Cell adhesion modeling method coupling matrix fractal features and viscoelastic deformation

Abstract

This invention discloses a cell adhesion modeling method coupling matrix fractal characteristics and viscoelastic deformation, comprising: 1. establishing a mechanical model of cell-matrix adhesion, related analysis, and hypotheses; 2. calculating closed molecular bond forces; 3. calculating the instantaneous molecular bond dissociation rate; 4. calculating the instantaneous molecular bond binding rate; 5. evaluating the effects of matrix creep, matrix stiffness, matrix fractal characteristics, and molecular bond distribution on molecular bond forces, molecular bond binding rates, and molecular bond dissociation rates. This invention reveals a novel mechanism of cell-matrix adhesion, comprehensively quantifying the influence of receptor-ligand distribution, matrix fractal characteristics, and the time scale of cell and matrix deformation (such as cell and matrix creep effects) on cell adhesion, thus aiding in the treatment of cell adhesion-related diseases. This invention can be applied to the preparation of biomaterials and in vitro cell culture, providing solutions for the application of bio-3D printing technology.

Description

Technical Field

[0001] This invention belongs to the field of cell adhesion mechanism modeling and analysis technology, and particularly relates to a cell adhesion modeling method that couples matrix fractal characteristics and viscoelastic deformation. Background Technology

[0002] Cell adhesion is fundamental to important physiological processes such as cell migration, proliferation, and differentiation, and serves as a channel for intercellular information exchange. Cells sense the physical properties (stiffness, thickness, geometry, and deformation) and mechanical stimuli of the extracellular environment through cell adhesion. Quantitative research on cell-matrix interactions is of great significance for the treatment of diseases related to cell adhesion, and also provides theoretical references for the preparation of biomaterials, bio-additive manufacturing, and in vitro cell culture.

[0003] Cell-matrix adhesion primarily occurs through adhesion plaques, which are mainly composed of multiple receptor-ligand bonds. Receptors in adhesion plaques, acting as transmembrane proteins, interact with ligand proteins on the matrix to generate cell-matrix interactions. Bell was the first to propose a model of cell-matrix interactions, simulating molecular bond clusters as springs and considering both cells and matrix as rigid bodies. Based on Bell's theories, leading researchers have established continuous-medium adhesion models that consider the elasticity or viscoelasticity of the cell and matrix to study the mechanisms of cell-matrix interactions.

[0004] From a materials perspective, cells are highly dynamic viscoelastic materials; they exist within a highly dynamic three-dimensional viscoelastic matrix. They communicate with their surroundings in a highly dynamic and complex manner, forming highly dynamic viscoelastic tissues. Cells can continuously read microenvironmental cues, such as matrix stiffness and geometry, and respond to them in a mechanosensitive manner to maintain cell and tissue health. The extracellular matrix, in which cells reside, is also essentially a viscoelastic material. Compared to elastic matrices, viscoelastic matrices can dissipate stress acting upon them significantly (stress relaxation), which is beneficial for cell adhesion and proliferation—a property that has been experimentally confirmed. However, existing studies treat cells and the matrix as rigid, or only consider the viscoelastic deformation of one (cell or matrix), failing to comprehensively consider the influence of viscoelastic deformation of both cells and the matrix, as well as the fractal characteristics (geometry) of the matrix, thus failing to accurately assess the interaction between cells and the matrix. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides a cell adhesion modeling method that couples matrix fractal characteristics and viscoelastic deformation. This method aims to accurately assess the influence of factors such as matrix material viscoelasticity, matrix fractal characteristics, ligand density in the matrix material, and external forces on the interaction between cells and the matrix. Furthermore, this method can be applied to the preparation of bio-hydrogel matrix materials, bio-additive manufacturing, and in vitro cell culture.

