A constitutive modeling method applicable to J-type soft tissue

Abstract

This invention relates to the field of soft tissue biomechanical modeling technology, specifically to a constitutive modeling method suitable for J-type soft tissue. The method includes: processing the soft tissue using tissue staining to obtain the volume fractions of matrix, collagen fibers, and elastic fibers; determining an isotropic matrix term based on the characteristics of mesenchymal cells and endothelial cells in the matrix; determining a collagen fiber term based on the characteristics of collagen fiber curling, straightening, fiber rotation, and interfiber slippage; determining an elastic fiber term based on the fiber rotation characteristics of elastic fibers, thus obtaining a model of undetermined parameters; adding the volume fractions of matrix, collagen fibers, and elastic fibers in the soft tissue to the model of undetermined parameters; and using a nearest-nearest global optimization differential evolution algorithm to solve for the undetermined parameters in the model of undetermined parameters, thereby obtaining a hyperelastic constitutive model. This invention can improve the accuracy of the biomechanical property model of J-type soft tissue.

Description

Technical Field

[0001] This invention relates to the field of soft tissue biomechanical modeling technology, and specifically to a constitutive modeling method applicable to J-type soft tissue. Background Technology

[0002] With the increasing precision of mechanical and optical experimental devices, more physical information has been provided for soft tissue modeling. Over the long course of evolution, soft tissue has gradually developed into one of the most remarkable materials in nature, possessing exceptional deformation capabilities. Reproducing the mechanical properties of natural tissues has always been a research goal in materials science and mechanics. The structure of soft tissue is composed of a mixture of various components, exhibiting significant overall mechanical properties, especially in large deformations. This characteristic has become an important research topic in bioengineering. Scientists are dedicated to exploring its complex mechanical mechanisms in order to accurately predict the mechanical behavior of these materials. Therefore, developing constitutive models that can effectively describe the mechanical characteristics at different length scales is particularly important.

[0003] In the process of realizing this invention, the inventors discovered at least the following problems in the prior art: Constitutive modeling is a key technical method for studying soft tissue. Traditional biological soft tissue modeling usually relies on tensor invariants of the strain, often employing exponential or power-law functions. These invariant-based formulas show good accuracy in the fitting process, but their prominent shortcomings are that the physical meaning of the parameters in the constitutive model is relatively unclear, the mechanical contributions of each component cannot be separated, and the complex motion of fibers is not taken into account. Summary of the Invention

[0004] In view of the above problems, the present invention provides a constitutive modeling method applicable to J-type soft tissue, which solves the technical problems of unclear physical meaning of parameters in constitutive models and inability to quantitatively express fiber motion in the prior art.

[0005] This invention provides a constitutive modeling method suitable for J-type soft tissue, comprising the following steps:

[0006] Step S1: The soft tissue is treated using tissue staining methods to obtain the volume fractions of matrix, collagen fibers and elastic fibers in the soft tissue;

[0007] Step S2: Determine the isotropic matrix item based on the characteristics of the mesenchymal cells and endothelial cells in the matrix; determine the collagen fiber item based on the characteristics of collagen fiber curling and straightening, fiber rotation and interfiber slippage; determine the elastic fiber item based on the fiber rotation characteristics of elastic fibers;

[0008] Step S3: Combine the matrix term, collagen fiber term, and elastic fiber term to obtain a parameter model to be determined;

[0009] Step S4: Add the volume fractions of matrix, collagen fibers and elastic fibers in the soft tissue to the undetermined parameter model; use the nearest global optimization differential evolution algorithm to solve the undetermined parameters in the undetermined parameter model to obtain the hyperelastic constitutive model;

[0010] Step S5: Use the hyperelastic constitutive model to obtain multiple mechanical parameters of soft tissue fibers.

[0011] Preferably, step S1 specifically includes:

[0012] Different staining reagents were used to label and stain the matrix, collagen fibers and elastic fibers in soft tissue. The stained soft tissue was imaged and analyzed using an optical microscope. The volume fraction of matrix, collagen fibers and elastic fibers in soft tissue was calculated using image analysis software.

