Method for predicting stress distribution of biological scaffold through recursive network

Abstract

The invention relates to the technical field of biomedical engineering, in particular to a method for predicting stress distribution of a biological scaffold by using a recursive network, which comprises the following steps: S1, acquiring geometric structure parameters and in-vitro culture environment parameters of the biological scaffold; s2, constructing a three-dimensional geometric model of the biological scaffold, and calculating the porosity of the scaffold and the shape characteristics of the support columns; s3, simulating a flow velocity field, a pressure field and shear stress distribution in the support; s4, calculating initial stress distribution of the biological scaffold under the action of fluid mechanics; s5, calculating the additional stress generated in the cell growth process, and iteratively updating the stress distribution of the stent through the recurrent neural network. According to the method, by combining the recurrent neural network and the cell proliferation kinetic model, the stress distribution of the biological scaffold in the cell growth process is accurately predicted, the scaffold design is optimized, and the biocompatibility and the mechanical stability of the scaffold are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of biomedical engineering, and particularly to a method for predicting the stress distribution of a biological scaffold using a recurrent network. Background Art

[0002] Biological scaffolds are widely used in tissue engineering to support cell growth and tissue repair; the design and application effect of biological scaffolds are closely related to their mechanical properties. Especially during the process of cell growth and proliferation, the stress distribution of the scaffold will change with the interaction between cells and the scaffold; as cells proliferate and migrate, they will generate traction forces on the surface of the scaffold, thereby inducing additional stresses, and the changes in these stresses will affect the structural stability of the scaffold and its performance in vivo; therefore, accurately predicting the stress distribution of a biological scaffold during cell growth is the key to optimizing scaffold design and improving its application effect.

[0003] However, the existing technologies have certain limitations in the stress prediction of biological scaffolds; although traditional finite element analysis methods can be used to calculate the stress distribution of scaffolds under the action of fluids, these methods usually ignore the mechanical changes during cell growth and cannot dynamically update the stress distribution of the scaffold; in addition, most of the existing methods rely on static stress analysis and do not fully consider the impact of cell proliferation on the scaffold, so they cannot provide accurate stress predictions. Summary of the Invention

[0004] Based on the above purposes, the present invention provides a method for predicting the stress distribution of a biological scaffold using a recurrent network.

[0005] A method for predicting the stress distribution of a biological scaffold using a recurrent network, comprising the following steps:

[0006] S1: Obtain the geometric structure parameters and in vitro culture environment parameters of the biological scaffold, wherein the geometric structure parameters include the porosity gradient distribution value, the strut diameter change rate, and the pore connectivity; the culture environment parameters include the viscosity of the culture medium and the perfusion flow rate;

[0007] S2: According to the geometric structure parameters obtained in S1, construct a three-dimensional geometric model of the biological scaffold, calculate the porosity of the scaffold and the shape characteristics of the struts, and generate the geometric data of the scaffold;

[0008] S3: Based on the geometric data generated in S2, calculate the fluid flow path inside the scaffold, and simulate the flow velocity field, pressure field, and shear stress distribution inside the scaffold according to the viscosity of the culture medium and the perfusion flow rate;

[0009] S4: According to the flow velocity field, pressure field, and shear stress distribution data obtained in S3, use finite element analysis to calculate the preliminary stress distribution of the biological scaffold under the action of fluid mechanics;

[0010] S5: Based on S4, combined with the cell proliferation characteristics of the biological scaffold, calculate the additional stress generated during cell growth, and iteratively update the stress distribution of the scaffold through a recurrent neural network.

[0011] Optionally, S1 specifically includes:

[0012] S11: Obtain the three-dimensional geometric image data of the biological scaffold through a three-dimensional scanner or computed tomography technology, and calculate the porosity gradient distribution value of the biological scaffold based on the three-dimensional geometric image data;

[0013] S12: Calculate the diameter change rate of the scaffold struts based on the three-dimensional geometric image data;

[0014] S13: Calculate the pore connectivity of the biological scaffold based on the three-dimensional geometric data through a pore connectivity analysis method;

[0015] S14: Use a rheological instrument to measure the viscosity of the culture medium, and the measurement method is to perform viscosity testing through a rotational viscometer or a capillary rheometer;

[0016] S15: Measure the perfusion flow rate of the culture medium by setting a flow meter and a flow rate sensor, and the flow rate measurement method is to use an ultrasonic flow meter or an electromagnetic flow meter to monitor the flow rate of the culture medium in the biological scaffold in real time.

[0017] Optionally, S2 specifically includes:

[0018] S21: Based on the three-dimensional geometric image data obtained in S1, use computer-aided design software to parameterize the geometric data of the scaffold and generate a three-dimensional geometric model of the scaffold;

[0019] S22: Calculate the porosity of the scaffold according to the three-dimensional geometric model generated in S21, and the formula is: where φ is the porosity of the scaffold, V void is the volume of the pores in the scaffold, and V total is the total volume of the scaffold;

[0020] S23: Based on the three-dimensional geometric model generated in S21, calculate the shape characteristics of the scaffold struts, including the diameter change, curvature, and length of the struts, and generate the shape characteristic data of the struts;

[0021] S24: Combine the porosity and the shape characteristic data of the struts obtained in S22 and S23 to generate the geometric data of the scaffold.