[0006] To solve the above problems, the present invention adopts the following technical solution:

[0007] The cell adhesion modeling method proposed in this invention, which couples matrix fractal features and viscoelastic deformation, includes the following steps:

[0008] Step 1: Considering the influence of matrix fractal characteristics, matrix and cell viscoelastic effects on cell-matrix adhesion, establish a viscoelastic-viscoelastic infinite half-space adhesion model;

[0009] Step 1.1: Considering the fractal characteristics of the matrix and the viscoelastic effects of the matrix and cells on cell-matrix adhesion, two viscoelastic infinite half-spaces are used to simulate the cell and matrix. The cell and matrix are connected by adhesion plaques, and receptor-ligand bonds are uniformly distributed in the adhesion plaques. The receptor-ligand bonds are simulated using elastic springs. Assume that the width of the adhesion plaque is 2a, the width of the receptor-ligand bond is a0, the number of receptor-ligand bonds is N, N = 2a / a0, and the coordinate of each molecular bond on the horizontal axis is x. i The value of i ranges from 1 to N. Considering a plane stress-strain problem, let the width of the viscoelastic infinite half-space be the width b of the acceptor-ligand bond. An external force F acts at the center positions of the two viscoelastic half-spaces respectively;

[0010] Step 1.2: The WM fractal function is a typical function used to represent random contours. The WM fractal function is used to accurately simulate and reconstruct the matrix surface with fractal properties. The WM fractal function is Z... s (x),

[0011]

[0012] In equation (1), Z s (x) represents the height of the matrix surface morphology; x represents the position coordinates of the matrix; D is the fractal dimension, which describes the function Z. s (x) Irregularity at all scales; G is the surface feature length scale coefficient, which reflects Z s (x) Amplitude; γ is the spatial frequency of the surface profile. For random profiles following a normal distribution, to suit high spectral density and phase randomness, γ is generally taken as 1.5. n is the frequency exponent, and n1 is the ordinal number corresponding to the lowest cutoff frequency ω1 of the matrix surface. Since the matrix is ​​a non-stationary random process, the lowest frequency is related to the matrix sampling length L, and is γ. n1 =1 / L, where n1 is the ordinal number corresponding to the lowest cutoff frequency ω1 on the matrix surface.

[0013] Step 1.3: Calculate the force F(x) from the closed bond. i The x-axis at any closed bond position in the viscoelastic half-space caused by ,t,z) j normal displacement,

[0014]

[0015] In equation (2), Q c (x j ,x i )=2(1-υ c 2 )ln|(x ∞ -x i ) / (x j -x i )| / πb,

[0016] Q s (x j ,x i )=2(1-υ s 2 )ln|(x ∞ -x i ) / (x j -x i )| / πb,υ c and υ s Poisson's ratio for cells and matrix, respectively, C c (t) and C s (t) represents the creep compliance of the cell and matrix, respectively, and n is the number of closed bonds. When i = j, the distributed force F(x) is used. i ,t,z) / a0 replaces the concentrated force F(x) i If ,t,z), then Q(x) i ,x i )=2(1-υ 2 )C0 / πb.

[0017] Step 1.4: Calculate the force F(x) from the closed bond. j x caused by ,t,z) j Elastic elongation L(x) at the location of the closed key j ,t,z), Where k r Stiffness of elastic molecular bonds.

[0018] Step 1.5: In x j Closure location, matrix surface morphology height Z s (x j The displacement w of the upper and lower viscoelastic half-spaces c (x j ,t,z) and w s (x j ,t,z), elastic elongation of molecular bonds L(x) j ,t,z), resting length of molecular bond l b Satisfy the following equation:

[0019] Z s (x j )+w c (x j ,t,z)+w s (x j ,t,z)+L(x j ,t,z)+l b =H(t, z) (4)

[0020] In equation (4), H(t,z) is the distance between the two interfaces at infinity.

[0021] Since the entire system is in force equilibrium, it satisfies the following equation:

[0022]

[0023] In equation (5), Z r (x 0ff x, t, z) is x off The amount of spring elongation caused by thermal disturbance to the free receptor;

[0024] Step 2: Calculate the closed molecular bond force F(x) j ,t,z);

[0025] Step 2.1: The number of closure bonds is n, and the value of j ranges from 1 to n. From equation (4), we know that by changing the value of j, we can obtain n equations. Adding equation (5), we have a total of n+1 equations, which can solve for n+1 unknowns, namely F(x1,t,z), F(x2,t,z), ..., F(x n H(t,z) and H(t,z);

[0026] Step 2.2: The equation in Step 2.1 holds true at any time t. Decompose the time interval [0~t] into k intervals. When any time interval Δt r =t r+1 -t r When the value of r is sufficiently small (from 0 to k-1), the force of the closed molecular bond F(x) j F(x,t,z) can be considered constant over arbitrarily small time intervals. j (t, z) can be expressed as the following formula:

[0027]

[0028] In equation (6), U(t) is the unit step function.

