How to Analyze Particle Motor Activity

Abstract

The method for analyzing the locomotor activity of particles using a motion detector 1 comprises the steps of contacting at least one particle with a flexible support 2, detecting at least one time-dependent signal indicative of a deflection of the flexible support 2 due to the motion of the at least one particle, and evaluating the detected time-dependent signal, wherein the evaluation comprises analysing the time-dependence of the signal to derive therefrom a number of signal parameters characterising the variation of the signal as a function of time, and executing a linking algorithm having as input variables an input vector comprising at least one selection of said signal parameters and having as output variable at least one activity indicator indicative of the locomotor activity of the particle.

Description

[Technical field]

[0001] The present invention relates to a method for analyzing the locomotor activity of particles using a motion detector. In particular, the present invention relates to the analysis of the locomotor activity of particles exhibiting motion at very low scales, for example having sizes in the range of Angstroms to micrometers. The present invention is particularly, but not exclusively, related to the analysis of the movement or internal dynamics of such particles. [Background technology]

[0002] Nanomechanical oscillators are widely used as sensors to detect small changes in the mass of particles. In US Pat. No. 5,399,633, a microcantilever is used to detect and measure the nanoscale vibrations (or nanomotions) of particles attached to its surface. The particles can be of chemical or biological nature, including, inter alia, proteins, lipids, carbohydrates, viruses, bacteria, yeasts, or mammalian cells. This system makes it possible to distinguish the state of the tested particles in the presence or absence of a stimulus, allowing, for example, antibiotic susceptibility detection. For this purpose, the dispersion of the nanoscale vibrations of the microcantilever is analyzed, and an increase in the dispersion attests to the vibrations or motions induced by the particles.

[0003] However, variance alone, i.e. using a single statistical parameter, is insufficient to distinguish between different states in each case. For example, in measurements of sensitive and resistant strains of bacteria particles, overlapping populations is common. Therefore, better methods of separating populations are needed. Furthermore, live and dead cells are an example of an extreme difference in metabolic activity, but a distinction between less extreme cases or the analysis of other kinetic activities of the particles, such as respiration level, growth rate, etc., is also needed. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] International Publication No. 2013 / 054311 Summary of the Invention

[0005] It is an object of the present invention to provide a method that allows an improved analysis of the locomotor activity of particles, in particular under similar or complex conditions.

[0006] This object is achieved by the method according to claim 1. That is, a method for analyzing the kinetic activity of particles using a kinetic detector is provided. The kinetic detector comprises a flexible support configured to deflect, e.g. bend, a detection device for detecting a signal generated upon deflection of the flexible support, and an evaluation device for evaluating the detected signal. The method comprises the steps of i) bringing at least one particle into contact with the flexible support, ii) detecting at least one time-dependent signal indicative of deflection of the flexible support due to the motion of the at least one particle using the detection device, and iii) evaluating the detected time-dependent signal using the evaluation device. Steps i) to iii) are preferably performed consecutively in said order. The evaluation of the detected time-dependent signal comprises a) analyzing the time-dependence of the signal to derive from the signal a number of signal parameters characterizing the variation of the signal as a function of time, and b) executing a linking algorithm having as input variables an input vector comprising at least one selection of the signal parameters and as output variables at least one activity indicator indicative of the kinetic activity of the particle. It is preferred that steps a) and b) are carried out consecutively in that order, ie step b) is preferably carried out after step a).

[0007] The invention is based on the insight that particles in contact with a flexible support give rise to random signals, i.e. signals that vary with time but do not follow a simple vibration pattern and that appear random at first glance, in other words signals that are buried in noise backgrounds, measurement artefacts etc., but which contain useful information about the particle's motor activity, which information can be extracted using mathematical methods. Indeed, the method of the invention allows the extraction of said information by analysing the temporal evolution of the signal characteristics. That is, in the method according to the invention, the time-dependent signal is analysed using mathematical methods. The mathematical methods can be applied to the detected signal in the time domain and / or to the transformed signal obtained by transforming the detected signal into the frequency domain. In any case, the signal is detected for multiple time points in order to obtain the time dependence of the signal, which is analysed to determine time-independent signal parameters. These signal parameters characterise the temporal evolution of the signal. A selection of at least one of these signal parameters is then fed as an input variable to a linking algorithm, which provides, based on the input variables, at least one output variable which is at least one activity indicator indicative of the particle's motor activity.

[0008] The flexible support may be a cantilever, preferably an AFM cantilever, a fiber such as a hollow fiber or a glass fiber, a membrane, a wire, a sponge, a flexible electrode, etc. It is further preferred that the particles are attached to the surface of the flexible support before being analyzed. The attachment is preferably carried out according to methods known in the state of the art, such as by functionalizing the surface of the flexible support or by using attachment compounds known in the art, respectively. It is particularly preferred that the particles are attached to the surface of the flexible support as described in WO 2021 / 130339, which is incorporated herein by reference. That is, it is preferred to disperse the particles in a solution comprising at least one of a gelling agent, a gellable agent and a thickening agent, and then add the dispersion to the surface of the flexible support.

[0009] Moreover, the motion detector preferably corresponds to a nanoscale motion detector as disclosed in US Pat. No. 6,399,363, also incorporated herein by reference. The deflection of the flexible support is therefore preferably measured by an optical level detection method, and the change in the position of the spot caused by the laser light reflected from the surface of the flexible support is measured using an optical detector such as a photodetector, particularly preferably a position-sensitive photodetector. The change in the position of the spot causes a change in the signal recorded by the detector. As will be explained in more detail below, the signal is preferably processed before signal parameters are derived therefrom. The signal can therefore also be referred to as raw input signal (RIS).

[0010] The method preferably includes, in the step of analysing the time dependence of the signal, defining a plurality of time intervals, the time dependence of the signal being analysed separately within each time interval to obtain a value for each of a plurality of signal estimators for each time interval, and the time series of each signal estimator being analysed to obtain a respective one of the signal parameters.

[0011] The signal estimate may be determined in the time domain or in the frequency domain, in the latter case the power spectrum is preferably estimated for each time interval of the signal.

[0012] Each signal estimator value is preferably determined by fitting a noise model to the power spectrum of the signal and / or by applying at least one statistical algorithm to the signal. The signal estimators are preferably estimators of moments of a probability density function and / or geometric properties of a power spectral density function and / or percentiles of a probability density function and / or correlation parameters and / or partial correlation parameters and / or parameters of an autoregressive moving average model and / or parameters of a non-linear autoregressive moving average model.

[0013] The noise model is preferably selected from a flicker noise model, a white noise model, a band noise model, or a combination thereof. α The white noise model is preferably represented as a weighted sum of functions, where f denotes frequency and alpha (α) is a free parameter. The white noise model is preferably represented as a constant or a constant modulated by the frequency response of the motion detector. The band noise model is preferably represented as a rational function of an order that is preferably optimized for the particular application. For example, a second order band noise model can correspond to a damped harmonic oscillator based model in susceptibility testing of E. coli strains. Examples of geometric properties of the power spectral density function are extrema points, inflection points, areas under different parts of the curve, or horizontal and vertical distances between them.

[0014] Regarding the estimators of the moments of the probability density function, it should be noted that they can have moments of different orders, can be standardized or not, etc. For example, the estimators of the moments of the probability density function can be variance, skewness, kurtosis, etc. They are further preferably optimized for a particular application, e.g., for E. coli antibiotic susceptibility detection, the variance can be utilized. Regarding the percentiles of the probability density function, it should be noted that they can have different percentile ranks. For example, the percentile ranks can be the 25th percentile, the 50th percentile (median), the 75th percentile, etc. The percentile ranks are further preferably optimized for a particular application, e.g., for classification of metabolic activities, the median can be used.

[0015] As outlined above, signal analysis can be based on signal parameters associated with different noise models, and signal estimates are determined, for example, by fitting noise models to the power spectral density function of the signal. However, these theoretical models are only as useful as practice follows theory. To properly analyze cases where the estimated spectrum deviates from the theoretical model, geometric properties of the spectrum are useful.

[0016] Therefore, analyzing the time dependence of a signal using the power spectral density function is a useful way to analyze random signal characteristics in the frequency domain.

[0017] Thus, in the method according to the invention, each signal estimator can be a geometrical property of the power spectral density function.

[0018] Various methods of determining the power spectral density function are possible and known in the art. For example, the power spectral density function can be determined by Welch's method.

[0019] The geometrical characteristic may be an extreme point of the power spectral density function, an inflection point of the power spectral density function, an area under the curve described by the power spectral density function, or a horizontal and / or vertical distance between them. Examples of extreme points of the power spectral density function are global or local maxima or global or local minima of the power spectral density function. An inflection point of the power spectral density function is understood as a point at which the power spectral density function changes the direction of its curvature. The area under the curve described by the power spectral density function is understood as the area under the power spectral density function between two points on the power spectral density function. The area is preferably determined by integrating the power spectral density function between the two points. For this purpose, any two points on the power spectral density function can be used. The horizontal and / or vertical distance between them is, for example, the horizontal and / or vertical distance between the extreme points or between the inflection points.

[0020] Signal parameters derived from such signal estimators can be considered as spectral signal parameters. Quantile signal parameters are a generalization of spectral signal parameters. As outlined above, spectral signal parameters can be calculated based on the power spectral density function. The power spectral density function of a signal is estimated as the mean of the signal periodogram, where the periodogram is the squared magnitude of the Fourier transform of a signal segment. The power spectral density function is a statistic. This means that it reveals the properties of a random signal (a stochastic process). If the mean of the periodogram is used, some sporadic but high amplitude events will deteriorate this statistic. For this reason, robust statistics such as for example the median are very often used. However, if these sporadic events convey useful information, it turns out that not only the median of the periodogram but also the probability distribution is useful to capture said information.

[0021] Thus, in the method according to the invention, at least one signal estimate can be obtained by determining a number of periodograms for each time interval. For every periodogram, at least one quantile is determined for at least one frequency range. The quantiles are preferably percentiles. These signal parameters can be referred to as quantile signal parameters.

[0022] Quantiles, in particular percentiles, can be determined for various frequency ranges. For example, the frequency range for which the quantiles or percentiles of the periodogram are estimated can be 0 Hz to 10 Hz, 10 Hz to 100 Hz, etc., but other frequency ranges are conceivable as well. In other words, for each periodogram, quantiles, such as percentiles, of a particular frequency range are determined. Thus, a set of time series of signal estimators, which are quantiles of the periodogram, in particular quantiles, such as percentiles, of a specified frequency range, is obtained.

[0023] This set of time series can be extended and at least one signal parameter is obtained from the extended time series, In other words, the time series of the signal estimator can be extended by combining the time series of the signal estimators and the signal estimator is obtained from the combined time series.

[0024] In particular, at least one time series of the signal estimators may be extended to form an extended time series by combining at least two signal estimators into their difference and / or ratio.

[0025] Additionally or alternatively, the time series of at least one of the signal estimators can be extended to form an extended time series by converting a number of quantiles, in particular percentiles, into values ​​of an empirical probability density function. In particular, all quantiles, such as all percentiles, can be converted into values ​​of an empirical probability density function (EPDF), and two consecutive quantiles, such as percentiles, are used to calculate one EPDF value. Furthermore, at least one distance between the values ​​of the empirical probability density function and the values ​​of the theoretical probability density function can be determined. For example, the distance can be measured between all EPDF values ​​and the theoretical value of the chi-squared probability density function. Examples of distances are the Kullback-Leibler divergence and the Jensen-Shannon distance, but other distances are conceivable as well. Additionally or alternatively, at least one geometric property of the empirical probability density function and / or various moments of the EPDF (mean, variance, skewness, kurtosis, etc.) can be determined.