[0013] Preferably, step S2 specifically includes:

[0014] Step S2-1: For the matrix composed of mesenchymal cells and endothelial cells, establish a matrix term based on isotropic properties. The matrix term calculates the stress response of the matrix based on the matrix strain tensor, matrix stiffness parameters and the first strain tensor invariant.

[0015] Step S2-2: Establish a collagen fiber term based on the characteristics of collagen fiber crimping and straightening, fiber rotation and interfiber slippage. The collagen fiber term includes fiber tensile stress response and slippage stress response.

[0016] Step S2-3: Establish an elastic fiber term based on the stress response of the elastic fiber containing rotational motion. The elastic fiber term is based on the modulus and strain of the elastic fiber to calculate the stress response of the elastic fiber.

[0017] Preferably, in step S2-1, the stress response S of the matrix... m The expression is:

[0018]

[0019] Among them, κ m I1 represents the first strain tensor invariant; p is the Lagrange multiplier; and C represents the Cauchy-Green strain tensor.

[0020] Preferably, step S2-2 specifically includes:

[0021] Step S2-2-1: Determine the relationship between the waviness of a single fiber and its uniaxial strain during the crimping and straightening process of a single fiber, and determine the crimping and straightening stress response of the fiber assembly based on the relationship characteristics of the single fiber.

[0022] Step S2-2-2: Based on the described curling and straightening stress response, and combined with the fiber rotation characteristics, determine the fiber tensile stress response;

[0023] Step S2-2-3: Based on the slip characteristics of collagen fibers, determine the slip stress response of the fiber assembly.

[0024] Preferably, in step S2-2-2, the curling and straightening stress response S f The expression is:

[0025]

[0026] Where, n f κ represents the number of fibrils. c d represents the stiffness parameter of collagen fibers. c The parameter represents the degree of nonlinearity of collagen fibers during deformation; θ is the calibrated angle along the circumferential axis, Γ c (θ) is a normal distribution of the calibrated angles along the circumferential axis, λ x ,λ y These are the elongation rates along the x and y axes, respectively. Let α represent the uniaxial strain of the fiber bundle, α represent the ratio of fiber slip length to bearing elongation, and λ represent the uniaxial strain of the fiber bundle. f The total stretch excluding fiber slippage is represented by D(w), where D(w) indicates that the fiber waviness follows a normal distribution, and N represents the direction in the tissue space. It represents the outer product.

[0027] Preferably, in step S2-2-3, the slip stress response S of the fiber assembly pg The expression is:

[0028]

[0029] Among them, κ pg d represents the average stiffness of a collagen fiber composed of multiple fibrils. pg A parameter representing the degree of nonlinearity of collagen fibers during slip deformation. D(λ) represents the slip strain of the fiber bundle. f ) represents the normal distribution of ripple. Substituting λ f The value, D is the spacing between fibers, L f It is the arc length of a single collagen fiber.

[0030] Preferably, in steps S2-3, the stress response S of the elastic fiber is... e The expression is:

[0031]

[0032] Among them, κ e It is the modulus of effective elastin fibers, E f For the strain of elastin fibers, d e This is a parameter representing the degree of nonlinearity of the elastic fiber during deformation.

[0033] Preferably, the expression for the undetermined parameter model in step S3 is:

[0034]

[0035] Where S represents the tissue-level stress response, θ i This represents the calibration angle of the i-th circumferential axis, n c n represents the number of typical directions in which collagen fibers exhibit behavior after being subjected to force. e N represents the number of typical directions in which the elastic fiber exhibits its behavior under stress. i φ represents the i-th typical direction. c ,φ e ,φ m These are the volume fractions of collagen fibers, elastic fibers, and matrix, respectively.

[0036] Preferably, the volume fractions of matrix, collagen fibers, and elastic fibers obtained through experimental measurements in step S1 are substituted into the undetermined parameter model, and then the parameters are fitted using a differential evolution algorithm, with a loss function... for:

[0037]

[0038] in, It is the experimental data of the j-th data point in direction 1. This is the calculated value of the j-th data point in the second direction. n represents the number of data points in the test points, including circumferential and radial data points.

