Method for evaluating mechanical properties of live cell surface based on gsa-optimized neural network

Abstract

The application provides a GSA-based optimization neural network representation method for evaluating biological cell mechanical characteristics, and belongs to the fields of micro-nano manipulation technology and cell biomechanics. The method obtains the surface mechanical characteristic parameters of biological cells under physiological conditions by using a nanoindentation technology, establishes a single-factor multi-level cell biomechanics sample set by using a factorial design method, and carries out neural network optimization on the sample set to inversely calculate a cell mechanics model. The neural network clustering analysis of the mechanical data of different types of cells in different regions solves the difficulty that the surface mechanical parameters in the cell mechanical characteristics cannot be subjected to clustering analysis. The network weight values of the neural network are optimized by combining a simulated annealing algorithm with a genetic algorithm, so that the problems of being easily trapped in a local minimum and a convergence speed in the weight value optimization process are solved. The optimization neural network is used for modeling, so that the cell mechanics evaluation result has good generalization ability and conforms to the biological cell mechanics law.

Description

Technical Field

[0001] This invention relates to the fields of micro-nano manipulation technology and cell biomechanics, and particularly to a method for evaluating the mechanical properties of biological cells based on GSA-optimized neural networks. Background Technology

[0002] The study of biomechanics is crucial for understanding various fundamental cellular behaviors, such as movement, differentiation, and proliferation, and has attracted significant attention in the fields of tissue engineering, cell biology, and cancer therapy. [1] In recent years, experts and scholars both domestically and internationally have conducted extensive experimental research on biomechanics, with particular focus on the mechanical properties of single cells. Studies have shown that the mechanical properties of cells play a crucial role in physiological activities such as cell migration, division, differentiation, adhesion, and nanoparticle endocytosis. Research on the mechanical properties of single cells will help us better understand the pathogenesis of diseases (including cancer) and provide theoretical basis and new research methods for early disease screening and diagnosis. [2] Therefore, the precise measurement of cellular mechanical properties is of great significance for understanding the nature of life activities and maintaining human health.

[0003] However, the constitutive equations of cells measured by researchers based on different linear viscoelastic models are still difficult to unify. Often, a large number of viscoelastic parameters are needed to fit the measurement data from their own experiments, yet they cannot predict the mechanical response of the same cells under different loading conditions in other researchers' experiments. In the development of mechanics, researchers often conduct theoretical analysis by proposing idealized mechanical models. These idealized models generally have relatively regular geometric shapes, boundary conditions, and material response functions described by explicit expressions, abstracting real complex mechanical problems into simple mathematical models, and then seeking analytical solutions. The emergence of computational mechanics methods has made it possible to solve problems with more complex geometric models and boundary conditions. [3] Neural networks have advantages in this regard. First, supervised learning of neural networks can quickly obtain the mapping relationship between input and output based on iterative learning of known examples. This mapping relationship is represented in the form of connection weights and thresholds, similar to neurons in the brain, and can describe various nonlinear relationships. [4] Secondly, neural networks have generalization ability, meaning that they can still produce reasonable outputs for data that were not encountered during the training (learning) process.

[0004] However, in practical applications, the difference surface of the BP network has many local minima. Under certain initial conditions, the algorithm's results may get stuck in local minima, and the convergence speed of the BP network training is very slow. Considering that SA has the ability to escape local optima but has a slow convergence speed, while GA can converge faster due to its simple data processing method, this paper proposes a method to improve the mechanical model established by the neural network based on GSA, making it more universally applicable.

[0005] [1]Ding Yue, Xu Guang-Kui, Wang Gang-Feng. On the determination of elastic moduli of cells by AFM based indentation.[J]. Scientific reports, 2017, 7{5}.

[0006] [2] Bu Yang. Measurement of cell viscoelastic mechanical properties based on atomic force microscopy [D]. Lanzhou University, 2020.

[0007] [3]Belytschko T, Liu WK, Moran B, et al. Nonlinear Finite Elements for Continua and Structures. Hoboken: John Wiley & Sons, 2013.