[0026] At least one signal parameter may be derived from at least one time series of the signal estimators and / or from at least one extended time series of the signal estimators by: i) defining a plurality of subseries for the time series and / or the extended time series and determining statistical properties for each subseries, preferably further determining at least one of their ratios, differences and difference ratios; and / or ii) fitting one or more parameterized curves comprising one or more parameters to the time series and / or the extended time series; and / or iii) defining a plurality of subseries for the time series and / or the extended time series and fitting one or more parameterized curves comprising one or more parameters for each subseries to obtain fitted parameters, preferably further determining their ratios, differences and difference ratios.

[0027] Possible statistical properties are for example percentiles and moments. Possible curves are exponential, polynomial, trigonometric curves, as well as linear and non-linear mixtures thereof.

[0028] The power spectral density functions of certain particle signals showed strong 1 / f characteristics. This kind of spectrum is often associated with the self-affinity of the signal. The self-affinity can be analyzed by detrended fluctuations analysis (DFA) and its generalization multifractal detrended fluctuations analysis (MF-DFA). In these methods, the dependence of the statistical properties of the signal on the time scale is investigated.

[0029] Thus, in a method according to the invention, evaluating the detected time-dependent signal with the evaluation device may comprise detecting the time-dependent signal during a time t, and analysing the time dependence of the signal may comprise: Dividing a signal of time t into time intervals of length T; For each time interval j=1, ..., t / T, calculating a digital integral of the signal within each time interval; Dividing the time interval into at least one number of subintervals; for each subinterval, detrending the digital integral of the signal by applying a detrending algorithm to the digital integral of the signal; for at least one number of subintervals, combining the subintervals into a detrended interval; and determining at least one generalized average of the detrended signal of the detrended interval for at least one number of sub-intervals, thereby obtaining at least one signal parameter and / or initial signal parameter; and It is preferred that the compound contains

[0030] Digital integration is applied to the signal in every time interval. The result is that the signal in each time interval is the integrated signal. For any digital signal x of N samples, i The digital integration of can be defined by the following equation:

[0031]

number

[0032] The detrending algorithm preferably fits a polynomial of any order (i.e., second order) to the integrated signal and then subtracts the fit from the integrated signal. The fit residual is the detrended integrated signal. Detrending is preferably applied to every subinterval separately. The result is that every subinterval becomes a detrended subinterval.

[0033] The integrated and detrended signals for all subintervals of the particular number of subintervals that the time interval is divided into are then combined back into one signal for the entire time interval (e.g., a 20 minute interval of a signal is integrated, then divided into four 5 minute subintervals, each of which is detrended, and all combined back into a 20 minute signal). The result of the detrending depends on the number of subintervals that the signal time interval is divided into; that is, it depends on the length of each subinterval.

[0034] At least one generalized average (integrated, detrended for at least one number of subintervals, and combined back) of the signal time interval is calculated (e.g., F2(128) means a generalized average with index 2 and 128 subintervals).

[0035] Any digital signal x of length N i The generalized mean with a non-zero exponent / power q of is defined by the following equation:

[0036]

number

[0037] Any signal x of length N i The generalized mean with zero exponent / power q of is defined by the following equation:

[0038]

number

[0039] A generalized mean with an index of 2 is simply the standard deviation, and a generalized mean with an index of 0 is the geometric mean.

[0040] The signal parameters are preferably obtained from generalized averages and / or their ratios and / or differences.

[0041] In particular, signal parameters can be derived from other signal parameters, such as by combining two or more signal parameters into their ratios and / or differences, such that the resulting signal parameters are independent of certain factors, such as environmental changes.

[0042] Preferably, the method further comprises running a feature selection algorithm to automatically select a subset of the signal parameters to obtain the input vector to be fed to the linking algorithm. The feature selection algorithm is preferably configured to select the subset of the signal parameters such that the subset is optimal for a multi-objective criterion.

[0043] Preferred feature selection algorithms implement univariate selection such as F-tests, mutual information, chi-squared, penalty-based methods such as L1, L2 and elastic net, as well as forward or backward feature selection based on properties of particular linking algorithms (such as coefficients in logistic regression or importance in tree-based algorithms) or based on various forms of cross-validation or bootstrapping using multi-objective criteria.

[0044] The multi-objective criterion is preferably at least one of accuracy, sensitivity, specificity, mean squared error, mean absolute error, root mean squared error, proportion of unexplained variance, coefficient of determination, number of signal parameters, or generalization gap.

[0045] For example, the input vector may include signal parameters that are optimal in the Pareto sense. Optimal in the Pareto sense is understood to be a non-dominated solution in which no improvement of all criteria is possible. In other words, improving one criterion will worsen at least one other criterion. As an example, if the feature selection algorithm corresponds to forward selection using a cross-validation algorithm, the selection of signal parameters may be performed when the cross-validation score is not improved in the Pareto sense. Additionally or alternatively, the input vector may include signal parameters that are optimal with respect to a single criterion composed of, for example, a linear combination of two or more of all the criteria. The use of a linear combination of two or more criteria may be understood as capturing some aspects of the evaluation of the linking algorithm. Additionally or alternatively, the input vector may include signal parameters that are optimal with respect to one of the above-mentioned criteria, but under constraints, for example constraints defined by the skilled person, or other criteria such as a specificity of 80% or more. These constraints may be defined after the analysis of the Pareto optimal solutions.

[0046] Drift cancellation is preferably applied to the signal prior to deriving signal parameters from the signal, i.e. drift cancellation is preferably applied to the first mentioned raw input signal, i.e. the RIS, In other words again, the signal estimate is preferably determined after drift cancellation.

[0047] Drift cancellation preferably involves a curve fitting procedure or high pass filtering to model the drift component of the signal, with the goal of cancelling the drift of the motion detector that appears in the detected signal, which can be caused by a variety of factors such as changes in temperature, humidity, surrounding fluid conditions, etc.

[0048] For example, drift cancellation can be performed by dividing the signal, in particular the RIS, into intervals and then applying curve fitting to model the drift component of the drift. Examples of fitted curves are polynomials, exponentials, trigonometric functions, or mixtures thereof. The fitted curves can be defined in linear and non-linear form. The type of curve, the number of fitting parameters, and the length of the time interval are preferably optimized for a particular application. The fitting error is preferably used by the next steps of the analysis, in particular in the calculation of the time series of the signal estimator.

[0049] Another example of drift cancellation involves the application of curve fitting as described above, but in a moving window regime, with the fitting parameters adapted continuously. The fitting errors are preferably used by the next steps of the analysis, in particular in the calculation of the time series of signal estimates.

[0050] In this example, the fitting is preferably repeated for every single point of the signal, in particular the RIS, using a buffer, such as a circular buffer, that stores the last samples of the signal. The fitting is preferably modified to efficiently update the curve fitting parameters so that millions of signal points can be processed. Similarly, the type of curve, the number of fitting parameters, and the length of the buffer are preferably optimized for a particular application.

[0051] Another example of drift cancellation involves the application of high-pass filtering to the signal, in particular the RIS, preferably having a particular order, type and parameters including phase shift. Examples of types are Butterworth, Chebyshev I and Chebyshev II, Kaiser, Elliptic, etc. The filter output is preferably used by the next steps of the analysis, in particular in the calculation of the time series of the signal estimator.

[0052] The drift cancellation algorithm is preferably a detrending algorithm, which is preferably arranged to detrend the signal.

[0053] In particular, when at least one signal parameter is a spectral signal parameter as described above, it is particularly preferred that a detrending algorithm is applied to the signal before the time dependence of the signal is analysed within a time interval.

[0054] Where at least one signal parameter is determined from a signal estimator which is a quantile, such as a percentile, of a probability density function of a periodogram, it is particularly preferred that a detrending algorithm is applied to the signal before the periodogram is determined, and a number of periodograms are determined for the detrended signal for each time interval.

[0055] For example, the detrending algorithm may be a fitting algorithm that fits a kth order polynomial to the signal and subtracts the fitted polynomial from the signal, thereby detrending the signal. By detrending the signal, drift in the signal may be removed.

[0056] The linking algorithm is particularly preferably a regression algorithm or a classification algorithm.

[0057] In case the linking algorithm is a regression algorithm, said multi-objective criterion is preferably at least one of the mean squared error, the mean absolute error, the root mean squared error, the proportion of unexplained variance, the coefficient of determination etc., the number of signal parameters, or the generalization gap.

[0058] In case the linking algorithm is a classification algorithm, the aforementioned multi-objective criteria is preferably at least one of accuracy, sensitivity, specificity, and the like.

[0059] More preferably, the linking algorithm is a machine learning (ML) algorithm.

[0060] In some embodiments, the ML algorithm may be an ML regression algorithm, in particular an ML algorithm implementing linear regression, decision tree regression, random forest regression, gradient boosting tree regression, kernel regression, multi-perceptron neural network, and RBF neural network regression, such algorithms being known in the art.

[0061] In other embodiments, the ML algorithm may be an algorithm implementing an ML classification algorithm, in particular a logistic regression, a decision tree, a random forest, a gradient boosting tree, a support vector machine, a multi-perceptron neural network, and a radial basis function (RBF) neural network, and these types of algorithms are known in the art.

[0062] Many other suitable ML algorithms are known in the art and can be used.

[0063] The particles are preferably biological objects and / or parts thereof and / or non-biological objects and / or parts thereof. Preferred biological objects are cells, such as prokaryotic or eukaryotic cells, spores, viruses, phages, and substances of biological origin, such as vesicles, peptides, proteins, polysaccharides, lipids, carbohydrates, nucleic acids and copolymers, protein-RNA copolymers, RNA-DNA copolymers, protein-DNA copolymers, RNA / DNA-protein copolymers, protein-protein copolymers, or capsules. Preferred parts of biological objects are organelles. Preferred non-biological objects are proteins, lipids, nucleic acids, such as DNA, and nanodevices. The cells are preferably living cells, and / or the organelles are preferably living organelles. The cells may be prokaryotic and / or eukaryotic cells. The cells may be motile and / or non-motile cells. The cells are preferably bacterial cells and / or fungal cells, such as yeast cells, and / or mammalian cells and / or insect cells and / or plant cells. The organelles are preferably mitochondria and / or nuclei or any other intracellular structure.

[0064] Activity indicators include metabolic activity of particles, physiological state of particles, respiration level of particles, ATP level of particles, and NADH / NAD + Preferably, the particle exhibits at least one of the following: a ratio of the particle's membrane potential, a growth rate of the particle, a mortality rate of the particle, an interaction of the particle with other particles, and an interaction of the particle with an environmental factor of the particle, or any combination thereof.

[0065] The environmental factors can be of a chemical nature, e.g., metabolites or drugs, e.g., antibiotics, toxins, denaturants or any other chemical compounds that affect the activity of the particles. However, the environmental factors can also be of a physical nature, e.g., temperature, humidity, viscosity, oxygen level, redox potential, radiation, pressure, or any other influence that affects the activity of the particles. The interaction of the particles with the environmental factors can be understood as the response of the particles to the environmental factors. The metabolic activity of the particles can be understood as the response of the particles to the environmental factors. The metabolic activity of the particles can be understood as the response of the particles to the environmental factors. +The physiological state of the particle may be a response to one or more of the aforementioned environmental factors. The interaction of the particle with other particles may be killing, proliferation, phagocytosis, conjugation, quorum sensing, or conformational changes of membrane complexes and / or protein complexes and / or other cellular complexes and / or macromolecular complexes.

[0066] The particles are preferably subjected to at least one chemical stimulus and / or at least one physical stimulus. The chemical stimulus is preferably the addition of a drug, such as an antibiotic or a compound that affects the metabolism or viability of the particles, such as cells. The chemical stimulus can also be a change in environmental conditions, such as culture conditions. The physical stimulus is preferably the application of a stress.

[0067] Preferably, the activity index is determined before and / or during and / or after the particles are subjected to a chemical and / or physical stimulus, and further preferably, the activity indexes thus determined are compared with each other.

[0068] For example, when analyzing the effectiveness of a drug against a particle, such as an antibiotic against bacteria, the activity index can be determined before and after adding the antibiotic to the bacteria. If the antibiotic is effective, the difference in the activity index is determined. For example, dead bacteria no longer exhibit metabolic activity. Furthermore, dying or sensitive bacteria may change their metabolic activity upon exposure to the antibiotic. That is, the bacteria do not die immediately.

