Computational mechanical analysis system for evaluating bone growth induced by bone healing scaffold

Abstract

The invention discloses a computational mechanical analysis system for evaluating bone growth induced by a bone healing scaffold, and relates to the technical field of bone healing evaluation, and the computational mechanical analysis system is specifically characterized in that under unified external load and time gating, quantitative indexes such as a regional average osteogenesis rate curve, an accumulated bone mass, time for reaching a preset healing threshold value, a cross section bridging rate and the like are used for evaluating bone growth induced by a bone healing scaffold; the induction osteogenesis effects of different stent structures are fairly compared, shape scoring and subjective weight are avoided, reproducibility and calibration are emphasized, the method can be used for preoperative structure screening and parameter sensitivity analysis and can also be in butt joint with follow-up images and experimental data, online calibration and treatment course optimization of individualized digital twinning are further supported, and the method is suitable for popularization and application. According to the method, the period boundary, the time-varying supply gating and the multi-physics field coupling of the RVE can be unified into the same calculation framework, and the defects of the prior art in microscopic geometric maintenance, time rhythm expression and biomechanical closed loop are effectively overcome.

Description

Technical Field

[0001] This invention belongs to the field of bone healing evaluation technology, and in particular relates to a computational mechanics analysis system for evaluating bone growth induced by bone healing scaffolds. Background Technology

[0002] Fracture healing involves multi-scale, multi-field processes, including mechanical transfer, tissue permeation, angiogenesis, and stem cell migration and differentiation. Existing scaffold evaluation methods mostly rely on static or quasi-static single-field simulations. Common practices include using average modulus or equivalent permeability to represent the complex porous framework, describing biological supply with constant boundary conditions or empirical constants, or weakly coupling between separate mechanical and biological models.

[0003] The existing techniques for evaluating bone healing have the following problems: (1) Equivalence processing will smooth out the micro-geometric features such as channel connectivity, tortuosity and wall shear, resulting in a distortion in the spatial distribution estimation of osteogenic-related stimuli; (2) Boundary supply is often set to constant or steady state, which makes it difficult to express the inhibition at postoperative zero time, the linear recovery in the following days and the stable process of the plateau phase, thus not consistent with the clinical follow-up rhythm; (3) The lack of a unified differentiable mechanism between mechanics, permeation, diffusion and cell fate makes it difficult to map shear stimulation and perfusion capacity together to differentiation rate; (4) In existing work, RVE is mostly used to calculate the equivalent modulus and equivalent permeability, and then back to the macroscopic model. This will hide the channel scale and local shear environment that are most critical to the final osteogenic formation. (5) Evaluation indicators often rely on subjective scoring or a single endpoint, lacking comparable hard indicators for clinical use, resulting in the inability to reproduce conclusions between different structures. Summary of the Invention

[0004] The purpose of this invention is to provide a computational mechanics analysis system for evaluating bone growth induced by bone healing scaffolds, thereby addressing the problems raised in the background art.

[0005] To achieve the above objectives, the embodiments of the present invention provide the following technical solutions: A computational mechanics analysis system for evaluating bone growth induced by bone healing scaffolds, the system comprising a time-varying boundary condition module, a multiphysics bone healing coupling module, and a bone scaffold structure evaluation module, wherein: The time-varying boundary condition module is used to set linear piecewise gating functions for the boundary access ratio and regional diffusion gain of the blood vessel density field and the stem cell field respectively, with the current time as the independent variable. During numerical solution, it is automatically assembled into Dirichlet boundary values ​​and regional diffusion coefficients of blood vessels and stem cells. The multiphysics field bone healing coupling module is used to establish a unified solution framework for porous elasticity, Darcy flow, vascular diffusion, stem cell diffusion and response in the fracture area based on the Dirichlet boundary value and the regional diffusion coefficient. It combines the neighborhood equivalent stiffness to give a unified differentiation rate and drive the closed-loop update of tissue lineage evolution and material properties. The bone scaffold structure evaluation module is used to perform periodic boundary modeling and periodic laying of selected microcellular structures within the fracture gap, participate in the global solution on explicit geometry, and evaluate feasibility using hard indicators of bone formation.

[0006] As a further limitation of the technical solution of this invention, the specific process of automatically assembling the Dirichlet boundary values ​​and regional diffusion coefficients of blood vessels and stem cells during numerical solution by setting linear piecewise gating functions for the boundary access ratio and regional diffusion gain of the blood vessel density field and stem cell field respectively is as follows: Construct anatomical boundaries and region sets; A linear piecewise gating function for the boundary access ratio is constructed to determine the access ratio of the vascular density field and the stem cell field; A linear piecewise gating function for the regional diffusion gain is constructed to determine the regional diffusion gain of the vascular density field and the stem cell field; Assemble Dirichlet boundary values ​​and regional diffusion coefficients; Perform time-progression and coupling sequence processing; Generate numerical values ​​and constraint strategies.