[0008] [4] HAYKIN S. Neural Networks and Machine Learning [M]. 3rd ed. Beijing: China Machine Press, 2016: 1-22. Summary of the Invention

[0009] This invention addresses the problem of overcoming the shortcomings of existing technologies by providing a method for characterizing and evaluating the mechanical properties of biological cells based on a GSA-optimized neural network, characterized by high fitting accuracy. Appropriate mechanical models can be established for different cell types based on their mechanical parameters, helping researchers to study cell mechanical characteristics more quickly and accurately.

[0010] The technical solution adopted by this invention to solve the technical problem is as follows: A method for evaluating the mechanical properties of biological cells based on GSA optimized neural network: collecting the mechanical properties of living biological cells under physiological conditions, cell viscoelasticity testing, creating a sample set of cell mechanical parameters, GSA neural network optimization algorithm, prediction of cell surface mechanical features, cell surface mechanical modeling, cluster analysis of cell mechanical parameters, and cell mechanical evaluation model.

[0011] The specific steps are as follows.

[0012] Step 1: Collect biomechanical properties of living cells under physiological conditions. Conduct cell mechanical property experiments using an atomic force microscopy system under physiological conditions. Use an atomic force probe to perform a mechanical test on the undulating morphology of the cell surface through an approximation-hold-withdrawal process. Record cell mechanical parameters and store the data in a spreadsheet. Ensure the reproducibility of the experiment and the good condition of the cells by using room temperature, liquid phase, and probe amplitude uniformity.

[0013] Step 2: Cell viscoelasticity test. A self-built viscoelastic model is used to describe the cell's mechanical characteristics, employing either the Hertz or Sneddon model to obtain the elastic modulus at each point on the cell. Preliminary screening of cell parameters is performed during the viscoelasticity test to ensure that the error is within an acceptable range.

[0014] Step 3: Create a sample set of cell mechanical parameters. Filter the mechanical characteristic parameters and their value ranges using mechanical data obtained from mechanical tests. Divide each parameter into equal levels and remove extreme values. Construct a calculation scheme based on factorial design, and generate training samples after finite element simulation. The training samples are further divided into training set, validation set, and test set in a 70%, 15%, and 15% ratio, respectively.

[0015] Step 4: GSA Neural Network Optimization Algorithm. First, the overall programming and modeling are performed in the data analysis software. The overall structure of the neural network is constructed based on the sample set obtained from factorial design. Then, the GA genetic algorithm is initialized according to the preset number of input and output nodes and connection method of the network. Parametric encoding is used to construct a six-dimensional structure from the contact point depth, contact point stress, overall cell height, local elastic modulus of the cell, viscoelastic coefficient, and relaxation time in the sample set as the initial population. The maximum number of iterations for the population is 100, the population size is 50, and the crossover and mutation probabilities are 0.1 and 0.3, respectively. Next, the initial temperature and cooling coefficient of the simulated annealing are initialized, with T0=100 and alpha=0.8, respectively.

[0016] Genetic iteration is performed within a simulated annealing loop. First, the initially trained network weights undergo elite-mode genetic iteration. If the fitness value of the best individual in the offspring population is less than the fitness value of the best individual in the current population, then the best individual in the current population, or multiple individuals with fitness values ​​greater than the best offspring individual's fitness, are directly copied to the offspring, randomly replacing a corresponding number of individuals in the worst-performing next generation. After each iteration, the current temperature is determined, and a new fitness function is applied. This loop is repeated until the periodic cooling reaches the termination temperature, yielding the optimal network weights. Based on these weights, the input-output relationship is predicted.

[0017] Step 5: Predicting cell surface mechanical features. Using the established neural network model, numerical calculations are performed to obtain new force-displacement curve feature data. The difference between this data and the force-displacement curve data measured in mechanical experiments is used as an optimization clue. The error formula is as follows: F1 and F2 are simulated characteristic stress values, and Fr and Fe are the stress values ​​at the needle insertion point and curve indentation point and peak point in the actual measurement, respectively. The optimal parameters are obtained through the parameter optimization algorithm, which are the characterization values ​​of the cell in the current region. Based on this, the same type of cells are collected multiple times and in multiple regions at different times to obtain mechanical parameters under different conditions, and the cell mechanical characteristics are extracted through the neural network algorithm.

