A machine active learning method for calculating elastic modulus of cells on substrates

Abstract

The present invention belongs to the field of cell mechanics and relates to a machine active learning method for calculating the elastic modulus of cells on a substrate. The present invention can accurately extract the cell elastic modulus E c , and eliminate the influence of indentation depth d, cell radius R, probe radius r, cell thickness t, and substrate stiffness E s on the extraction of E c . This means that the influence caused by not satisfying the small deformation assumption, the infinite half-space assumption, and substrate deformation can be effectively eliminated. Compared with traditional machine learning methods, the AL model method can effectively screen the data set and automatically find the data that can significantly improve the model accuracy. It takes both computational accuracy and computational efficiency into account. The modeling process of the method of the present invention is simple, avoiding complex equation solving. At the same time, the influence of multiple factors can be considered during modeling.

Description

Technical Field

[0001] The invention belongs to the field of cell mechanics and relates to a machine active learning method for calculating the elastic modulus of cells on a matrix. Background Art

[0002] Studies have shown that the cell elastic modulus (E c ) is affected by the elastic modulus of the matrix (E s ) and is associated with cell growth, proliferation, differentiation, and migration. For example, E c With E s The increase of E c Cells with higher expression levels showed higher growth and proliferation abilities and lower drug resistance. The migration ability of mouse embryonic fibroblasts showed similar c Neural stem cell E c On softer gels, E is lower and tends to differentiate into neurons; on stiffer gels, E c higher, and tend to differentiate into glial cells. c It has been used as an important mechanical index to correlate matrix stiffness with cell biological behavior.

[0003] From a mechanical perspective, changes in the elastic modulus of cells caused by the matrix may come from two aspects: (1) intrinsic changes in cell composition and structure. (2) The elastic modulus E c The error caused by the extraction method. At present, the Hertz model is often used to fit the atomic force microscope (AFM) indentation curve. The Hertz model (Formula 1) is used to extract E c .

[0004]

[0005] Where P is the indentation force, E is the elastic modulus, μ is Poisson's ratio, r is the probe radius, and d is the indentation depth.

[0006] The use of the Hertz model to extract the elastic modulus of cells may result in errors due to the following reasons: (1) The small deformation assumption and the infinite half-space assumption cannot be well satisfied. In AFM indentation cell experiments, the indentation depth and the probe radius are usually of the same order of magnitude. This is because the ratio of the compression depth to the cell thickness must exceed a certain value to ensure that the determined contact point does not significantly affect the calculation results. Therefore, limiting the ratio of the compression depth to the probe radius to satisfy the small deformation assumption is not applicable to cell indentation. In addition, since the cell size cannot be regarded as an infinite half-space relative to the size of the probe, the extracted E c(2) In the AFM indentation experiment, the matrix to which the cells are attached will deform due to the force applied by the AFM probe. The actual indentation depth measured by AFM is the sum of cell deformation and matrix deformation, but the Hertz model cannot eliminate matrix deformation.

[0007] In order to more accurately calculate E c , to reduce the impact of the calculation method, the Hertz correction model was proposed to reduce the impact of the indentation depth, and the CoCS model was proposed to reduce the impact of matrix deformation. However, there is no more advanced method that can eliminate the above errors at the same time. This is because considering multiple influencing factors will make it difficult to establish and solve the Hertz correction model. Introducing a machine learning model that is good at establishing a nonlinear relationship between input and output variables can effectively solve the problem of considering multiple variables. However, the accuracy of traditional machine learning models depends on the training data. Blindly training with a large amount of data will increase the burden of data collection and training processes and make modeling inefficient. However, training with a small amount of random data will significantly reduce the accuracy of the model. Therefore, to eliminate the impact of multiple errors on the extracted E c The key challenge is how to use algorithms to select the data sets that are most needed for training, and to improve the calculation accuracy as much as possible with as little data as possible, so as to balance calculation efficiency and accuracy.

[0008] This patent introduces active learning (AL) for the first time to solve this problem. ABAQUS finite element analysis (FE) is used to simulate the cell deformation scenarios on different substrates in the AFM indentation experiment to provide data. The established AL model can automatically find data that can significantly improve the accuracy of the model to establish a nonlinear correspondence between input variables and output variables, thereby establishing a model that can be used to extract the elastic modulus of cells on the substrate. Compared with traditional machine learning models, the introduction of the AL model not only significantly saves the time of finite element analysis, but also improves the prediction accuracy of the model. Summary of the invention

[0009] This patent uses ABAQUS finite element analysis (FE) to simulate the deformation scenarios of cells on different substrates in AFM indentation experiments to provide data. An AL model is established that can automatically find data that can significantly improve the accuracy of the model. The introduction of the AL model can significantly reduce the FE time and greatly improve the prediction accuracy of the model. Finally, an effective model that can be used to extract the elastic modulus of cells on the substrate is established.