[0022] Optionally, S23 specifically includes:

[0023] S231: Based on the three-dimensional geometric model generated in S21, first extract the cross-sectional data of the stent struts at different positions, and calculate the diameter change of the struts through the following formula: where D rate is the diameter change rate of the strut, D max is the maximum diameter of the strut at a certain position, D min is the minimum diameter of the strut at the same position;

[0024] S232: Fit the geometric shape of the strut by the surface fitting method, and calculate the curvature of the strut by the least squares method. The formula is: where κ is the curvature of the strut, and R is the local radius of the strut surface at a certain position;

[0025] S233: Calculate the total length of the strut by calculating the length of each segment of the three-dimensional geometric model of the strut. Specifically, the integral method is used for calculation, and its formula is: where L is the total length of the strut, x, y, z are the coordinates of the strut in three-dimensional space, a and b are the starting and ending positions of the strut, and t is the parameter on the strut.

[0026] Optionally, the specific steps of S3 include:

[0027] S31: Based on the geometric data generated in S2, use the computational fluid dynamics method to perform mesh division on the geometric structure of the stent, discretize the three-dimensional stent model into multiple computational units, and generate a mesh model for fluid flow calculation;

[0028] S32: Calculate the flow path of the fluid in the stent by numerically solving the Navier-Stokes equations. The expression of the Navier-Stokes equations is: where ρ is the density of the fluid, v is the velocity vector of the fluid, p is the pressure of the fluid, μ is the viscosity of the fluid, f is the external body force, is the Laplace operator, represents the pressure gradient;

[0029] S33: According to the viscosity of the culture medium and the perfusion flow rate, combined with the geometric structure of the stent, use CFD simulation software to calculate the flow velocity field. The flow velocity field is calculated by the following formula: where v is the average flow velocity of the fluid, Q is the perfusion flow rate of the fluid, and A is the cross-sectional area of the fluid flow path;

[0030] S34: Use CFD simulation software to solve the pressure field and shear stress distribution. The pressure field is calculated by the following formula: where is the pressure field, ρ is the density of the fluid, μ is the viscosity of the fluid, is the time change rate of the flow velocity, is the convective term of the flow velocity, and f is the external body force; the shear stress is calculated by the following formula: where τ is the shear stress and μ is the viscosity of the fluid, is the velocity gradient, representing the frictional force between the fluid and the surface of the scaffold.

[0031] Optionally, S4 specifically includes:

[0032] S41: According to the velocity field, pressure field, and shear stress distribution data obtained in S3, first combine the three-dimensional geometric model of the scaffold with the fluid mechanics data, perform finite element mesh division, and discretize the scaffold model into a finite number of elements;

[0033] S42: Solve the stress distribution of the biological scaffold under the action of fluid mechanics through finite element analysis. The stress analysis equation expression used is: σ = E·∈, where σ is the stress, E is the Young's modulus of the scaffold, and ∈ is the strain;

[0034] S43: Combine the pressure field, velocity field, and shear stress distribution generated by the fluid to calculate the stress values at each position within the scaffold;

[0035] S44: Synthesize the calculated stress values to obtain a preliminary stress distribution map of the scaffold.

[0036] Optionally, S5 specifically includes:

[0037] S51: On the basis of S4, determine the cell proliferation characteristics in combination with the biological model. Based on the cell proliferation rate, migration rate, and growth density, predict the distribution and growth trend of cells on the surface of the scaffold to determine the additional stress generated by the cells on the scaffold during the growth process;

[0038] S52: Calculate the additional stress generated by each cell on the surface of the scaffold according to the traction force during cell growth, the interaction force between cells, and the pressure exerted by the cells on the surface of the scaffold, and map it onto the geometric model of the scaffold;

[0039] S53: Combine the additional stress calculated in S52 with the fluid mechanics stress distribution data obtained in step S4 to obtain the total stress distribution generated by the scaffold during cell growth;

[0040] S54: Use a recurrent neural network to take the current stress distribution as input, perform multiple iterative optimizations to learn the law of stress changes during cell growth, and update the stress distribution map of the scaffold to obtain a more accurate stress prediction.

[0041] Optionally, S51 specifically includes:

[0042] S511: First, calculate the number of cells growing on the scaffold surface per unit time through the kinetic model of cell proliferation. The formula is: N(t) = N 0 e rt , where N(t) is the number of cells at time t, N 0 is the initial number of cells, r is the proliferation rate of cells, and t is time;

[0043] S512: Based on the cell distribution model, calculate the process of gradual diffusion of cells on the scaffold surface. The formula is: where, is the change rate of cell density, D is the cell diffusion coefficient, is the spatial gradient of cell concentration, and r is the cell proliferation rate;

[0044] S513: Through the cell distribution data obtained in S512, calculate the additional stress exerted by cells on the scaffold surface. The formula is: σ cell = αN(t)·F traction , where σ cell is the additional stress exerted by cells, α is the stress gain factor, N(t) is the cell density, and F traction is the traction force exerted by cells on the scaffold surface;

[0045] S514: Combine the geometric shape of the scaffold, the cell density distribution, and the additional stress, and predict the stress change trend of cells after growing on the scaffold surface through the following formula, and then obtain the total additional stress generated during cell growth: σ total = ∫ Ω σ cell (x, t)dΩ, where σ total is the total additional stress generated by cells on the scaffold during cell growth, Ω is the scaffold surface area, and σ cell (x, t) is the local stress exerted by cells at position x and time t.