[0039] R, a measure of fitting ability 2 The calculation formula is as follows:

[0040]

[0041] Where y j It is the j-th data value. It is the constitutive model prediction value corresponding to the j-th data point. It is the average value of the j-th experimental data. After parameter fitting, the hyperelastic constitutive model of the J-type soft tissue is finally obtained.

[0042] Compared with the prior art, the present invention has at least the following beneficial effects:

[0043] (1) The present invention obtains the volume fraction of matrix, collagen fibers and elastic fibers in soft tissue by tissue staining method, which not only avoids the problem of fuzzy physical information in traditional methods, but also makes the most of existing physical information, so that the model has stronger physical meaning and accuracy.

[0044] (2) This invention fully considers the mechanical properties of each component of soft tissue, including the isotropic characteristics of the matrix, the crimping and straightening of collagen fibers, fiber rotation and interfiber slippage characteristics, and the fiber rotation characteristics of elastic fibers. By mathematically modeling and combining these properties, the quantitative separation of the mechanical contributions of each component is successfully achieved, enabling the model to more comprehensively describe the mechanical behavior of soft tissue.

[0045] (3) This invention uses a differential evolution algorithm with the nearest global optimization to determine the model parameters, ensuring the convergence of the solution process and the reliability of the results. Test verification using planar biaxial tensile data shows that the model can accurately capture the J-shaped stress curve characteristics of soft tissues and has accurate predictive capabilities. Attached Figure Description

[0046] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0047] Figure 1 A flowchart of the present invention's modeling method applicable to J-type soft tissue.

[0048] Figure 2 A detailed flowchart of the present invention's modeling method applicable to J-type soft tissue.

[0049] Figure 3 This is a schematic diagram illustrating three complex movements of collagen fibers provided by the present invention.

[0050] Figure 4 The fitting effect diagram of the biaxial stretching data of the tricuspid valve provided by the present invention. Detailed Implementation

[0051] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0052] To illustrate the effectiveness of the method proposed in this invention, the following detailed description of the above technical solution is provided through a specific embodiment. For example, a specific implementation of this invention... Figure 1As shown, a constitutive modeling method applicable to J-type soft tissue is disclosed, and the specific implementation steps are as follows:

[0053] Step S1: The soft tissue is treated using tissue staining methods to obtain the volume fractions of matrix, collagen fibers and elastic fibers in the soft tissue.

[0054] In some embodiments, the specific steps of treating soft tissue using tissue staining methods may include: labeling and staining the matrix, collagen fibers, and elastic fibers in the soft tissue using different staining reagents; acquiring and analyzing images of the stained soft tissue using an optical microscope or imaging device; calculating the volume fractions of the matrix, collagen fibers, and elastic fibers in the soft tissue using image analysis software; and using the obtained volume fractions as known parameters for subsequent model construction.

[0055] By predetermining these volume fractions, the number of three parameters that need to be fitted in the constitutive model can be reduced. The reduction in the number of parameters helps to improve the model fitting efficiency and the overall robustness of the model.

[0056] Step S2: Determine the isotropic matrix item based on the characteristics of the mesenchymal cells and endothelial cells in the matrix; determine the collagen fiber item based on the characteristics of collagen fiber curling and straightening, fiber rotation and interfiber slippage; determine the elastic fiber item based on the fiber rotation characteristics of elastic fibers;

[0057] This invention decouples the strain energy density of soft tissue, decomposing the overall tissue's mechanical response into contributions from three main components: elastic fibers (e), collagen fibers (c), and a matrix (m) composed of connective tissues such as interstitial cells and endothelial cells. The mechanical contributions of these three components are weighted by their respective volume fractions. The expression for the strain energy density function is as follows:

[0058] Ψ(C)=φ c Ψ c (C)+φ e Ψ e (C)+φ m Ψ m (C)

[0059] Where C represents the Cauchy-Green strain tensor, Ψ(C) is the total strain energy density, and Ψ c (C),Ψ e (C),Ψ m (C) represents the strain energy density of collagen fibers, elastic fibers, and the matrix, respectively. c ,φ e ,φ m These are the volume fractions of collagen fibers, elastic fibers, and matrix, respectively.