[0007] As a further limitation of the technical solution of this invention, in the set of anatomical boundaries and regions, the outer surface of the solution domain is divided into three types of boundaries according to anatomical meaning: outside the callus bone marrow ends and On the soft tissue side; the set of subdomains adjacent to the boundary within the domain is defined as follows: The access ratio of the blood vessel density field and the stem cell field is: and , The expression for the linear piecewise gating function of the boundary access ratio is: ; ; in, Indicates the proportion of patients receiving immediate post-operative care; This indicates the platform's supply level has been restored. The delay time for the start of access; This is the linear recovery time; The regional diffusion gain of the blood vessel density field and the stem cell field is: and , The expression for the linear piecewise gating function of the region diffusion gain is: ; ; in, Indicates the lower limit of early-stage transparency; This indicates the platform's transparency.

[0008] As a further limitation of the technical solution of this embodiment of the invention, the expression for the assembly Dirichlet boundary value is: ; ; in, and The corresponding external reference value for the boundary; Normalized blood vessel density; MSC concentration; The expression for the diffusion coefficient of the assembly area is: ; ; in, Indicates the first One region; and The regional baseline diffusion coefficient; This is the strain suppression function; For equivalent change; Blood vessel density in spatial location and time The speed of spread; For mesenchymal stem cells in spatial location and time The rate of diffusion and migration; The calculation order for the time advancement and coupling sequence processing is as follows: calculate ;Will Write to the Dirichlet boundary, Diffusion coefficient of the writing region; The mechanical, seepage, and diffusion equations are solved by the multiphysics bone healing coupling module. In the numerical generation and constraint strategy, the constraints are: .

[0009] As a further limitation of the technical solution of this invention, the specific process of establishing a unified solution framework for porous elasticity, Darcy flow, vascular diffusion, stem cell diffusion and response within the fracture region based on the Dirichlet boundary value and the regional diffusion coefficient, and combining the equivalent stiffness of the neighborhood to give a unified differentiation rate, driving the closed-loop update of tissue lineage evolution and material properties is as follows: Determine the constitutive and variable properties of the porous elastic structure and construct the mechanical equilibrium equations; Darcy flow and mass conservation calculations were performed, and stimulus quantity extraction and unified force flow influence factors were established. Based on the Dirichlet boundary value and the regional diffusion coefficient, angiogenesis diffusion field is calculated; Stem cell diffusion and reaction are performed based on the Dirichlet boundary value and the regional diffusion coefficient. Perform neighborhood equivalent stiffness calculations and unify the differentiation rate; Simultaneous updates and write-backs of other cell lineage evolutions and material properties.

[0010] As a further limitation of the technical solution of this embodiment of the invention, the expression for the porous elastic constitutive model and variables is as follows: ; ; ; in, This is the total stress tensor; For displacement; For small strain tensors, For the partial strain tensor; Unit tensor; Shear modulus; Material parameters; Pore ​​pressure; For Biot coefficients; The trace of the small strain tensor; Represents partial differential operators; The expression for the mechanical equilibrium equation is: ; in, Body density; The formula for calculating Darcy flow and mass conservation is as follows: ; ; ; in, Darcy speed; For penetration rate; For fluid viscosity; For source terms; Porosity; , These are the bulk moduli of the fluid and the skeleton, respectively. Skempton coefficient; Darcy velocity is the velocity vector that a fluid exhibits in a porous medium. The formula for calculating the stimulus amount extraction is: ; ; in, For octahedral shear strain; The volume-average Darcy velocity; Unit volume; The expression for the unified force flow influence factor is: ; in, , For reference standard quantity, It is a dimensionless quantity.

[0011] As a further limitation of the technical solution of this embodiment of the invention, the expression of the angiogenesis diffusion field is: ; in, Normalized blood vessel density; The attenuation rate; To generate source terms; The regional baseline diffusion coefficient; Provided by the time-varying boundary condition module; , These are the threshold and the slope, respectively. The expression for stem cell diffusion and response is as follows: ; in, MSC concentration; , These represent proliferation and apoptosis rates, respectively. For path rate; The regional baseline diffusion coefficient; Provided by the time-varying boundary condition module; MSC concentration; express Cell type; Indicates fibroblasts; It represents chondrocytes; Indicates osteoblasts; The formula for calculating the equivalent stiffness of the neighborhood is: ; ; in, For unit The neighborhood set; The unit center distance (m); The weighting scale is (m). The neighborhood radius (m); It is a unit step function; Let i be the equivalent elastic modulus of element i; The formula for calculating the uniform differentiation rate is: ; in, It is a continuously differentiable and scalable Logistic or Hill form; To determine the path differentiation rate, multiple paths are assigned, including: , , , and ; Let be the effect function of force flow stimulation; The function representing the influence of blood vessel density; This is the local stiffness influence function; In the evolution of other cell lineages, the evolutionary expressions for the fibrous, cartilaginous, and bone lineages are as follows: ; in, Indicates the uniform differentiation rate, and is simultaneously affected by , , Joint regulation; The rate of MSC differentiation into fibroblasts; The rate of MSC differentiation into chondrocytes; This represents the rate of MSC differentiation into osteoblasts. The rate of differentiation of fibroblasts into osteoblasts; The rate of chondrocyte differentiation into osteoblasts; , and These represent fibroblasts, chondrocytes, and osteoblasts, respectively. , and These represent the proliferation rates of fibroblasts, chondrocytes, and osteoblasts, respectively. , and These represent the apoptosis rates of fibroblasts, chondrocytes, and osteoblasts, respectively. The expression for synchronous updating and writing back of material properties is: ; ; ; ; ; in, This refers to the volume fraction of granulation tissue, fiber, cartilage, and bone. , , and These are the baseline parameters for granulation tissue, fibers, cartilage, and bone, respectively; subscripts. This indicates the equivalent value of the time step.