[0046] Optionally, S52 specifically includes:

[0047] S521: Calculate the traction force generated by each cell on the scaffold surface. The traction force is generated by the interaction between the cell and the scaffold surface, and the traction force is calculated through the following formula: F traction = k·Δx, where F traction is the traction force generated by cells, k is the elastic coefficient between the cell and the scaffold surface, and Δx is the displacement amount exerted by cells on the scaffold surface;

[0048] S522: Calculate the additional stress generated by cells on the scaffold surface. The additional stress is related to the traction force and the contact area of the scaffold surface, and is calculated through the following formula: where σcell is the additional stress generated by the cell on the surface of the scaffold, F traction is the traction force applied by the cell, A contact is the contact area between the cell and the surface of the scaffold;

[0049] S523: Spatially map the calculated additional stress σ cell according to the position of the cell on the surface of the scaffold, and using the geometric data of the scaffold, distribute the additional stress to each node of the scaffold through a grid mapping algorithm;

[0050] S524: Combine the growth state and cell distribution information of each cell on the surface of the scaffold, and gradually update the additional stress to the geometric model of the scaffold in a weighted average manner to obtain the final additional stress value of each node.

[0051] Optionally, the S54 specifically includes:

[0052] S541: Prepare the input data of the recurrent neural network, use the current stress distribution map of the scaffold as the input feature, and the additional stress, hydrodynamic stress generated during cell growth, and geometric characteristics of the scaffold as additional information to form the input vector of the neural network;

[0053] S542: Input the input vector into the recurrent neural network, make a preliminary prediction according to the existing weights and biases, and obtain the stress value of each node;

[0054] S543: Calculate the error between the network output and the true stress distribution through the backpropagation algorithm;

[0055] S544: Based on the error, use the gradient descent algorithm to adjust the weights and biases of the network to optimize the prediction ability of the network;

[0056] S545: Iterate multiple times until the prediction result converges; after convergence, the output stress distribution map is the final stress prediction during cell growth.

[0057] Advantages of the present invention:

[0058] In the present invention, by introducing a recurrent neural network and a cell proliferation kinetics model, it is possible to accurately predict the stress distribution of a biological scaffold during cell growth on the basis of considering hydrodynamic stress; through multiple iterations and optimizations, the recurrent neural network can effectively learn the law of stress changes during cell growth and dynamically update the stress distribution map of the scaffold, thereby providing a more accurate stress prediction; this process combines the interaction between hydrodynamics and biomechanics, enabling a comprehensive and dynamic simulation of the mechanical behavior of the scaffold during cell proliferation.

[0059] The present invention, through dynamically adjusting stress prediction, can help designers take into account the influence of cell behavior on mechanical properties during the stent design process, optimize the structure and material selection of the stent, improve its biocompatibility and mechanical stability, and ultimately enhance the reliability and effectiveness of the biostent in clinical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] To more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only those of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0061] Figure 1 It is a schematic diagram of the method for predicting the stress distribution of the biostent according to an embodiment of the present invention;

[0062] Figure 2 It is a schematic diagram of the process for iteratively updating the stress distribution through a recurrent neural network according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0063] The present invention will be described in detail below in conjunction with the drawings and specific embodiments. At the same time, it should be noted here that in order to make the embodiments more detailed, the following embodiments are the best and preferred embodiments. For some well-known technologies, those skilled in the art can also adopt other alternative methods for implementation; moreover, the drawings are only for more specifically describing the embodiments, and are not intended to specifically limit the present invention.

[0064] It should be pointed out that in the specification, when referring to "an embodiment", "embodiments", "exemplary embodiments", "some embodiments", etc., it indicates that the described embodiments may include specific features, structures or characteristics, but not necessarily every embodiment includes such specific features, structures or characteristics. In addition, when combining an embodiment to describe a specific feature, structure or characteristic, implementing such a feature, structure or characteristic in combination with other embodiments (whether explicitly described or not) should be within the knowledge scope of those skilled in the relevant art.

[0065] Generally, the terms can be understood at least in part from their use in the context. For example, at least in part depending on the context, the term "one or more" used herein can be used to describe any feature, structure or characteristic in a singular sense, or can be used to describe a combination of features, structures or characteristics in a plural sense. In addition, the term "based on" can be understood as not necessarily intended to convey a set of exclusive factors, but rather, at least in part depending on the context, allowing for the existence of other factors that may not be explicitly described.

[0066] Such as Figure 1 - Figure 2As shown in the figure, a method for predicting the stress distribution of a biological scaffold using a recursive network includes the following steps:

[0067] S1: Obtain the geometric structure parameters and in vitro culture environment parameters of the biological scaffold. Among them, the geometric structure parameters include the porosity gradient distribution value, the strut diameter change rate, and the pore connectivity; the culture environment parameters include the viscosity of the culture medium and the perfusion flow rate.

[0068] S2: According to the geometric structure parameters obtained in S1, construct a three-dimensional geometric model of the biological scaffold, calculate the porosity of the scaffold and the shape characteristics of the struts, and generate the geometric data of the scaffold.

[0069] S3: Based on the geometric data generated in S2, calculate the fluid flow path inside the scaffold, and simulate the flow velocity field, pressure field, and shear stress distribution inside the scaffold according to the viscosity of the culture medium and the perfusion flow rate.

