Construction modeling method suitable for J-shaped soft tissue

Abstract

The invention relates to the technical field of soft tissue mechanical modeling, in particular to a modeling method suitable for J-type soft tissue, which comprises the following steps: treating the soft tissue by adopting a tissue dyeing method to obtain the volume fractions of matrix, collagenous fiber and elastic fiber in the soft tissue; determining isotropic matrix items according to the characteristics of interstitial cells and endothelial cells in the matrix; determining a collagenous fiber item based on the characteristics of curl straightening, fiber rotation, and slippage between fibers of the collagenous fibers; determining an elastic fiber item based on the fiber rotation characteristic of the elastic fiber, and obtaining an undetermined parameter model; adding the volume fractions of matrix, collagenous fiber and elastic fiber in the soft tissue into an undetermined parameter model; and solving the to-be-determined parameters in the to-be-determined parameter model by adopting a recent global optimization differential evolution algorithm to obtain the hyperelastic constitutive model, and the accuracy of the J-type soft tissue mechanical property model can be improved.

Description

Technical Field

[0001] The invention relates to the technical field of soft tissue mechanics modeling, and in particular to a constitutive modeling method suitable for J-shaped soft tissue. Background Art

[0002] With the improvement of the accuracy of mechanical and optical experimental devices, more physical information is provided for soft tissue modeling. In the long process of biological evolution, soft tissue has gradually developed into one of the most outstanding materials in nature, with extremely outstanding deformation ability. How to reproduce the mechanical properties of natural tissues has always been a research goal in the fields of materials science and mechanics. The structure of soft tissue is composed of a mixture of multiple components, showing remarkable overall mechanical properties, especially in large deformation. This property has become an important research topic in bioengineering. Scientists are committed to in-depth exploration of its complex mechanical mechanisms in order to accurately predict the mechanical behavior of these materials. Therefore, it is particularly important to develop constitutive models that can effectively describe the mechanical characteristics at different length scales.

[0003] In the process of realizing the present invention, the inventors found that there are at least the following problems in the prior art: A key technical method for studying soft tissue is constitutive modeling. Traditional biological soft tissue modeling usually relies on tensor invariants of strain variables, often using exponential functions or power law functions. These invariant-based formulas show good accuracy in the fitting process, but their outstanding shortcomings are that the physical meaning of the parameters in the constitutive model is relatively unclear, and the mechanical contribution of each component cannot be separated, and the complex movement of the fiber is not considered. Summary of the invention

[0004] In view of the above problems, the present invention provides a constitutive modeling method suitable for J-type soft tissue, which solves the technical problems in the prior art that the physical meanings of parameters in the constitutive model are unclear and the fiber movement cannot be quantitatively expressed.

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

[0006] Step S1, processing the soft tissue using a tissue staining method to obtain the volume fractions of matrix, collagen fibers and elastic fibers in the soft tissue;

[0007] Step S2, determining an isotropic matrix item based on the characteristics of the interstitial cells and endothelial cells in the matrix; determining a collagen fiber item based on the characteristics of curling and straightening of collagen fibers, fiber rotation, and inter-fiber slippage; and determining an elastic fiber item based on the fiber rotation characteristics of elastic fibers;

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

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

[0010] Step S5: using 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 mark and stain the matrix, collagen fibers and elastic fibers in the soft tissue. The images of the stained soft tissue were collected and analyzed using an optical microscope. The volume fractions of the matrix, collagen fibers and elastic fibers in the soft tissue were calculated using image analysis software.

[0013] Preferably, step S2 specifically includes:

[0014] Step S2-1, for a matrix composed of interstitial cells and endothelial cells, a matrix term is established based on the isotropic property, wherein 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;

[0015] Step S2-2, establishing a collagen fiber term based on the curling and straightening characteristics of the collagen fibers, the fiber rotation, and the slippage between the fibers, wherein the collagen fiber term includes a fiber tensile stress response and a slip stress response;

[0016] Step S2-3, establishing an elastic fiber term based on the stress response of the elastic fiber with rotational motion, wherein 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 represents the stiffness parameter of the matrix, I1 represents the first strain tensor invariant; p is the Lagrange multiplier; C represents the Cauchy-Green strain tensor.

