Method for regulating mechanical properties of human soft tissue simulation material by using surrogate model

Abstract

The application provides a method for regulating mechanical properties of soft tissue simulation material of human body by using a surrogate model, and specifically comprises the following steps: (1) extracting sample points of different material parameters, and performing mechanical test on the sample points to obtain mechanical property indexes of the soft tissue simulation material; (2) establishing a surrogate model capable of quantitatively describing the regulation law of the material parameters on the mechanical property indexes of the soft tissue simulation material; and (3) using the model to predict and calculate the mechanical properties of different parameter materials, and regulating the mechanical properties thereof. The method for regulating mechanical properties of soft tissue simulation material of human body by using a surrogate model can establish an approximate mathematical model between material components and mechanical parameters by using a surrogate model, predict the mechanical parameters of different component materials, reversely guide material preparation, and regulate the mechanical properties.

Description

Technical Field

[0001] This invention relates to the field of human target technology, specifically a method for using a surrogate model to regulate the mechanical properties of simulated human soft tissue materials. Background Technology

[0002] High-speed impacts are widespread in human engineering practices and activities, causing significant damage to human tissues and organs. In scenarios such as traffic accidents, extreme sports, explosive impacts, ballistic impacts, and blunt force trauma, the soft tissues of the brain, chest, and abdomen often suffer non-fatal injuries such as lacerations and contusions, as well as fatal injuries such as bullet penetration and explosions. In kinetic energy testing, targets can be divided into biological targets and non-biological targets. Biological targets include human corpses, living or dead animals, and excised biological tissues, which can accurately reflect the mechanical response of organisms in kinetic energy injury. However, their application is limited due to ethical issues, difficulties in obtaining them, and differences in biological activity and physiological structure. Researchers have developed non-biological targets based on human physiological structure and tissue mechanical characteristics, including physical targets and biomimetic targets. Physical targets, such as rigid walls, provide relatively limited data through sensors and lack simulation of human anatomical structures and the dynamic mechanical response of soft tissues, resulting in low simulation accuracy. Biomimetic targets, such as soft tissue human body targets, can overcome the shortcomings of the above-mentioned kinetic energy testing and biomechanical research by simulating human internal organs through various soft tissue simulation materials such as clay, soap, gelatin, SEBS gel and polymer materials.

[0003] However, the composition of human soft tissue is extremely complex, with vastly different microstructures and compositions. For example, the liver contains abundant blood vessels with pre-stressed structures, the lungs include numerous tiny alveoli, and muscles exhibit typical anisotropy due to the arrangement of muscle fibers. These differences in stress response hysteresis characteristics among different soft tissues and organs lead to significant variations in their mechanical properties. Commonly used materials for human targets, such as clay and gelatin, serve as homogeneous simulation materials. However, these materials differ considerably from the complex viscoelasticity and heterogeneous mechanical characteristics of human soft tissue. The differences in the structure and mechanical properties of simulated materials compared to biological soft tissue materials prevent a true reflection of the mechanical response characteristics of biological soft tissue under high-speed impact. Therefore, developing simulation materials that more closely approximate the mechanical properties of human soft tissue, and controlling their mechanical properties, are crucial for the development of highly realistic biological soft tissue dummies and the upgrading of target technology. Summary of the Invention

[0004] This invention addresses the technical problem of how to regulate the mechanical properties of soft tissue simulation materials, and provides a method for regulating the mechanical properties of human soft tissue simulation materials using a proxy model.

[0005] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0006] A method for regulating the mechanical properties of simulated human soft tissue materials using a surrogate model includes the following steps:

[0007] (1) Extract sample points of material parameters and conduct mechanical tests on the sample point materials to obtain the mechanical performance index of the soft tissue simulation material; (2) Establish a proxy model that can quantitatively describe the regulation law of material parameters on the mechanical performance index of the soft tissue simulation material; (3) Use the model to predict and calculate the mechanical properties of different material synthesis parameters to obtain the material synthesis parameters whose mechanical properties are close to those of the target soft tissue.

[0008] The material parameters include at least one of the following: material molecular weight, material concentration, proportion of different components, and preparation condition parameters.