[0010] The present invention is implemented according to the following technical solutions:

[0011] An active learning method for calculating the elastic modulus of cells on a substrate, the steps are as follows:

[0012] The first step is to set the finite element calculation parameters. The data is obtained through numerical calculation using the finite element software ABAQUS, and the cell model is a homogeneous cylinder. The schematic diagram of the parameters that need to be set for finite element modeling is as follows Figure 2 As shown. According to the actual working conditions, the cell thickness t, cell radius R, probe radius r, cell elastic modulus E are set respectively. c , matrix elastic modulus E s , probe displacement. Since the probe ball hardly deforms during the indentation process, the probe is set as a rigid body.

[0013] The second step is to establish a finite element calculation model. The bottom of the matrix is ​​set to be fixed and the side is free. The cells are set to be bound to the matrix. An axisymmetric model is created in ABAQUS. The unit is set to CAX4RH. A mesh convergence analysis is performed, and a mesh size with high calculation accuracy and efficiency is selected for calculation. Through ABAQUS parametric modeling and multiple calculations, the relationship between the compression force P and the indentation depth d is extracted.

[0014] The third step is to establish the AL model and adopt the committee query method. The process is as follows Figure 3 As shown. First, the number of initial committees is set to N according to the requirements, and each model of the committee is named m j (j≤N). The committee query method needs to evaluate an initial data set with n data points first. The initial data set is the starting data set for the AL model iteration, which needs to be obtained by setting different finite element calculation parameters in the first step. The error rate σ is calculated using Equation 2.

[0015]

[0016] where f j is the neural network model corresponding to member j. The calculation result is. X i =[x 1 , x 2 , x 3 , x 4 ] i represents the i data point. target The neural network model is built using the open source framework pytorch. The input layer of the network structure has 4 neurons and requires four variables x 1 , x 2 , x 3 , x 4 As input. The output layer has 1 neuron, representing the label y. Except for the output layer, the activation function of each layer uses the nonlinear LeakyReLU function. The loss function is the mean square error loss function. The optimization function is the Adam algorithm.

[0017] The error rate σ is calculated to screen the members of the initial committee. The initial committee trains the initial data set until convergence and calculates the error rate σ. Committee members with an error rate σ < 10% are considered qualified. Unqualified committee members are removed and the remaining m models form a new committee. The new committee evaluates the parameter space used in the finite element modeling set in the first step and evaluates the new data points that need to be put into training. The evaluation criteria of the committee are defined as Equation 3.

[0018]

[0019] is the average of the predictions of the m members. In each iteration, the top data points of η are found, calculated by FE, and merged with the initial data set to form a new data set. The merged data set is retrained until convergence to evaluate the test data set. The test data set does not participate in the training and needs to be obtained by finite element calculation. After completing multiple iterations, when the error rate defined in Equation 4 is When , the data set is considered to be converged, and the AL model is completed, which can be used for the accurate calculation of the cell elastic modulus.

[0020]

[0021] The present invention has the following technical advantages:

[0022] (1) Accurately extract the cell elastic modulus E c , eliminating the indentation depth d, cell radius R, probe radius r, cell thickness t, matrix stiffness E s That is to say, the influence of not satisfying the small deformation assumption, the infinite half-space assumption, the matrix deformation, etc. on Ec can be effectively eliminated at the same time.

[0023] (2) Compared with traditional machine learning methods, the AL model method can effectively screen the data set and automatically find data that can significantly improve the model accuracy, taking into account both computational accuracy and computational efficiency.

[0024] (3) The modeling process of the method is simple, avoiding the need to solve complex equations. At the same time, the influence of multiple factors can be directly considered during modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Flowchart for modeling the Al model in the technical implementation solution;

[0026] Figure 2 Schematic diagram of the finite element calculation and all considered variables;

[0027] Figure 3 It is the specific iterative process diagram of the AL model;

[0028] Figure 4 Compute comparison charts for traditional machine learning models and AL models;

[0029] Figure 5 This is the AL model prediction error rate graph;

[0030] Figure 6 This is the predicted value diagram of the AL model under different input parameters. DETAILED DESCRIPTION

[0031] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions. Figure 2 is a schematic diagram of the model with finite element calculation and all considered variables. Figure 3 It is the specific iterative process of the AL model. Figure 4 is the error rate of the traditional machine learning model and AL model Comparison of the amount of data required. Figure 5 is the prediction error rate of the AL model.

[0032] Example 1

[0033] According to the first step of the technical solution, set the finite element parameters, such as Figure 2 As shown, the cell thickness t is set to 10 μm, the cell radius R is set to 8 μm to 50 μm, and the probe radius r is set to 2 μm to 20 μm. Cell elastic modulus E c Set to 2 kPa, the matrix elastic modulus E s The pressure was set to 0.4 kPa to 20 kPa. The probe displacement was set to 0.1 μm to 2 μm. The matrix radius was set to 500 μm and the thickness was set to 100 μm. The cell and matrix Poisson's ratio was set to 0.49.