[0029] Step 2.3: Substitute equations (2), (3), and (6) into equation (4) and combine them with equation (5) to obtain the result at any time t. rhave:

[0030]

[0031] Step 2.4: Record X on = [x1,x2,x3,…x n ] T x i F(t) represents the x-coordinate of the closed bond. r ,z)=[F(x1,t r ,z),F(x2,t r ,z),……F(x n ,t r ,z)] T Z s (x)=[Z s (x1),Z s (x2),…Z s (x n )] T Z S (x i ) represents the x-coordinate i The morphology height of the matrix surface,

[0032]

[0033]

[0034]

[0035]

[0036] I is an n×n identity diagonal matrix, ε={1} n×1 , A is an n×n matrix;

[0037] Step 2.5: From Steps 2.3 and 2.4, the expression for the closed molecular bond force can be obtained.

[0038]

[0039] (8) Among them,

[0040] Step 3: The closed molecular bond forces affected by matrix fractal characteristics and viscoelastic deformation are iterated to obtain the expression of the change of closed molecular bond forces with time at any time. The dissociation rate of closed molecular bonds at any time is further analyzed by Bell theory.

[0041] Step 4: Calculate the molecular bond binding rate. The process of breaking the bond and freeing the acceptor to bind to the ligand is simulated as the acceptor undergoing Brownian motion in a potential well, where the potential well U(t) is the ligand. rThe size of z depends on the change in the elastic properties of the polymer that connects to the free acceptor;

[0042] Step 4.1: Calculate the actual distance ξ that the free receptor moves when it binds to the ligand. off (t r );

[0043] Step 4.2: Calculate the potential well U(t) based on the elongation of the polymer connecting the free acceptor. r The size of z);

[0044] Step 4.3: Calculate the molecular bond binding rate depending on matrix fractal characteristics and cell and matrix viscoelastic deformation.

[0045] Step 5: Use MATLAB programming to calculate the molecular bond forces, molecular bond binding rates, and molecular bond dissociation rates described in steps 1 to 4. Change the creep time, matrix stiffness, matrix fractal characteristics, and molecular bond distribution parameters, and evaluate their effects on the molecular bond forces, molecular bond binding rates, and molecular bond dissociation rates.

[0046] Compared with the prior art, the beneficial effects of the present invention are reflected in:

[0047] This invention reveals a novel mechanism of cell-matrix adhesion, comprehensively quantifying the effects of receptor-ligand distribution, matrix fractal characteristics, and the temporal scales of cell and matrix deformation (such as cell and matrix creep effects) on the binding and breaking rates of molecular bonds during cell adhesion. Specifically, the beneficial effects are as follows: matrix receptor-ligand distribution guides the preparation of materials that promote cell adhesion; the influence of the temporal scales of cell and matrix deformation on the binding and breaking rates of molecular bonds during cell adhesion can explain experiments on cell adhesion to viscoelastic substrates and further guide the preparation of viscoelastic materials that promote cell adhesion; and the influence of matrix fractal characteristics on cell adhesion guides the geometric design of 3D-printed scaffolds for in vitro cell culture.

[0048] This invention can be applied to the preparation of biomaterials and the in vitro culture of cells, providing solutions for the application of bio-3D printing technology, and also assisting in the treatment of diseases related to cell adhesion. Attached Figure Description

[0049] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0050] Figure 1(a) is a schematic diagram of cells adhering to the substrate through adhesion spots;

[0051] Figure 1(b) is a schematic diagram of the adhesion spot structure;

[0052] Figure 2Flowchart for modeling and analyzing cell adhesion;

[0053] Figure 3(a) is a schematic diagram of the mechanical model of molecular bond clusters distributed between cells and matrix;

[0054] Figure 3(b) is a magnified schematic diagram of the matrix surface morphology;

[0055] Figure 4(a) is a schematic diagram of the mechanical model of closed molecular bonds;

[0056] Figure 4(b) is a schematic diagram of the mechanical model of breaking molecular bonds.