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

[0021] Step S2-2-1, determining the relationship characteristics between the waviness and uniaxial strain of a single fiber during the curling and straightening process of the single fiber, and determining the curling and straightening stress response of the fiber assembly based on the relationship characteristics of the single fiber;

[0022] Step S2-2-2, determining the fiber tensile stress response based on the curling and straightening stress response and combining the fiber rotation characteristics;

[0023] Step S2-2-3: Based on the slip characteristics of the 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] Among them, n f is the number of fibrils, κ c represents the stiffness parameter of collagen fibers, d c The parameter representing the nonlinearity of collagen fibers during deformation; θ is the calibration angle along the circumferential axis, Γ c (θ) is the normal distribution of the calibration angle along the circumferential axis, λ x ,λ y are the elongation rates of the x and y axes, is the uniaxial strain of the fiber bundle, α is the ratio of the fiber slip length to the load elongation, and λ f is the total stretch excluding fiber slip, D(w) indicates that the fiber waviness w conforms to the normal distribution, N is the direction in the tissue space, Represents the outer product.

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

[0028]

[0029] Among them, κ pg represents the average stiffness of collagen fibers composed of multiple fibrils, d pg The parameter that indicates the nonlinearity of collagen fibers during the slip deformation process, represents the slip strain of the fiber bundle, D(λ f ) represents the normal distribution of waviness. Substitute into λ f The value of D is the distance between fibers, L f is the arc length of a single collagen fiber.

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

[0031]

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

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

[0034]

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

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

[0037]

[0038] in, is the experimental data of the jth data 1 direction, is the model calculation value of the jth data in the 2nd direction. n represents the number of data in the test point, including circumferential and radial data points.

[0039] Evaluation of fitting ability R 2 The calculation formula is as follows:

[0040]

[0041] where y j is the jth data value, is the predicted value of the constitutive model corresponding to the jth data, is the average value of the jth experimental data. After parameter fitting, the hyperelastic constitutive model of 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 fractions of matrix, collagen fibers and elastic fibers in soft tissues through tissue staining methods, which not only avoids the problem of physical information ambiguity in traditional methods, but also makes the most of existing physical information, making the model have stronger physical meaning and accuracy.

[0044] (2) The present invention fully considers the mechanical properties of each component of soft tissue, including the isotropic characteristics of the matrix, the curling and straightening of collagen fibers, fiber rotation and inter-fiber slip characteristics, and the fiber rotation characteristics of elastic fibers. By mathematically modeling and combining these characteristics, the quantitative separation of the mechanical contribution of each component is successfully achieved, enabling the model to more comprehensively describe the mechanical behavior of soft tissue.

[0045] (3) The present invention uses the differential evolution algorithm of the nearest global optimization to determine the model parameters, which ensures the convergence of the solution process and the reliability of the results. The test verification of the planar biaxial tensile data shows that the model can accurately capture the J-type stress curve characteristics of soft tissue and has accurate prediction capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The drawings are only for the purpose of illustrating particular embodiments and are not to be construed as limiting the invention.

[0047] Figure 1 A flow chart of the constitutive modeling method for J-shaped soft tissue provided by the present invention.

[0048] Figure 2 A detailed flow chart of the constitutive modeling method for J-shaped soft tissue provided by the present invention.

[0049] Figure 3 Schematic diagrams of three complex movements of collagen fibers provided by the present invention.

[0050] Figure 4 This is a fitting effect diagram of the tricuspid valve biaxial stretching data tested by the present invention. DETAILED DESCRIPTION

[0051] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. In addition, the present invention can also be implemented in other ways different from those described herein, and therefore, the protection scope of the present invention is not limited by the specific embodiments disclosed below.

[0052] In order to illustrate the effectiveness of the method proposed in the present invention, the above technical solution of the present invention is described in detail below through a specific embodiment. Figure 1As shown, a constitutive modeling method suitable for J-shaped soft tissue is disclosed, and the specific implementation steps are as follows:

[0053] Step S1: Process the soft tissue using a tissue staining method to obtain the volume fractions of matrix, collagen fibers and elastic fibers in the soft tissue.

[0054] In some embodiments, the specific steps of processing the soft tissue using the tissue staining method may include: using different staining reagents to mark and stain the matrix, collagen fibers and elastic fibers in the soft tissue. The stained soft tissue is imaged and analyzed using an optical microscope or imaging equipment, and the volume fractions of the matrix, collagen fibers and elastic fibers in the soft tissue are calculated using image analysis software, and the obtained volume fractions are used as known parameters for subsequent model construction.

