherein the initial dye matrix includes calibrated spectral dye data; An updated dye matrix is ​​generated based on the initial dye matrix and the estimated crosstalk substitution value; The updated dye matrix is ​​adjusted to meet a calculated optimized value, wherein the calculated optimized value is based on the estimated crosstalk substitution value and the filtered signal data; An improved dye matrix is ​​generated based on the adjusted and updated dye matrix; and Spectral adjustment data is generated based on the improved dye matrix. 2. The method as described in Example 1, wherein adjusting the updated dye matrix further comprises satisfying a plurality of calculated optimized values, wherein each calculated optimized value is calculated based on each fluorescent dye used in the multiplex fluorescence assay. 3. The method as described in any one of Examples 1 to 2, wherein the calculated optimized value is further calculated based on the cross-correlation between the intermediate updated dye matrix and the dyes used in the multiplex fluorescence assay. 4. The method as described in any one of Examples 1 to 3, further comprising: The filtered signal data is deconvolved to determine individual dye data; Adjust the baseline of discontinuous fixed data to reduce measurement noise; Calculate the cross-correlation matrix of the signal from each fluorescent dye used in the multiplex fluorescence assay; and The estimated crosstalk substitution value is used to generate the calculated optimized value to weight the data in the cross-correlation matrix. 5. The method as described in any one of Examples 1 to 4, The improved dye matrix (DM) 经改善 It approximates the true dye matrix DM0 and is as follows: DM 经改善 DM - DM e Among them DM 经改善 It is an improved dye matrix, where DM is the initial dye matrix, and DM e It is the error of the initial dye matrix. 6. The method as described in any one of Examples 1 to 5, wherein adjusting the updated dye matrix is ​​an iterative process. 7. The method as described in any one of Examples 1 to 6, further comprising: The spectral data is used to generate quantitative results. 8. The method as described in any one of Examples 1 to 7, further comprising: Detecting discontinuities in the filtered signal data, wherein a discontinuity is a significant increase or decrease in the filtered signal data between two time points; and Adjusted and filtered signal data is generated based on the detected discontinuities, wherein the calculated optimized values ​​are further based on the adjusted and filtered signal data. 9. The method as described in Example 8, wherein generating the adjusted filtered signal data based on the detected discontinuities includes using a polynomial fitting curve. 10. A system for reducing spectral crosstalk in multiplex measurements, the system comprising: A detector configured to receive filtered signal data from multiple fluorescence measurements; A memory configured to store an initial dye matrix, wherein the initial dye matrix includes calibrated spectral dye data; Processor, the processor being configured to: An updated dye matrix is ​​generated based on the initial dye matrix and the estimated crosstalk substitution value; The updated dye matrix is ​​adjusted to meet a calculated optimized value, wherein the calculated optimized value is based on the estimated crosstalk substitution value and the filtered signal data; An improved dye matrix is ​​generated based on the adjusted and updated dye matrix; and Spectral adjustment data is generated based on the improved dye matrix. 11. The system as described in Example 10, wherein the processor is further configured to: The updated dye matrix is ​​adjusted to satisfy multiple calculated optimized values, each of which is calculated based on each fluorescent dye used in the multiplex fluorescence assay. 12. The system of any one of Examples 10 to 11, wherein the calculated optimized value is further calculated based on the cross-correlation between the intermediate updated dye matrix and the dyes used in the multiplex fluorescence assay. 13. The system of any one of embodiments 10 to 12, wherein the processor is further configured to: The filtered signal data is deconvolved to determine individual dye data; Adjust the baseline of discontinuous fixed data to reduce measurement noise; Calculate the cross-correlation matrix of the signal from each fluorescent dye used in the multiplex fluorescence assay; and The estimated crosstalk substitution value is used to generate the calculated optimized value to weight the data in the cross-correlation matrix. 14. The system as described in any one of Examples 10 to 13, The improved dye matrix (DM) 经改善 It approximates the true dye matrix DM0 and is as follows: DM 经改善 DM - DM e Among them DM 经改善 It is an improved dye matrix, where DM is the initial dye matrix, and DM e It is the error of the initial dye matrix. 15. The system of any one of Examples 10 to 14, wherein the processor is configured to adjust the updated dye matrix during iteration. 16. The system of any one of embodiments 10 to 15, wherein the processor is further configured to: The spectral data is used to generate quantitative results. 17. The system of any one of embodiments 10 to 16, wherein the processor is further configured to: Detecting discontinuities in the filtered signal data, wherein a discontinuity is a significant increase or decrease in the filtered signal data between two time points; and Adjusted and filtered signal data is generated based on the detected discontinuities, wherein the calculated optimized values ​​are further based on the adjusted and filtered signal data. 18. The system as described in Example 17, wherein the processor generates the adjusted filtered signal data based on the detected discontinuities by using a polynomial fitting curve. 19. A computer-readable medium encoded with computer-readable instructions that, when executed by a processor of a computer, cause the computer to perform the method as described in any one of Examples 1 to 9. 20. A system comprising a processor and a storage medium storing instructions, the instructions, when executed by the processor, causing the system to perform the method as described in any one of Embodiments 1 to 9. Although the invention has been described with reference to certain exemplary embodiments, examples and applications, it will be apparent to those skilled in the art that various modifications and changes can be made thereto without departing from the invention.