[0060] Through the derivation of the 2nd-Piola-Kirchhoff stress tensor, the expression for the tissue stress response S is obtained as follows:

[0061]

[0062] Where E = (CI) / 2 is the Green-Lagrange strain tensor, I is the unit tensor, and p is the Lagrange multiplier, which is introduced to describe the incompressibility of the tissue.

[0063] In this way, the present invention decomposes the soft tissue mechanical response into the contribution of each component, and can directly measure the volume fraction through the experimental means in step S1, thus simplifying the model construction.

[0064] (1) For the matrix composed of connective tissues such as mesenchymal cells and endothelial cells, this invention uses isotropic modeling to model it. The 2nd Piola Kirchhoff stress response S of the matrix term composed of connective tissues such as mesenchymal cells and endothelial cells is shown. m The expression is:

[0065]

[0066] Among them, κ m I represents the stiffness parameter of the matrix, and I1 represents the first strain tensor invariant.

[0067] S m As the matrix term.

[0068] (2) For collagen fibers, this invention analyzes their mechanical properties and establishes a collagen fiber term. For a single fiber, such as... Figure 3 As shown, fiber elongation deformation includes fiber crimping and straightening, and fiber slippage. The density function Ψ of the collagen fiber term... c (C) consists of two parts, namely Ψ c (C)=Ψ f (C)+Ψ pg (C), where Ψ f (C) represents the strain energy density during fiber straightening, Ψ pg (C) represents the strain energy density of fiber slip.

[0069] For the straightening of fiber crimp, such as Figure 3 As shown, L f L is the arc length of a single collagen fiber, where L is the end-to-end length. Assume the fiber waviness is equal to L. f / L, w>1, the larger the w value, the higher the crimp of a single fiber. Total tensile strength excluding fiber slippage. Where λ sIt is relaxation stretching, which means stretching a single fiber before it is straightened. This refers to the actual stretching of the fiber. The end-to-end distance after stretching is l. When l > L f hour, Assuming the fiber bears only tensile loads and not compressive loads, therefore when w < λ f Only when the fiber is subjected to load. The fiber's strain tensor.

[0070] The waviness w of the fiber follows a normal distribution D(w). Collagen fibers with common orientation are considered to be undergoing uniaxial strain. Fiber assembly, uniaxial strain The expression is:

[0071]

[0072] Collagen fibers with common orientation are considered as a fiber assembly undergoing uniaxial strain, and the strain energy Ψ of the fiber assembly is... ens (E f It must meet the following form:

[0073]

[0074] Among them, κ c d represents the stiffness parameter of collagen fibers. c A parameter representing the degree of nonlinearity of collagen fibers during deformation.

[0075] Then it contains n f The expression for the 2nd Piola Kirchhoff stress response generated by the fibers formed from the root fibrils is:

[0076]

[0077] Where α represents the ratio of fiber slip length to load elongation.

[0078] Since collagen fibers have a certain orientation within tissues, it is assumed that the orientation of collagen fibers along the circumferential axis, denoted by angle θ, follows a normal distribution Γ. c (θ). Under the affine assumption, the stress response expression for the straightening of tissue-level collagen fibers is: 2ndPiolaKirchhoff stress.

[0079]

[0080] Where N represents the direction in the tissue space, N(θ) = [cos(θ), sin(θ), 0], and θ is the calibrated angle along the circumferential axis. It represents the outer product.

[0081] Let Γ1(β) be the fiber orientation distribution in the deformed state, and Γ0(θ) be the fiber orientation distribution in the reference state. Since adjacent fibers remain adjacent, the number of fibers dN around angle β remains unchanged after rotation and reorientation at angle θ, as follows:

[0082] Γ1(β)dβ=Γ0(θ)dθ=dN

[0083] Therefore, the angular distribution of the fiber after rotation is:

[0084]

[0085] Where, λ x ,λ y These are the elongation rates along the x and y axes, respectively. D is the spacing between fibers.