[0055] By predetermining these volume fractions, the 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, determining an isotropic matrix item based on the characteristics of the interstitial cells and endothelial cells in the matrix; determining a collagen fiber item based on the characteristics of curling and straightening of collagen fibers, fiber rotation, and inter-fiber slippage; and determining an elastic fiber item based on the fiber rotation characteristics of elastic fibers;

[0057] The present invention decouples the strain energy density of soft tissue and decomposes the mechanical response of the whole tissue into the contribution of three main components, including: elastic fibers (e), collagen fibers (c) and matrix (m) composed of connective tissues such as interstitial cells and endothelial cells. The mechanical contributions of the three are weighted by their respective volume fractions. The expression of the strain energy density function is:

[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, Ψ c (C),Ψ e (C),Ψ m (C) are the strain energy densities of collagen fibers, elastic fibers and matrix terms, φ c ,φ e ,φ m are the volume fractions of collagen fibers, elastic fibers and matrix terms, respectively.

[0060] By deducing the 2nd-Piola-Kirchhoff stress tensor, the expression of 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. p is introduced to describe the incompressibility of the tissue.

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

[0064] (1) For the matrix composed of connective tissues such as interstitial cells and endothelial cells, the present invention adopts isotropy to model it. The 2nd Piola Kirchhoff stress response S of the matrix composed of connective tissues such as interstitial cells and endothelial cells is m The expression is:

[0065]

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

[0067] S m as the matrix item.

[0068] (2) For collagen fibers, the present invention analyzes their mechanical properties and establishes collagen fiber terms. For a single fiber, Figure 3 As shown in Figure 2, the elongation deformation of the fiber includes fiber curling and straightening and fiber sliding. The density function of the collagen fiber term Ψ c (C) consists of two parts, namely, Ψ c (C)=Ψ f (C)+Ψ pg (C), where Ψ f (C) is the strain energy density of fiber curling and straightening, Ψ pg (C) is the strain energy density of fiber slip.

[0069] For the straightening of the curled fibers, Figure 3 As shown, L f is the arc length of a single collagen fiber, and L is the end-to-end length. Assume that the fiber waviness w = L f / L, w>1, the larger the w value, the higher the curling degree of the single fiber. Total stretching excluding fiber slippage where λ sIt is a relaxation stretch, which means stretching a single fiber before it is straightened. is the actual stretching of the fiber. The end-to-end distance after stretching is l. When l>L f hour, Assume that the fiber does not bear compressive loads but only tensile loads, so when w<λ f The fiber is loaded only when

[0070] The fiber waviness w conforms to the normal distribution D(w), and the collagen fibers with common orientation are considered to be subjected to uniaxial strain. Fiber assembly, uniaxial strain The expression is:

[0071]

[0072] The collagen fibers with common orientation are regarded as a fiber collection subjected to uniaxial strain. The strain energy of the fiber collection is ens (E f ) satisfies the following form:

[0073]

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

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

[0076]

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

[0078] Since collagen fibers have a certain orientation in tissues, it is assumed that the orientation of collagen fibers along the circumferential axis is calibrated at an angle θ that follows a normal distribution Γ c (θ). Under the affine assumption, the 2nd PiolaKirchhoff stress response expression of collagen fiber curling and straightening at the tissue level is:

[0079]

[0080] Where N is the direction in tissue space, N(θ) = [cos(θ), sin(θ), 0], θ is the calibration angle along the circumferential axis, 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 the angle β remains unchanged after the angle θ is rotated and reoriented, as follows:

[0082] Γ1(β)dβ=Γ0(θ)dθ=dN

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

[0084]

[0085] Among them, λ x ,λ y are the elongation rates of the x and y axes, D is the distance between fibers.

[0086] n f For a fiber formed by a root fibril, the strain of the fiber bundle in the direction of θ is:

[0087]

[0088] Among them, λ p The calculation expression is

[0089] The strain energy density of PGs satisfies:

[0090]

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

[0092] The stress response of fiber slip is for:

[0093]

[0094] Among them, D(λ f ) represents the normal distribution of waviness. Substitute into λ f The value of .

[0095] The 2nd Piola Kirchhoff stress response of collagen fibers at the tissue level considering fiber curling, straightening, rotation and slippage is:

[0096]

[0097] Among them, S f and S pg are the fiber tensile stress response and sliding stress response, respectively.f and S pg Together they form the collagen fibers.

[0098] Through the above-mentioned method, the present invention establishes collagen fiber terms including curling and straightening, rotational reorientation and sliding of the fibers, which can describe and predict the mechanical response of the collagen fibers.

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

[0100]

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

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

[0103]

[0104] S e As the spandex item.