[0069] In a further aspect, there is provided a method for generating a training dataset for a machine learning algorithm, the method comprising: a) contacting at least one particle with a flexible support; b) detecting, using a detection device, at least one time-dependent signal indicative of a deflection of the flexible support due to the movement of the at least one particle; c) evaluating the detected time-dependent signal using an evaluation device, where the evaluation of the detected time-dependent signal comprises analysing the time dependence of the signal in order to derive from the signal a number of signal parameters characterising the variation of the signal as a function of time; d) performing an independent measurement to derive at least one relevant activity indicator indicative of the particle's kinetic activity; e) storing the plurality of signal parameters and at least one associated activity indicator in a training data set; f) repeating steps a) to e) for a number of particles exhibiting different locomotor activities; Includes.

[0070] The training data set therefore includes a number of signal parameters and associated activity indices for a number of particles.

[0071] In a further aspect, a method for training a machine learning algorithm is provided, the machine learning algorithm being trained using the training dataset described above.

[0072] That is, the machine learning algorithm is trained with the signal parameters and the associated activity indices, and thus can make predictions of the activity indices based on the signal parameters and vice versa, without requiring knowledge of the particles and their motion activity.

[0073] For example, training can be based on a training data set that includes the experimental results detected by the detection device of the motion detector.Then, this training data set is preferably labeled with the results of a reference experiment that measures the metabolic activity of a subject using a reference method, such as the sensitivity of strains measured by the Kirby-Bauer test.Then, the labeled data is used to select signal parameters, optimize all stages of the linking algorithm, and evaluate performance using cross-validation techniques.

[0074] Preferred embodiments of the present invention will now be described with reference to the drawings, which are illustrative of presently preferred embodiments of the invention and are not intended to limit the invention. [Brief description of the drawings]

[0075] [Figure 1] FIG. 1 is a schematic diagram of preferred steps of the method according to the invention. [Diagram 2] FIG. 2 shows a diagram of a signal detected with a motion detector subjected to drift cancellation during evaluation with the method according to the invention. [Diagram 3] FIG. 3 shows a signal detected using a motion detector subjected to fitting of a noise model in determining the signal estimator under evaluation using the method according to the invention. [Figure 4] FIG. 4 is a graph showing the accuracy of different algorithms for different numbers of signal parameters to identify a Pareto-optimal feature selection algorithm suitable for the method according to the invention. [Figure 5a] FIG. 5a shows a schematic diagram of a motion detector with a cantilever with live bacteria attached (top) and a time series of signal estimates determined during evaluation using the method according to the invention (bottom panel). [Figure 5b] FIG. 5b shows a schematic diagram of a kinetic detector with a cantilever with dead bacteria attached (top) and a time series of signal estimates determined during evaluation using the method according to the invention (bottom panel). [Figure 6a] FIG. 6a is a graph illustrating a signal estimate determined during the evaluation shown in FIGS. 5a and 5b. [Figure 6b] FIG. 6b is a graph showing the fluorescence over time determined for the live and dead bacteria used in the assays shown in FIGS. 5a and 5b. [Figure 7a] FIG. 7a is a graph showing the signal detected using a kinetic detector for E. coli strain ATCC-25922 under different conditions and for which signal estimates over time were determined during evaluation using the method according to the invention. [Figure 7b]FIG. 7b is a graph showing the signal detected using a kinetic detector for E. coli strain BAA-2452 under different conditions and for which signal estimates over time were determined during evaluation using the method according to the invention. [Figure 8a] FIG. 8a is a graph showing further signal parameters determined during evaluation using the method according to the invention for signals detected using a kinetic detector for E. coli strain ATCC-25922 and E. coli strain BAA-2452 under different conditions. [Figure 8b] FIG. 8b is a graph showing a linear combination of further signal parameters of FIG. 8a. [Figure 9] FIG. 9 is a graph showing linear combinations of further signal parameters determined during evaluation using a method according to the invention for signals detected using a kinetic detector for E. coli strain ATCC-25922 and E. coli strain BAA-2452 under different conditions. [Figure 10] FIG. 10 is a graph showing signal parameters-median values ​​of signal estimates and time series of signal estimates determined during evaluation using the method according to the invention for signals detected using a kinetic detector for a NARA-5032 resistant E. coli strain under different conditions. [Figure 11] FIG. 11 is a graph illustrating the determination of signal parameters by linear and exponential fitting to the signal estimator shown in FIG. [Figure 12] FIG. 12 is a table showing the performance of feature selection algorithms suitable for evaluation by the method according to the invention for different input vectors. [Figure 13a] FIG. 13a is a graph showing the correlation between the signal parameters of the method according to the invention and the mortality determined using standard microbiological methods. [Figure 13b] FIG. 13b is a graph showing the correlation between other signal parameters of the method according to the invention and the mortality determined by standard microbiological methods. [Figure 13c]FIG. 13c is a graph showing the correlation between a linear combination of the signal parameters of FIGS. 13a and 13b and the mortality rate determined by standard microbiological methods. [Figure 14a] FIG. 14a is a graph showing the time series of signal estimates determined with the method according to the invention for E. coli ATCC-25922 under different conditions. [Figure 14b] FIG. 14b is a graph showing the time series of signal estimates determined with the method according to the invention for E. coli ATCC-25922 under different conditions. [Figure 15a] FIG. 15a is a graph showing signal parameters determined from the time series of the graphs of FIGS. 14a and 14b. [Figure 15b] FIG. 15b is a graph showing a combination of signal parameters determined from the time series of the graphs of FIGS. 14a and 14b. [Figure 16a] FIG. 16a is a graph showing a linear combination of further signal parameters determined from the time series of the graphs of FIGS. 14a and 14b. [Figure 16b] FIG. 16b is a graph showing ATP (adenosyl triphosphate) concentrations (a marker for metabolic activity) of E. coli ATCC-25922 under the culture conditions measured in the graphs of FIGS. 14a and 14b. [Figure 17] FIG. 17 is a schematic diagram of a motion detector. [Figure 18a] FIG. 18a shows the distribution of Klebsiella pneumoniae strains by reference MIC for ciprofloxacin (CIP). [Figure 18b] FIG. 18b illustrates the performance of the linking algorithm, which is a classification algorithm depending on the number of signal parameters (SP). [Figure 19] FIG. 19 illustrates the performance of the classification model, linking algorithm, with different numbers of SPs for Klebsiella pneumoniae and ciprofloxacin. [Figure 20a]FIG. 20a shows the scores for each experiment used to train model 1 of FIG. 19 using one SP plotted against the reference MIC of ciprofloxacin. [Figure 20b] FIG. 20b shows the scores for each experiment used to train model 4 in FIG. 19 using the four SPs plotted against the reference MIC of ciprofloxacin. [Figure 21a] FIG. 21a shows the distribution of E. coli and Klebsiella pneumoniae strains according to their reference MIC for ceftriaxone (CRO). [Figure 21b] FIG. 21b shows the scores for each experiment used to train the CRO model of FIG. 24 plotted against the reference MIC of ceftriaxone. [Figure 22a] FIG. 22a shows the distribution of E. coli strains according to their reference MIC for ciprofloxacin (CIP). [Figure 22b] FIG. 22b shows the scores for each experiment used to train the CIP model of FIG. 24 plotted against the reference MIC of CIP. [Figure 23a] FIG. 23a shows the distribution of E. coli strains according to their reference MIC for cefotaxime (CTX). [Figure 23b] FIG. 23b shows the scores for each experiment used to train the CTX model of FIG. 24 plotted against the reference MIC of CTX. [Figure 24] FIG. 24 shows the performance of the classification models for the data shown in FIG. 21b (CRO), FIG. 22b (CIP) and FIG. 22c (CTX). [Figure 25a] FIG. 25a is a graph showing the signal detected using a motion detector for the cancer cell line SW480 under different conditions (with doxorubicin) and for which signal estimates over time were determined during evaluation using the method according to the invention. [Figure 25b]FIG. 25b is a graph showing the signal detected using a kinetic detector for the cancer cell line SW480 under different conditions (medium control) and for which signal estimates over time were determined during evaluation using the method according to the invention. [Figure 26] Figure 26 shows the geometrical properties of the vibration power spectral density function. These are used to calculate the integrals N1-N5, distances and ratios listed. Using the 20Hz-200Hz section, a line is fitted to the log-log plot to determine N0 and alpha (slope and intercept of the log-log line fit). [Figure 27] Figure 27 shows a comparison between the quantile spectrum and the power spectral density. The 50th percentile spectrum (P50) is close to the classical power spectral density function (PSD). The other percentiles introduce additional information about the probability distribution of the Fourier components. [Figure 28] 28 shows the empirical probability density function (EPDF) calculated based on the spectral percentiles of the three Fourier components 10 Hz, 100 Hz, and 1000 Hz. Although the EPDF is chi-squared distributed conditional on the transformed noise being Gaussian, estimation of this statistic for cellular oscillatory signals revealed its discriminatory power. [Figure 29] Figure 29 shows the MF-DFA signal parameters used in the embodiment. They are calculated as the ratio of Fq (number of subintervals) for the last 20 minutes of the drug phase and the first 20 minutes of the drug phase. Thus, the signal parameter "F0" is F-10 (1024) for the last 20 minutes of the drug phase divided by F-10 (1024) for the first 20 minutes of the drug phase. [Diagram 30] FIG. 30 illustrates the dependence of the performance of the classification algorithm, the linking algorithm, on the signal parameters selected by the method described in the present invention in the problem of classification of the metabolic response to two antibiotics, namely ceftriaxone and ciprofloxacin. [Diagram 31]FIG. 31 illustrates the dependence of the performance of the classification algorithm, the linking algorithm, on the signal parameters selected by the method described in this invention in the problem of classification of the metabolic response of a physical stressor-temperature. [Diagram 32] FIG. 32 illustrates the dependence of the performance of the classification algorithm, the linking algorithm, on the signal parameters selected by the method described in the present invention in the problem of classification of colon cancer cells metabolized in the presence and absence of antibiotics. [Diagram 33] 33 illustrates the results of applying the linking algorithm, a linear regression algorithm, with quantile signal parameters of the prediction of metabolic response to changing drug concentrations. High values ​​of the coefficient of determination indicate a strong dependence between the linking algorithm output and the actual value of the drug concentration. [Diagram 34] FIG. 34 illustrates the dependence of the performance of the regression algorithm, the linking algorithm, on some signal parameters selected by the method described in the present invention in the problem of estimating the quantitative metabolic response to increasing concentrations of antibiotics. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0076] Various aspects of the present invention will now be described with reference to the drawings.

[0077] As mentioned above, the invention allows an improved analysis of the motion activity of particles by means of a motion detector 1 comprising a flexible support 2 arranged to be in contact with the particles to be analysed and to deflect due to the motion of the particles (see Fig. 17). As can be further seen from Fig. 17, the motion detector 1 comprises a radiation source, such as a laser 5, for irradiating electromagnetic radiation onto the flexible support 2, and further comprises a detection device 3 for detecting a signal in the form of reflected electromagnetic radiation and generated upon deflection of the flexible support 2, and an evaluation device 4 for evaluating the detected signal and for finally outputting at least one activity indicator indicative of the motion activity of the particles. In the illustrated example, the motion detector corresponds to a motion detector as described in US Pat. No. 5,399,323.

[0078] For illustrative purposes only, preferred steps and the preferred sequence of these steps enabling the analysis of the locomotor activity of particles according to the method of the invention are summarized below with reference to FIG.

[0079] S0: The starting point of the analysis is at least one time-dependent signal representative of the deflection of the flexible support of the motion detector, said signal being referred to as the raw input signal RIS.

[0080] In order to cancel any drift in the RIS, the method preferably subjects the RIS to drift cancellation.