[0070] S4: According to the flow velocity field, pressure field, and shear stress distribution data obtained in S3, use finite element analysis to calculate the preliminary stress distribution of the biological scaffold under the action of fluid mechanics.

[0071] S5: On the basis of S4, combined with the cell proliferation characteristics of the biological scaffold, calculate the additional stress generated during cell growth, and iteratively update the stress distribution of the scaffold through a recursive neural network.

[0072] S1 specifically includes:

[0073] S11: Obtain the three-dimensional geometric image data of the biological scaffold through a three-dimensional scanner or computer tomography (CT) technology, and calculate the porosity gradient distribution value of the biological scaffold based on the three-dimensional geometric image data. The porosity gradient distribution value reflects the change of the porosity of each part of the scaffold in space; the porosity gradient distribution value is calculated by the following formula: where φ(x, y, z) is the porosity of the biological scaffold at the position (x, y, z), V void is the void volume at this position, and V total is the total volume at this position;

[0074] S12: Based on the three-dimensional geometric image data, calculate the strut diameter change rate of the scaffold. The strut diameter change rate represents the degree of diameter change of each strut in the scaffold at different positions; the strut diameter change rate is calculated by the following formula: where D rate is the strut diameter change rate, D max is the maximum diameter of the strut at a certain position, and D min is the minimum diameter of the strut at the same position;

[0075] S13: By means of the pore connectivity analysis method, calculate the pore connectivity of the biological scaffold based on the three-dimensional geometric data. The pore connectivity reflects the connection degree between the pores in the scaffold and is used to evaluate the fluid channel characteristics of the scaffold. The pore connectivity is calculated by the following formula: where C comect is the pore connectivity, V connected is the volume of the connected pores in the scaffold, and V total is the total volume of the scaffold;

[0076] S14: Use rheological instruments to measure the viscosity of the culture medium. The measurement method is to conduct viscosity tests through a rotational viscometer or a capillary rheometer to obtain the flow characteristics of the culture medium at different shear rates;

[0077] S15: By setting a flow meter and a flow rate sensor, measure the perfusion flow rate of the culture medium. The flow rate measurement method is to use an ultrasonic flow meter or an electromagnetic flow meter to monitor the flow velocity of the culture medium in the biological scaffold in real time. Through the above steps, the geometric structure parameters and in vitro culture environment parameters of the biological scaffold can be accurately obtained, providing accurate basic data for subsequent fluid mechanics simulation and stress analysis.

[0078] S2 specifically includes:

[0079] S21: Based on the three-dimensional geometric image data obtained in S1, use computer-aided design (CAD) software to parameterize the geometric data of the scaffold and generate a three-dimensional geometric model of the scaffold. The model accurately describes each geometric feature of the scaffold, including struts, pores, and the connection relationship between pores;

[0080] S22: According to the three-dimensional geometric model generated in S21, calculate the porosity of the scaffold. The formula is: where φ is the porosity of the scaffold, V void is the volume of the pores in the scaffold, and V total is the total volume of the scaffold. The porosity reflects the proportion of voids in the scaffold;

[0081] S23: Based on the three-dimensional geometric model generated in S21, calculate the shape characteristics of the scaffold struts, including the diameter change, curvature, and length of the struts, and generate the shape characteristic data of the struts;

[0082] S24: Combine the porosity and the shape characteristic data of the struts obtained in S22 and S23 to generate the geometric data of the scaffold for subsequent fluid mechanics simulation and stress analysis. Through the specific implementation of the above steps, a three-dimensional geometric model of the biological scaffold can be accurately constructed, and the porosity and the shape characteristics of the struts can be accurately calculated. These accurate data provide the basis for subsequent fluid mechanics simulation and stress distribution prediction, ensuring the optimization of the scaffold design and the accurate simulation of biomechanical behavior.

[0083] The specific calculation of the shape characteristics of the support struts in S23 includes:

[0084] S231: Based on the three-dimensional geometric model generated in S21, first extract the cross-sectional data of the support struts at different positions, and calculate the diameter change of the struts through the following formula: where D rate is the diameter change rate of the strut, D max is the maximum diameter of the strut at a certain position, D min is the minimum diameter of the strut at the same position;

[0085] S232: Fit the geometric shape of the strut by the surface fitting method, and calculate the curvature of the strut using the least squares method. The formula is: where κ is the curvature of the strut, R is the local radius of the strut surface at a certain position, the curvature reflects the bending degree of the strut, and represents the geometric shape characteristics of the strut;

[0086] S233: Calculate the total length of the strut by calculating the length of each segment of the three-dimensional geometric model of the strut. Specifically, the integral method is used for calculation, and its formula is: where L is the total length of the strut, x, y, z are the coordinates of the strut in three-dimensional space, a and b are the starting and ending positions of the strut, and t is the parameter on the strut; this formula is used to accurately calculate the length of the strut; by calculating the diameter change, curvature and length of the support strut in detail, the geometric shape characteristics of the strut can be comprehensively understood; these shape characteristics provide detailed structural parameters for the subsequent prediction of stress distribution, which helps to optimize the support design and ensure its performance and stability in practical applications.