[0012] As a further limitation of the technical solution of this invention, the specific process of performing periodic boundary modeling and periodic laying of the selected microcellular structure within the fracture gap, participating in the overall solution in explicit geometry, and evaluating the feasibility using hard indicators of bone formation is as follows: RVE cell geometry and domain decomposition constructs cells periodically laid out in three-dimensional space, and divides the skeletal solid domain and the pore fluid domain within the cells. Periodic boundary conditions are set to apply periodic constraints on displacement and flow on the opposite surfaces of the cell. The periodic structure is laid out as a macroscopic framework and incorporated into the global solution domain; Determine the Dirichlet boundary values ​​and write them into the time-gated diffusion coefficient; Evaluation output is based on bone formation.

[0013] As a further limitation of the technical solution of this embodiment of the invention, the geometric scale of the cell is: The skeletal solid domain is The pore fluid domain is .

[0014] As a further limitation of the technical solution of this embodiment of the invention, the expression for the mechanical periodic displacement condition in the periodic constraint is as follows: ; in, This indicates the front face of the opposite side of a cell. This represents the negative aspect of the cell's opposite side. Represents the displacement vector. Represents the macroscopic average strain tensor; The expression for the traction consistency between opposing surfaces in the periodic constraint is: ; in, Represents the surface traction vector; The expression for the seepage periodicity condition in the periodic constraint is as follows: ; ; in, Represents the fluid velocity vector; This represents the macroscopic average pressure gradient; In the periodic constraint, the expression for the no-slip and impermeable conditions of the inner wall of the skeleton is as follows: ; in, It is the surface normal vector; Indicates the surface located within a solid framework; The expression for copying cell elements to the fracture gap region using integer translation vectors, where the periodic structure is laid out as a macroscopic framework and incorporated into the global solution domain, is as follows: ; in, To translate the basic RVE to a spatial position Translation vector; Indicates an integer index; The periodic structure is laid out into a macroscopic framework and incorporated into the global solution domain, resulting in the macroscopic framework solid domain and the explicit pore domain as follows: ; in, Represents a macroscopic-scale scaffold solid domain; A spatial domain representing a macroscopic scale; This represents the union operator. A representative volume unit representing a solid domain. A representative volume unit representing a fluid domain; The periodic structure is laid out into a macroscopic framework and incorporated into the global solution domain. The tissue domain for fracture healing is denoted as... The global solution domain is: ; in, It represents the entire computational domain, including healing tissue, scaffold, and voids; This represents the area where new tissue is formed during the fracture healing process.

[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention, through a unified external load and time gating, uses quantitative indicators such as regional average osteogenic rate curves, cumulative bone mass, time to reach a preset healing threshold, and cross-sectional bridging rate to fairly compare the induced osteogenic effects of different scaffold structures. This avoids shape scoring and subjective weighting, emphasizes reproducibility and calibrability, and can be used for preoperative structure screening and parameter sensitivity analysis. It can also be integrated with follow-up images and experimental data to further support online calibration and treatment optimization of individualized digital twins. It can unify the periodic boundaries, time-varying supply gating, and multi-physics coupling of RVE into the same computational framework, effectively making up for the shortcomings of existing technologies in maintaining microscopic geometry, expressing temporal rhythms, and biomechanical closed loops. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention.

[0017] Figure 1 An application architecture diagram of the system provided in an embodiment of the present invention is shown. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0019] To address the problems of existing technologies, this invention, under unified external load and time gating, uses quantitative indicators such as regional average osteogenic rate curve, cumulative bone mass, time to reach a preset healing threshold, and cross-sectional bridging rate to fairly compare the induced osteogenic effects of different scaffold structures. This avoids shape scoring and subjective weighting, emphasizes reproducibility and calibrability, and can be used for preoperative structure screening and parameter sensitivity analysis, as well as for integration with follow-up images and experimental data. It further supports online calibration and treatment optimization of individualized digital twins, and can unify the periodic boundaries, time-varying supply gating, and multi-physics coupling of RVE into the same computational framework, effectively compensating for the shortcomings of existing technologies in maintaining microscopic geometry, expressing temporal rhythms, and establishing biomechanical loops.

[0020] Figure 1 An application architecture diagram of the system provided in an embodiment of the present invention is shown.

[0021] Specifically, a computational biomechanical analysis system for evaluating bone growth induced by bone healing scaffolds includes: The time-varying boundary condition module 101 is used to set linear piecewise gating functions for the boundary access ratio and regional diffusion gain of the blood vessel density field and the stem cell field respectively, with the current time as the independent variable. During numerical solution, it is automatically assembled into Dirichlet boundary values ​​and regional diffusion coefficients of blood vessels and stem cells.