[0086] n f For fibers formed from root fibrils, the strain of a fiber bundle with direction θ is:

[0087]

[0088] Where, λ p The calculation expression is as follows

[0089] The strain energy density of PGs satisfies:

[0090]

[0091] Among them, κ pg d represents the average stiffness of a collagen fiber composed of multiple fibrils. pg A parameter representing the degree of nonlinearity of collagen fibers during slip deformation.

[0092] The stress response of fiber slip for:

[0093]

[0094] Where D(λ) f ) represents the normal distribution of ripple. Substituting λ f The value of .

[0095] The tissue-level collagen fiber stress response considering fiber crimping, straightening, rotation, and slippage is as follows:

[0096]

[0097] Among them, S f and S pg These are the fiber tensile stress response and slip stress response, respectively.f and S pg Together they constitute the collagen fiber item.

[0098] Through the above methods, the present invention establishes a collagen fiber term that includes fiber crimping, straightening, rotational redirection, and slippage, which can describe and predict the mechanical response of collagen fibers.

[0099] (3) For elastic fibers, considering the rotation of the elastic fibers, the following elastin strain energy function is used:

[0100]

[0101] Among them, κ e It is the modulus of effective elastin fibers, E f For the strain of elastin fibers, d e This is a parameter representing the degree of nonlinearity of the elastic fiber during deformation.

[0102] The orientation of elastin fibers follows a normal distribution. e (θ), then the stress response S of the elastin fiber containing rotational motion e The expression is:

[0103]

[0104] S e As the elastic fiber item.

[0105] Step S3: Combine the matrix term, collagen fiber term, and elastic fiber term to obtain a parameter model to be determined.

[0106] The complete constitutive model expression for the undetermined parameters is:

[0107] S=φ c S c +φ e S e +φ m S m

[0108] Where S represents the tissue-level stress response.

[0109] In fiber stretching, fibers often exhibit a family of fibers in a few representative directions under load. However, since this constitutive model involves multiple integrations in practical applications, computational efficiency is low. Therefore, this problem is addressed by decoupling the distribution of collagen fibers in the tissue into typical directions N. i The sum of the fiber bundles under the following typical direction is characterized by the gradual recruitment of fibers in soft tissue under a tensile force S at the tissue level, resulting in fiber bundles with multiple principal directions and clear physical significance. The 2nd Piola Kirchhoff stress response at this point is:

[0110]

[0111] Where, θ i This represents the calibration angle of the i-th circumferential axis, n f n represents the number of fibrils contained in a collagen fiber. c n represents the number of typical directions in which collagen fibers exhibit behavior after being subjected to force. e This represents the number of typical directions in which the elastic fiber exhibits its behavior under stress, and is taken as n. c ,n e =3. N i This represents the i-th typical direction.

[0112] The tissue-level stress response S is determined as the undetermined parameter model.

[0113] Step S4: Add the volume fractions of matrix, collagen fibers and elastic fibers in the soft tissue to the undetermined parameter model; use the nearest global optimization differential evolution algorithm to solve for the undetermined parameters in the undetermined parameter model to obtain the hyperelastic constitutive model.

[0114] In this step, the volume fractions of matrix, collagen fibers, and elastic fibers obtained through experimental measurement in step S1 are substituted into the undetermined parameter model to reduce the number of parameters that need to be fitted.

[0115] Then, the parameters are fitted using the differential evolution algorithm. Loss function for:

[0116]

[0117] in, It is the experimental data of the j-th data point in direction 1. This is the calculated value of the j-th data point in the second direction. n represents the number of data points in the test points, including circumferential and radial data points.

[0118] R, a measure of fitting ability 2 The calculation formula is as follows:

[0119]

[0120] Where y j It is the j-th data value. It is the constitutive model prediction value corresponding to the j-th data point. It is the average value of the j-th experimental data.