[0081] S1: From the signal, from the RIS, but preferably after its drift cancellation, the method calculates a time series of signal estimators. The calculation of the time series of signal estimators can be done in the time domain or in the frequency domain.

[0082] When a signal estimate in the time domain is calculated, the signal is divided into time intervals, the time dependence of the signal is analyzed separately within each time interval to obtain a signal estimate, and the time series of the signal estimates is analyzed to obtain the signal parameters. For example, the signal estimate can be determined by using at least one of the following: estimators of the moments of the probability density function, percentiles of the probability density function, Results of correlation, partial correlation, or auto-regressive moving average (ARMA) and nonlinear auto-regressive moving average (NARMA) modeling.

[0083] The values ​​of the signal estimator, e.g. a particular statistical algorithm or a noise model such as time-varying noise model parameters, are preferably sampled into new time series. These new time series of signal estimators preferably consist of fewer points and reveal characteristic patterns, which can be used as input for the determination or extraction of signal parameters (see further below).

[0084] If a signal estimate in the frequency domain is calculated, the signal is preferably divided into intervals where the power spectrum is estimated. The estimation and windowing methods are preferably optimized for a particular application. Then, various noise models are preferably fitted to the given spectrum and the signal estimators, here the fitting parameters, are preferably used as samples of a new time series. Apart from the signal estimators, which are parameters of the noise models, geometric properties of the estimated spectrum can also be measured (e.g. extreme points, inflection points, areas under different parts of the curve, horizontal and vertical distances between them).

[0085] The result is a set of time series, each of which is a signal estimator, fitting specific parameters or characteristics, and in this way the number of points can be significantly reduced and the extraction of the signal parameters allows the identification of patterns or shapes in the time series characteristics of a given metabolic activity (see further below).

[0086] S2: After computing the time series of signal estimators, convert the time series of signal estimators in the time or frequency domain into a vector of signal parameters. This conversion is preferably performed by one of the following three methods: The estimated time series is divided into intervals. Statistical properties such as percentiles or moments are calculated for each interval. These form a vector of basic signal parameters. Ratios, differences, and difference ratios of the basic signal parameters can then be used to calculate a vector of extended signal parameters. In this way, the signal parameters become more robust to environmental conditions. The estimated time series is fitted using a curve, preferably of a type and parameterization optimized for the particular application. The type of curve can be exponential, polynomial, trigonometric, and linear and nonlinear mixtures thereof. The third method of signal parameter extraction is a combination of the first two methods. For this purpose, fitting is preferably not performed on the entire signal, but only within intervals, and blending using ratios and differences is performed.

[0087] The result of the extraction of the signal parameters is a large vector of real numbers (usually more than 200). This vector is preferably shortened by selecting a subset of the signal parameters by running a feature selection algorithm.

[0088] S3: Thus, after the extraction of the signal parameters, the selection of the signal parameters is carried out by a feature selection algorithm. In this way, the robustness and generalization level of the classification or in a sense prediction algorithm is provided. The feature selection algorithm for selecting the signal parameters is preferably optimized for the specific application and can be one of the following: Univariate selection (F-test, mutual information, chi, chi-square, etc.), Penalty-based methods (L1, L2, Elastic Net), Forward or backward selection of signal parameters based on the properties of a particular model, or based on cross-validation or bootstrapping.

[0089] The concept of model Pareto optimality can be used to select the vector of signal parameters that is optimal for a multi-objective criterion in forward or backward selection. The number of signal parameters must be minimal and the accuracy must be maximal. Usually, it is not possible to reduce the number of signal parameters used without decreasing the accuracy. Therefore, from these Pareto optimal algorithms, the final linking algorithm containing the optimal input vector of signal parameters is preferably selected based on a domain-specific criterion, for example with the assistance of a human expert. This additional criterion can be the performance of a special test data set or additional requirements defined by the experts.

[0090] S4: The input vector obtained after the selection of the signal parameters is fed to a linking algorithm, which uses the input vector of signal parameters to output an activity index of the particles. This activity index can be discrete, and the input vector of the signal parameters extracted and selected in the previous step is used as input of a classification algorithm. That is to say, the linking algorithm corresponds in this case to a classification algorithm. The classification algorithm can be one of the following: Logistic regression, Decision trees, Random forest, Gradient Boosting Trees, Support Vector Machine, Multi-perceptron neural network, Radial basis function (RBF) neural networks. The type of linking algorithm and the values ​​of its hyper-parameters are preferably optimized for a particular application.

[0091] The activity index may also be a real number, and the input vector of signal parameters is also used as input for a regression algorithm, i.e. the linking algorithm corresponds in this case to a regression algorithm. The regression algorithm is preferably one of the following: Linear regression, Decision tree regression, Random forest regression, Gradient Boosting Tree Regression, Kernel Regression, Multi-perceptron neural network, RBF neural network regression. The type of linking algorithm and the values ​​of its hyper-parameters are preferably optimized for a particular application.

[0092] More practically speaking, particles in contact with the flexible support induce random signals buried in a significant noise background with useful information encoded in both the time and frequency domains. Particles such as organisms evolve over time under various stimuli (nutrients, antibiotics, chemicals, etc.) that affect the properties of the random signal. For example, signal properties providing diagnostic information can be extracted using the method according to the invention, for example by observing their temporal evolution under appropriately optimized measurement conditions. Due to biological variability between the tested organisms and between the different conditions measured, the method proposed herein has proven to be a powerful tool allowing to separate diagnostic information from measurement artifacts and noise background. Relating this example to the analysis outline shown in Fig. 1, the detected signal is transformed into a time series of signal estimators encoding, for example, i) changes in the living state of the organism, and ii) changes in the state of the measurement environment itself. The time series resemble different shapes and patterns that need to be quantified and related to the phenomenon of interest. These time series are then subjected to the extraction of signal parameters, which here define for example a single experiment and are stable in a given application domain, in order to detect a given phenomenon or to measure its strength. A selection of signal parameters is performed in order to optimize the set of signal parameters to increase the strength of the relationship between the signal parameters and the phenomenon of interest in the next stage of the analysis outline. Finally, an indicator indicative of the phenomenon of interest is output.

[0093] 2 shows a signal detected with a motion detector, subjected to drift cancellation during evaluation with the method according to the invention. In the example shown, the drift is cancelled by fitting a linear curve, in fact a first order polynomial, with a duration interval of 5 minutes.

[0094] 3 shows a signal detected by a motion detector and subjected to fitting of a noise model in determining a signal estimate. The noise model here corresponds to a mixture of white noise and band noise and includes four fitting parameters: amplitude of the band noise, frequency of the poles of the band noise, bandwidth, and level of the white noise.

[0095] Figure 4 shows the identification of Pareto optimal feature selection algorithms that can be used in the method according to the invention. The Pareto optimal feature selection algorithms are based on the accuracy and number of signal parameters.

[0096] Figures 5a and 5b show that the method according to the invention can be used to distinguish between live and dead cells, or more broadly cells that show extreme differences in metabolic activity. This example can be seen as an introduction to the method and as a very elementary and uncomplicated case. In particular, these figures show, on top, in each case a flexible support in the form of a microcantilever of a motion detector, which contains live (Figure 5a) and dead (Figure 5b) bacteria attached to the microcantilever.

[0097] In this experiment, the Gram-negative Escherichia coli reference strain ATCC-25922 was cultured at late logarithmic growth phase (OD ) under standard laboratory conditions (i.e., Miller's Luria Bertani broth (LB), aerobic, 37°C). 600 =1=10 9The bacteria were cultured to 1000 ng / mL (cells / mL) and harvested using centrifugation (2000 g, 3 ft). The pellet was separated and divided into two groups for subsequent analysis. The first group of bacteria was left viable at room temperature, while the second group was exposed to 60°C for 20 min to generate non-viable bacteria by denaturation of enzyme complexes and other cell essential processes. As expected and confirmed by independent measurements, in this latter group we were unable to detect any metabolic activity using the redox-dependent fluorescent dye resazurin, whose emission / excitation spectrum shifts with respiratory activity, a major indicator of the metabolic state of the cells.

[0098] Before the start of the experiment, the microcantilever of the motion detector was functionalized with the necessary linking agent to achieve a sustainable cell attachment that would reliably persist throughout the nanomotion recording. The attachment was performed as described in WO 2021 / 130339. Indeed, in this experimental setup, positively charged poly-D-lysine (PDL: Poly-D-Lysine) was used, since it is able to promote the attachment of E. coli cells that exhibit a negatively charged lipopolysaccharide surface. In fact, most cells exhibit a negative net charge on their surface, and if this is not the case, functionalizing agents can be adapted (see also WO 2021 / 130339). Here, a solution of 0.1 mg / ml poly-D-lysine in ultrapure water was applied for 20 min on the microcantilever, which was then rinsed again with ultrapure water and allowed to dry. Using the motion detector, the deflection of the functionalized bare microcantilever was recorded in 1 / 2 concentrated LB, which was used as a blank for the subsequent measurements of the two groups of E. coli cells. Both viable and heat-killed populations of E. coli cells were then attached to the microcantilever in parallel recordings, i.e., two phases of signal recording were performed: a Blank phase, measuring the deflection of an empty cantilever, followed by a Bac phase, measuring the deflection of the cantilever with attached bacteria.

[0099] From the microcantilever deflections and after drift cancellation using linear detrending (first order polynomial) for intervals of 10 seconds length, the time series of signal estimates, in this case the variance (second moment of the probability density function), are calculated and plotted for 20 minutes, firstly for bare microcantilevers (blank phase) and secondly for microcantilevers with ATCC-25922 attached for each group of live and non-live cells (Bac phase). In other words, in FIG. 5a, the variance of these deflections of a microcantilever carrying immobilized E. coli ATCC-25922 in 1 / 2 LB after incubation in LB at 37° C. is shown. As mentioned above, these are live bacteria. FIG. 5b shows the variance of a microcantilever carrying bacteria of the same strain after exposure to 60° C. for 20 minutes, where the bacteria are dead.

[0100] From the variance, i.e. signal estimates, the signal parameters, i.e. median variance over the 20 min recording for the blank and Bac phases, were calculated. For the blank phase, the mean μ was 1.6×10 -6 V 2 / V 2 After attachment of live cells, in the Bac phase, the dispersion was 1.5 × 10 -5 V 2 / V 2 whereas the median variance of heat-killed nonviable bacteria in the Bac phase remained at the level of the blank phase (μ viable =1.5×10 -5 V 2 / V 2 vs. μ heatkilled =2.5×10 -6 V 2 / V 2 , p=0.0013, t-test, μ of variance calculated over 20 min), which is consistent with other metabolic activity assessments, such as using the fluorescent dye resazurin mentioned above.

[0101] Figure 6a shows the median variance in the Bac phase of five experiments (bars represent medians, t-test p<0.005). As can be seen in Figure 6a, in this extreme case of viable and non-viable bacteria, the use of a single signal parameter was sufficient to distinguish between the two metabolically distinct groups.

[0102] With reference to further figures, more complex scenarios in which there are less extreme differences between groups (in terms of biological quality or phenotype) are analysed by the method according to the invention.

[0103] To this end, Figures 7a to 12 show the investigation of the response of cells to a changing environment that can be used for classification, where the changing environment corresponds to a change from a favorable culture environment to a stressful environment. In particular, these figures illustrate antibiotic susceptibility testing (AST) performed using the method according to the invention, where sensitive and resistant E. coli strains are attached to the microcantilever of a kinetic detector and exposed to the antibiotic ceftriaxone.

[0104] Indeed, the ceftriaxone-susceptible E. coli strain ATCC-25922 was used in the analysis shown in Fig. 7a, whereas the ceftriaxone-resistant E. coli strain BAA-2452 was used in the analysis shown in Fig. 7b. Fig. 7a and Fig. 7b show plots of the signal estimate over time, i.e. here the variance of the microcantilever deflection, for (i) bare functionalized microcantilevers (Blank), (ii) microcantilevers with attached bacteria under culture conditions (Bac), and (iii) attached bacteria exposed to ceftriaxone (drug). In this example, 1 / 2LB was used as the culture medium for the blank and Bac phases, and the drug phase was supplemented with 32 μg / mL ceftriaxone.