[0018] Step 6: Cell surface mechanical modeling. The obtained mechanical parameters representing different regions of the cell are re-introduced into the original self-built model to obtain the current mechanical model of the cell, and the error rates of the traditional model, neural network and GSA optimized network are compared.

[0019] Step 7: Cluster analysis of cell mechanical parameters. Based on numerical simulation, the upper and lower limits of cell elastic modulus and adhesion force are determined. The two parameters and their corresponding cell height positions are input into a BP neural network for cluster analysis, and the distribution of mechanical parameters is marked according to the gridded positions.

[0020] Step 8: Cell mechanical assessment model, used to establish the mechanical distribution characteristics of different cell types, retrain the neural network to obtain its mechanical model.

[0021] Furthermore, the mechanical properties of living biological cells under the physiological state are collected, and a nanoindentation viscoelasticity test experiment is performed on the cell surface to obtain the force-displacement curve and force-time curve of cell surface viscoelasticity, as well as mechanical parameters such as indentation depth, holding time, contact stress, and cell height.

[0022] Furthermore, the cell viscoelasticity test, using the Hertz model, is... Suitable for atomic force probes with microspherical tips; the Sneddon model is... Suitable for atomic force probes with tapered tips, used to record the mechanical parameters of the approach-hold-withdrawal process on the cell surface, among which... It is the normal pressure applied to the probe. The radius of the microsphere probe tip. It is the depth of the indentation. It is half the angle of a cone. It is the elastic modulus of the sample. The sample Poisson's ratio (generally considered to be 0.5); the self-built viscoelastic model is... Where E is the effective elastic modulus, F is the contact stress, h is the indentation depth, and α is the probe half-angle. Adhesion work is a quantitative relationship established between cell height, adhesion work, and contact stress elastic modulus.

[0023] Furthermore, the sample set of cell mechanical parameters is selected and determined to include the contact stress at the contact point, the contact stress at which the indentation peak is reached, the cell height, and the indentation depth, while the output mechanical parameters are the elastic modulus and the adhesion force.

[0024] Furthermore, the experimental data test method used for the cell mechanical parameter sample set is factorial design, which can study the effects of a single factor at multiple levels, as well as whether there are interactions between factors, and find the optimal combination, so that the subsequent neural network model mapping relationship and the optimized parameters are more accurate and more targeted to different cell regions.

[0025] Furthermore, the neural network algorithm employs a combination of simulated annealing and genetic algorithms to optimize the neural network model, and the overall algorithm execution flow is described.

[0026] Step 1: Construct training samples. Classify the data using self-learned features from the dataset, with the fitness function being... , generate training samples.

[0027] Step 2: Initialize the BP neural network. Determine the number of input and output nodes of the BP neural network based on the dimensions of the input and output sets, according to the formula... The hidden layer nodes are obtained by traversing the layer, where l is the number of hidden layer nodes, m is the number of input layer nodes, n is the number of output layer nodes, and a is a positive integer less than 10.

[0028] Step 3: Optimize the weights of the BP network using the genetic simulated annealing algorithm. After determining the overall network structure, initialize the genetic algorithm with parameterized encoding based on the number of network layers, the number of neurons in each layer, and the interconnection method of each layer. The population size is preset to 50, and the maximum number of iterations is 100. Then, preset the initial temperature T0=100, the annealing rate to 0.8, and the termination temperature T1=0.0001 for the simulated annealing algorithm. After iterative optimization, the optimal weights of the BP network are finally obtained.

[0029] Step 4: Use the obtained network weights to train and learn the BP neural network. The genetic iteration process is carried out in the annealing simulation loop. After the initial training, the individual fitness is constituted by the network input-output error. Then, the optimal offspring are obtained through an iterative method based on an elite selection model. Then, through the annealing loop, the optimal weights of the network are obtained in the periodic cooling process.

[0030] Furthermore, the cell surface mechanical feature prediction involves dividing the cell surface into 8×8 grids for sequential indentation when performing nanoindentation on different cell regions, so as to ensure that the collected mechanical parameters can be regionally clustered and easily located.

[0031] Furthermore, the cell surface mechanical feature prediction will characterize the mechanical properties of different cell types, and use traditional methods to compare the error rates of neural networks and improved neural networks to demonstrate the robustness of the algorithm.