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

[0106] The expression of the complete constitutive model with 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 the tensile process of fibers, they are often expressed as fiber families in several representative directions under load. In practical applications, this constitutive model involves multiple integrations, which results in low computational efficiency. i The sum of the fiber bundles under the typical direction is that under the tension of the tissue level S, the fibers in the soft tissue are gradually recruited and manifested as fiber bundles in multiple main directions, which has a clear physical meaning. At this time, the 2nd Piola Kirchhoff stress response is:

[0110]

[0111] Among them, θ i represents the calibration angle of the ith circumferential axis, n f Indicates the number of protofibrils contained in the collagen fiber, n c Indicates the number of typical directions of collagen fibers after being stressed, n e It represents the typical number of directions of elastic fiber after being stressed, and is taken as n c ,n e =3. N i represents the i-th typical direction.

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

[0113] Step S4, adding the volume fractions of the matrix, collagen fibers and elastic fibers in the soft tissue to the undetermined parameter model; using the nearest global optimal differential evolution algorithm to solve the undetermined parameters in the undetermined parameter model to obtain a hyperelastic constitutive model.

[0114] In this step, the volume fractions of the matrix, collagen fibers and elastic fibers obtained by 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 differential evolution algorithm is used to fit the parameters. Loss function for:

[0116]

[0117] in, is the experimental data of the jth data 1 direction, is the model calculation value of the jth data in the 2nd direction. n represents the number of data in the test point, including circumferential and radial data points.

[0118] Evaluation of fitting ability R 2 The calculation formula is as follows:

[0119]

[0120] where y j is the jth data value, is the predicted value of the constitutive model corresponding to the jth data, is the average value of the jth experimental data.

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

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

[0123] In some embodiments, the tensile physical parameters are input into the hyperelastic constitutive model of the J-type soft tissue to obtain corresponding multiple mechanical parameters, which include matrix membrane stress, elastic fiber membrane stress, collagen fiber membrane stress, and membrane stress corresponding to straightening, rotation and slippage of curled fibers.

[0124] Through the hyperelastic constitutive model, the present invention can separate the mechanical contribution of each component and quantitatively calculate the kinematic mechanical behavior of various fibers. Specifically, the present invention can obtain the stress proportions of various components such as matrix term, elastic fiber term and elastic fiber term, and can obtain the stress proportions of various kinematic mechanical behaviors such as fiber straightening, rotation and slippage.

[0125] In order to verify the validity of the constitutive model proposed in this invention, the biaxial tensile test data of the tricuspid valve is used for verification. Figure 3 As shown in Table 1, under the given conditions, the method proposed in the present invention is compared with the traditional Fung exponential constitutive model. The results are shown in the table. The analysis of the fitting accuracy shows that the hyperelastic constitutive model of the J-type soft tissue provided by the present invention can fully couple physical information under the condition of biaxial tension in the plane, and each physical parameter involved has a distinct physical meaning, while the fitting accuracy is higher. This shows that the constitutive model proposed in the present invention makes full use of the physical information of the tissue and shows a strong descriptive potential in fitting this J-type soft tissue material.

[0126] Table 1

[0127]

[0128] Although the specific embodiments of the present invention depict various actions or steps in a specific order, this should be understood as requiring such actions or steps to be performed in the specific order shown or in a sequential order, or requiring all illustrated actions or steps to be performed to obtain the desired results. Under certain circumstances, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these should not be interpreted as limiting the scope of the present disclosure. Certain features described in the context of a separate embodiment can also be implemented in a single implementation in combination. On the contrary, the various features described in the context of a single implementation can also be implemented in multiple implementations individually or in any suitable sub-combination. The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or replacements that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

[0129] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A constitutive modeling method for J-shaped soft tissue, characterized in that: The following steps are involved: Step S1, processing the soft tissue using a tissue staining method to obtain the volume fractions of matrix, collagen fibers and elastic fibers in the soft tissue; Step S2, determining an isotropic matrix item according to the characteristics of the interstitial cells and endothelial cells in the matrix; The collagen fiber term is determined based on the characteristics of curling and straightening of collagen fibers, fiber rotation, and inter-fiber slippage; Determining an elastic fiber term based on the fiber rotation characteristics of the elastic fibers; Step S3, combining the matrix item, collagen fiber item and elastic fiber item to obtain a parameter model to be determined; Step S4, adding the volume fractions of the matrix, collagen fibers and elastic fibers in the soft tissue to the undetermined parameter model; using the nearest global optimal differential evolution algorithm to solve the undetermined parameters in the undetermined parameter model to obtain a hyperelastic constitutive model; Step S5: using the hyperelastic constitutive model to obtain multiple mechanical parameters of the soft tissue.

2. The constitutive modeling method for J-shaped soft tissue according to claim 1, characterized in that: The step S1 specifically includes: Different staining reagents were used to mark and stain the matrix, collagen fibers and elastic fibers in the soft tissue. The images of the stained soft tissue were collected and analyzed using an optical microscope. The volume fractions of the matrix, collagen fibers and elastic fibers in the soft tissue were calculated using image analysis software.