[0105] The two patterns recognizable in Figures 7a and 7b are characteristic of sensitive and resistant strains, but when the analysis is not performed visually by the human eye but by a machine, the assessment is not always clear-cut and not easy to distinguish.

[0106] For this, signal parameters were calculated and thresholded to determine whether a given strain was sensitive or resistant. That is, if the value of the signal parameter is greater than the threshold, the strain is determined to be resistant, and if the value is less than or equal to the threshold, the strain is determined to be sensitive. To determine whether cells with different responses to antibiotic stress can be classified, the signals of two additional sensitive clinical isolates RN-26 and RN-49 from a Swiss hospital, as well as two additional resistant clinical isolates B1 and B15, were detected with a kinetic detector. A total of 67 experiments with these strains exposed to ceftriaxone were recorded. Signal parameters were extracted from the single signal estimator that gave one of the best separations between the two different groups, for example as the median of the first 30 min of the drug phase normalized to the median of the entire drug phase, or the median of the last 30 min of the drug phase normalized to the median of the entire drug phase.

[0107] Figure 8a shows two signal parameters: the median from the first 30 minutes of the drug phase normalized to the median of the entire drug phase (lower graph) and the median from the last 30 minutes of the drug phase normalized to the median of the entire drug phase (upper graph). From these graphs it is clear that both signal parameters (SP) have different values ​​for sensitive and resistant strains. Both examples of signal parameters show significantly different populations for a number of experiments using the same conditions for a number of additional sensitive and resistant strains (t-test, p<0.00005). However, using a single signal parameter is insufficient in each case to distinguish a single record of a sensitive strain from a record of a resistant strain, since there is an overlap between both populations. Therefore, a better method of separation of the two populations is required. This is shown in Figure 8b, where the separation of the sensitive and resistant populations, each composed of different strains, is strengthened by using both signal parameters from Figure 8a.

[0108] From FIG. 8b, the combination of the signal parameters will result in a better separation of the two metabolic states, for example as sensitive and resistant strains. That is, the separation of the sensitive and resistant populations, each composed of different strains, is enhanced by using both signal parameters from FIG. 8a. In the illustrated example, the two signal parameters are represented as a linear combination, and the separation line is neither vertical nor horizontal, but diagonal, and mathematically represented as a linear combination of these two signal parameters. That is, the two signal parameters are added together to form a classification index that can be weighted and thresholded by two constants. This approach can be generalized, and several signal parameters can be extracted from the time series of signal estimators weighted by corresponding constants and thresholded to classify sensitive and resistant strains, where the optimal number of signal parameters achieves the highest accuracy. The optimal weights and thresholds can be estimated using a logistic regression algorithm. That is, the linking algorithm here is a logistic regression algorithm.

[0109] In FIG. 9 it is shown that a linear combination of more than two signal parameters (in this case four signal parameters) can further improve the separation. This linear combination of signal parameters becomes the classification index. That is, FIG. 9 shows how adding an additional signal parameter improves the classification accuracy (proportion of correctly classified experiments). The weighted sum of the signal parameters is thresholded in such a way that negative values ​​indicate resistant strains and positive values ​​indicate susceptible strains. In this set of 67 experiments, one signal parameter alone (ratio of median variance in the last 30 minutes of the drug phase to median variance throughout the drug phase) achieved an accuracy of 85.1%. A weighted sum of four signal parameters (median variance of the last 30 min of the drug phase relative to median variance of the entire drug phase, median variance of the first 30 min of the drug phase relative to median variance of the entire drug phase, median variance from 60 to 90 min of the drug phase relative to median variance from 30 to 60 min of the drug phase, and median variance from 60 to 90 min of the drug phase relative to median variance of the entire drug phase) increased the accuracy of separation of both classes to 89.6%. For this limited data set, the weights and thresholds were optimized with a logistic regression algorithm to demonstrate the potential of this solution.

[0110] However, in practical applications, the extraction and selection of signal parameters must be carefully optimized. A large number of signal parameters leads to so-called overfitting of the algorithm. In this case, the high performance of the dataset used for fitting is not maintained when the algorithm is used in practical conditions. For this reason, a cross-validation procedure is applied, in which the dataset is divided into k subsets. The algorithm is fitted on the k-1 subsets and validated on the last subset that was not used for fitting. This process is repeated k times, each time excluding a new subset. In this way, the estimated average accuracy reveals the overfitting problem (overfitted algorithms are less accurate than non-overfitted algorithms).

[0111] Cross-validation helps to select only those signal parameters that carry useful information. The selection starts with one signal parameter, successively increasing the number of parameters by one (forward selection), and then starts removing signal parameters down to a single parameter (backward selection). Cross-validation helps to evaluate how the addition or removal of signal parameters affects the indicator performance measured by a specified single or multi-objective criterion. This procedure makes it possible to extract many signal parameters from the signal estimator of many time series and select only the most important ones.

[0112] In the examples presented above, a very small data set was used. In the following and with reference to Figures 10-12, the method of the invention is applied to a much larger data set, comprising 1102 experiments with 84 clinical strains of E. coli isolated from patient samples tested with ceftriaxone. 561 of these experiments were performed against susceptible strains and 541 against resistant strains.

[0113] In a first step, drift cancellation of the detected RIS was performed. For this purpose, the detected RIS was divided into 10 second intervals. A linear fitting of a first order polynomial to the RIS of 10 second intervals was then applied to calculate the fitting error, which is the input for the calculation of the signal estimate, in the following the variance (estimator of the second moment of the probability density function). In this way, the signal estimate over time, i.e. the variance signal s(t) with a sampling frequency of 0.1 Hz, is obtained.

[0114] In the frequency domain, an 85 second interval is used for power spectrum estimation and fitting with a mixture of white noise and second-order band noise models using the common equation (1).

[0115]

number

[0116] where f denotes frequency, A, f0, Q are the band noise parameters, and B is the white noise parameter (constant). This results in four additional signals (A(t), f0(t), Q(t), and B(t)) with a sampling frequency of about 0.01 Hz (1 / 85). These (time series of statistical estimators), together with the variance signal s(t), are the inputs for the determination of the signal parameters.

[0117] In this determination of the signal parameters, the signal parameters are calculated. The signals s(t), A(t), f0(t), Q(t), B(t) are divided into 20 minute long intervals for the Bac phase and 30 minute long intervals for the drug phase, and are denoted by m2 through m7 and m9 through m8, respectively. 12 See Figure 10, which shows intervals of . For each interval, we calculate its median (50th percentile) along with all their possible ratios. Equation (2) shows the definition of the median ratio:

[0118]

number

[0119] In the formula, m i ,m j is the median within the i-th and j-th intervals as defined in FIG.

[0120] For the dispersion signal in the drug phase, linear and exponential fitting are also applied, and the fitted parameters are the additional four signal parameters (slope a, cross point b, growth / decay rate τ, and magnitude c). Equation (3) defines the exact formula.

[0121]

number

[0122] where the coefficients of determination for both the fit and the ratios c / τ and b / a are in the set of extracted signal parameters. An illustration of the linear and exponential fits is shown in FIG.

[0123] As a result, a set of 192 signal parameters is determined or extracted and subjected to a signal parameter selection stage, i.e. fed into a feature selection algorithm.

[0124] In the table shown in Figure 12, the performance of the feature selection algorithm based on Pareto optimality is shown. Apart from the accuracy (fraction of correctly classified experiments), the sensitivity (fraction of correctly classified experiments with a sensitive strain) and the specificity (fraction of correctly classified experiments with a resistant strain) are estimated. N means the number of signal parameters used by the algorithm. In the presented example, the feature selection algorithm was a classification algorithm of cellular antibiotic susceptibility estimated by 300 iterations of three-fold stratified cross-validation. The results were obtained for a data set counting 1102 experiments with clinical strains of E. coli and the antibiotic - ceftriaxone. 561 experiments were performed with a sensitive strain and 541 experiments with a resistant strain. Each column of the table corresponds to a different vector of signal parameters that are the input of the Pareto optimal classification algorithm with the maximum accuracy and the minimum number of signal parameters. The accuracy ranges from 84.8% for the algorithm based on a single signal parameter to 86.7% for the algorithm based on five signal parameters. The addition of subsequent signal parameters improves the sensitivity from 84.8% to 86.7%.

[0125] Correlation with mortality rate of organisms With reference to Figures 13a-c, it is shown that the method according to the present invention correlates with the mortality rate of the organism.

[0126] That is, susceptible cells exposed to a toxin or antibiotic show a decrease in viability, which ultimately leads to death. In the case of bacteria exposed to a bactericidal antibiotic, the mortality can be measured by determining the change in the number of colony-forming units (CFU) at different time points. A CFU is thereby defined as a bacterium (=unit) that forms a visible colony on a growth medium through multiple replication cycles. The number of these CFUs is therefore a measure of the concentration of viable bacteria in the bacterial suspension of interest. Multiple samplings over time help to evaluate the change in the number of CFUs of viable bacteria and thus to calculate the mortality rate. This method has been a very reliable standard technique for more than a century, already applied by, for example, Robert Koch.

[0127] However, one of its main drawbacks is its dependence on growth and therefore the time required for bacteria to form visible colonies for analysis. Rapidly growing bacteria such as K. pneumoniae form visible colonies in 10 hours, whereas slow growing pathogens such as Mycobacterium tuberculosis take several weeks. Either way, it is a very reliable but slow method.

[0128] In this example shown in Figures 13a-c, different susceptible strains of the bacterium K. pneumoniae exhibit different mortality rates when exposed to the antibiotic ceftriaxone, depending on various reasons and biological components. In our test group of six K. pneumoniae isolates, mortality rates were >0.05 CFU. * minutes -1 ~0.25 CFU * minutes -1For the determination of the mortality, the strains were cultured as described above and exposed to the same concentrations of ceftriaxone. The population was sampled every 20 min, colonies were plated and the number of viable bacteria was determined by the number of CFUs after overnight incubation of the culture plates. At least three experiments were performed per strain. The same strains were used in parallel to detect the deflection of the flexible support with a motion detector in the same sequence of recording phases, as shown in Figures 7a and 7b. The same two signal parameters SP1:Median VAR-DRUG0-30min / Median VAR-DRUG0-120min and SP2:Median VAR-DRUG90-120min / Median VAR-DRUG0-120min were used separately to test the correlation between the detected signal and the mortality rate. In doing so, at least three signal recordings using the kinetic detector with a complete blank phase, Bac phase, and drug phase were used to calculate the mean and SEM of both signal parameters derived from the drug phase. SP1 = 0.81 and R SP2 A positive correlation with ρ = 0.5 was observed, suggesting a correlation between the deflection of the flexible support of the motion detector and the mortality rate (see Figures 13a and 13b).

[0129] However, as can be seen in Figure 13c, the correlation improved significantly by increasing the number of signal parameters for which the classification index is calculated (in this case, four signal parameters: Median VAR-DRUG90-120min / Median VAR-DRUG0-120min , Median VAR-DRUG0-30min / Median VAR-DRUG0-120min , Median VAR-DRUG60-90min / Median VAR-DRUG30-60min , Median VAR-DRUG60-90min / Median VAR-DRUG0-120min Mortality rate (CFU * minutes -1) and the correlation with the classification index from the signal improved to R = 0.98. Thus, the linear combination of three or more signal parameters to calculate the classification index helps to describe the biological phenomenon of the response to a stress environment (antibiotic susceptibility) more accurately. Therefore, in summary, it can be said that the signal of the motility detector reflects the mortality rate of the organism, and the linear combination of the signal parameters improves the correlation with the mortality rate determined by standard microbiological methods. A high correlation of the classification index means that the mortality rate can be predicted, which is an example of a linear regression algorithm.

[0130] Classification of metabolic activities With reference to Figures 14a to 16b, it is shown that the method according to the present invention can be used to classify metabolic activity.

