A composite signal denoising method for biological cell adhesion force extraction

Abstract

The application discloses a composite signal denoising method for biological cell adhesion force extraction. Firstly, a preliminary treatment is performed on a living cell mechanics parameter collected under a physiological state to obtain a cell force-displacement curve. A Hankle matrix is used to construct the force-displacement data to a two-dimensional matrix space. Secondly, a matrix H constructed by the force-displacement data is decomposed according to a singular value decomposition theory to obtain corresponding left and right singular matrices and singular values arranged in descending order. A slope of singular value change is calculated k Then, several larger singular value points are reserved, and the singular value points are used to approximate the original matrix H to complete matrix reconstruction. A Symlets7 wavelet is selected as a base function to perform four-layer wavelet decomposition on the force-displacement data after singular value decomposition denoising. A hard threshold function is used to perform wavelet reconstruction on the force-displacement data, so that the denoised force-displacement curve is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of cell biomechanics measurement, in particular to a composite signal denoising method for extracting biological cell adhesion force. BACKGROUND

[0002] As the most basic unit of biological structure and function, the activities such as division, migration, differentiation and apoptosis of biological cells are closely related to the physiological activities such as growth and development of organisms, so the in-depth study of biological cell behavior has been widely concerned. Experiments have shown that the mechanical properties of cells play an important role in the behavior of cells, and they play a crucial role in cell processes such as adhesion, migration, signal, sensing and tissue development, especially the properties related to cell deformation such as elasticity and adhesion, which not only participate in the regulation of each process of the cell, but also can reflect the state of the cell in real time. Therefore, the study of the mechanical properties of cells can help to analyze the running mechanism from the physical point of view.

[0003] However, the current nanoindentation technology is mostly based on the morphology map obtained by scanning, and after human observation, the target point is randomly selected at the center position of the morphology map for mechanical characteristic information extraction, and then the mechanical property index is obtained by gradually processing the obtained curve. The measurement technology has certain contingency, and due to the influence of the environment and the limitation of the hardware itself, there will always be a large amount of random noise in the obtained force-displacement data. Noise will affect the judgment of the fracture peak and thus affect the extraction of adhesion force characteristic index, so it is necessary to suppress the noise in the measured force-displacement curve and restore the true force-displacement curve to improve the accuracy of the mechanical property index extraction algorithm. SUMMARY

[0004] In order to solve the above technical problems, the present application provides a composite signal denoising method for extracting biological cell adhesion force.

[0005] In order to achieve the above purpose, the present application is implemented according to the following technical solutions:

[0006] A composite signal denoising method for extracting biological cell adhesion force, comprising the following steps:

[0007] S1, collecting the mechanical properties of living biological cells under physiological conditions: using an atomic force microscope mechanical testing system to perform nanoindentation viscoelasticity test experiment on the surface of living biological cells, and recording the force-displacement curve and force-time curve of the viscoelasticity of the cell surface by performing mechanical test on the cell surface through the approach-hold-withdraw process of the atomic force probe;

[0008] S2, cell viscoelasticity test and mechanical property curve acquisition: determine the mechanical relationship model between the atomic force probe and the cell from the actually measured data, draw the force-displacement curve using the DMT contact model; and delete the loading curve in the force-displacement curve, and only keep the rollback curve, i.e. the mechanical property curve;

[0009] S3, mechanical property curve noise reduction processing: sequentially perform median filter noise reduction processing, singular value decomposition noise reduction processing and wavelet transform noise reduction processing on the noise in the obtained mechanical property curve.

[0010] Further, the median filter noise reduction processing in step S3 includes:

[0011] According to the noise size and signal characteristics in the mechanical property curve, a fixed size sliding window is determined, the data in the window is sorted according to the size, and the middle value is taken as the new value of the current data point. The window is slid to the position of the next data point, and the above steps are repeated until the sliding window traverses the entire signal.

[0012] Further, the singular value decomposition noise reduction processing in step S3 includes:

[0013] A two-dimensional Hankle matrix space is constructed using the mechanical property curve data after median filter noise reduction processing: Wherein, N is the number of data in the force-displacement curve; L is the length of the set intercept window; when N is even, L takes the value of N / 2, and when N is odd, L takes the value of (N-1) / 2; the Hankle matrix is decomposed according to A=UΣV T , to obtain singular matrices and singular values U, V T , Σ; wherein U is an m-order square matrix orthogonal to each other between rows and columns, which is a set of unit orthogonal bases of AA T ; V T (V transpose matrix) is an n-order square matrix orthogonal to each other between rows and columns, and Σ is an m-row n-column diagonal matrix whose diagonal elements are the singular values of A; according to the singular values, the slope k of the change is calculated: Wherein: (p n , q n ) is the coordinate of the nth singular value, (p n-1 , q n-1 ) is the coordinate of the n-1th singular value, and s is the total number of singular values; a number of larger singular value points are retained, and the approximate matrix H is removed, and the front and rear rows of data can retain the main information of the mechanical property, thereby reducing the memory requirement of data storage.