[0057] Specific Implementation Examples

[0058] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0059] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0060] In this embodiment, as shown in Figure 1(a), cells adhere to the substrate through adhesion plaques and sense the substrate's stiffness, geometry, deformation, and mechanical stimulation through these plaques. Figure 1(b) shows the structure of the adhesion plaque, which consists of multiple integrin-ligand bonds. The integrin forms receptor-ligand bonds with the substrate ligands and simultaneously binds to stress fibers.

[0061] According to the embodiments Figure 2 The flowchart shown is implemented, and the specific steps are as follows:

[0062] Step 1: Considering the influence of matrix fractal characteristics, matrix and cell viscoelastic effects on cell-matrix adhesion, establish a viscoelastic-viscoelastic infinite half-space adhesion model as shown in Figure 3(a);

[0063] Step 1.1: As shown in Figure 3(a), two viscoelastic infinite half-spaces are used to simulate the cell and matrix. The cell and matrix are connected by adhesion spots. The receptor-ligand bonds are uniformly distributed in the adhesion spots. The receptor-ligand bonds are simulated by elastic springs.

[0064] Assume the width of the adhesion plaque is 2a, the width of the receptor-ligand bond is a0, the number of receptor-ligand bonds is N, N = 2a / a0, and the coordinate of each molecular bond on the horizontal axis is x. i The value of i ranges from 1 to N. Considering a plane stress-strain problem, let the width of the viscoelastic infinite half-space be a0, which is the width of the acceptor-ligand bond. An external force F acts on the center positions of the two viscoelastic half-spaces respectively; initially, assuming the number of closed bonds is n, the number of open bonds is Nn. The positions of the closed bonds are recorded using a set X. onThe location of the disconnect key is represented by X. off express.

[0065] Step 1.2: The cell matrix is ​​not perfectly smooth, as shown in Figure 3(b), which is a magnified schematic diagram of the matrix morphology. The WM fractal function is a typical function used to represent random contours. The WM fractal function is used to accurately simulate and reconstruct the matrix surface with fractal properties. The WM fractal function is Z... s (x),

[0066]

[0067] In equation (1), Z s (x) represents the height of the matrix surface morphology; x represents the position coordinates of the matrix; D is the fractal dimension, which describes the function Z. s (x) Irregularity at all scales; G is the surface feature length scale coefficient, which reflects Z s (x) Amplitude; γ is the spatial frequency of the surface profile. For random profiles following a normal distribution, to suit high spectral density and phase randomness, γ is generally taken as 1.5. n is the frequency exponent, and n1 is the ordinal number corresponding to the lowest cutoff frequency ω1 of the matrix surface. Since the matrix is ​​a non-stationary random process, the lowest frequency is related to the matrix sampling length L, and is γ. n1 =1 / L, where n1 is the ordinal number corresponding to the lowest cutoff frequency ω1 on the matrix surface.

[0068] Step 1.3: Calculate the force F(x) from the closed bond. i The x-axis at any closed bond position in the viscoelastic half-space caused by ,t,z) j normal displacement,

[0069]

[0070] In equation (2), Q c (x j ,x i )=2(1-υ c 2 )ln|(x ∞ -x i ) / (x j -x i )| / πb,Q s (x j ,x i )=2(1-υ s 2 )ln|(x ∞ -x i ) / (x j -x i )| / πb,υ c and υs Poisson's ratio for cells and matrix, respectively, C c (t) and C s (t) represents the creep compliance of the cell and matrix, respectively, and n is the number of closed bonds. When i = j, the distributed force F(x) is used. i ,t,z) / a0 replaces the concentrated force F(x) i If ,t,z), then Q(x) i ,x i )=2(1-υ 2 )C0 / πb.

[0071] Step 1.4: Calculate the force F(x) from the closed bond. j x caused by ,t,z) j Elastic elongation L(x) at the location of the closed key j ,t,z), Where k r Stiffness of elastic molecular bonds.