[0131] In the example shown in Figures 14a and 14b, the time series of the signal estimator, the resonant frequency, is analyzed and signal parameters are extracted, similar to the previous examples. Figure 14a shows the signal estimator for E. coli ATCC-25922 attached to a microcantilever when exposed to 1 / 2LB and then to 1 / 8LB, i.e., when the E. coli cells experience different nutrient availability and therefore different metabolic activity. In the control experiment shown in Figure 14b, the same strain is exposed to 1 / 2LB and replaced with 1 / 2LB. Comparing Figures 14a and 14b, it becomes clear that the increase in resonant frequency is less pronounced for the change from 1 / 2LB to 1 / 2LB (the "no change" condition) compared to the exchange of medium from 1 / 2LB to 1 / 8LB. Thus, in principle, signal parameters can be extracted and used to distinguish metabolic states of the same organism.

[0132] Figures 15a and 15b show the extracted signal parameters determined from the resonant frequency region. As can be seen from the graph shown in Figure 15a, none of them can separate or distinguish the two populations to an acceptable degree (t-test, p>0.05). From the graph shown in Figure 15b showing the coupling of the two signal parameters SP1 and SP2, it follows that there is an overlap of the recordings of E. coli at 1 / 2LB and E. coli at 1 / 8LB.

[0133] As mentioned above and shown in FIG. 16a, the linear separation of the populations exposed to 1 / 2LB and 1 / 8LB can be represented by a linear combination of these two signal parameters. In fact, the separation can be further improved by using a linear combination of more than two signal parameters (three in this case). This linear combination of signal parameters becomes the classification index. As can be seen from FIG. 16a, the accuracy of separating the two populations increases from 70.6% when only one signal parameter is used to 88.2% when three signal parameters are used. The weights and thresholds are estimated using a logistic regression algorithm, i.e., the linking algorithm is a logistic regression algorithm here.

[0134] To structure the description of signal parameters, Polish Notation is used along with some formal structure for signal parameter names.

[0135] The signal parameter names have the following structure: TIME_SERIES_NAME_PHASE_NAME_START_TIME-END_TIME_STATISTICS_USED (For example, f0_Bac_80-90_p50 means the f0 signal estimator where the 50th percentile is calculated for the bac phase over the time interval from 80 to 90 minutes.) The statistics used are percentile, mean, standard deviation (std), and slope.

[0136] Polish Notation is a way of encoding arithmetic expressions without the use of parentheses. For example, / +ab-ab is equivalent to (a+b) / (ab). It is used to automatically encode signal parameters that are ratios and differences of other signal parameters.

[0137] The feature selection algorithm selected the following noise signal parameters as Pareto optimal based on the accuracy and number of signal parameters: -f0_Bac_80-90_p50 f0_Bac_0-10_p50 -A_Bac_110-120_p50 A_Bac_0-120 / Q_Bac_80-90_p50 f0_Bac_20-30_p50 / f0_Bac_110-120_p50 Q_Bac_70-80_p50 -f0_Bac_0-10_p50 f0_Bac_0-120_p50

[0138] Figure 16b relates to an independent experiment using a chemiluminescence method to measure ATP concentration. Similar to the measurements presented for Figures 15a-16a, the energy status of the cells can be assessed by the concentration of ATP in different media (1 / 2 LB and 1 / 8 LB) with different nutrient availability, and by using an enzymatic assay (BacTiter-Glo™) using chemiluminescence generated by the ATP-dependent enzymatic activity of luciferase.

[0139] As can be seen from FIG. 16b, one metabolic marker of the metabolic activity of the cells similarly results in two partially overlapping populations, with each symbol in the graph representing one measurement. Thus, similar to when one signal parameter is used to analyze the signal of the flexible support in the kinetic detector, using only one metabolic marker is insufficient to separate two metabolic states of the same type of cells in closely related environments (in this case 1 / 2LB and 1 / 8LB). Thus, the combination of signal parameters, i.e., the use of classifiers, can again be understood as capturing several aspects of the metabolic state of the cells. Increasing the number of signal parameters can be understood similarly to increasing the number of metabolic markers.

[0140] The following embodiments investigate three aspects of the time dependence of the signal evaluated by the evaluation device: complex aspects of the power spectral density that are not covered by theoretical noise models, aspects related to particle oscillation rare events in the signal that may be lost during power spectral density estimation, and the auto-affinity of cellular oscillations.

[0141] Specifically, typical spectra and signal estimators that can be derived from a signal detected with a motion detector and analyzed with the method according to the invention are presented in Figure 26. For this type of spectrum, the following list of 60 time series signal estimators is defined, which are estimated every 2 minutes: Spectral minimum (f min and p min ) Spectral maximum (f max , p max ) The midpoint of the perpendicular distance between the minimum and maximum, p left =p right =(p max +p min ) / 2 and the corresponding frequency (f left , f right ) Flicker noise parameters (N0, α) for the frequency range 20Hz to 200Hz

[0142]

number

[0143] Five frequency ranges N1 to N5 (20 Hz, f min ), (f min , f left ), (f left , f max ), (f max , f right ), (f right , 20 kHz). Area under the curve for 20 equidistant frequency ranges (20Hz-28Hz, 28Hz-39Hz, ..., 224Hz-316Hz, 316Hz-447Hz, ..., 10023Hz-14158Hz, 14158Hz-20000Hz) on a logarithmic scale NE1-NE20. The normalized power normN for all i i and normNE i N i / (N1+N2+N3+N4+N5) and NE i / (N1+N2+N3+N4+N5)

[0144] These time series of signal estimators can be used to calculate signal parameters and / or their ratios and differences.

[0145] As can be seen from figures 27 and 28, the quantiles, in particular the percentiles, of the periodogram (see figure 27) can be used to take into account the shape of the probability distribution of the periodogram (see figure 28). In the described solution, nine percentiles from 10, 20, ..., 90 are used, which are calculated for a given frequency range. In the presented embodiment, the following frequency ranges are used: 0Hz-10Hz, 10Hz-100Hz, 100Hz-200Hz, 200Hz-400Hz, 400Hz-1000Hz, 1000Hz-2000Hz, 2000Hz-4000Hz, 4000Hz-5000Hz, 5000Hz-6000Hz, 6000Hz-7000Hz, 7000Hz-8000Hz, 8000Hz-10000Hz (p10_1000-2000 means the 10th percentile of the frequency range 1000Hz-2000Hz). Furthermore, the following extended time series are created: KLPQ - Kullback-Leibler divergence between the chi-squared probability density function and the empirical probability density function calculated based on percentiles, KLQP - the Kullback-Leibler divergence between the empirical probability density function calculated based on percentiles and the chi-squared probability density function; Kurtosis - The kurtosis (moment) of the empirical probability density function, JS - the Jensen-Shannon distance between the chi-squared probability density function and the empirical probability density function, MO-(p 60 -p 40 ) / (p 90 -p 10 ) (ratio and difference), EEPDF - Mean (moment) of the empirical probability density function.

[0146] These provide 5-minute samples of signal estimators for 112 time series, from which signal parameters for different percentiles, frequency ranges and time intervals, as well as their ratios and differences, are calculated. These are the objects of the feature selection algorithm.

[0147] Current knowledge on cellular oscillations has revealed that their power spectral density functions have strong 1 / f characteristics. This kind of spectrum is often associated with the autoaffinity of the signal. Autoaffinity can be analyzed by Detrended Fluctuation Analysis (DFA) and its generalization Multifractal Detrended Fluctuation Analysis (MF-DFA). In these methods, the dependence of signal statistical properties on the time scale is investigated. In the presented embodiment, MF-DFA based signal parameters were used. In particular, the following 21 generalized mean exponents / powers are used: -10.0, -8.0, -6.0, -4.0, -2.0, -1.0, -0.8, -0.6, -0.4, -0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0, 2.0, 4.0, 6.0, 8.0, 10.0. With 9 subintervals (4, 8, 16, 32, 64, 128, 256, 512, 1024) 189 signal parameters are obtained from which ratios and / or differences can be further calculated.

[0148] In FIG. 29, a table of signal parameters used in the presented embodiment is shown. They are F for the last 20 minutes of the drug phase and F for the first 20 minutes of the drug phase. q (number of subintervals). Thus, the signal parameter "F0" is the ratio of F -10 (1024) for the first 20 min of the drug phase -10 (1024). These signal parameters are mixed again by calculating their ratio (for example, F146_F129 means F146 / F129).

[0149] Similar to the examples consisting of relatively small data sets shown in Figures 7a-12 and 14-16a, the linking of signal parameters (SPs) substantially improves the performance of the classification algorithm, the linking algorithm, on big data sets containing highly diverse analytes. Again, we used the response of cells changing from a favorable culture environment to a stressful environment, this time with the antibiotic ciprofloxacin (CIP), for classification. We used 83 different clinical isolates of Klebsiella pneumoniae strains with different minimal inhibitory concentrations (MICs) to ciprofloxacin, ranging over four orders of magnitude, considered to be either clinically susceptible or resistant, shown as ≦S and >R, respectively, in Figure 18a. MICs were determined by standard diagnostic reference methods (E-test or broth microdilution). The level of resistance to ciprofloxacin is due to different resistance mechanisms and other genetic determinants of the different strains. Despite the diversity of the strains mentioned, the nanomotion of the 83 strains was measured in 233 experiments with only one concentration of CIP, 8 μg / ml ("concentration" in FIG. 18a), in the experimental setup of nanomotion recording described above for FIG. 7a and FIG. 7b. Briefly, in each experiment, the bacterial specimen attached to the micromechanical sensor was exposed to the culture medium (1 / 2 concentrated LB) for 120 min, followed by exposure to CIP for 120 min.

[0150] In Fig. 18b the performance improvement as the number of SPs increases is visualized, while Fig. 19 lists all the metrics evaluated for the classification algorithm, the linking algorithm, on this dataset. Accuracy, sensitivity and specificity are calculated as follows: Accuracy (%) = 100 × (true positive + true negative) / (true positive + true negative + false positive + false negative) Sensitivity (%) = 100 × (true positive) / (true positive + false negative) Specificity (%) = 100 × (true negative) / (true negative + false positive)

[0151] Here, true positives are considered as experiments that were correctly classified for the susceptible strain, true negatives are experiments that were correctly classified for the resistant strain, false positives are experiments in which the resistant strain was misclassified, and false negatives refer to experiments in which the susceptible strain was misclassified.

[0152] Classification model number 1 (classification model is an instance of the classification algorithm, the linking algorithm) is based on a single SP (F128), which probably has the greatest impact, resulting in a classification accuracy of 85.8%. Model number 2 with two SPs (F128, F61) achieves an accuracy of 89.7%, three SPs (F128, F61, F146_F129) achieve an accuracy of 91.4%, and finally model number 4, which combines four SPs (F128, F61, F146_F129, F7_F0), reaches an accuracy of 93.1% (summarized in Figure 19). Figure 18b also shows an increase in sensitivity and specificity.

[0153] The scores, i.e., classification indices, for each of the 233 experiments are benchmarked against a reference MIC that is considered either susceptible (S reference) or resistant (R reference) in Figure 20a for model number 1 based on one SP and in Figure 20b for model number 4 based on four SPs. The scores take positive values ​​for predicted susceptible (S invention) and negative values ​​for predicted resistant (R invention). Correctly classified experiments are shown in light grey for susceptible strains (true positives) and dark grey for resistant strains (true negatives). Misclassified experiments (false positives and false negatives) are shown as open circles. The number of misclassified experiments drops from an initial 33 for model number 1 to 16 for model number 4. All models are classification algorithms that are logistic regression algorithms using MF-DFA signal parameters, the linking algorithm.

[0154] In conclusion, one SP, which can be considered as a single aspect of the nanomotion signal, is less suitable than four SPs to describe the diverse responses to drugs found in such a diverse dataset of 83 different strains. The increase in SPs and their combinations significantly improves the performance of the classification algorithm.