[0014] Further, the wavelet transform noise reduction processing in step S3 includes:

[0015] The Symlets wavelet family is selected for wavelet decomposition. j，k The fixed threshold denoising is carried out. Wherein, N is the data length, lambda is the threshold size, and sigma is the standard deviation of noise.

[0016] Compared with the prior art, the cell mechanics parameter collected under the physiological state is preliminarily processed to obtain the cell force-displacement curve, which is used for subsequent denoising processing. The Hankle matrix is used to construct the force-displacement data to the two-dimensional matrix space, and then the matrix H constructed by the force-displacement data is decomposed according to the singular value decomposition theory to obtain the corresponding unit orthogonal bases and the singular values arranged in descending order. Next, the slope k of the singular value change is calculated, a plurality of larger singular value points are retained, the singular value points are used to approximate the matrix H for matrix reconstruction, the force-displacement data after singular value decomposition denoising is selected as the base function for 4-layer wavelet decomposition, the hard threshold function is selected as the threshold function, the fixed threshold denoising is carried out, the wavelet reconstruction of the force-displacement data is carried out, and the denoised force-displacement curve is obtained. Therefore, the present application can effectively remove the random noise caused by environmental influence and equipment hardware limitation, solve the problem of too many interference values in the extracted force-displacement curve in the cell adhesion force characteristic index extraction process, and prove the superiority of the denoising algorithm from the simulation and experimental data. The force-displacement data of each point on the cell surface is extracted, and the real force-displacement curve is restored, so that the accuracy of the mechanics characteristic index extraction algorithm is improved. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 The flowchart of an embodiment of the present application.

[0018] Figure 2 The partial curve graph used in the present application.

[0019] Figure 3 The simulation original signal curve graph used in the present application.

[0020] Figure 4 The simulation denoised signal curve graph used in the present application.

[0021] Figure 5 The force-displacement curve graph obtained by denoising the actually measured partial curve by using the median filtering, singular value decomposition and wavelet transformation in the present application.

[0022] Figure 6 The composite denoising method used in the application is compared with other common denoising methods in terms of denoising effect on actual measured force-displacement signals. DETAILED DESCRIPTION

[0023] To make the objectives, technical solutions and advantages of the application clearer, the application will be further described in detail below with reference to examples. The specific examples described herein are only used to explain the application and do not limit the application.

[0024] As shown in Figure 1 , the embodiment exemplarily provides a composite signal denoising method for extracting biological cell adhesion force, comprising the following steps:

[0025] S1, collecting the mechanical properties of living cells under physiological conditions: performing nanoindentation viscoelasticity test experiment on the surface of living cells by using an atomic force microscope mechanical test system, performing mechanical test on the surface of cells through the approach-hold-withdraw process of the atomic force probe, and recording the force-displacement curve and force-time curve of the viscoelasticity of the cell surface;

[0026] S2, cell viscoelasticity test and mechanical property curve acquisition: determining the mechanical relationship model between the atomic force probe and the cell from the actual measured data, and drawing the force-displacement curve by using the DMT contact model; and deleting the loading curve in the force-displacement curve and only retaining the back-off curve, i.e. the mechanical property curve, as shown in Figure 2 ;

[0027] S3, denoising processing of the mechanical property curve: sequentially performing median filter denoising processing, singular value decomposition denoising processing and wavelet transform denoising processing on the noise in the obtained mechanical property curve;

[0028] The median filter denoising processing comprises:

[0029] According to the size of the noise in the mechanical property curve and the signal characteristics, a fixed-size sliding window is determined, the data in the window is sorted according to the size, and the middle value is taken as the new value of the current data point. The window is slid to the position of the next data point, and the above steps are repeated until the sliding window traverses the entire signal.