[0032] Furthermore, the cell surface mechanical parameter clustering analysis includes cell elastic modulus and adhesion force, and the range is defined based on the sample set of numerical simulation.

[0033] In addition, according to an example of the present invention, a method for evaluating the biomechanical properties of biological cells based on a GSA optimized neural network is provided. Specifically, the method for acquiring cell mechanical parameter data in the cell mechanical parameter sample set is as follows: an atomic force probe performs a Z-direction approach-hold-withdrawal process test at a certain position on the cell surface under different conditions. In a single test, the atomic force probe approaches the cell from a constant height, creates an indentation on the cell surface until the cantilever beam loading force of the probe reaches a set value, the probe holds for a certain period of time, and then the probe is withdrawn from the cell surface to the initial position.

[0034] Compared with traditional methods, the present invention has the following advantages.

[0035] This invention presents a method for characterizing and evaluating the mechanical properties of biological cells based on a GSA-optimized neural network. Compared to traditional cell mechanical modeling methods, this method achieves higher fitting accuracy and provides a targeted approach for establishing mechanical models of multiple cells, facilitating faster and more accurate research into cell mechanical characteristics. It also addresses the problems of slow convergence speed and overfitting inherent in previous artificial neural networks. Through neural network clustering analysis of mechanical data from different cell types and regions, it overcomes the challenge of clustering surface mechanical parameters in cell mechanical properties. By combining simulated annealing with a genetic algorithm to optimize the network weights, it solves the problems of easily getting trapped in local minima and slow convergence during weight optimization. Modeling using this optimized neural network results in cell mechanical evaluation results with good generalization ability, conforming to the laws of biological cell mechanics. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of a method for characterizing the mechanical properties of biological cells based on GSA-optimized neural networks. The system includes: 1. Atomic force microscope mechanical testing system; 2. Cell viscoelasticity testing; 3. Cell mechanical parameter sample set; 4. Neural network algorithm; 5. Cell surface mechanical characteristics; 6. Cell mechanical modeling; 7. Characterization of the cell under test; 8. Cell mechanical model. Figure 2 This is a diagram of the BP neural network topology used in this invention; Figure 3 This is a comparison of the force-displacement curves of atomic force microscopy on liver cancer cells (SMCC-7721) using the method of this invention; Figure 4 This is a comparison of the force-displacement curves of human breast cancer cells obtained by atomic force microscopy using the method of this invention; Figure 5 Comparison of average error rates when applying traditional models, neural network models, and GSA-optimized neural network models to different cells. Detailed Implementation

[0037] The present invention will be further described below with reference to the accompanying drawings.

[0038] like Figure 1 As shown, a method for evaluating the mechanical properties of biological cells based on GSA optimized neural network includes: 1. collecting mechanical properties of living biological cells under physiological conditions; 2. cell viscoelasticity testing; 3. creating a sample set of cell mechanical parameters; 4. GSA neural network optimization algorithm; 5. prediction of cell surface mechanical features; 6. cell surface mechanical modeling; 7. cluster analysis of cell mechanical parameters; 8. cell mechanical evaluation model. Cellular mechanical properties were tested under physiological conditions using an atomic force probe nanoindentation system (1), and the cell mechanical parameters were recorded in a spreadsheet. Cellular viscoelasticity testing technology (2) was used, combined with elasticity models such as Hertz or Sneddon and a self-built viscoelastic model, to obtain mechanical parameter data of the atomic force probe's approach-hold-withdrawal process on the cell surface, establishing a cell mechanical parameter sample set (3). Based on the GSA neural network optimization algorithm (4), modeling was performed in the data analysis, using the cell mechanical parameter sample set for training and testing, and optimizing the neural network model of the cell mechanical parameters. Using the cell mechanical parameter data as input, the optimal cell surface mechanical parameters were predicted (5). The obtained characterization mechanical parameters of different cell regions were reintroduced into the original self-built model to obtain the current cell mechanical model (6). The cell elastic modulus, adhesion force, and cell height obtained from the data simulation were clustered using a BP neural network to obtain a gridded distribution of cell surface mechanical features (7). For different types of cells, finite element modeling was used to model their mechanical distribution characteristics and optimal parameters to obtain their mechanical models (8).