[0022] In this embodiment of the invention, by constructing an anatomical boundary and region set, and constructing a linear piecewise gating function for the boundary access ratio, the access ratio of the vascular density field and the stem cell field is determined. Simultaneously, a linear piecewise gating function for the region diffusion gain is constructed to determine the region diffusion gain of the vascular density field and the stem cell field. Then, Dirichlet boundary values ​​and region diffusion coefficients are assembled, and time-progression and coupling sequence processing are performed to generate numerical and constraint strategies. Specifically, in the anatomical boundary and region set, the outer surface of the solution domain is divided into three types of boundaries according to anatomical significance: outside the callus bone marrow ends and On the soft tissue side; the set of subdomains adjacent to the boundary within the domain is defined as follows: The integration ratio of the vascular density field and the stem cell field is: and , The expression for the linear piecewise gating function of the boundary access ratio is: ; ; in, Indicates the proportion of patients receiving immediate post-operative care; This indicates the platform's supply level has been restored. The delay time for the start of access; This is the linear recovery time; The regional diffusion gain of the vascular density field and the stem cell field is and , The expression for the linear piecewise gating function of the region diffusion gain is: ; ; in, Indicates the lower limit of early-stage transparency; This indicates the platform's transparency. The expression for the assembly Dirichlet boundary values ​​is: ; ; in, and The corresponding external reference value for the boundary; Normalized blood vessel density; MSC concentration; The expression for the diffusion coefficient of the assembly area is: ; ; in, Indicates the first One region; and The regional baseline diffusion coefficient; This is the strain suppression function; For equivalent change; Blood vessel density in spatial location and time The speed of spread; For mesenchymal stem cells in spatial location and time The rate of diffusion and migration; The computational order for time advancement and coupling sequence processing is as follows: calculate ;Will Write to the Dirichlet boundary, Diffusion coefficient of the writing region; The mechanical, seepage, and diffusion equations are solved using a multiphysics bone healing coupling module. In the numerical generation and constraint strategy, the constraints are: .

[0023] It is understandable that, with time as the sole independent variable, linear piecewise gating functions are set for the boundary access ratio and regional diffusion gain of the vascular density field and the stem cell field, respectively. Then, during numerical solution, the Dirichlet boundary values ​​and regional diffusion coefficients of the vascular and stem cells are automatically assembled. This does not change the material constants and constitutives, does not introduce any spatial piecewise functions, does not participate in equivalence, and only provides the boundary and coefficients that evolve with time as input to the multiphysics bone healing coupling module 102.

[0024] It is understandable that the input is the current time t and the external reference value. Compared with the regional baseline diffusion coefficient Output four sets of time functions with each timetable parameter. The assembled boundary values ​​and regional coefficient fields are connected to the multiphysics bone healing coupling module 102. They are executed before the field equations are solved at each time step. Their output is directly used to evaluate the relationship between the coefficients of the Dirichlet boundary and diffusion tensor of blood vessels and stem cells and the bone scaffold structure evaluation module 103. No microstructure processing is performed. It only provides the influence of time-gated real geometry on the flow path and shear environment in the multiphysics solution. It can describe the exogenous access of blood vessels and stem cells and the permeability within the domain with linear piecewise functions. It reproduces the time history of postoperative supply limitation and gradual recovery with the minimum parameter set. The time-driven mode of boundary and coefficient is completely decoupled from the explicit geometry, which is convenient to work with the structure laid in the RVE cycle. Under the premise of ensuring function continuity and physical boundedness, it improves the stability of global time progression and provides a calibrated and reproducible source of boundary data for subsequent differentiation rate calculation and bone mass growth.

[0025] The multiphysics field bone healing coupling module 102 is used to establish a unified solution framework for porous elasticity, Darcy flow, vascular diffusion, stem cell diffusion and response in the fracture area based on the Dirichlet boundary value and the regional diffusion coefficient. It combines the neighborhood equivalent stiffness to give a unified differentiation rate and drive the closed-loop update of tissue lineage evolution and material properties.