[0072] Step 1.5: As shown in Figure 4(a), at x j Closure location, matrix surface morphology height Z s (x j The displacement w of the upper and lower viscoelastic half-spaces c (x j ,t,z) and w s (x j ,t,z), elastic elongation of molecular bonds L(x) j ,t,z), resting length of molecular bond l b Satisfy the following equation:

[0073] Z s (x j )+w c (x j ,t,z)+w s (x j ,t,z)+L(x j ,t,z)+l b =H(t, z) (4)

[0074] In equation (4), H(t,z) is the distance between the two interfaces at infinity.

[0075] Since the entire system is in force equilibrium, it satisfies the following equation:

[0076]

[0077] In equation (5), Z r (x 0ff x, t, z) is x off The amount of spring elongation caused by thermal disturbance to the free receptor;

[0078] Step 2: Calculate the closed molecular bond force F(x) j ,t,z);

[0079] Step 2.1: The number of closure bonds is n, and the value of j ranges from 1 to n. From equation (4), we know that by changing the value of j, we can obtain n equations. Adding equation (5), we have a total of n+1 equations, which can solve for n+1 unknowns, namely F(x1,t,z), F(x2,t,z), ..., F(x n H(t,z) and H(t,z);

[0080] Step 2.2: The equation in Step 2.1 holds true at any time t. Decompose the time interval [0~t] into k intervals. When any time interval Δt r =t r+1 -t r When the value of r is sufficiently small (from 0 to k-1), the force of the closed molecular bond F(x) j F(x,t,z) can be considered constant over arbitrarily small time intervals. j (t, z) can be expressed as the following formula:

[0081]

[0082] In equation (6), U(t) is the unit step function.

[0083] Step 2.3: Substitute equations (2), (3), and (6) into equation (4) and combine them with equation (5) to obtain the result at any time t. r have:

[0084]

[0085] Step 2.4: Record X on = [x1,x2,x3,…x n ] T x i F(t) represents the x-coordinate of the closed bond. r ,z)=[F(x1,t r ,z),F(x2,t r ,z),……F(x n ,t r ,z)] T Z s (x)=[Z s (x1),Z s (x2),…Z s (x n )] T Z S (x i) represents the x-coordinate i The morphology height of the matrix surface,

[0086]

[0087]

[0088]

[0089]

[0090] I is an n×n identity diagonal matrix, ε={1} n×1 , A is an n×n matrix;

[0091] Step 2.5: From Steps 2.3 and 2.4, the expression for the closed molecular bond force can be obtained.

[0092]

[0093] (8) Among them,

[0094] Step 3: The closed molecular bond forces affected by matrix fractal characteristics and viscoelastic deformation are iterated to obtain the expression of the change of closed molecular bond forces with time at any time. The dissociation rate of closed molecular bonds at any time is further analyzed by Bell theory.

[0095] k off (t)=k0exp(F(t) / F b (9)

[0096] Step 4: Calculate the molecular bond binding rate, simulating the binding process of the free acceptor and ligand as the acceptor undergoing Brownian motion in a potential well, where the potential well U(t) r The size of z depends on the change in the elastic properties of the polymer that connects to the free acceptor;

[0097] Step 4.1: Calculate the actual distance ξ that the free receptor moves when it binds to the ligand. off (t r As shown in Figure 4(b), let the position of the disconnect key be x. off When z = 0, the elongation of the broken molecular bond is 0, which is the initial position where the closed bond begins to react. The broken bond elongates under thermal perturbation, simultaneously causing rigid displacement of the upper viscoelastic half-space. The following two equations are satisfied at the position of the broken bond:

[0098] z(x off , t r )=z r (x m , t r ,z)+[wc (x off , t r ,z)-w c (x off , t r ,0)]+[H(0,0)-H(t r ,z)] (10)

[0099] δ(x off ,t r ,z)=H(t r ,z)-w c (x off ,t r ,z)-l b -z r (x off ,t r ,z)-w s (x off ,t r ,z)-Z s (x off (11) ξ is the actual distance ξ that the free receptor moves when the receptor and ligand bind. off (t r When combined, ξ off (t r )=z(x off ,t r At this time, the receptor-ligand spacing δ(x) off ,t r ,ξ off (t r ))=0, calculated as follows

[0100]

[0101] Step 4.2: Calculate the size of the potential well based on the elongation of the polymer connecting the free acceptor. During the binding process between the acceptor and ligand, the acceptor needs to overcome the deformation energy U(t) of the spring connected to it. r ,z),

[0102]

[0103] Step 4.3: Calculate the molecular bond binding rate depending on matrix fractal characteristics and cell and matrix viscoelastic deformation.