[0034] Step 2: Set the AL model parameters. N is set to 50. In the initial data set, d is set to (0.1, 0.6, 1.1, 1.6) in μm. r is set to (2, 8, 14) in μm. R is set to (8, 20, 32, 44) in μm. E s The data are set to (0.4, 2.4, 4.4, 6.4, 8.4, 10.4, 12.4, 14.4, 16.4, 18.4) in kPa, with a total of 480 data. The error rate σ is calculated using equation 2 to screen the committee members, and the result is that 30 committee members are qualified. In the test data set, d is set to (0.25, 0.45, 0.65, 0.85, 1.05, 1.25, 1.45, 1.65, 1.85) in μm. r is set to (5, 7, 9, 11, 13, 15, 17) in μm. R is set to (11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31) in μm. E sSet to (1, 3, 5, 7, 9, 11, 13, 15, 17) units kPa. Figure 3 The iterative calculation is performed as shown in the figure. Each iteration finds the top 200 data points of η. After 7 iterations, the error rate When the model converges, the AL model is built. The AL model error rate The amount of data required is much smaller than that of traditional methods, such as Figure 4 The prediction error rate of the AL model is shown in 5. It can be seen that the predicted value and the label value have good consistency. The AL model makes predictions under different input parameters and compares them with the existing models. It can be seen that the AL calculation accuracy is good. Figure 6 shown.

[0035] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. An active learning method for calculating the elastic modulus of cells on a substrate, It is characterized in that Here are the steps: The first step is to set the finite element calculation parameters; the data is obtained through numerical calculation of the finite element software ABAQUS, and the cell model is a homogeneous cylinder; the cell thickness t, cell radius R, probe radius r, cell elastic modulus E are set respectively. c , matrix elastic modulus E s , probe displacement; set the probe to a rigid body; The second step is to establish a finite element calculation model; the bottom of the matrix is ​​set to be fixed and the side is free; the cells are set to be bound to the matrix; Create an axisymmetric model in ABAQUS; the unit is set to CAX4RH; Conduct mesh convergence analysis, select mesh size with higher calculation accuracy and efficiency for calculation, and extract the relationship between compression force P and indentation depth d through ABAQUS parametric modeling and calculation; The third step is to establish the AL model and adopt the committee query method. First, the number of initial committees is set to N according to the requirements, and each model of the committee is named m. j (j≤N); The committee query method needs to evaluate the initial data set with n data points first, and the initial data set is the starting data set of the AL model iteration, which needs to be obtained by the user through the first step of setting different finite element calculation parameters; use formula (2) to calculate the error rate σ; Where: y target Indicates a label; The error rate σ is calculated to screen the members of the initial committee; the initial committee trains the initial data set until convergence and calculates the error rate σ; the committee members with an error rate σ < 10% are considered qualified; unqualified committee members are eliminated, and the remaining m models form a new committee; the new committee evaluates the parameter space used in the finite element modeling set in the first step and evaluates the new data points that need to be put into training; the evaluation criteria of the committee are defined as formula (3); in, is the average of the predictions of m members; In each iteration, the data points with the highest η ranking are found, calculated by FE, and merged with the initial data set to form a new data set; the merged data set is retrained until convergence to evaluate the test data set; the test data set does not participate in the training and needs to be obtained through finite element calculation; after completing multiple iterations, when the error rate defined in formula (4) When , the data set is considered to be converged, and the AL model is completed for the accurate calculation of the cell elastic modulus; 2. An active learning method for calculating the elastic modulus of cells on a substrate as claimed in claim 1, It is characterized in that In the third step, the output layer has one neuron, representing the label y; except for the output layer, the activation function of each layer uses the nonlinear LeakyReLU function; the loss function is the mean square error loss function; and the optimization function is the Adam algorithm.

3. An active learning method for calculating the elastic modulus of cells on a substrate as claimed in claim 1 or 2, It is characterized in that In the first step, the cell and matrix Poisson's ratio was set to 0.

49.

4. An active learning method for calculating the elastic modulus of cells on a substrate as claimed in claim 1 or 2, It is characterized in that In the first step, the cell thickness t is set to 10 μm, the cell radius R is set to 8 μm to 50 μm, and the probe radius r is set to 2 μm to 20 μm; the cell elastic modulus E c Set to 2 kPa, the matrix elastic modulus E s Set to 0.4kPa~20kPa.

5. An active learning method for calculating the elastic modulus of cells on a substrate as claimed in claim 3, It is characterized in that In the first step, the cell thickness t is set to 10 μm, the cell radius R is set to 8 μm to 50 μm, and the probe radius r is set to 2 μm to 20 μm; the cell elastic modulus E c Set to 2 kPa, the matrix elastic modulus E s Set to 0.4kPa~20kPa.

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