3. The constitutive modeling method for J-shaped soft tissue according to claim 2, characterized in that: The step S2 specifically includes: Step S2-1, for a matrix composed of interstitial cells and endothelial cells, a matrix term is established based on the isotropic property, wherein 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, establishing a collagen fiber term based on the curling and straightening characteristics of the collagen fibers, the fiber rotation, and the slippage between the fibers, wherein the collagen fiber term includes a fiber tensile stress response and a slip stress response; Step S2-3, establishing an elastic fiber term based on the stress response of the elastic fiber with rotational motion, wherein the elastic fiber term is based on the modulus and strain of the elastic fiber to calculate the stress response of the elastic fiber.

4. The constitutive modeling method for J-shaped soft tissue according to claim 3, characterized in that: In step S2-1, the stress response S of the matrix m The expression is: Among them, κ m represents the stiffness parameter of the matrix, I1 represents the first strain tensor invariant; p is the Lagrange multiplier; C represents the Cauchy-Green strain tensor.

5. The constitutive modeling method for J-shaped soft tissue according to claim 4, characterized in that: The step S2-2 specifically includes: Step S2-2-1, determining the relationship characteristics between the waviness and uniaxial strain of a single fiber during the curling and straightening process of the single fiber, and determining the curling and straightening stress response of the fiber assembly based on the relationship characteristics of the single fiber; Step S2-2-2, determining the fiber tensile stress response based on the curling and straightening stress response and combining the fiber rotation characteristics; Step S2-2-3: Based on the slip characteristics of the collagen fibers, determine the slip stress response of the fiber assembly.

6. The constitutive modeling method for J-shaped soft tissue according to claim 5, characterized in that: In the step S2-2-2, the curling and straightening stress response S f The expression is: Among them, n f is the number of fibrils, κ c represents the stiffness parameter of collagen fibers, d c The parameter representing the nonlinearity of collagen fibers during deformation; θ is the calibration angle along the circumferential axis, Γ c (θ) is the normal distribution of the calibration angle along the circumferential axis, λ x ,λ y are the elongation rates of the x and y axes, is the uniaxial strain of the fiber bundle, α is the ratio of the fiber slip length to the load elongation, and λ f is the total stretch excluding fiber slippage, D(w) indicates that the fiber waviness w conforms to the normal distribution, N is the direction in the tissue space, Represents the outer product.

7. The constitutive modeling method for J-shaped soft tissue according to claim 6, characterized in that: In the step S2-2-3, the sliding stress response S of the fiber assembly pg The expression is: Among them, κ pg represents the average stiffness of collagen fibers composed of multiple fibrils, d pg The parameter that indicates the nonlinearity of collagen fibers during the slip deformation process, represents the slip strain of the fiber bundle, D(λ f ) represents the normal distribution of waviness. Substitute into λ f The value of D is the distance between fibers, L f is the arc length of a single collagen fiber.

8. The constitutive modeling method for J-shaped soft tissue according to claim 7, characterized in that: In step S2-3, the stress response S of the elastic fiber e The expression is: Among them, κ e is the effective elastin fiber modulus, E f is the elastin fiber strain, d e It is a parameter of the nonlinear degree of elastic fiber during deformation.

9. The constitutive modeling method for J-shaped soft tissue according to claim 8, characterized in that: The expression of the undetermined parameter model in step S3 is: Where S represents the tissue-level stress response, θ i represents the calibration angle of the ith circumferential axis, n c Indicates the number of typical directions of collagen fibers after being subjected to force, n e Indicates the number of typical directions in which elastic fibers are subjected to force, N i represents the i-th typical direction, φ c ,φ e ,φ m are the volume fractions of collagen fibers, elastic fibers and matrix terms, respectively.

10. The constitutive modeling method for J-shaped soft tissue according to claim 9, characterized in that: The step S4 specifically includes: The volume fractions of matrix, collagen fibers and elastic fibers obtained by experimental measurement in step S1 are substituted into the undetermined parameter model, and then the parameters are fitted using the differential evolution algorithm. The loss function for: in, is the experimental data of the jth data 1 direction, is the model calculation value of the jth data in the 2nd direction, n represents the number of data in the test point, including circumferential and radial data points, Evaluation of fitting ability R 2 The calculation formula is as follows: where y j is the jth data value, is the predicted value of the constitutive model corresponding to the jth data, is the average value of the jth experimental data. After parameter fitting, the hyperelastic constitutive model of J-type soft tissue is finally obtained.

Images