[0039] like Figure 2 As shown in the diagram, the topology of the neural network is set according to the force-displacement relationship. There are four possible input layer node configurations based on the input data type, with a maximum of four nodes. The selection of hidden layer nodes in the neural network has no absolute theoretical basis; it is generally adjusted continuously based on training performance and experience to obtain the optimal values. After debugging, the number of hidden layers was set to three, with eight nodes per layer, and the output layer had one node.

[0040] like Figure 3 The figure shown is a comparison of the force-displacement curves of liver cancer cells fitted using the method of this invention under atomic force microscopy. Nanoindentation of cells was performed using atomic force microscopy, and the obtained data was processed using the Sneddon contact model to obtain relevant mechanical parameters, which were then input into a network. The network was trained to retrieve the parameters, yielding the corresponding viscoelastic coefficients, which were then fitted using a formula to obtain... Figure 3 The comparison shows that the force-displacement curve of the cell mechanics data, after being trained by a neural network, has a better fit to the actual measured values ​​and is superior to traditional mechanical modeling methods.

[0041] like Figure 4 The figure shown is a comparison of the force-displacement curves of human breast cancer cells fitted using atomic force microscopy according to this invention. Nanoindentation of cells was performed using atomic force microscopy, and the obtained data was processed using the Sneddon contact model to obtain relevant mechanical parameters, which were then input into the network. The network was trained to retrieve the parameters, yielding the corresponding viscoelastic coefficients, which were then fitted using the formula to obtain... Figure 4 The comparison shows that the force-displacement curve of the cell mechanics data, after being trained by a neural network, has a better fit to the actual measured values ​​and is superior to traditional mechanical modeling methods.

[0042] like Figure 5 As shown in the figure, the GSA-optimized neural network model analysis of the mechanical characterization process of different cell surfaces shows that the average relative error of the cell surface mechanical characteristics is smaller than that of the neural network and is significantly better than that of the traditional model.

[0043] This invention provides a modeling process for a method to characterize and evaluate the mechanical properties of biological cells based on a GSA-optimized neural network. The process involves obtaining mechanical parameters such as adhesion force, indentation depth, retention time, and Young's modulus by performing force-displacement and force-time curves on the cell surface using atomic force microscopy (AFM) viscoelasticity testing experiments. Under physiological conditions, cell surface viscoelasticity tests are conducted using an AFM mechanical testing system. Cell surface mechanical parameters under different conditions are collected, a dataset is established, and the data is analyzed. The dataset of cell mechanical parameters is then introduced into a neural network (e.g.,...). Figure 2 The model is trained using the GSA algorithm (as shown in the figure). Cell mechanical parameters are used as input, and cell viscoelastic parameters are used as output. The input-output relationship is predicted by the neural network to perform cell mechanical modeling. Cell surface mechanical parameters marked with grids are obtained by collecting data from the same type of cells at different times and in multiple regions. Their distribution characteristics are obtained by BP neural network clustering analysis. For different types of cells, their mechanical distribution characteristics and optimal parameters are modeled using finite element method to obtain their mechanical models.

[0044] Example 1: like Figure 3 The figure shown is a comparison of the force-displacement curves of liver cancer cells fitted using the method of this invention via atomic force microscopy. Nanoindentation was performed on SMCC-7721 liver cancer cells using an atomic force microscope with a pyramidal probe. The maximum indentation depth was 0.6 μm, and the maximum stress was 4.2 nN. The obtained data were processed using the Sneddon contact model to obtain relevant mechanical parameters, determining the elastic modulus range to be 0.9-3.2 Kp. After data analysis and numerical simulation, the parameters were input into a network. The parameters were then trained and inverted using GSA optimization neural network to obtain the corresponding viscoelastic coefficients, which were then fitted using a formula to obtain... Figure 3 The comparison shows that after training with a neural network, the force-displacement curve of the cell mechanics data fits the actual measured value better than the traditional mechanical modeling method, with an error of about 6%.