[0026] In this embodiment of the invention, by determining the porous elastic constitutive and variables, constructing mechanical equilibrium equations, performing Darcy flow and mass conservation calculations, extracting stimulus amounts and unifying force flow influencing factors, then calculating the angiogenesis diffusion field based on Dirichlet boundary values ​​and regional diffusion coefficients, performing stem cell diffusion and response, calculating neighborhood equivalent stiffness, unifying differentiation rates, and synchronously updating and rewriting other cell lineage evolutions and material properties. Specifically, the expressions for the porous elastic constitutive and variables are as follows: ; ; ; in, This is the total stress tensor; For displacement; For small strain tensors, For the partial strain tensor; Unit tensor; Shear modulus; Material parameters; Pore ​​pressure; For Biot coefficients; The trace of the small strain tensor; Represents partial differential operators; The expression for the mechanical equilibrium equation is: ; in, Body density; The formulas for Darcy flow and mass conservation are as follows: ; ; ; in, Darcy speed; For penetration rate; For fluid viscosity; For source terms; Porosity; , These are the bulk moduli of the fluid and the skeleton, respectively. Skempton coefficient; Darcy velocity is the velocity vector that a fluid exhibits in a porous medium. The formula for calculating the stimulus amount extraction is: ; ; in, For octahedral shear strain; The volume-average Darcy velocity; Unit volume; The expression for the unified force flow influence factor is: ; in, , For reference standard quantity, It is a dimensionless quantity; The expression for the angiogenesis diffusion field is: ; in, Normalized blood vessel density; The attenuation rate; To generate source terms; The regional baseline diffusion coefficient; Provided by the time-varying boundary conditions module; , These are the threshold and the slope, respectively. The expression for stem cell diffusion and response is: ; in, MSC concentration; , These represent proliferation and apoptosis rates, respectively. For path rate; The regional baseline diffusion coefficient; Provided by the time-varying boundary condition module; MSC concentration; express Cell type; Indicates fibroblasts; It represents chondrocytes; Indicates osteoblasts; The formula for calculating the equivalent stiffness of the neighborhood is: ; ; in, For unit The neighborhood set; The unit center distance (m); The weighting scale is (m). The neighborhood radius (m); It is a unit step function; Let i be the equivalent elastic modulus of element i; The formula for calculating the uniform differentiation rate is: ; in, It is a continuously differentiable and scalable Logistic or Hill form; To determine the path differentiation rate, multiple paths are assigned, including: , , , and ; Let be the effect function of force flow stimulation; The function representing the influence of blood vessel density; This is the local stiffness influence function; In the evolution of other cell lineages, the evolutionary expressions for the fibrous, cartilaginous, and bone lineages are as follows: ; in, Indicates the uniform differentiation rate, and is simultaneously affected by , , Joint regulation; The rate of MSC differentiation into fibroblasts; The rate of MSC differentiation into chondrocytes; This represents the rate of MSC differentiation into osteoblasts. The rate of differentiation of fibroblasts into osteoblasts; The rate of chondrocyte differentiation into osteoblasts; , and These represent fibroblasts, chondrocytes, and osteoblasts, respectively. , and These represent the proliferation rates of fibroblasts, chondrocytes, and osteoblasts, respectively. , and These represent the apoptosis rates of fibroblasts, chondrocytes, and osteoblasts, respectively. The expression for material property synchronization update and write-back is: ; ; ; ; ; in, This refers to the volume fraction of granulation tissue, fiber, cartilage, and bone. , , and These are the baseline parameters for granulation tissue, fibers, cartilage, and bone, respectively; subscripts. This indicates the equivalent value of the time step.

[0027] It is understandable that a unified solution framework for porous elasticity, Darcy flow, vascular diffusion, stem cell diffusion and response is established within the fracture region. Shear and flow stimuli are simultaneously extracted and synthesized into dimensionless influence quantities. Combined with the equivalent stiffness of the neighborhood, a continuously differentiable unified differentiation rate is given, driving tissue lineage evolution and material properties (including…). The closed-loop update of the boundary value and diffusion coefficient is performed without structural equivalence; the time-varying gating of the boundary value and diffusion coefficient is provided by the time-varying boundary condition module 101.

[0028] It is understandable that the output of the time-varying boundary condition module can be directly read from the blood vessel and MSC fields. To set Dirichlet boundary values, read Using the diffusion coefficient of the assembly region, if an explicit skeleton and channels constructed by RVE and periodic boundaries exist within the domain, their geometry is directly reflected in the mesh and contact interface conditions. No equivalent microstructure is applied; all fields are solved on the explicit geometry, and the output... Used for evaluating bone formation and healing time, by synthesizing shear and permeation stimuli into a dimensionless quantity. The uniform differentiation rate is given by the continuous function product of blood supply and neighborhood stiffness. Without introducing piecewise functions or performing structural equivalence, a closed-loop iterative framework is formed that allows for consistent and calibrable force, flow, generation, and material properties, with material properties being synchronously written back. Ensuring that Darcy flux and coupling strength evolve together with tissue maturity provides a physical and biological basis for time-varying boundary gating and RVE structure evaluation.

[0029] The bone scaffold structure evaluation module 103 is used to perform periodic boundary modeling and periodic laying of the selected micro-cell structure within the fracture gap, participate in the overall solution in explicit geometry, and evaluate the feasibility using hard indicators of bone formation.