[0087] S3 specifically includes:

[0088] S31: Based on the geometric data generated in S2, use the computational fluid dynamics (CFD) method to mesh the geometric structure of the support, discretize the three-dimensional support model into multiple computational units, and generate a grid model for fluid flow calculation;

[0089] S32: Calculate the flow path of the fluid in the support by numerically solving the Navier-Stokes equations. The expression of the Navier-Stokes equations is: where ρ is the density of the fluid, v is the velocity vector of the fluid, p is the pressure of the fluid, μ is the viscosity of the fluid, f is the external volume force, is the Laplace operator, represents the pressure gradient; this equation is used to calculate the flow path of the fluid inside the support;

[0090] S33: According to the viscosity of the culture medium and the perfusion flow rate, combined with the geometric structure of the scaffold, use CFD simulation software to calculate the flow velocity field, and the flow velocity field is calculated by the following formula: where v is the average flow velocity of the fluid, Q is the perfusion flow rate of the fluid, A is the cross-sectional area of the fluid flow path, and this formula is used to simulate the flow velocity distribution of the fluid in the scaffold;

[0091] S34: Use CFD simulation software to solve the pressure field and shear stress distribution. The pressure field is calculated by the following formula: where, is the pressure field, ρ is the density of the fluid, μ is the viscosity of the fluid, is the rate of change of flow velocity with time, is the convective term of the flow velocity, and f is the external body force; the shear stress is calculated by the following formula: where τ is the shear stress, μ is the viscosity of the fluid, is the flow velocity gradient, representing the frictional force between the fluid and the surface of the scaffold; the above steps can more accurately describe the hydrodynamic environment inside the scaffold by simulating the fluid flow path, flow velocity field, pressure field and shear stress distribution, ensuring the uniform distribution and effective transfer of the fluid inside the scaffold. These data are crucial for subsequent stress analysis and biological reaction simulation, helping to optimize the design of the biological scaffold and improve its performance and usage effect.

[0092] S4 specifically includes:

[0093] S41: According to the flow velocity field, pressure field and shear stress distribution data obtained in S3, first combine the three-dimensional geometric model of the scaffold with the hydrodynamic data, perform finite element mesh division, and discretize the scaffold model into a finite number of elements for stress analysis. This step uses finite element analysis software to mesh the scaffold and generate a finite element mesh suitable for stress calculation;

[0094] S42: Solve the stress distribution of the biological scaffold under hydrodynamic action through finite element analysis. The stress analysis equation expression used is: σ = E·∈, where σ is the stress, E is the Young's modulus of the scaffold, and ∈ is the strain, and the strain is calculated by the following formula: where ΔL is the displacement of the scaffold deformation and L is the initial length; the stress generated by the fluid mainly includes the deformation caused by the flow velocity, pressure and shear stress;

[0095] S43: Combine the pressure field, flow velocity field and shear stress distribution generated by the fluid, and calculate the stress values at each position inside the scaffold respectively. Among them, the fluid pressure and shear stress affect the stress distribution of the scaffold through the following formulas: σ pressure = p·A and σ shear = τ·A; where, σ pressureis the stress generated by pressure, p is the pressure of the fluid, and A is the force-bearing area of the bracket surface; σ shear is the stress generated by shear force, and τ is the shear stress of the fluid; the calculated pressure and shear stress act on each node of the bracket to obtain the stress distribution;

[0096] S44: Synthesize the calculated stress values to obtain a preliminary stress distribution diagram of the bracket, which shows the stress states of the bracket at different positions under the action of the fluid.

[0097] S5 specifically includes:

[0098] S51: On the basis of S4, determine the cell proliferation characteristics in combination with the biological model, and predict the distribution and growth trend of cells on the bracket surface based on the cell proliferation rate, migration rate, and growth density, so as to determine the additional stress generated by the cells on the bracket during the growth process;

[0099] S52: Calculate the additional stress generated by each cell on the bracket surface according to the traction force during cell growth, the interaction force between cells, and the pressure exerted by cells on the bracket surface, and map it to the geometric model of the bracket, considering the influence of cell proliferation and migration dynamics on the bracket stress;

[0100] S53: Combine the additional stress calculated in S52 with the hydrodynamic stress distribution data obtained in step S4 to obtain the total stress distribution generated by the bracket during cell growth;

[0101] S54: Use a recurrent neural network to take the current stress distribution as input and perform multiple iterative optimizations to learn the law of stress change during cell growth, and update the stress distribution diagram of the bracket to obtain a more accurate stress prediction; by combining cell proliferation characteristics with recurrent neural network to optimize the stress distribution, it is possible to dynamically simulate and predict the influence of cell growth on the stress distribution of the biological bracket, accurately capture the mechanical changes during cell growth, provide a scientific basis for bracket design optimization, and thus improve the stability and performance of the bracket in biomedical applications.

[0102] S51 specifically includes:

[0103] S511: First, calculate the number of cells growing on the bracket surface per unit time through the kinetic model of cell proliferation. This model is based on the cell growth rate, cell migration rate, and the cell density that can be accommodated on the bracket surface. The formula is: N(t) = N 0 e rt , where N(t) is the number of cells at time t, N 0 is the initial number of cells, r is the proliferation rate of cells, and t is the time;

[0104] S512: Calculate the process of the gradual diffusion of cells on the surface of the scaffold based on the cell distribution model. The formula is as follows: where is the change rate of cell density, D is the cell diffusion coefficient, is the spatial gradient of cell concentration, and r is the cell proliferation rate;