[0104]

[0105] in k B Let l be Boltzmann's constant, T be absolute temperature, and l be the constant. bind denoted as the molecular bond adhesion radius.

[0106] Step 5: Use MATLAB programming to calculate the molecular bond forces, molecular bond binding rates, and molecular bond dissociation rates described in steps 1 to 4. Change the creep time, matrix stiffness, matrix fractal characteristics, and molecular bond distribution parameters, and evaluate their effects on the molecular bond forces, molecular bond binding rates, and molecular bond dissociation rates.

[0107] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A cell adhesion modeling method coupled with matrix fractal characteristics and viscoelastic deformation, characterized by: Includes the following steps: Step 1: Considering the influence of matrix fractal characteristics, matrix and cell viscoelastic effects on cell-matrix adhesion, establish a viscoelastic-viscoelastic infinite half-space adhesion model; Includes the following steps: Step 1.1: Two viscoelastic infinite half-spaces are used to simulate cells and matrix. Cells and matrix are connected by adhesion spots. Receptor-ligand bonds are uniformly distributed in the adhesion spots. Receptor-ligand bonds are simulated by elastic springs. Step 1.2: Accurately simulate and reconstruct the matrix surface with fractal properties using WM fractal functions; Step 1.3: Calculate the force F(x) of the closed molecular bond. i The x-axis at any closed bond position in the viscoelastic half-space caused by ,t,z) j ; normal displacement; Step 1.4: Calculate the force F(x) of the closed molecular bond. j x caused by ,t,z) j Elastic elongation L(x) at the location of the closed key j ,t,z); Step 1.5: In x j Closure location, matrix surface morphology height Z s (x j The displacement w of the upper and lower viscoelastic half-spaces c (x j ,t,z) and w s (x j ,t,z), elastic elongation of molecular bonds L(x) j ,t,z), resting length of molecular bond l b Satisfy the following equation: Z s (x j )+w c (x j ,t,z)+w s (x j ,t,z)+L(x j ,t,z)+l b =H(t,z) (4) In equation (4), H(t,z) is the distance between the two interfaces at infinity; Since the entire system is in force equilibrium, it satisfies the following equation: In equation (5), Z r (x Off x, t, z) is x off The amount of spring elongation caused by thermal disturbance to the free receptor; Step 2: Based on the model in Step 1, calculate the closed molecular bond forces; Step 3: The closed molecular bond forces affected by matrix fractal characteristics and viscoelastic deformation are obtained through iteration to obtain the expression of the change of closed molecular bond forces with time at any time, and then the dissociation rate of closed molecular bonds at any time is analyzed. Step 4: Calculate the molecular bond binding rate depending on matrix fractal characteristics and cell and matrix viscoelastic deformation; Step 5: Evaluate the effects of matrix creep, matrix stiffness, matrix fractal characteristics, and molecular bond distribution on molecular bond forces, molecular bond binding rate, and molecular bond dissociation rate.

2. The cell adhesion modeling method based on matrix fractal features and viscoelastic deformation coupling as described in claim 1, characterized in that, In step 1.1, it is assumed that the width of the adhesion plaque is 2a, the width of the receptor-ligand bond is a0, the number of receptor-ligand bonds is N, N = 2a / a0, and the coordinate of each molecular bond on the horizontal axis is x. i The value of i ranges from 1 to N; considering the plane stress-strain problem, let the width of the viscoelastic infinite half-space be the width of the acceptor-ligand molecular bond b; the external force F acts on the center position of the two viscoelastic half-spaces respectively.