[0009] The mechanical performance indicators mentioned in step (1) include at least one of Young's modulus, Shore hardness, storage modulus, dissipation modulus, relaxation modulus, and creep compliance.

[0010] The mechanical performance indicators also include at least one of the material parameters from models such as the Mooney-Rivlin model, the Ogden model, and the Neo-Hookean model, which characterize hyperelastic properties.

[0011] The method for establishing the surrogate model in step (2) is one of the following: Kriging model, artificial neural network, radial basis function, support vector regression model, and multinomial regression model.

[0012] The soft tissue simulation material is a polyvinyl alcohol-plant gel composite hydrogel, and the material parameters are the concentration of polyvinyl alcohol aqueous solution, the concentration of plant gel aqueous solution, the ratio of polyvinyl alcohol to plant gel, the freeze-thaw temperature of the hydrogel, and the freeze-thaw time of the hydrogel.

[0013] In step (1), the Latin hypercube sampling method is used to combine the three parameters of polyvinyl alcohol aqueous solution concentration, plant gel aqueous solution concentration and polyvinyl alcohol / plant gel ratio to form all sample points. Quasi-static mechanical compression test and Hopkinson bar high strain rate compression test are performed on all sample points to obtain Young's modulus and Ogden hyperelastic model material index of polyvinyl alcohol-plant gel hydrogel under different strain rates.

[0014] A proxy model is established using the Kriging model method.

[0015] The soft tissue simulation material is a polymer poly(dodecanoic acid glycerol), and the material parameters are the glycerol / dodecanoic acid ratio and the thermosetting time. In step (1), the Latin hypercube sampling method is used to combine the two parameters of the poly(dodecanoic acid glycerol) ratio and the thermosetting time to form sample points. Stress relaxation test and creep test are performed on all sample point materials to obtain the relaxation modulus and creep compliance of poly(dodecanoic acid glycerol).

[0016] In step (2), an artificial neural network is used to establish a proxy model for polydodecanoic acid glyceride.

[0017] In step (3), the material synthesis parameters are adjusted, and its mechanical properties are predicted using a surrogate model. The mechanical properties are then controlled until the error in the mechanical properties is less than or equal to 10%, resulting in material synthesis parameters whose mechanical properties closely approximate those of the target soft tissue. The method of using a surrogate model to control the mechanical properties of simulated materials for human soft tissue, as described in this invention, has the following advantages:

[0018] The method for regulating the mechanical properties of simulated human soft tissue materials using a surrogate model, as described in this invention, establishes an approximate mathematical model between material components and mechanical parameters through a surrogate model. This model predicts the mechanical parameters of materials with different components, and inversely guides material preparation, thereby controlling its mechanical properties. The process of regulating the mechanical properties of simulated human soft tissue materials according to this invention is as follows: First, a sampling scheme is selected to sample material concentration and components. The distribution and number of sample points greatly affect the accuracy of the surrogate model; therefore, a suitable number of evenly distributed sample points must be selected. Based on the material concentration and components obtained from the sampling, simulated materials are experimentally synthesized, and then the mechanical properties of the simulated materials are obtained through various mechanical tests. As a preferred embodiment, the mechanical property indicators include Young's modulus, Shore hardness, storage modulus, dissipation modulus, relaxation modulus, and creep compliance, which characterize viscoelastic properties, as well as material parameters characterizing hyperelastic properties such as the Mooney-Rivlin model, Ogden model, and Neo-Hookean model. The advantage of this setup is that diverse mechanical parameters can characterize the material's stiffness, hardness, nonlinear mechanical properties under different strain rates, strain rate dependence, and soft tissue-like viscous characteristics in multiple dimensions, enabling reverse-guided synthesis of materials that possess a variety of biomimetic mechanical properties.

[0019] The method for regulating the mechanical properties of human soft tissue simulation materials using a surrogate model as described in this invention establishes the surrogate model using one of the following methods: Kriging model, artificial neural network, radial basis function, support vector regression model, and multinomial regression model. By using the established surrogate model, various mechanical properties of simulation materials with different concentrations and component ratios can be predicted, and the mechanical properties of the simulation materials can be regulated.