[0030] In this embodiment of the invention, RVE cell geometry and domain decomposition construct cells periodically laid out in three-dimensional space. Within each cell, a skeleton solid domain and a pore fluid domain are divided. Periodic boundary conditions are set, and periodic constraints on displacement and flow are applied to the opposite surfaces of the cells. This periodically lays out a macroscopic skeleton and loads it into the global solution domain. Dirichlet boundary values ​​are then determined, and time-gated diffusion coefficients are written. Finally, the evaluation output is based on bone formation. Specifically, the geometric scale of the cell is... ; The framework solid domain is The pore fluid domain is The expression for the mechanical periodic displacement condition in a periodic constraint is: ; in, This indicates the front face of the opposite side of a cell. This represents the negative aspect of the cell's opposite side. Represents the displacement vector. Represents the macroscopic average strain tensor; The expression for the traction consistency between opposite surfaces in a periodic constraint is: ; in, Represents the surface traction vector; The expression for the periodicity condition of seepage in periodic constraints is: ; ; in, Represents the fluid velocity vector; This represents the macroscopic average pressure gradient; In periodic constraints, the expression for the no-slip and impermeable conditions of the inner wall of the skeleton is as follows: ; in, It is the surface normal vector; Indicates the surface located within a solid framework; The expression for copying cell elements to the fracture gap region using integer translation vectors, after periodically laying out a macroscopic skeleton and loading it into the global solution domain, is as follows: ; in, To translate the basic RVE to a spatial position Translation vector; Indicates an integer index; Periodically laid out to form a macroscopic framework and incorporated into the global solution domain, the macroscopic framework solid domain and explicit pore domain are obtained as follows: ; in, Represents a macroscopic-scale scaffold solid domain; A spatial domain representing a macroscopic scale; This represents the union operator. A representative volume unit representing a solid domain. A representative volume unit representing a fluid domain; The periodic structure is laid out as a macroscopic framework and loaded into the global solution domain. The tissue domain for fracture healing is denoted as... The global solution domain is: ; in, It represents the entire computational domain, including healing tissue, scaffold, and voids; This represents the area of ​​newly formed tissue during the fracture healing process. The Dirichlet boundary values ​​for blood vessel density and stem cell concentration, which are time-gated at the external anatomical boundary, are calculated using the following formula: ; ; in, Indicates at the boundary Place Blood vessel density at any given time; The boundary access ratio representing blood vessel density; Indicates the first Exogenous reference vessel density at class boundaries; Indicates at the boundary Place MSC concentration at time; This indicates the percentage of stem cells that can be accessed at the boundary. Indicates the first The concentration of exogenous reference stem cells at the class boundary; In evaluating bone formation as the target, within a given evaluation region... With time window Based on the unified differentiation rate and cell evolution results calculated by the multiphysics bone healing coupling module 102, several hard indicators are output, including: Local osteogenic rate density: .

[0031] in, In spatial location ,time osteoblast generation rate density; The rate of differentiation of mesenchymal stem cells into osteoblasts; This represents the concentration of mesenchymal stem cells. The rate of differentiation of fibroblasts into osteoblasts; This refers to the concentration of fibroblasts. The rate of differentiation of chondrocytes into osteoblasts; This refers to the concentration of chondrocytes. Regional mean osteogenic rate curve: ; in, For time The regional average osteogenic rate; Indicates the region of interest; Cumulative osteogenic mass: ; in, This represents the cumulative osteogenic amount within the time window 0-T; Increase in bone volume fraction: ; in, This refers to the increase in bone volume fraction. Let be the bone tissue volume fraction field at the termination time; The initial bone tissue volume fraction field; Time to reach the healing threshold: ; in, The time required to reach the healing threshold; This is a preset healing threshold; Bridging rate: ; in, For a moment bridging rate; This represents the bone volume fraction threshold for determining a valid bone bridging. Mechanical safety factor: .

[0032] in, For mechanical safety factor; The maximum allowable strain; For a moment The maximum strain; The maximum allowable stress; For a moment The maximum stress.

[0033] It is understandable that the time-varying boundary condition module 101 provides... After completing the boundary and diffusion coefficient assembly, the multiphysics bone healing coupling module 102 solves the mechanics, permeation, blood vessel and stem cell diffusion in the global domain of explicit geometry, promotes the unified differentiation rate and cell lineage evolution, and simultaneously counts multiple indicators until the termination condition is met or a given time is reached. All evaluation quantities and curves are output and summarized by case or structure for easy horizontal comparison.

[0034] Understandably, by using periodic boundaries to strictly embed micro-cells into the explicit geometry of macro-fracture gaps, the solution occurs directly on the real channels and skeleton without any equivalent processing, shape weights or subjective scoring. Under uniform external load and time gating, it provides structural feasibility conclusions with hard indicators such as bone rate, cumulative bone mass, healing threshold time and bridging rate. It has the advantages of being reproducible, comparable and simple to implement in engineering.

[0035] It should be understood that although the steps in the flowcharts of the various embodiments of the present invention are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the various embodiments may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0036] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0037] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0038] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

[0039] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A computational biomechanical analysis system for evaluating bone growth induced by bone healing scaffolds, characterized in that, The system includes a time-varying boundary condition module, a multi-physics field bone healing coupling module, and a bone scaffold structure evaluation module, wherein: The time-varying boundary condition module is used to set linear piecewise gating functions for the boundary access ratio and regional diffusion gain of the blood vessel density field and the stem cell field respectively, with the current time as the independent variable. During numerical solution, it is automatically assembled into Dirichlet boundary values ​​and regional diffusion coefficients of blood vessels and stem cells. The multiphysics field bone healing coupling module is used to establish a unified solution framework for porous elasticity, Darcy flow, vascular diffusion, stem cell diffusion and response in the fracture area based on the Dirichlet boundary value and the regional diffusion coefficient. It combines the neighborhood equivalent stiffness to give a unified differentiation rate and drive the closed-loop update of tissue lineage evolution and material properties. The bone scaffold structure evaluation module is used to perform periodic boundary modeling and periodic laying of selected microcellular structures within the fracture gap, participate in the global solution on explicit geometry, and evaluate feasibility using hard indicators of bone formation.