[0121] After parameter fitting, the hyperelastic constitutive model of J-type soft tissue was finally obtained.

[0122] Step S5: Use the hyperelastic constitutive model to obtain multiple mechanical parameters of soft tissue fibers.

[0123] In some embodiments, tensile physical parameters are input into the hyperelastic constitutive model of the J-shaped soft tissue to obtain a plurality of corresponding mechanical parameters, including matrix membrane stress, elastic fiber membrane stress, collagen fiber membrane stress, and membrane stress corresponding to straightening, rotation, and slippage of coiled fibers.

[0124] By employing a hyperelastic constitutive model, this invention can separate the mechanical contributions of each component and quantitatively calculate the kinematic behavior of various fibers. Specifically, this invention can obtain the stress proportions of multiple components, such as the matrix term, elastic fiber term, and elastic fiber term, and can also obtain the stress proportions of various kinematic behaviors, such as fiber straightening, rotation, and slippage.

[0125] To verify the effectiveness of the constitutive model proposed in this invention, biaxial tensile test data of the tricuspid valve were used for validation. The fitting results are as follows: Figure 3 As shown in Table 1, under the given conditions, the method proposed in this invention is compared with the traditional Fung exponential constitutive model. Analysis of the fitting accuracy shows that the hyperelastic constitutive model of J-type soft tissue provided by this invention can comprehensively couple physical information under planar biaxial tension, with each physical parameter having a distinct physical meaning, and exhibiting higher fitting accuracy. This indicates that the constitutive model proposed in this invention fully utilizes the physical information of the tissue and demonstrates strong descriptive potential in fitting this type of J-type soft tissue material.

[0126] Table 1

[0127]

[0128] While the specific embodiments of the present invention depict actions or steps in a particular order, this should be understood as requiring such actions or steps to be performed in the shown specific order or sequential order, or requiring all illustrated actions or steps to be performed to achieve the desired result. In certain environments, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these should not be construed as limiting the scope of this disclosure. Certain features described in the context of individual embodiments may also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may also be implemented individually or in any suitable sub-combination in multiple implementations. The above descriptions are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention.

[0129] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A constitutive modeling method applicable to J-type soft tissue, characterized in that, Includes the following steps: Step S1: The soft tissue is treated using tissue staining methods to obtain the volume fractions of matrix, collagen fibers and elastic fibers in the soft tissue; Step S2: Determine the isotropic matrix terms based on the characteristics of the mesenchymal cells and endothelial cells in the matrix; The collagen fiber term is determined based on the characteristics of collagen fiber crimping and straightening, fiber rotation, and interfiber slippage; The elastic fiber term is determined based on the fiber rotation characteristics of elastic fibers; Step S3: Combine the matrix term, collagen fiber term, and elastic fiber term to obtain a parameter model to be determined; Step S4: Add the volume fractions of matrix, collagen fibers and elastic fibers in the soft tissue to the undetermined parameter model; use the nearest global optimization differential evolution algorithm to solve for the undetermined parameters in the undetermined parameter model to obtain the hyperelastic constitutive model; Step S5: Obtain multiple mechanical parameters of the soft tissue using the hyperelastic constitutive model; Step S2 specifically includes: Step S2-1: For the matrix composed of mesenchymal cells and endothelial cells, establish a matrix term based on isotropic properties. The matrix term calculates the stress response of the matrix based on the strain tensor of the matrix, the stiffness parameter of the matrix, and the first strain tensor invariant. Step S2-2: Establish a collagen fiber term based on the characteristics of collagen fiber crimping and straightening, fiber rotation and interfiber slippage. The collagen fiber term includes fiber tensile stress response and slippage stress response. Step S2-3: Establish an elastic fiber term based on the stress response of the elastic fiber containing rotational motion. The elastic fiber term is based on the modulus and strain of the elastic fiber to calculate the stress response of the elastic fiber. In step S2-1, the stress response S of the matrix m The expression is: Among them, κ m The matrix stiffness parameter is represented by I1, which represents the first strain tensor invariant; p is the Lagrange multiplier; and C represents the Cauchy-Green strain tensor. Step S2-2 specifically includes: Step S2-2-1: Determine the relationship between the waviness of a single fiber and its uniaxial strain during the crimping and straightening process of a single fiber, and determine the crimping and straightening stress response of the fiber assembly based on the relationship characteristics of the single fiber. Step S2-2-2: Based on the described curling and straightening stress response, and combined with the fiber rotation characteristics, determine the fiber tensile stress response; Step S2-2-3: Based on the slip characteristics of collagen fibers, determine the slip stress response of the fiber assembly; Step S4 specifically includes: The volume fractions of matrix, collagen fibers, and elastic fibers obtained through experimental measurements in step S1 are substituted into the undetermined parameter model, and then the parameters are fitted using the differential evolution algorithm, with the loss function... for: in, It is the experimental data of the j-th data point in direction 1. It is the model calculation value of the j-th data point in the 2nd direction, and n represents the number of data points in the test point, including circumferential and radial data points; R, a measure of fitting ability 2 The calculation formula is as follows: Where y j It is the j-th data value. It is the constitutive model prediction value corresponding to the j-th data point. It is the average value of the j-th experimental data. After parameter fitting, the hyperelastic constitutive model of the J-type soft tissue is finally obtained.