[0030] The singular value decomposition denoising processing comprises:

[0031] The mechanical property curve data after the median filter denoising processing is used to construct a two-dimensional Hankle matrix space: Wherein, N is the number of data in the force-displacement curve; L is the length of the set intercept window; when N is even, L takes the value of N / 2, and when N is odd, L takes the value of (N-1) / 2; the Hankle matrix is constructed according to A=UΣV TDecomposition is carried out to obtain singular matrix and singular value U, V T , Σ; wherein U is an m-order matrix orthogonal between rows and columns, and is a set of unit orthogonal bases of AA T ; V T (V transpose matrix) is an n-order matrix orthogonal between rows and columns, and Σ is an m-row n-column diagonal matrix, diagonal elements of which are singular values of A; according to the singular value, the slope k of the change is calculated: Wherein: (p n , q n ) is the coordinate of the nth singular value, (p n-1 , q n-1 ) is the coordinate of the (n-1)th singular value, and s is the total number of singular values; the singular value point with the largest slope and all singular values before it are retained, and the singular values after it are set to zero, then the data is reconstructed into a matrix, and the data in the first row and the last column of the data matrix are extracted to obtain the effective force-displacement curve data containing a small amount of noise.

[0032] The wavelet transform denoising processing includes:

[0033] The Symlets wavelet family is selected for wavelet decomposition. For different wavelet basis function lengths and decomposition scales of the Symlets series, the Symlets7 wavelet function with a wavelet decomposition scale of 4 is selected as the basis function for processing the mechanical property data, the obtained wavelet decomposition coefficients W j，k are recorded, and fixed threshold denoising is adopted: Wherein: N is the data length, λ is the threshold size, and σ is the standard deviation of noise; according to the processed wavelet decomposition coefficients, wavelet reconstruction is performed on the force-displacement data to obtain the denoised force-displacement curve.

[0034] In order to verify the feasibility of the denoising method of the present application, simulation signal effect evaluation and denoising effect test are carried out respectively. Among them:

[0035] The simulation signal effect evaluation is specifically:

[0036] Based on the DMT cell model, the simulation force-displacement data without noise is set as: The simulation original signal curve is shown in Figure 3 ; wherein A0 is a probe related constant, which is set as -1 according to idealized parameters; A1 is the curve offset of the adhesion part, which is set as 0.25 for the convenience of combining with the elastic part curve; D is the curve segmentation point, which is 2048nm; the elastic part parameters a0 is 1 and a1 is 0 are determined according to the adhesion part curve. Considering the possible noise environment, 6db Gaussian white noise is introduced as random noise, and four narrow-band noises with different frequencies are superimposed to simulate the noise signal: Wherein: wgn is Gaussian white noise; A iFor the amplitude of the interference noise, the amplitudes of the four narrow-band noises are 0.1nN, 0.1nN, 0.2nN, and 0.2nN, respectively; f i For the frequency of the interference noise, the four frequencies are 1kHz, 2kHz, 3kHz, and 4kHz, respectively; For the initial phase of the interference noise, the four phases are set to 30°, -30°, 0°, and 60°, respectively; a simulated noisy signal curve is shown in Figure 4 .

[0037] Then, the noisy signal is denoised by using the median filtering denoising method, the singular value decomposition denoising method, and the wavelet transform denoising method. The first 10 singular values are plotted, and the maximum slope point is calculated. According to the calculated slope, the first two singular values are retained, and all the singular values except the first two singular values are set to zero. The matrix is reconstructed to obtain the signal after singular value decomposition denoising. For the signal obtained after singular value decomposition, the Symlets series wavelet is selected as the wavelet basis function. After comparison based on the signal-to-noise ratio, root mean square error, and other criteria, the Sym7 is selected as the wavelet basis function for further denoising. The denoising result is shown in Figure 5 .

[0038] The denoising effect test is as follows:

[0039] For the real force-displacement data, the fitting curve reliability of the force-displacement data is evaluated by using the curve fitting goodness evaluation after denoising by using the median filtering, singular value decomposition, and wavelet transform according to the algorithm design scheme. The calculated fitting curve is obtained after the composite denoising method.