2. The computational biomechanical analysis system for evaluating bone growth induced by bone healing scaffolds according to claim 1, characterized in that, The specific process of automatically assembling the Dirichlet boundary values ​​and regional diffusion coefficients of blood vessels and stem cells during numerical solution by setting the boundary access ratio and regional diffusion gain for the vascular density field and stem cell field respectively is as follows: Construct anatomical boundaries and region sets; A linear piecewise gating function for the boundary access ratio is constructed to determine the access ratio of the vascular density field and the stem cell field; A linear piecewise gating function for the regional diffusion gain is constructed to determine the regional diffusion gain of the vascular density field and the stem cell field; Assemble Dirichlet boundary values ​​and regional diffusion coefficients; Perform time-progression and coupling sequence processing; Generate numerical values ​​and constraint strategies.

3. The computational biomechanical analysis system for evaluating bone growth induced by bone healing scaffolds according to claim 2, characterized in that, In the aforementioned set of anatomical boundaries and regions, the outer surface of the solution domain is divided into three types of boundaries according to anatomical significance: outside the callus bone marrow ends and On the soft tissue side; the set of subdomains adjacent to the boundary within the domain is defined as follows: The access ratio of the blood vessel density field and the stem cell field is: and , The expression for the linear piecewise gating function of the boundary access ratio is: ； ； in, Indicates the proportion of patients receiving immediate post-operative care; This indicates the platform's supply level has been restored. The delay time for the start of access; This is the linear recovery time; The regional diffusion gain of the blood vessel density field and the stem cell field is: and , The expression for the linear piecewise gating function of the region diffusion gain is: ； ； in, Indicates the lower limit of early-stage transparency; This indicates the platform's transparency.

4. The computational biomechanical analysis system for evaluating bone growth induced by bone healing scaffolds according to claim 3, characterized in that, The expression for the assembly Dirichlet boundary value is: ； ； in, and The corresponding external reference value for the boundary; Normalized blood vessel density; MSC concentration; The expression for the diffusion coefficient of the assembly area is: ； ； in, Indicates the first One region; and The regional baseline diffusion coefficient; This is the strain suppression function; For equivalent change; Blood vessel density in spatial location and time The speed of spread; For mesenchymal stem cells in spatial location and time The rate of diffusion and migration; The calculation order for the time advancement and coupling sequence processing is as follows: calculate ;Will Write to the Dirichlet boundary, Diffusion coefficient of the writing region; The mechanical, seepage, and diffusion equations are solved by the multiphysics bone healing coupling module. In the numerical generation and constraint strategy, the constraints are: 。 5. The computational biomechanical analysis system for evaluating bone growth induced by bone healing scaffolds according to claim 4, characterized in that, The specific process of establishing a unified solution framework for porous elasticity, Darcy flow, vascular diffusion, stem cell diffusion and response within the fracture region based on the Dirichlet boundary value and the regional diffusion coefficient, and combining it with the equivalent stiffness of the neighborhood to give a unified differentiation rate, driving the closed-loop update of tissue lineage evolution and material properties is as follows: Determine the constitutive and variable properties of the porous elastic structure and construct the mechanical equilibrium equations; Darcy flow and mass conservation calculations were performed, and stimulus quantity extraction and unified force flow influence factors were established. Based on the Dirichlet boundary value and the regional diffusion coefficient, angiogenesis diffusion field is calculated; Stem cell diffusion and reaction are performed based on the Dirichlet boundary value and the regional diffusion coefficient. Perform neighborhood equivalent stiffness calculations and unify the differentiation rate; Simultaneous updates and write-backs of other cell lineage evolutions and material properties.

6. The computational biomechanical analysis system for evaluating bone growth induced by bone healing scaffolds according to claim 5, characterized in that, The expressions for the porous elastic constitutive and variable are as follows: ； ； ； in, This is the total stress tensor; For displacement; For small strain tensors, For the partial strain tensor; Unit tensor; Shear modulus; Material parameters; Pore ​​pressure; For Biot coefficients; The trace of the small strain tensor; Represents partial differential operators; The expression for the mechanical equilibrium equation is: ； in, Body density; The formula for calculating Darcy flow and mass conservation is as follows: ； ； ； in, For Darcy's speed; For penetration rate; For fluid viscosity; For source terms; Porosity; , These are the bulk moduli of the fluid and the skeleton, respectively. Skempton coefficient; Darcy velocity is the velocity vector that a fluid exhibits in a porous medium. The formula for calculating the stimulus amount extraction is: ； ； in, For octahedral shear strain; The volume-average Darcy velocity; Unit volume; The expression for the unified force flow influence factor is: ； in, , For reference standard quantity, It is a dimensionless quantity.