2. The constitutive modeling method for J-type soft tissue according to claim 1, characterized in that, Step S1 specifically includes: Different staining reagents were used to label and stain the matrix, collagen fibers and elastic fibers in soft tissue. The stained soft tissue was imaged and analyzed using an optical microscope. The volume fraction of matrix, collagen fibers and elastic fibers in soft tissue was calculated using image analysis software.

3. The constitutive modeling method for J-type soft tissue according to claim 2, characterized in that, In step S2-2-2, the curling and straightening stress response S f The expression is: Where, n f κ represents the number of fibrils. c d represents the stiffness parameter of collagen fibers. c The parameter represents the degree of nonlinearity of collagen fibers during deformation; θ is the calibrated angle along the circumferential axis, Γ c (θ) is a normal distribution of the calibrated angles along the circumferential axis, λ x ,λ y These are the elongation rates along the x and y axes, respectively. Let α represent the uniaxial strain of the fiber bundle, α represent the ratio of fiber slip length to bearing elongation, and λ represent the uniaxial strain of the fiber bundle. f The total stretch excluding fiber slippage is represented by D(w), where D(w) indicates that the fiber waviness follows a normal distribution, and N represents the direction in the tissue space. It represents the outer product.

4. The constitutive modeling method for J-type soft tissue according to claim 3, characterized in that, In step S2-2-3, the slip stress response S of the fiber assembly pg The expression is: Among them, κ pg d represents the average stiffness of a collagen fiber composed of multiple fibrils. pg A parameter representing the degree of nonlinearity of collagen fibers during slip deformation. D(λ) represents the slip strain of the fiber bundle. f ) represents the normal distribution of ripple. Substituting λ f The value, D is the spacing between fibers, L f It is the arc length of a single collagen fiber.

5. The constitutive modeling method for J-type soft tissue according to claim 4, characterized in that, In steps S2-3, the stress response S of the elastic fiber e The expression is: Among them, κ e It is the modulus of effective elastin fibers, E f For the strain of elastin fibers, d e This is a parameter representing the degree of nonlinearity of the elastic fiber during deformation.

6. The constitutive modeling method for J-type soft tissue according to claim 5, characterized in that, The expression for the undetermined parameter model in step S3 is: Where S represents the tissue-level stress response, θ i This represents the calibration angle of the i-th circumferential axis, n c n represents the number of typical directions in which collagen fibers exhibit behavior after being subjected to force. e N represents the number of typical directions in which the elastic fiber exhibits its behavior under stress. i φ represents the i-th typical direction. c ,φ e ,φ m These are the volume fractions of collagen fibers, elastic fibers, and matrix, respectively.

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