[0155] In another example, an even larger and more diverse dataset of 487 samples including 160 clinical isolates of two different bacterial species, E. coli and K. pneumoniae, was exposed to one concentration of ceftriaxone (shown as "concentration", FIG. 21a). The nanomotion of bacterial cells was measured in the same experimental setup described for 7a and 7b with a 120 min medium phase (1 / 2 concentrated LB) followed by a 120 min drug exposure phase (ceftriaxone, CRO), with the 160 strains again spanning a wide range of several orders of magnitude of MIC (FIG. 21a, using standard reference methods for MIC). Signal parameters derived from signal estimators that are geometric properties of the power spectral density function are used. The feature selection algorithm selected the following signal parameters based on the concepts of accuracy, number of signal parameters, and Pareto optimality: / NE0_Drug_90-120_p50 NE0_Drug_0-30_p50 / normNE19_Drug_90-120_p50 normNE19_Drug_60-90_p50 / normNE13_Bac_90-120_p50 normNE13_Bac_90-120_p50 / normNE1_Drug_90-120_p50 normNE1_Drug_0-120_p50

[0156] The linking algorithm, a classification algorithm with high performance to separate experiments with resistant strains from those with susceptible strains, is based on the combination of the four signal parameters mentioned above resulting in a score, i.e. a classification index that takes positive values ​​for experiments with predicted susceptibility (S invention) and negative values ​​for experiments with predicted resistance (R invention). An accuracy of 91.6%, sensitivity of 89.0% and specificity of 94.6% were reached (Figure 24). The scores of each sample were plotted against the reference MIC according to the method shown in Figure 21b. Correctly classified experiments are shown in light grey for susceptible strains (true positives) and in dark grey for resistant strains (true negatives). Incorrectly classified experiments (false positives and false negatives) are shown as open circles.

[0157] A similar analysis of 210 samples of 127 E. coli strains exposed to 8 μg / ml ciprofloxacin (CIP, shown as "concentration" in Figures 22a and 22b) was measured in the nanomotion setup described for Figures 7a and 7b. After processing of the nanomotion signals, the quantiles and MF-DFA signal parameters are used with the linking algorithm, which in this embodiment is a classification algorithm that is a logistic regression. The signal parameters selected by the feature selection algorithm are as follows: / / / -p90_0-10_Drug_90-120_mean p50_0-10_Drug_90-120_mean -p50_0-10_Drug_90-120_mean p10_0-10_Drug_90-120_mean / -p90_5000-6000_Drug_90-120_mean p50_5000-6000_Drug_90-120_mean -p50_5000-6000_Drug_90-120_mean p10_5000-6000_Drug_90-120_mean / / -p90_0-10_Drug_0-30_mean p50_0-10_Drug_0-30_mean -p50_0-10_Drug_0-30_mean p10_0-10_Drug_0-30_mean / -p90_5000-6000_Drug_0-30_mean p50_5000-6000_Drug_0-30_mean -p50_5000-6000_Drug_0-30_mean p10_5000-6000_Drug_0-30_mean / / p20_200-400_Drug_90-120_mean p20_10-100_Drug_90-120_mean / p20_200-400_Drug_30-60_mean p20_10-100_Drug_30-60_mean / p30_10-100_Bac_60-90_mean p30_0-10_Bac_60-90_mean F75

[0158] The classification algorithm, the final linking algorithm, was based on the four SPs and correctly classified 190 out of 210 samples. It therefore achieved an accuracy of 90.5%, a sensitivity of 89.8% and a specificity of 91.2% (Figure 24). The majority of the 20 misclassified samples (shown as open circles in Figure 22b) were found around the clinical breakpoint that marks the boundary between susceptible (≦S) and resistant (R>) strains defined by the reference AST method.

[0159] Furthermore, in another analysis, 155 samples of 125 diverse E. coli strains from a collection of different strains were exposed to a third antibiotic, cefotaxime (CTX). In the same nanomotion measurement setup as described in 7a and 7b, we used 32 μg / ml of cefotaxime (shown as "concentration" in Figures 23a and 23b). Quantile and MF-DFA signal parameters, as well as a linking algorithm, a classification algorithm that is a logistic regression, are used in this embodiment. The signal parameters selected by a feature selection algorithm based on the accuracy and number of signal parameters and based on the concept of Pareto optimality are as follows: / / p50_400-1000_Drug_90-120_mean p50_100-200_Drug_90-120_mean / p50_400-1000_Drug_0-30_mean p50_100-200_Drug_0-30_mean / / / -p50_200-400_Drug_30-60_mean p10_200-400_Drug_30-60_mean - p90_200-400_Drug_30-60_mean p50_200-400_Drug_30-60_mean / -p50_100-200_Drug_30-60_mean p10_100-200_Drug_30-60_mean - p90_100-200_Drug_30-60_mean p50_100-200_Drug_30-60_mean / / -p50_200-400_Drug_0-30_mean p10_200-400_Drug_0-30_mean - p90_200-400_Drug_0-30_mean p50_200-400_Drug_0-30_mean / -p50_100-200_Drug_0-30_mean p10_100-200_Drug_0-30_mean - p90_100-200_Drug_0-30_mean p50_100-200_Drug_0-30_mean F186_F64 F45_F38 / / p70_1000-2000_Drug_90-120_mean p70_100-200_Drug_90-120_mean / p70_1000-2000_Drug_00-30_mean p70_100-200_Drug_0-30_mean

[0160] The linking algorithm, a classification algorithm based on five SPs, resulted in only 11 incorrect classifications, with an accuracy of 92.9%, a sensitivity of 91.7% and a specificity of 94% (Figure 24). The scores, i.e., classification indices, of each sample are again benchmarked against the reference AST method in Figure 22b.

[0161] In summary, for each of the four bacteria-drug combinations in Figures 18a-24, a different highly performing linking algorithm, a classification algorithm, was developed based on a small number of SPs calculated from the signal estimator time series. In each case, the group of resistant cells could be almost completely separated from the sensitive cells based on the different cellular and metabolic responses within 120 min of exposure to three different drugs, namely ceftriaxone, ciprofloxacin and cefotaxime.

[0162] The two aforementioned drugs, cefotaxime and ciprofloxacin, interfere with different cellular processes in bacterial cells. Cefotaxime belongs to the family of beta-lactam antibiotics that interfere with cell wall metabolism, while ciprofloxacin, as a quinolone, binds to topoisomerases involved in replication and DNA folding, a process that effectively affects all processes in which DNA is involved. Proper functioning of both drug targets is essential. For both, their disturbance is detrimental to the cell in the long run, but the cellular stress responses they induce are both different.

[0163] For a total dataset size of 404 experiments, 202 of which were performed with a susceptible E. coli strain and 32 μg / ml cefotaxime, and an equal number of experiments were performed with a susceptible E. coli strain and 8 μg / ml ciprofloxacin, a combination of nanomotion recordings and machine learning was applied to develop a classification algorithm, the Linking Algorithm, that separates the information associated with the nanomotion response to cefotaxime from ciprofloxacin. All 404 experiments were used simultaneously to develop a classification model. If an experiment was performed with cefotaxime and was then correctly predicted by the method, it was considered correctly classified. The same was true for ciprofloxacin. The experimental setup was again identical to that described for Figures 7a and 7b, with a 120 minute medium phase followed by 120 minutes of exposure to either of the two drugs. For benchmarking, MICs were determined by the reference method.

[0164] The classification algorithm used was quantile signal parameters and the linking algorithm was a support vector machine algorithm with a radial basis function. The feature selection algorithm selected the following Pareto optimal signal parameters based on accuracy and number of signal parameters: -KLQP_200-400_Drug_90-120_p95 KLQP_200-400_Drug_0-30_p95 / EEPDF_0-10_Drug_090-120_p95 EEPDF_0-10_Drug_0-30_p95 / Kurtosis_0-10_Drug_90-120_p10 JS_0-10_Drug_90-120_p10 -EEPDF_Drug_90-120_mean JS_2000-4000_Drug_0-30_mean MO_0-10_Drug_90-120_p75 MO_100-200_Drug_30-60_std KLQP_0-10_Drug_0-30_std

[0165] In the classification algorithm, the linking algorithm, predicted susceptibility responses to ciprofloxacin were assigned a negative score value, while predicted responses to cefotaxime were assigned a positive score value (similar to the classification algorithm for the R and S phenotypes). Thus, incorrectly classified experiments received a positive value for ciprofloxacin and a negative value for cefotaxime. In the high-performance classification algorithm based on the seven SPs, the accuracy for both drugs reached 85.4%. 87.0% of the ciprofloxacin experiments were correctly classified, and 83.7% for cefotaxime. The influence of all additional signal parameters is shown in Figure 30. Thus, information accompanying the nanomotion signals caused by different stressors can be extracted and described by the classification algorithm.

[0166] In addition to chemical stressors, physical stressors can also affect cellular and metabolic activity and thus cellular nanomotion, as shown for different drugs (Figures 7a-12 and 18a-24) and different levels of nutrient supply (Figures 14-16a). To that end, the nanomotion of several different strains of E. coli differing in genetic composition was recorded for 30 min in culture medium (1 / 2 concentrated LB). Half of these experiments were performed at room temperature, while the other half were exposed to 37 °C (76 experiments at 37 °C, 72 at RT). The metabolic rate at 37 °C was expected to be higher as the bacterium E. coli adapts to a lifestyle within the human gut microbiome. Using spectral signal parameters and a logistic regression classification algorithm. The feature selection algorithm selected the following Pareto-optimal signal parameters based on accuracy and number of signal parameters: / NE17_Bac_0-15_p25 NE12_Bac_0-15_p25 / NE17_Bac_15-30_p10 NE13_Bac_15-30_p10 / NE16_Bac_15-30_p75 NE15_Bac_15-30_p75 -NE19_Bac_15-30_p10 NE19_Bac_0-15_p10 N1_Bac_0-15_std

[0167] The accuracy of the classification algorithm in separating both conditions, comparing nanomotions at two different temperatures and thus anticipating very global changes in the metabolic activity of the cells, ranges from 97% with a single SP to 99% with five SPs. In Figure 31, the dependence of the algorithm performance on the number of signal parameters selected based on accuracy and on the concept of Pareto optimality is shown.

[0168] Drug sensitivity testing for cancer cells Figures 25a and 25b show that the method according to the invention can be used to perform a drug sensitivity test (DST) on cancer cells attached to a microcantilever. In particular, these figures show the deflection dispersion of a microcantilever attached with the human colon cancer cell line SW480 (Figure 25a) and the dispersion of cells maintained in cell culture medium (Figure 25b), measured in cell culture medium and then exposed to an inhibitory concentration of the drug doxorubicin.

[0169] Doxorubicin-sensitive SW480 were cultured in cell culture flasks under standard laboratory conditions (i.e., cell culture medium (Dulbecco's modified Eagle's medium (DMEM) containing 10% heat-inactivated fetal calf serum (FCS) at 37 °C and 5% CO2). In preparation for nanomotion experiments, cells were detached, collected in cell culture medium and washed in DMEM containing 10% FCS. The cell suspension was used for attachment to the cantilever and all nanomotion measurements with the device were performed in DMEM containing 10% FCS. The experiments were carried out in a kinetic detector. Colon cancer cells were attached to the cantilever. Three phases of signal recording were performed: (i) a blank phase, in which the deflection of the bare cantilever was measured, (ii) a medium phase, in which the deflection of the cantilever with SW480 attached was measured, followed by (iii) a drug phase, in which the deflection of the cantilever with SW480 attached was recorded after exposure to a drug, or a second medium phase without doxorubicin. The recordings shown below were performed in a kinetic detector placed in a CO2-supplied incubator to allow optimal culture conditions for the cancer cells.