[0020] The method for regulating the mechanical properties of simulated human soft tissue using a surrogate model in this invention, for polyvinyl alcohol-plant gel composite hydrogels, the material parameters are the concentration of polyvinyl alcohol aqueous solution, the concentration of plant gel aqueous solution, and the ratio of polyvinyl alcohol to plant gel. Simultaneously, step (1) uses the Latin hypercube sampling method to combine the three parameters to form all sample points. Quasi-static mechanical compression tests and high strain rate compression tests are performed on all sample points to obtain the Young's modulus and Ogden hyperelastic model material indices of the polyvinyl alcohol-plant gel hydrogel at different strain rates. In step (2), a Kriging surrogate model is selected to establish the surrogate model. The advantage of this setup is that, for the simulated target liver soft tissue, the most prominent mechanical indices are selected to establish the Kriging surrogate model. By regulating its nonlinear mechanical properties and rate-dependent characteristics through material composition, its mechanical properties during high strain rate impact are made close to those of liver tissue.

[0021] The method for regulating the mechanical properties of simulated human soft tissue using a surrogate model in this invention, for poly(dodecanoic acid glycerol) (PGD), the material parameters are the glycerol / dodecanoic acid ratio and the thermosetting time. Step (1) uses the Latin hypercube sampling method to combine these two parameters to form all sample points. Stress relaxation and creep tests are performed on all sample points to obtain the relaxation modulus and creep compliance of the viscoelastic properties of PGD. In step (2), an artificial neural network is selected to establish a surrogate model. The advantage of this setup is that, for the simulated intervertebral disc nucleus pulposus soft tissue, the most prominent mechanical indicators are selected to establish an artificial neural network surrogate model. By regulating its viscoelastic mechanical properties through material composition, its mechanical properties are made close to those of the nucleus pulposus tissue.

[0022] To make the technical solution of the method for regulating the mechanical properties of human soft tissue simulation materials using a proxy model as described in this invention clearer, the invention will be further described in detail below with reference to specific embodiments. Detailed Implementation

[0023] Example 1

[0024] This embodiment provides a method for regulating the mechanical properties of human soft tissue simulation materials using a surrogate model. The simulation material is a polyvinyl alcohol-plant gel (PVA-PHY) composite hydrogel, and includes the following steps: (1) selecting a sampling scheme to sample material concentration and component sample points; (2) obtaining the Young's modulus and hyperelastic mechanical parameters of the simulation material through compression mechanics testing; (3) selecting the Kriging surrogate model modeling method; and (4) predicting and regulating the mechanical properties of the simulation material.

[0025] The sampling scheme described in this embodiment can be Latin hypercube sampling (LHS). LHS is a method for obtaining an approximately random distribution from a multivariate parameter distribution. It belongs to stratified sampling and is one of the most widely used sampling methods. This method, from the perspective of spatial coverage, ensures the comprehensiveness and uniformity of the sample projection in the probability space. Its key is to stratify each design variable with equal probability and then sample from it. For PVA-PHY hydrogel, sampling x1, x2, and x3 are the concentrations of PVA aqueous solution, PHY aqueous solution, and PVA / PHY mixing ratio, respectively. According to the material solubility limitation, the sampling intervals are [0, 20%], [0, 5%], and [0.25, 4]. Combining the three parameters forms all sample points. In this example, 50 sample points are sampled as follows:

[0026]

[0027]

[0028] The mechanical properties of the human soft tissue simulation material described in this embodiment include Young's modulus and Ogden hyperelastic model material parameters under quasi-static and high strain rate conditions. All sample points were subjected to strain rate testing at 0.01 s-1 using a universal testing machine and a Hopkinson bar apparatus. -1 and 1000s -1 Compression test. The formula for calculating Young's modulus is:

[0029]

[0030] The measured stress-strain curves were fitted using the Ogden model, with elongation as the independent variable to describe large deformation conditions. The strain energy function is:

[0031]

[0032] Where N is the order of the model, usually a number between 1 and 3; λ1, λ2, and λ3 are the first, second, and third principal elongation rates, respectively, and α... i and μ i These are the material parameters. In this embodiment, a first-order Ogden model is used, and the material parameters include α1 and μ1.