[0045] Implementation Example 2: like Figure 4 The figure shown is a comparison of the force-displacement curves of human breast cancer cells fitted using atomic force microscopy according to this invention. Nanoindentation was performed on human breast cancer cells MCF-7 using an atomic force microscope with a pyramidal probe. The maximum indentation depth of human breast cancer cells was 0.8 micrometers, and the maximum stress was 8.6 nN. The obtained data was processed using the Sneddon contact model to obtain relevant mechanical parameters, and the elastic modulus range of 1.7-4.5 Kp was determined. After data analysis and numerical simulation, the parameters were obtained and input into the network. The parameters were then trained and inverted using GSA optimization neural network to obtain the corresponding viscoelastic coefficients, which were then fitted using the formula to obtain... Figure 4 The comparison shows that after training with a neural network, the force-displacement curve of the cell mechanics data fits the actual measured value better than the traditional mechanical modeling method, with an error of about 6.5%.

[0046] like Figure 5 The figure shown is a comparison of the error rates after mechanical modeling different types of cancer cells in different ways, namely the traditional Hertzian model, the BP neural network model, and the optimized neural network model.

[0047] The present invention provides a method for evaluating the mechanical properties of biological cells based on GSA optimized neural networks. Compared with traditional cell mechanical modeling methods, it has a higher degree of fit and can provide a targeted means for establishing mechanical models of multicellular structures.

[0048] The foregoing has provided a detailed description of a method for characterizing the mechanical properties of biological cells based on a GSA-optimized neural network, as provided by this invention. The examples provided are merely to aid in understanding the method and are not intended to limit the scope of the invention. The scope of this invention is defined by the appended claims. All equivalent substitutions and modifications made without departing from the spirit and principles of this invention should be included within its scope.

Claims

1. A method for characterizing and evaluating the mechanical properties of biological cells based on a GSA-optimized neural network, comprising: collecting mechanical information of living cells under physiological conditions; cell viscoelasticity testing; creating a sample set of cell mechanical parameters; applying a GSA neural network optimization algorithm; predicting cell surface mechanical features; modeling cell surface mechanics; performing cluster analysis of cell mechanical parameters; and establishing a cell mechanical evaluation model; characterized in that... The specific steps are as follows: Step 1: Collect biomechanical information of living cells under physiological conditions. Conduct cell mechanical property experiments using an atomic force microscopy system under physiological conditions. Use an atomic force probe to perform mechanical tests on the undulating morphology of the cell surface during the approach-hold-withdraw process. Summarize and store the recorded cell mechanical parameters in a spreadsheet for easy conversion into usable data files later. Step 2: Cell viscoelasticity test, Hertz model is Suitable for atomic force probes with microspherical tips; the Sneddon model is... Suitable for atomic force probes with tapered tips, used to record the mechanical parameters of the approach-hold-withdrawal process on the cell surface, among which... It is the normal pressure applied to the probe. The radius of the microsphere probe tip. It is the depth of the indentation. It is half the angle of a cone. It is the elastic modulus of the sample. The sample Poisson's ratio (generally considered to be 0.5); the self-built viscoelastic model is... Where E is the effective elastic modulus, F is the contact stress, h is the indentation depth, and α is the probe half-angle. For adhesion work, a quantitative relationship is established between cell height, adhesion work, and contact stress elastic modulus; considering cell viscoelasticity, a self-built viscoelastic model is used to obtain cell mechanical characteristic parameters, and the elastic modulus at each point of the cell is obtained through Hertz or Sneddon models. Step 3: Create a sample set of cell mechanical parameters. Filter and determine the mechanical characteristic parameters and their value ranges through mechanical data obtained from mechanical testing. Divide each parameter into equal levels. Establish an experimental set of mechanical parameters for different regions of the cell surface based on the factorial design scheme. Finally, generate training samples after finite element simulation. Compile all generated training samples into a data file. Step 4: GSA Neural Network Optimization Algorithm. This step combines simulated annealing and genetic algorithms to optimize the neural network model. The overall algorithm execution flow is as follows: Construct training samples, learn features from the dataset for classification, and use the fitness function as... Generate training samples; initialize the BP neural network, determining the number of input and output nodes based on the dimension of the input and output sets, according to the formula... The number of hidden layer nodes is obtained by traversing the network, where l is the number of hidden layer nodes, m is the number of input layer nodes, n is the number of output layer nodes, and a is a positive integer less than 10. The weights of the BP network are optimized using a genetic simulated annealing algorithm. After determining the overall network structure, the genetic algorithm is initialized with parameterized encoding based on the number of network layers, the number of neurons per layer, and the interconnection method of each layer. The population size is preset to 50, and the maximum number of iterations is 100. The initial temperature T0 of the simulated annealing algorithm is preset to 100, the annealing rate is 0.8, and the termination temperature T1 is 0.0001. Through iterative optimization, the optimal weights of the BP network are finally obtained. The network weights are used to train and learn a backpropagation (BP) neural network. The genetic iteration process is carried out in the annealing simulation loop. After initial training, the individual fitness is constituted by the network input-output error. The optimal offspring are obtained through an iterative method based on an elite selection model. The optimal weights of the network are obtained through the annealing loop and periodic cooling. The neural network is designed based on the simulated input-output parameters and their mechanical relationship in the data analysis software. The number of weights and thresholds to be optimized is determined. The network weights are improved by the GSA algorithm, i.e., the genetic simulated annealing algorithm, and the neural network is trained to predict the input-output relationship. Step 5: Predicting the mechanical features of cell surface. Using the established neural network model, numerical calculations are performed to obtain new force-displacement curve feature data. The difference between this data and the force-displacement curve data measured in mechanical experiments is used as an optimization clue. The optimal parameters are obtained through a parameter optimization algorithm, which is the characterization value of the cell in the current region. Multiple samples are collected from the same type of cells at different times and in multiple regions to obtain mechanical parameters under different conditions. The cell mechanical features are then extracted through a neural network algorithm. Step 6: Cell surface mechanical modeling. The characterization mechanical parameters of different regions of the obtained living cell are re-introduced into the original self-made model to obtain the surface mechanical model of the current cell. Step 7: Cluster analysis of mechanical parameters on cell surface. Cluster analysis is performed on the mechanical characteristic parameters in different regions on the surface of living cells. An unsupervised BP neural network is used, and the weight optimization also uses the genetic simulated annealing algorithm. Step 8: Cell mechanical assessment model, used to establish the mechanical distribution characteristics of different cell types, retrain the neural network to obtain its mechanical model.