[0105] S513: Calculate the additional stress exerted by the cells on the surface of the scaffold through the cell distribution data obtained in S512. This additional stress is closely related to cell density, traction force, and intercellular interaction force. The formula is: σ cell = αN(t)·F traction , where σ cell is the additional stress exerted by the cells, α is the stress gain factor, N(t) is the cell density, and F traction is the traction force exerted by the cells on the surface of the scaffold;

[0106] S514: Combine the geometric shape of the scaffold, cell density distribution, and additional stress. Predict the stress change trend of the cells after growing on the surface of the scaffold through the following formula, and then obtain the total additional stress generated during the cell growth process: σ total = ∫ Ω σ cell (x, t)dΩ, where σ total is the total additional stress generated by the cells on the scaffold during the growth process, Ω is the surface area of the scaffold, and σ cell (x, t) is the local stress exerted by the cells at position x and time t. This integral calculates the additional stress generated by cell growth on the entire surface area of the scaffold; By accurately calculating the stress change trend of the cells after growing on the surface of the scaffold and combining the additional stress of the cells with the geometric shape of the scaffold and cell distribution, the total additional stress generated during the cell growth process can be dynamically predicted. This prediction provides accurate stress data for the design optimization of biological scaffolds, helping to improve the biocompatibility, mechanical properties, and service life of the scaffolds.

[0107] S52 specifically includes:

[0108] S521: Calculate the traction force generated by each cell on the surface of the scaffold. The traction force is generated by the interaction between the cell and the surface of the scaffold. The traction force is calculated through the following formula: F traction = k·Δx, where F traction is the traction force generated by the cell, k is the elastic coefficient between the cell and the surface of the scaffold, and Δx is the displacement amount exerted by the cell on the surface of the scaffold. This force describes the stretching or compression effect of the cell on the surface of the scaffold;

[0109] S522: Calculate the additional stress generated by cells on the surface of the scaffold. The additional stress is related to the traction force and the contact area between the scaffold surface, and is calculated by the following formula: where, σ cell is the additional stress generated by cells on the surface of the scaffold, F traction is the traction force applied by cells, A contact is the area of contact between cells and the scaffold surface. This formula reflects the stress distribution applied when cells come into contact with the scaffold surface;

[0110] S523: Perform spatial mapping on the calculated additional stress σ cell according to the position of cells on the scaffold surface. Using the geometric data of the scaffold, distribute the additional stress to each node of the scaffold through a mesh mapping algorithm; specifically, according to the geometric position of each node on the scaffold surface mesh and the cell distribution, use the interpolation method to map the additional stress generated by each cell at its location to the nodes of the scaffold model;

[0111] S524: Combine the growth state of each cell on the scaffold surface and the cell distribution information, and gradually update the additional stress to the geometric model of the scaffold in a weighted average manner to obtain the final additional stress value of each node; by accurately calculating the traction force and additional stress generated by cells on the scaffold surface and mapping them to the geometric model of the scaffold, the impact of cell growth on the mechanical properties of the scaffold can be dynamically simulated. This process provides detailed stress distribution information for the design optimization of biological scaffolds, ensuring that the scaffold can effectively withstand the mechanical loads generated during cell growth, thereby improving the stability and biocompatibility of the scaffold.

[0112] S54 specifically includes:

[0113] S541: Prepare the input data for the recurrent neural network. Use the current stress distribution map of the scaffold as the input feature, and the additional stress, hydrodynamic stress generated during cell growth, and geometric characteristics of the scaffold as additional information to form the input vector of the neural network. Each input vector contains the stress distribution of the scaffold, the state of cell proliferation, and the additional stress at its corresponding position;

[0114] S542: Input the input vector into the recurrent neural network, make a preliminary prediction according to the existing weights and biases, and obtain the stress value of each node. The output of the recurrent neural network is calculated by the following formula:

[0115] y(t) = f(W·y(t - 1)+U·x(t)+b), where y(t) is the predicted stress value at time step t, x(t) is the input data, W is the recurrent weight matrix, U is the input weight matrix, b is the bias term, and f is the activation function. This formula represents the state update process of the recurrent neural network, which updates the network state based on the previous state and the current input;

[0116] S543: Calculate the error between the network output and the true stress distribution through the backpropagation algorithm, specifically calculated through the following error function: where L is the error function, y pred (i) is the predicted stress value of the i-th node, y true (i) is the true stress value, and N is the number of nodes. The error calculated through the error function will be used to adjust the parameters of the network;

[0117] S544: Based on the error, use the gradient descent algorithm to adjust the weights and biases of the network to optimize the prediction ability of the network; the process of updating the weights is achieved through the following formula: where η is the learning rate, is the gradient of the loss function with respect to the weight W. By continuously updating the weights and biases, the network can learn the law of stress change during cell growth;

[0118] S545: Iterate multiple times until the prediction result converges. In each iteration, the network continuously adjusts its internal parameters to more accurately predict the stress distribution; after convergence, the output stress distribution map is the final stress prediction during cell growth; through the iterative optimization process of the recurrent neural network, the above steps can accurately learn the law of stress change during cell growth and dynamically update the stress distribution map of the scaffold. This process not only improves the accuracy of stress prediction but also effectively captures the impact of cell growth on the mechanical properties of the scaffold, providing more accurate data support for the optimization of scaffold design, thereby enhancing the biocompatibility, stability, and reliability of the scaffold in practical applications.