7. The computational biomechanical analysis system for evaluating bone growth induced by bone healing scaffolds according to claim 6, characterized in that, The expression for the angiogenesis diffusion field is: ； in, Normalized blood vessel density; The attenuation rate; To generate source terms; The regional baseline diffusion coefficient; Provided by the time-varying boundary condition module; , These are the threshold and the slope, respectively. The expression for stem cell diffusion and response is as follows: ； in, MSC concentration; , These represent proliferation and apoptosis rates, respectively. For path rate; The regional baseline diffusion coefficient; Provided by the time-varying boundary condition module; MSC concentration; express Cell type; Indicates fibroblasts; It represents chondrocytes; Indicates osteoblasts; The formula for calculating the equivalent stiffness of the neighborhood is: ； ； in, For unit The neighborhood set; The unit center distance (m); The weight scale is (m); The neighborhood radius (m); It is a unit step function; Let i be the equivalent elastic modulus of element i; The formula for calculating the uniform differentiation rate is: ； in, It is a continuously differentiable and scalable Logistic or Hill form; To determine the path differentiation rate, multiple paths are assigned, including: , , , and ; Let be the effect function of force flow stimulation; The function representing the influence of blood vessel density; This is the local stiffness influence function; In the evolution of other cell lineages, the evolutionary expressions for the fibrous, cartilaginous, and bone lineages are as follows: ； in, Indicates the uniform differentiation rate, and is simultaneously affected by , , Joint regulation; The rate of MSC differentiation into fibroblasts; The rate of MSC differentiation into chondrocytes; This represents the rate of MSC differentiation into osteoblasts. The rate of differentiation of fibroblasts into osteoblasts; The rate of chondrocyte differentiation into osteoblasts; , and These represent fibroblasts, chondrocytes, and osteoblasts, respectively. , and These represent the proliferation rates of fibroblasts, chondrocytes, and osteoblasts, respectively. , and These represent the apoptosis rates of fibroblasts, chondrocytes, and osteoblasts, respectively. The expression for synchronous updating and writing back of material properties is: ； ； ； ； ； in, This refers to the volume fraction of granulation tissue, fiber, cartilage, and bone. , , and These are the baseline parameters for granulation tissue, fibers, cartilage, and bone, respectively; subscripts. This indicates the equivalent value of the time step.

8. The computational biomechanical analysis system for evaluating bone growth induced by bone healing scaffolds according to claim 7, characterized in that, The specific process of performing periodic boundary modeling and periodic laying of the selected microcellular structure within the fracture gap, participating in the global solution on an explicit geometric level, and evaluating feasibility using hard indicators of bone formation is as follows: RVE cell geometry and domain decomposition constructs cells periodically laid out in three-dimensional space, and divides the skeletal solid domain and the pore fluid domain within the cells. Periodic boundary conditions are set to apply periodic constraints on displacement and flow on the opposite surfaces of the cell. The periodic structure is laid out as a macroscopic framework and incorporated into the global solution domain; Determine the Dirichlet boundary values ​​and write them into the time-gated diffusion coefficient; Evaluation output is based on bone formation.

9. The computational biomechanical analysis system for evaluating bone growth induced by bone healing scaffolds according to claim 8, characterized in that, The geometric scale of the cell is The skeleton solid domain is The pore fluid domain is .

10. The computational biomechanical analysis system for evaluating bone growth induced by bone healing scaffolds according to claim 9, characterized in that, The expression for the mechanical periodic displacement condition in the periodic constraint is as follows: ； in, This indicates the front face of the opposite side of a cell. This represents the negative aspect of the cell's opposite side. Represents the displacement vector. Represents the macroscopic average strain tensor; The expression for the traction consistency between opposing surfaces in the periodic constraint is: ； in, Represents the surface traction vector; The expression for the seepage periodicity condition in the periodic constraint is as follows: ； ； in, Represents the fluid velocity vector; This represents the macroscopic average pressure gradient; In the periodic constraint, the expression for the no-slip and impermeable conditions of the inner wall of the skeleton is as follows: ； in, It is the surface normal vector; Indicates the surface located within a solid framework; The expression for copying cell elements to the fracture gap region using integer translation vectors, where the periodic structure is laid out as a macroscopic framework and incorporated into the global solution domain, is as follows: ； in, To translate the basic RVE to a spatial position Translation vector; Indicates an integer index; The periodic structure is laid out into a macroscopic framework and incorporated into the global solution domain, resulting in the macroscopic framework solid domain and the explicit pore domain as follows: ； in, Represents a macroscopic-scale scaffold solid domain; A spatial domain representing a macroscopic scale; This represents the union operator. A representative volume unit representing a solid domain. A representative volume unit representing a fluid domain; The periodic structure is laid out as a macroscopic framework and incorporated into the global solution domain. The tissue domain for fracture healing is denoted as... The global solution domain is: ； in, It represents the entire computational domain, including healing tissue, scaffold, and voids; This represents the area where new tissue is formed during the fracture healing process.

Images