[0033] The surrogate modeling method described in this embodiment selects the Kriging surrogate model. The Kriging model is one of the most widely used methods and is a way to functionally model stochastic processes; therefore, it is called a "stochastic process model." Its functional expression is:

[0034]

[0035] in, This represents the i-th sampling point, which has m variables; It is an approximate function applicable to n sampling points; β is the regression coefficient; z(X) i () is a expression with a mean of 0 and a variance of σ. 2 The spatial correlation of the random function is given by the following equation:

[0036]

[0037] Where R(θ,X) i ,X j ) is the Gaussian correlation function for θ, where θ represents the spatial correlation between two samples, which can be estimated by maximizing the probability of the sampling point, as shown in the following formula.

[0038]

[0039] A linear combination of the sample Y response values ​​can be used to estimate a new point X. * response value

[0040]

[0041] By minimizing the mean squared error (MSE) of this predictor variable through unbiased estimation, we arrive at:

[0042]

[0043] in,

[0044] r(X * )=[R(θ,X1,X * ),…,R(θ,X n ,X * )]

[0045] For a strain rate of 0.01s -1 and 1000s -1 Compression tests were conducted to establish mathematical models between Young's modulus (E) and the material parameters (α1, μ1) of the first-order Ogden model.

[0046]

[0047] Where E, α1, and μ1 represent 0.01s -1 Mechanical properties under quasi-static experimental conditions; E′, α′1, μ′1 represent 1000 s. -1 Mechanical properties under high strain rate experimental conditions; f i (i = 1, 2, 3) is 0.01s -1 surrogate model for strain rate test conditions, gj (j=1,2,3) is 1000s -1 A surrogate model for strain rate testing conditions. After establishing the model, inputting material parameters allows for the prediction of its mechanical properties. By continuously adjusting the material parameters, multiple mechanical properties predicted by the model can be obtained. The mechanical properties y of the target liver soft tissue as measured by mechanical experiments i For comparisons between (i = 1, 2, 3), the Mean Absolute Relative Error (MARE) can be used as an evaluation metric for model error. The calculation formula is as follows:

[0048]

[0049] By adjusting the combined material parameters to reduce the error until the error in the mechanical properties is less than or equal to 10%, material synthesis parameters with mechanical properties close to those of the target soft tissue are obtained.

[0050] Example 2

[0051] This embodiment provides a method for regulating the mechanical properties of a human soft tissue simulation material using a surrogate model. The simulation material is dodecanoic acid glycerol. The method includes the following steps: (1) selecting a sampling scheme to sample material concentration and component sample points; (2) obtaining the mechanical properties of the simulation material through stress relaxation and creep mechanical tests; (3) selecting a suitable surrogate model for modeling; and (4) predicting and regulating the mechanical properties of the simulation material and optimizing the material synthesis parameters using a genetic algorithm.

[0052] The sampling scheme described in this embodiment also uses Latin hypercube sampling. For dodecanoic acid glycerol ester, sampling x1 and x2 are the dodecanoic acid / glycerol ratio and thermosetting time, respectively. Based on the material synthesis conditions, the sampling intervals are limited to [0.25, 4] and [12, 240]. Combining the two parameters forms all sample points. In this example, 50 sample points are sampled as follows:

[0053]

[0054]

[0055] Stress relaxation and creep mechanical tests were performed on all sample points to obtain the relaxation modulus Y(t) and creep compliance J(t). Under constant load and constant deformation, the viscous effect of the simulated soft tissue material is manifested as creep and stress relaxation. The stress relaxation behavior over time can be quantified using a multinomial Prony sequence, and the relaxation modulus Y(t) and creep compliance J(t) are as follows:

[0056]

[0057] Where E0 represents the instantaneous modulus, τ i and τ j It is a characteristic time scale in classical creep and relaxation functions. In the Prony series, m and n are related to the complexity of the spring-sticker element.