[0119] This invention covers any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To enable the public to have a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments of this invention. However, those skilled in the art can fully understand this invention without the description of these details. Additionally, to avoid unnecessary confusion to the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0120] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for predicting stress distribution of biological scaffolds using a recursive network, characterized in that: The following steps are involved: S1: obtaining geometric structural parameters and in vitro culture environment parameters of the biological scaffold, wherein the geometric structural parameters include porosity gradient distribution value, pillar diameter change rate and pore connectivity; the culture environment parameters include viscosity of the culture fluid and perfusion flow rate; S2: Based on the geometric structure parameters obtained in S1, a three-dimensional geometric model of the biological scaffold is constructed, and the porosity of the scaffold and the shape characteristics of the pillars are calculated to generate geometric data of the scaffold; S3: Based on the geometric data generated by S2, the fluid flow path in the scaffold is calculated, and the flow velocity field, pressure field and shear stress distribution inside the scaffold are simulated according to the viscosity of the culture fluid and the perfusion flow rate; S4: Based on the velocity field, pressure field and shear stress distribution data obtained in S3, finite element analysis is used to calculate the preliminary stress distribution of the bioscaffold under the action of fluid mechanics; S5: Based on S4, combined with the cell proliferation characteristics of the biological scaffold, the additional stress generated during cell growth is calculated, and the stress distribution of the scaffold is iteratively updated through a recursive neural network.

2. The method for predicting stress distribution of a biological scaffold using a recursive network according to claim 1, characterized in that: The S1 specifically includes: S11: acquiring three-dimensional geometric image data of the bioscaffold by a three-dimensional scanner or computer tomography technology, and calculating a porosity gradient distribution value of the bioscaffold based on the three-dimensional geometric image data; S12: Calculate the diameter change rate of the stent strut based on the three-dimensional geometric image data; S13: Calculate the pore connectivity of the bioscaffold based on 3D geometric data using the pore connectivity analysis method; S14: using a rheological instrument to measure the viscosity of the culture solution, wherein the measuring method is to perform a viscosity test using a rotational viscometer or a capillary rheometer; S15: The perfusion flow rate of the culture solution is measured by setting a flow meter and a flow rate sensor. The flow rate measurement method is to use an ultrasonic flow meter or an electromagnetic flow meter to monitor the flow rate of the culture solution in the bioscaffold in real time.

3. The method for predicting stress distribution of biological scaffolds using a recursive network according to claim 1, characterized in that: The S2 specifically includes: S21: Based on the three-dimensional geometric image data obtained in S1, the geometric data of the stent is parameterized using computer-aided design software to generate a three-dimensional geometric model of the stent; S22: Based on the three-dimensional geometric model generated in S21, the porosity of the scaffold is calculated using the formula: Where, φ is the porosity of the scaffold, V void is the volume of the hole in the scaffold, V total is the total volume of the scaffold; S23: Based on the three-dimensional geometric model generated in S21, the shape characteristics of the stent struts are calculated, including the diameter change, curvature and length of the struts, and the shape characteristic data of the struts are generated; S24: Combining the porosity and pillar shape feature data obtained in S22 and S23 to generate geometric data of the scaffold.

4. The method for predicting stress distribution of a biological scaffold using a recursive network according to claim 3, characterized in that: The S23 specifically includes: S231: Based on the 3D geometric model generated by S21, the cross-sectional data of the stent struts at different positions are first extracted, and the diameter change of the struts is calculated using the following formula: Among them, D rate is the diameter change rate of the pillar, D max is the maximum diameter of the support at a certain position, D min is the minimum diameter of the pillar at the same position; S232: The geometric shape of the pillar is fitted by the surface fitting method, and the curvature of the pillar is calculated by the least square method. The formula is: Among them, κ is the curvature of the pillar, and R is the local radius of the pillar surface at a certain position; S233: Calculate the total length of the pillar by calculating the length of each section of the three-dimensional geometric model of the pillar. Specifically, the integral method is used for calculation, and the formula is: Among them, L is the total length of the pillar, x, y, z are the coordinates of the pillar in three-dimensional space, a and b are the starting and ending positions of the pillar, and t is a parameter on the pillar.

5. The method for predicting stress distribution of biological scaffolds using a recursive network according to claim 1, characterized in that: The S3 specifically includes: S31: Based on the geometric data generated in S2, the geometric structure of the bracket is meshed using the computational fluid dynamics method, the three-dimensional bracket model is discretized into multiple calculation units, and a mesh model for fluid flow calculation is generated; S32: The flow path of the fluid in the bracket is calculated by numerically solving the Navier-Stokes equation. The expression of the Navier-Stokes equation is: Where ρ is the density of the fluid, v is the velocity vector of the fluid, p is the pressure of the fluid, μ is the viscosity of the fluid, and f is the external volume force. is the Laplace operator, represents the pressure gradient; S33: Based on the viscosity of the culture medium and the perfusion flow rate, combined with the geometric structure of the scaffold, the flow velocity field is calculated using CFD simulation software. The flow velocity field is calculated using the following formula: Wherein, v is the average flow velocity of the fluid, Q is the perfusion flow rate of the fluid, and A is the cross-sectional area of ​​the fluid flow path; S34: CFD simulation software is used to solve the pressure field and shear stress distribution. The pressure field is calculated by the following formula: in, is the pressure field, ρ is the density of the fluid, μ is the viscosity of the fluid, is the time rate of change of flow velocity, is the convection term of the flow velocity, f is the external volume force; the shear stress is calculated by the following formula: Where τ is the shear stress, μ is the viscosity of the fluid, is the flow velocity gradient, which represents the friction between the fluid and the support surface.