[0170] Figure 25a shows the dispersion of nanomotion signals over time when SW480 colon cancer cells are allowed to attach under culture conditions and then supplemented with 32 μM doxorubicin in the drug phase. In the experiment shown in Figure 25b, where no doxorubicin is added, the cells are maintained in DMEM and a second medium phase is recorded. Comparing Figures 25a and 25b, the reduction in dispersion after exposure to the drug is significant compared to the unchanged condition. Based on 61 experiments with SW480 (32 with exposure to doxorubicin and 29 without doxorubicin), the spectral signal parameters are calculated and the linking algorithm, a logistic regression classification algorithm, is used to distinguish between both conditions.

[0171] The signal parameters selected by the feature selection algorithm based on Pareto optimality, accuracy, and number of signal parameters are as follows: / NE8_Drug_0-30_std NE2_Drug_0-30_std -NE0_Drug_90-120_p75 NE0_Drug_0-30_p75 / NE10_Drug_90-120_slope NE3_Drug_90-120_slope -NE19_Drug_90-120_std NE13_Drug_30-60_std -NE9_Drug_60-90_std NE5_Drug_0-30_std -NE7_Drug_0-30_std NE1_Drug_0-30_std NE4_Drug_0-30_p95

[0172] In fact, the accuracy of the Pareto-optimal linking algorithm ranges from 83.2% for one SP to 91.6% for seven SPs. In Fig. 32, the dependence of the algorithm performance on the accuracy, the number of signal parameters, and the number of signal parameters selected based on the concept of Pareto optimality is presented. The method is a forward selection method based on 300 iterations of three-fold cross-validation.

[0173] Quantification of metabolic activity In addition to the qualitative assessment of the metabolic state of cells by using classification models, the impact of interference in the metabolic activity of cells by drugs can be quantified using regression models. We used the clinical E. coli isolate IMHA-2155385, which is sensitive to the drug combination ceftazidime-avibactam. This cephalosporin / beta-lactamase inhibitor combination attacks the bacterial cell wall synthesis and simultaneously blocks the beta-lactamase mediated resistance mechanism. In Figure 33, we show the results of the regression of the metabolic state induced by various inhibitory concentrations of antibiotics (from 32 μg / ml to 512 μg / ml). The plot shows the relationship between the results of the prediction of the drug concentration by the model based on five signal parameters and the actual drug concentration. The coefficient of determination of the presented models ranges from 0.86 for a single signal parameter to 0.993 for five signal parameters. In Figure 34, the dependence of the algorithm performance on the number of signal parameters selected based on the mean squared error, the number of signal parameters, and the concept of Pareto optimality is shown. The method is a forward selection method based on 10-fold cross-validation. The linking algorithm, which is a linear regression algorithm, is used with the following selected signal parameters: / / - p50_8000-10000_Drug_90-120_mean p10_8000-10000_Drug_90-120_mean - p50_1000-2000_Drug_90-120_mean p10_1000-2000_Drug_90-120_mean / - p50_8000-10000_Drug_0-30_mean p10_8000-10000_Drug_0-30_mean - p50_1000-2000_Drug_0-30_mean p10_1000-2000_Drug_0-30_mean / / p10_6000-7000_Bac_90-120_mean p10_0-10_Bac_90-120_mean / p10_6000-7000_Bac_60-90_mean p10_0-10_Bac_60-90_mean / / p20_6000-7000_Drug_90-120_mean p20_5000-6000_Drug_90-120_mean / p20_6000-7000_Drug_60-90_mean p20_5000-6000_Drug_60-90_mean / / / - p90_7000-8000_Drug_90-120_mean p10_7000-8000_Drug_90-120_mean - p60_7000-8000_Drug_90-120_mean p40_7000-8000_Drug_90-120_mean / - p90_2000-4000_Drug_90-120_mean p10_2000-4000_Drug_90-120_mean - p60_2000-4000_Drug_90-120_mean p40_2000-4000_Drug_90-120_mean / / - p90_7000-8000_Drug_0-30_mean p10_7000-8000_Drug_0-30_mean - p60_7000-8000_Drug_0-30_mean p40_7000-8000_Drug_0-30_mean / - p90_2000-4000_Drug_0-30_mean p10_2000-4000_Drug_0-30_mean - p60_2000-4000_Drug_0-30_mean p40_2000-4000_Drug_00-30_mean / / p30_6000-7000_Drug_60-90_mean p30_5000-6000_Drug_60-90_mean / p30_6000-7000_Bac_60-90_mean p30_5000-6000_Bac_60-90_mean

[0174] The results presented confirm that the present invention makes it possible to measure the increasing effects of metabolic activity associated with increasing drug concentrations. [Explanation of symbols]

[0175] 1. Motion Detector 2 Flexible support 3. Detection Device 4. Evaluation device 5 Radiation source

Claims

1. A method for analyzing the motion activity of a particle using a motion detector (1), wherein the motion detector (1) is A flexible support (2) configured to bend, A detection device (3) for detecting a signal generated when the flexible support (2) is deflected, An evaluation device (4) for evaluating the detected signal, The method comprises, The steps include bringing at least one particle into contact with the flexible support (2), The steps include using the detection device (3) to detect at least one time-dependent signal indicating the deflection of the flexible support (2) due to the motion of at least one particle, The steps include evaluating the detected time-dependent signal using the evaluation device (4), Includes, The evaluation of the detected time-dependent signal is as follows: The process involves analyzing the time dependence of the signal and deriving from the signal a plurality of signal parameters that characterize the fluctuations of the signal as a function of time, The linking algorithm is executed, having an input vector as an input variable that includes at least one selection of the signal parameters, and at least one activity index indicating the motion activity of the particle as an output variable. The method, characterized by including the following:

2. The method according to claim 1, wherein, in the step of analyzing the time dependence of the signal, a plurality of time intervals are defined, the time dependence of the signal is analyzed separately within each time interval to obtain values ​​for each of a plurality of signal estimators for each time interval, and the time series of each signal estimator is analyzed to obtain each of the signal parameters.

3. Each signal estimate is determined by fitting a noise model to the signal and / or by applying at least one statistical algorithm to the signal and / or Each signal estimator is selected from a group consisting of estimators of the moments of the probability density function, the geometric properties of the power spectral density function, the percentiles of the probability density function, the correlation parameter, the partial correlation parameter, the parameters of the autoregressive moving average model, and the parameters of the nonlinear autoregressive moving average model. The method according to claim 2.

4. Each signal estimator is a geometrical characteristic of the power spectral density function. The method according to claim 2 or 3.

5. For each time interval, multiple periodograms are determined. For all periodograms, at least one quantile is determined for at least one frequency range, thereby obtaining the signal estimate. The method according to claim 2 or 3.

6. At least one of the signal estimates, the time series, The combination of at least two signal estimators, their difference and / or ratio, Converting multiple quantiles into empirical probability density function values. It is extended to form an extended time series by at least one of the following: The at least one signal parameter is obtained from the extended time series. The method according to claim 5.

7. At least one signal parameter is derived from at least one of the time series of the signal estimators, and / or from at least one of the extended time series of the signal estimators, Define multiple subseries for the aforementioned time series and / or the aforementioned extended time series, and determine the statistical characteristics of each subseries. Fitting one or more parameterized curves containing one or more parameters to the time series and / or the extended time series, Define multiple subseries for the aforementioned time series and / or the aforementioned extended time series, and for each subseries, fit one or more parameterized curves containing one or more parameters to obtain the fitted parameters, Derived by at least one of the following: The method according to claim 2 or 3.

8. Evaluating the detected time-dependent signal using the evaluation device (4) includes detecting the time-dependent signal during time t, and analyzing the time dependence of the signal. The steps of dividing the signal at time t into time intervals of length T, For each time interval j = 1, ..., t / T, A step of calculating the digital integral of the signal within each time interval, The steps of dividing the aforementioned time interval into at least one number of sub-intervals, For each sub-interval, the step of removing the trend from the digital integral of the signal by applying a trend removal algorithm to the digital integral of the signal, For at least one of the aforementioned partial intervals, the steps of combining the partial intervals with detangled intervals, For at least one number of sub-intervals, determine at least one generalized mean of the de-trended signal of the de-trended interval, thereby obtaining at least one signal parameter. The steps to implement, The method according to claim 1, including the method described in claim 1.

9. The method according to claim 8, wherein at least one signal parameter is derived from a ratio and / or difference between at least two signal parameters.

10. The further includes executing a feature selection algorithm to automatically select a subset of signal parameters and obtaining the input vector to be supplied to the linking algorithm, The method according to claim 1 or 2.

11. The drift cancellation algorithm is applied to the signal before the derivation of the signal parameters from the signal, The method according to claim 1 or 2.

12. The method according to claim 1 or 2, wherein the linking algorithm is a regression algorithm or a classification algorithm.

13. The method according to claim 1 or 2, wherein the linking algorithm is a machine learning algorithm.

14. The method according to claim 1 or 2, wherein the particles are at least one of a cell, prokaryotic cell, eukaryotic cell, spore, virus, phage, vesicle, peptide, protein, polysaccharide, lipid, carbohydrate, nucleic acid or copolymer thereof, protein-RNA copolymer, RNA-DNA copolymer, protein-DNA copolymer, RNA / DNA-protein copolymer, protein-protein copolymer, capsule, organelle, or nanodevice.

15. The method according to claim 1 or 2, wherein the activity indicator represents at least one of the metabolic activity of the particle, the physiological state of the particle, the respiratory level of the particle, the ATP level of the particle, the NADH / NAD+ ratio of the particle, the membrane potential of the particle, the growth rate of the particle, the mortality rate of the particle, the interaction between the particle and other particles, and the interaction between the particle and environmental factors, or any combination thereof.

16. The particles are subjected to at least one chemical stimulus and / or at least one physical stimulus. The method according to claim 1 or 2.

17. The method according to claim 16, wherein the activity index is determined before and / or while the particles are subjected to the chemical and / or physical stimulus, and the activity indexes thus determined are compared with one another.

18. A method for generating training datasets for machine learning algorithms, a) bringing at least one particle into contact with the flexible support (2), b) Using a detection device (3), detect at least one time-dependent signal indicating the deflection of the flexible support (2) due to the motion of at least one particle, c) Evaluating the detected time-dependent signal using an evaluation device (4), wherein the evaluation of the detected time-dependent signal includes analyzing the time dependence of the signal in order to derive from the signal a plurality of signal parameters that characterize the variation of the signal as a function of time, d) Performing independent measurements to derive at least one relevant activity index indicating the motion activity of the particles, e) Storing the plurality of signal parameters and the at least one associated activity index in the training dataset, f) Repeating steps a) to e) for multiple particles exhibiting different kinetic activities, The method, including the method described above.

19. A method for training a machine learning algorithm, wherein the machine learning algorithm is trained using a training dataset generated by the method of claim 18.

20. The method according to claim 4, wherein the geometrical characteristics are the extremum of the power spectral density function, the inflection point of the power spectral density function, the area under the curve described by the power spectral density function, or the horizontal and / or vertical distance between them.

21. The extended time series is obtained by converting a plurality of quantiles into the values ​​of an empirical probability density function, Determining at least one distance between the value of the empirical probability density function and the value of the theoretical probability density function, and / or Determining at least one geometrical property and / or various moments of the empirical probability density function. The method according to claim 6, further formed by...

22. Further determining at least one of the ratio, difference, and ratio of the difference of the statistical characteristics, and / or Further determine at least one of the ratio, difference, and ratio of the difference of the fitted parameters. The method according to claim 7.

23. The method according to claim 10, wherein the feature selection algorithm is configured to select a subset of the signal parameters in such a manner that the subset is optimal for a multi-objective criterion.

24. The drift cancellation algorithm includes a curve fitting procedure or high-pass filtering for modeling the drift component of the signal, and / or The aforementioned drift cancellation algorithm is a trend removal algorithm. The method according to claim 11.

25. The particles are cells, the chemical stimulus is the addition of at least one of the following: a drug, an antibiotic, a compound that affects the metabolism or viability of the cells, or a change in culture conditions or environmental conditions, and / or The aforementioned physical stimulus is the application of stress. The method according to claim 16.

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