2. The method for characterizing and evaluating the mechanical properties of biological cells based on GSA optimized neural networks according to claim 1, characterized in that: The mechanical properties of living biological cells under the physiological state were collected, and a nanoindentation viscoelasticity test experiment was performed on the cell surface to obtain the force-displacement curve and force-time curve of cell surface viscoelasticity, as well as mechanical parameters such as indentation depth, holding time, contact stress, and cell height.

3. The method for characterizing and evaluating the mechanical properties of biological cells based on GSA optimized neural networks according to claim 1, characterized in that: The sample set of cell mechanical parameters is selected and determined to include the contact stress at the contact point, the contact stress at which the indentation peak is reached, the cell height, and the indentation depth, while the output mechanical parameters are the elastic modulus and the adhesion force.

4. The method for characterizing and evaluating the mechanical properties of biological cells based on GSA optimized neural networks according to claim 1, characterized in that: The experimental data set of the cell mechanical parameters used is based on factorial design, which can study the effects of a single factor at multiple levels, as well as whether there are interactions between factors. It can also find the optimal combination, making the subsequent neural network model mapping relationship and the optimized parameters more accurate and more targeted to different cell regions.

5. The method for characterizing and evaluating the mechanical properties of biological cells based on GSA optimized neural networks according to claim 1, characterized in that: The prediction of cell surface mechanical characteristics involves dividing the cell surface into 8×8 grids for nanoindentation of different cell regions, ensuring that the collected mechanical parameters can be regionally clustered and easily located.

6. The method for characterizing and evaluating the mechanical properties of biological cells based on GSA optimized neural networks according to claim 1, characterized in that: The predicted cell surface mechanical characteristics will characterize the mechanical properties of different cell types, and the robustness of the algorithm will be demonstrated by comparing the error rates of traditional methods with those of neural networks and improved neural networks.

7. The method for characterizing and evaluating the mechanical properties of biological cells based on GSA optimized neural networks according to claim 1, characterized in that: The cell surface mechanical parameter clustering analysis includes cell elastic modulus and adhesion force, and the range is defined based on the sample set of numerical simulation.

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