[0058] After acquiring sample data, this embodiment selects an artificial neural network as the surrogate model. A neural network is a mathematical or computational model that mimics the structure and function of a biological brain's neural network, used to estimate or approximate functions. The material synthesis parameters of the sample points—the dodecanoic acid / glycerol ratio and the thermosetting time—are used as the input layer of the neural network, while the relaxation modulus Y(t) and creep compliance J(t) obtained from mechanical testing are used as the output layer. The neural network is then trained. Using the Matlab neural network toolbox and the BP neural network algorithm, the weights and activation functions of the nodes are adjusted to learn and adapt to different input patterns, producing the expected output results. In this embodiment, the material synthesis parameters are used as the input layer of the neural network, and the mechanical indices relaxation modulus and creep compliance are used as the output layer. Two hidden layers are set, with 40 samples as the training set and 10 samples as the test set, to obtain the approximate functional relationship at time t:

[0059] Y = F(x1, x2) = w 11 x1+w 12 x2+w 21 f1(x1)+w 22 f2(x2)+b

[0060] J = G(x1,x2) = w 11 x1+w 12 x2+w 21 g1(x1)+w 22 g2(x2)+b

[0061] Where Y is the relaxation modulus, J is the creep compliance, and x1 and x2 represent the dodecanoic acid / glycerol ratio and the thermosetting time, respectively. ij (i = 1, 2, 3; j = 1, 2, 3) represent the weights of the neural network, f i (i = 1, 2, 3) and g j (j=1,2,3) represent the activation functions of the relaxation modulus Y(t) and creep compliance J(t) neural networks, respectively, and b is the bias. After establishing the model, multiple mechanical properties can be predicted by inputting material parameters. The predicted mechanical properties can be obtained through continuous debugging. The mechanical properties of the target nucleus pulposus soft tissue y iFor comparisons between (i=1,2), the Mean Absolute Relative Error (MARE) of multiple indicators is used as the evaluation index for model error, calculated using the same formula as in Example 1. The error can be reduced by adjusting the combined material parameters until it is within an acceptable range. As a preferred embodiment, the error in the mechanical indicators should be less than or equal to 10%, resulting in material synthesis parameters whose mechanical properties closely approximate the target soft tissue.

[0062] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the claims.

Claims

1. A method for regulating the mechanical properties of simulated human soft tissue materials using a surrogate model, characterized in that, The soft tissue simulation material is a polyvinyl alcohol-plant gel composite hydrogel that simulates liver soft tissue. The method includes the following steps: (1) The Latin hypercube sampling method was adopted to combine three parameters: the concentration of polyvinyl alcohol aqueous solution, the concentration of plant gel aqueous solution, and the ratio of polyvinyl alcohol to plant gel to form all sample points. Quasi-static mechanical compression test and Hopkinson bar high strain rate compression test were carried out on all sample points to obtain the Young's modulus and Ogden hyperelastic model material index of polyvinyl alcohol-plant gel hydrogel under different strain rates. (2) A proxy model that can quantitatively describe the regulation law of material parameters on the mechanical property index of soft tissue simulation materials is established by using the Kriging model method; (3) The mechanical properties of different material synthesis parameters are predicted and calculated using the model, so as to obtain material synthesis parameters with mechanical properties close to the target soft tissue; Alternatively, the soft tissue simulation material is a polymer, poly(dodecanoic acid glyceride), which simulates the soft tissue of the intervertebral disc nucleus pulposus, and the method includes the following steps: (1) The Latin hypercube sampling method was used to combine the ratio of polydodecanoic acid to glycerol and the thermosetting time to form sample points. Stress relaxation test and creep test were performed on all sample point materials to obtain the relaxation modulus and creep compliance of polydodecanoic acid glycerol. (2) An artificial neural network was selected to establish a proxy model that can quantitatively describe the regulation law of material parameters on the mechanical property index of soft tissue simulation materials; (3) Adjust the material synthesis parameters, predict its mechanical properties through the surrogate model, and regulate its mechanical properties until the error of the mechanical properties is less than or equal to 10%, so as to obtain the material synthesis parameters with mechanical properties close to the target soft tissue.

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