Claims

1. A method for reducing spectral crosstalk in multiplex measurements, the method comprising: Receive filtered signal data from multiplex fluorescence measurements; Receive an initial dye matrix, wherein the initial dye matrix includes calibrated spectral dye data; An updated dye matrix is ​​generated based on the initial dye matrix and the estimated crosstalk substitution value; The updated dye matrix is ​​adjusted to meet a calculated optimized value, wherein the calculated optimized value is based on the estimated crosstalk substitution value and the filtered signal data; An improved dye matrix is ​​generated based on the adjusted and updated dye matrix; as well as Spectral adjustment data is generated based on the improved dye matrix.

2. The method of claim 1, wherein adjusting the updated dye matrix further comprises satisfying a plurality of calculated optimized values, wherein each calculated optimized value is calculated based on each fluorescent dye used in the multiplex fluorescence assay.

3. The method of any one of claims 1 to 2, wherein the calculated optimized value is further calculated based on the cross-correlation between the intermediate updated dye matrix and the dyes used in the multiplex fluorescence assay.

4. The method according to any one of claims 1 to 3, further comprising: The filtered signal data is deconvolved to determine individual dye data; Adjust the baseline of discontinuous fixed data to reduce measurement noise; Calculate the cross-correlation matrix of the signal of each fluorescent dye used in the multiplex fluorescence assay; as well as The estimated crosstalk substitution value is used to generate the calculated optimized value to weight the data in the cross-correlation matrix.

5. The method as described in any one of claims 1 to 4, The improved dye matrix (DM) 经改善 It approximates the true dye matrix DM0 and is as follows: DM 经改善 DM - DM e Among them DM 经改善 It is an improved dye matrix, where DM is the initial dye matrix, and DM e It is the error of the initial dye matrix.

6. The method of any one of claims 1 to 5, wherein adjusting the updated dye matrix is ​​an iterative process.

7. The method of any one of claims 1 to 6, further comprising: The spectral data is used to generate quantitative results.

8. The method of any one of claims 1 to 7, further comprising: Detecting discontinuities in the filtered signal data, wherein a discontinuity is a significant increase or decrease in the filtered signal data between two time points; as well as Adjusted and filtered signal data is generated based on the detected discontinuities, wherein the calculated optimized values ​​are further based on the adjusted and filtered signal data.

9. The method of claim 8, wherein generating the adjusted filtered signal data based on the detected discontinuities includes using a polynomial fitting curve.

10. A system for reducing spectral crosstalk in multiple determinations, the system comprising: A detector configured to receive filtered signal data from multiple fluorescence measurements; A memory configured to store an initial dye matrix, wherein the initial dye matrix includes calibrated spectral dye data; Processor, the processor being configured to: An updated dye matrix is ​​generated based on the initial dye matrix and the estimated crosstalk substitution value; The updated dye matrix is ​​adjusted to meet a calculated optimized value, wherein the calculated optimized value is based on the estimated crosstalk substitution value and the filtered signal data; An improved dye matrix is ​​generated based on the adjusted and updated dye matrix; as well as Spectral adjustment data is generated based on the improved dye matrix.

11. The system of claim 10, wherein the processor is further configured to: The updated dye matrix is ​​adjusted to satisfy multiple calculated optimized values, each of which is calculated based on each fluorescent dye used in the multiplex fluorescence assay.

12. The system of any one of claims 10 to 11, wherein the calculated optimized value is further calculated based on the cross-correlation between the intermediate updated dye matrix and the dyes used in the multiplex fluorescence assay.

13. The system of any one of claims 10 to 12, wherein the processor is further configured to: The filtered signal data is deconvolved to determine individual dye data; Adjust the baseline of discontinuous fixed data to reduce measurement noise; Calculate the cross-correlation matrix of the signal of each fluorescent dye used in the multiplex fluorescence assay; as well as The estimated crosstalk substitution value is used to generate the calculated optimized value to weight the data in the cross-correlation matrix.

14. The system as described in any one of claims 10 to 13, The improved dye matrix (DM) 经改善 It approximates the true dye matrix DM0 and is as follows: DM 经改善 DM - DM e Among them DM 经改善 It is an improved dye matrix, where DM is the initial dye matrix, and DM e It is the error of the initial dye matrix.

15. The system of any one of claims 10 to 14, wherein the processor is configured to adjust the updated dye matrix during the iteration process.

16. The system of any one of claims 10 to 15, wherein the processor is further configured to: The spectral data is used to generate quantitative results.

17. The system of any one of claims 10 to 16, wherein the processor is further configured to: Detecting discontinuities in the filtered signal data, wherein a discontinuity is a significant increase or decrease in the filtered signal data between two time points; and Adjusted and filtered signal data is generated based on the detected discontinuities, wherein the calculated optimized values ​​are further based on the adjusted and filtered signal data.

18. The system of claim 17, wherein the processor generates the adjusted filtered signal data based on the detected discontinuities by using a polynomial fitting curve.

19. A computer-readable medium encoded with computer-readable instructions that, when executed by a processor of a computer, cause the computer to perform the method as described in any one of claims 1 to 9.

20. A system comprising a processor and a storage medium storing instructions, the instructions, when executed by the processor, causing the system to perform the method as described in any one of claims 1 to 9.

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