[0040] In addition, in some embodiments, other denoising methods are used for comparison with the denoising method of the present application, and the results are shown in Figure 6 The atomic force microscope is used to perform nanoindentation on liver cancer cells SMCC-7721 by using a four-pyramid probe. The maximum indentation depth of the liver cancer cells is 0.6 microns, and the maximum stress is 4.2nN. After the relevant mechanical parameters are obtained by processing the data by using the DMT contact model, it is determined that the elastic modulus range is 0.9-3.2Kp. After median filtering denoising processing, a suitable window size is selected and applied to the entire signal. In each window, the median value is assigned to the center of the window to obtain a preliminary denoised signal. After singular value decomposition of the preliminary denoised signal, a singular value sequence is obtained, and a singular value curve is plotted. The point with the maximum slope value is retained, and the data matrix is reconstructed to obtain a further denoised signal. The further denoised signal is decomposed into four layers according to the sym7 wavelet, and the wavelet is reconstructed to obtain Figure 6 the curve after composite denoising, and the FIR high-pass filter curve and the emd denoising curve obtained by using other denoising methods are compared to obtain Figure 6The cell mechanics data is denoised by median filtering, singular value decomposition and wavelet transform, and the force displacement curve has good denoising effect, and the force-displacement curve after the composite denoising method is fitted, and the fitting degree is 0.9529, so the baseline determined according to the method has high reliability, and it is also proved from another aspect that the DWT model has higher matching degree on the force-displacement data under the experimental conditions of the present application, and is superior to the traditional mechanical modeling method.

[0041] The technical scheme of the present application is not limited to the above specific embodiments, and any technical modification made according to the technical scheme of the present application falls within the protection scope of the present application.

Claims

1. A composite signal denoising method for extracting biological cell adhesion force, characterized in that: The following steps are involved: S1. Collecting the mechanical properties of living cells under physiological conditions: Nanoindentation viscoelasticity tests were performed on the surface of living cells using an atomic force microscope mechanical testing system. The atomic force probe was used to perform mechanical tests on the cell surface's undulating morphology during the approach-hold-withdraw process, recording the force-displacement curves and force-time curves of the cell surface's viscoelasticity. S2. Cell viscoelasticity testing and mechanical property curve acquisition: Determine the mechanical relationship model between the atomic force probe and the cell from the actual measurement data, and use the DMT contact model to draw the mechanical property curve of the hold-withdraw process; S3. Noise reduction processing of mechanical characteristic curve: performing median filtering noise reduction processing, singular value decomposition noise reduction processing and wavelet transform noise reduction processing on the noise in the obtained mechanical characteristic curve in sequence.

2. The composite signal denoising method for extracting biological cell adhesion force according to claim 1, characterized in that: The median filtering noise reduction process in step S3 includes: A fixed-size sliding window is determined based on the noise level and signal characteristics in the mechanical characteristic curve. The data in the window is sorted by size, and the middle value is taken as the new value of the current data point. The window is slid to the position of the next data point and the above steps are repeated until the sliding window traverses the entire signal.

3. The composite signal denoising method for extracting biological cell adhesion force according to claim 2, characterized in that: The singular value decomposition denoising process in step S3 includes: The two-dimensional Hankle matrix space is constructed using the mechanical characteristic curve data after median filtering noise reduction: ; Where N is the number of data in the force-displacement curve; L is the length of the set interception window; when N is an even number, L is N / 2, when N is an odd number, L is (N-1) / 2; the Hankle matrix is ​​A=UΣV T Decompose to obtain singular matrix and singular values U 、V T ,Σ; where U is an m-order square matrix with orthogonal rows and columns, which is AA T A set of unit orthogonal bases; V T (The transposed matrix of V) is an n-order square matrix with orthogonal rows and columns. Σ is an m-row, n-column diagonal matrix whose diagonal elements are the singular values ​​of A. The slope k of its change is calculated based on the singular values: Among them: (p n ,q n ) is the coordinate of the nth singular value, (p n-1 ,q n-1 ) is the coordinate of the n-1th singular value, and s is the total number of singular values; retaining several larger singular value points to approximate the matrix H, and taking one row of data before and after can retain the main information of the mechanical properties, thus reducing the memory requirements for data storage.

4. The composite signal denoising method for extracting biological cell adhesion force according to claim 3, characterized in that: The wavelet transform noise reduction process in step S3 includes: The Symlets wavelet family is selected for wavelet decomposition. In view of the different lengths and decomposition scales of the wavelet basis functions of the Symlets series, the Symlets7 wavelet function with a wavelet decomposition scale of 4 is selected as the basis function for mechanical property data processing. The obtained wavelet decomposition coefficients are Record; use fixed threshold to denoise: ;in: N is the data length, is the threshold size, is the standard deviation of the noise; according to the wavelet decomposition coefficients recorded after processing, the force-displacement data is reconstructed by wavelet to obtain the denoised force-displacement curve.

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