6. The method for predicting stress distribution of biological scaffolds using a recursive network according to claim 1, characterized in that: The S4 specifically includes: S41: According to the velocity field, pressure field and shear stress distribution data obtained in S3, the three-dimensional geometric model of the stent is first combined with the fluid mechanics data, and finite element meshing is performed to discretize the stent model into a finite number of units; S42: The stress distribution of the biological scaffold under the action of fluid mechanics is solved by finite element analysis, and the stress analysis equation expression used is: σ=E·∈, where σ is stress, E is the Young's modulus of the scaffold, and ∈ is strain; S43: combining the pressure field, velocity field and shear stress distribution generated by the fluid, respectively calculating the stress value at each position in the bracket; S44: synthesizing the calculated stress values ​​to obtain a preliminary stress distribution diagram of the bracket.

7. The method for predicting stress distribution of biological scaffolds using a recursive network according to claim 1, characterized in that: The S5 specifically includes: S51: Based on S4, the cell proliferation characteristics are determined by combining biological models. Based on the cell proliferation rate, migration rate and growth density, the distribution and growth trend of cells on the scaffold surface are predicted to determine the additional stress on the scaffold during cell growth. S52: Based on the traction force during cell growth, the interaction force between cells and the pressure exerted by cells on the scaffold surface, the additional stress generated by each cell on the scaffold surface is calculated and mapped to the geometric model of the scaffold; S53: combining the additional stress calculated in S52 with the fluid mechanics stress distribution data obtained in step S4 to obtain the total stress distribution generated by the scaffold during cell growth; S54: A recursive neural network is used to take the current stress distribution as input and perform multiple iterative optimizations to learn the law of stress changes during cell growth and update the stress distribution map of the scaffold to obtain more accurate stress predictions.

8. The method for predicting stress distribution of biological scaffolds using a recursive network according to claim 7, characterized in that: The S51 specifically includes: S511: First, the number of cells growing on the scaffold surface per unit time is calculated using a cell proliferation kinetic model. The formula is: N(t) = N0e rt , where N(t) is the number of cells at time t, N0 is the initial number of cells, r is the cell proliferation rate, and t is time; S512: Based on the cell distribution model, the process of gradual diffusion of cells on the scaffold surface is calculated using the formula: in, is the rate of change of cell density, D is the cell diffusion coefficient, is the spatial gradient of cell concentration, r is the cell proliferation rate; S513: Calculate the additional stress exerted by cells on the surface of the scaffold using the cell distribution data obtained in S512. The formula is: σ cell =αN(t)@F traction , where σ cell is the additional stress applied to the cell, α is the stress gain factor, N(t) is the cell density, F traction is the traction force exerted by cells on the scaffold surface; S514: Combining the geometric shape of the scaffold, cell density distribution and additional stress, the following formula is used to predict the stress change trend after cells grow on the scaffold surface, and then the total additional stress generated during cell growth is obtained: σ total =∫ Ω σ cell (x, t)dΩ, where σ total is the total additional stress generated on the scaffold during cell growth, Ω is the scaffold surface area, and σ cell (x, t) is the local stress exerted by the cell at position x and time t.

9. The method for predicting stress distribution of biological scaffolds using a recursive network according to claim 8, characterized in that: The S52 specifically includes: S521: Calculate the traction force generated by each cell on the scaffold surface. The traction force is generated by the interaction between the cell and the scaffold surface. The traction force is calculated by the following formula: F traction = k·Δx, where F traction is the traction force generated by the cells, k is the elastic coefficient between the cells and the scaffold surface, and Δx is the displacement exerted by the cells on the scaffold surface; S522: Calculate the additional stress generated by the cells on the surface of the scaffold. The additional stress is related to the traction force and the contact area of ​​the scaffold surface and is calculated by the following formula: Among them, σ cell is the additional stress generated by cells on the scaffold surface, F traction is the traction force exerted by the cell, A contact is the contact area between cells and the scaffold surface; S523: The calculated additional stress σ cell According to the position of cells on the scaffold surface, spatial mapping is performed, and the geometric data of the scaffold is used to distribute the additional stress to each node of the scaffold through a grid mapping algorithm; S524: In combination with the growth state of each cell on the surface of the scaffold and the cell distribution information, the additional stress is gradually updated to the geometric model of the scaffold by weighted averaging to obtain the final additional stress value of each node.

10. The method for predicting stress distribution of biological scaffolds using a recursive network according to claim 9, characterized in that: The S54 specifically includes: S541: preparing input data for the recursive neural network, taking the current scaffold stress distribution map as input features, and the additional stress generated during cell growth, the fluid mechanics stress, and the geometric characteristics of the scaffold as additional information to form an input vector of the neural network; S542: Input the input vector into the recursive neural network, make a preliminary prediction based on the existing weights and biases, and obtain the stress value of each node; S543: Calculate the error between the network output and the true stress distribution through the back propagation algorithm; S544: Based on the error, the gradient descent algorithm is used to adjust the weights and biases of the network to optimize the prediction ability of the network; S545: Iterate multiple times until the prediction results converge; after convergence, the output stress distribution diagram is the final stress prediction during the cell growth process.

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