3. The cell adhesion modeling method based on matrix fractal features and viscoelastic deformation coupling as described in claim 1, characterized in that, In step 1.2, the WM fractal function is Z. s (x) In equation (1), Z s (x) represents the height of the matrix surface morphology; x represents the position coordinates of the matrix; D is the fractal dimension, which describes the function Z. s (x) Irregularity at all scales; G is the surface feature length scale coefficient, which reflects Z s (x) Amplitude; γ is the spatial frequency of the surface profile, with a value of 1.5; n is the frequency exponent; n1 is the ordinal number corresponding to the lowest cutoff frequency ω1 of the matrix surface; the relationship between the lowest frequency and the matrix sampling length L is given by γ. n1 =1 / L, where n1 is the ordinal number corresponding to the lowest cutoff frequency ω1 on the matrix surface.

4. The cell adhesion modeling method based on matrix fractal features and viscoelastic deformation coupling as described in claim 1, characterized in that, In step 1.4, the method for calculating the positional elastic elongation is as follows: In equation (2), Q c (x j ,x i )=2(1-υ c 2 )ln|(x ∞ -x i ) / (x j -x i )| / πb,Q s (x j ,x i )=2(1-υ s 2 )ln|(x ∞ -x i ) / (x j -x i )| / πb,υ c and υ s Poisson's ratio for cells and matrix, respectively, C c (t) and C s (t) represents the creep compliance of the cell and matrix, respectively, and n is the number of closed bonds; When i = j, use the distributed force F(x) i ,t,z) / a0 Substitution closing molecular bond force F(x i If ,t,z), then Q(x) i ,x i )=2(1-υ 2 )C0 / πb.

5. The cell adhesion modeling method based on matrix fractal features and viscoelastic deformation coupling as described in claim 1, characterized in that, The formula for calculating the elastic elongation in step 1.4 is as follows: Where k r Stiffness of elastic molecular bonds.

6. The cell adhesion modeling method coupled with matrix fractal features and viscoelastic deformation as described in claim 1, characterized in that, The calculation process for step 2 is as follows: Step 2.1: The number of closure bonds is n, and the value of j ranges from 1 to n. From equation (4), we know that by changing the value of j, we can obtain n equations. Adding equation (5), we have a total of n+1 equations, which can solve for n+1 unknowns, namely F(x1,t,z), F(x2,t,z), ..., F(x n H(t,z) and H(t,z); Step 2.2: The equation in Step 2.1 holds true at any time t. Decompose the time interval [0~t] into k intervals. For any integer r from 0 to k-1, the time interval Δt... r =t r+1 -t r When both are small enough, the force of the closed molecular bond F(x) j F(x,t,z) can be considered constant over arbitrarily small time intervals. j (t, z) can be expressed as the following formula: In equation (6), U(t) is the unit step function. Step 2.3: Substitute equations (2), (3), and (6) into equation (4) and combine them with equation (5) to obtain the result at any time t. r have Step 2.4: Record X on = [x1,x2,x3,…x n ] T x i F(t) represents the x-coordinate of the closed bond. r ,z)=[F(x1,t r ,z),F(x2,t r ,z),……F(x n ,t r ,z)] T Z s (x)=[Z s (x1),Z s (x2),…Z s (x n )] T Z S (x i ) represents the x-coordinate i The morphology height of the matrix surface, I is an n×n identity diagonal matrix, ε={1} n×1 , A is an n×n matrix; Step 2.5: From Steps 2.3 and 2.4, the expression for the closed molecular bond force can be obtained. in, 7. The cell adhesion modeling method based on matrix fractal features and viscoelastic deformation coupling as described in claim 1, characterized in that, The specific process of step 4 is as follows: Step 4.1: Calculate the actual distance ξ that the free receptor moves when it binds to the ligand. off (t r ); Step 4.2: Calculate the size of the potential well based on the elongation of the polymer connecting the free acceptor; Step 4.3: Calculate the molecular bond binding rate depending on matrix fractal characteristics and cell and matrix viscoelastic deformation.

8. The cell adhesion modeling method based on matrix fractal features and viscoelastic deformation coupling as described in claim 1, characterized in that, The specific process of step 5 is as follows: calculate the molecular bond force, molecular bond binding rate and molecular bond dissociation rate described in steps 1 to 4, change the creep time, matrix stiffness, matrix fractal characteristics and molecular bond distribution related parameters, and evaluate their effects on molecular bond force, molecular bond binding rate and molecular bond dissociation rate.

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