Fluid shear stress driven skeletal structure evolution method and system
The fluid shear stress-driven skeletal structure evolution method solves the problems of inaccurate driving signals and coarse boundary condition processing in existing technologies, and realizes stable and accurate simulation of skeletal structures under new mechanical environments.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-26
- Publication Date
- 2026-03-31
AI Technical Summary
Existing bone remodeling simulation methods suffer from inaccurate driving signals, coarse boundary condition processing, and insufficient mesh adaptability, leading to non-convergence of calculations and deviations from physiological realities.
Using fluid shear stress as the driving signal, and through stable boundary treatment and adaptive mesh optimization, accurate simulation of the skeletal structure is achieved.
It improves the biological accuracy and computational stability of skeletal remodeling simulation, ensures the long-term stability of boundary conditions and the adaptability of the mesh, and realizes the stable evolution of skeletal structures under new mechanical environments.
Smart Images
Figure CN121768682A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the fields of biomechanics and computational bionics, and in particular relates to a method and system for skeletal structure evolution driven by fluid shear stress, which is used to predict and simulate the adaptive growth and remodeling of bones under mechanical conditions. Background Technology
[0002] Skeleton is a typical intelligent biocomposite material capable of adaptive remodeling based on its mechanical environment to optimize its structure and achieve a "use it or lose it" effect. This process is known as "Wolff's Law." Traditional skeleton remodeling simulation methods are mostly based on global strain energy density or Mises equivalent stress as driving signals. However, increasing biological evidence suggests that the perception of mechanical stimuli by bone cells (such as osteoblasts and osteoclasts) mainly originates from the fluid shear stress generated by the fluid flow within the bone canaliculi in the bone microstructure.
[0003] In the field of computer simulation for adaptive remodeling of skeletal biomechanics, existing technologies mainly revolve around the following core approaches: 1. The method based on solid strain energy density (SED) treats bone as an optimized material, with the goal of making the strain energy density of the entire bone structure tend to a uniform and optimal "target value" or "dead zone".
[0004] 2. Based on the solid-state Mises equivalent stress method, Mises stress is used as a comprehensive mechanical stimulus signal. The remodeling rule is similar to that of the SED method: growth occurs in high-stress areas, and absorption occurs in low-stress areas.
[0005] 3. Methods based on solid principal strain or strain tensor use the maximum / minimum principal strain, certain invariants of the strain tensor, or strain in a specific direction as driving signals. For example, some theories suggest that bone is deposited along the direction of the maximum principal strain.
[0006] The aforementioned common existing technologies mainly have the following problems: 1. Inaccurate driving signal: Using solid strain energy, stress or strain as the driving signal fails to accurately reflect the fluid dynamic factors (i.e. fluid shear stress) actually perceived at the cellular level. Numerous studies have shown that bone tissue cells are more sensitive to fluid dynamic factors than solid mechanical factors, thus leading to a deviation between the predicted results and the actual physiological situation.
[0007] 2. Rough handling of boundary conditions: In simulations, it is often difficult to fix the boundaries of bones (such as articular surfaces) stably and accurately, which leads to non-physiological drift or distortion of boundary nodes during the reshaping process, affecting the stability of the calculation and the accuracy of the results.
[0008] 3. Insufficient mesh adaptability: During structural evolution, the mesh cannot be effectively refined and coarsened according to the distribution of the mechanical field, resulting in insufficient analysis accuracy in high gradient stress / strain regions or waste of computational resources in low gradient regions.
[0009] 4. Poor convergence: Due to the above problems, traditional simulation processes often suffer from mesh quality deterioration and computational non-convergence after multiple iterations, making it difficult to achieve complete and stable long-term evolution simulation.
[0010] To address the aforementioned problems, this invention proposes a method and system for skeletal structure evolution driven by fluid shear stress. Summary of the Invention
[0011] The purpose of this invention is to propose a skeletal structure evolution method and system based on fluid shear stress driving, with stable boundary treatment and adaptive mesh optimization capabilities, to solve the problems mentioned in the background art, thereby achieving a more biologically consistent, computationally more stable, and more accurate simulation of bone growth and remodeling.
[0012] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A fluid shear stress-driven method for skeletal structure evolution includes the following steps: S1. Initialization and Feature Recognition: Read the initial geometric model of the skeleton and automatically identify the mechanical boundary features of the model, including fixed constraint surfaces and load application surfaces; S2. Setting stable boundary conditions and defining the exclusion zone: Apply displacement constraints to the fixed constraint surface and define the elements of the surface as the reshaping exclusion zone. The surface elements in this zone will not participate in the addition or subtraction of elements in subsequent iterations. S3. Explicit dynamic analysis and fluid shear force extraction: Explicit dynamic analysis is used to perform fluid-structure interaction analysis on the skeletal model and output fluid shear force as a stress index driving bone remodeling. S4. Shear stress-driven bone remodeling: Based on the fluid shear force extracted in S3, calculate the average fluid shear force of each outer surface unit except for the remodeling exclusion area, set a reference stress value, and calculate whether this surface unit is a unit that needs to be added or removed based on the comparison relationship between the average fluid shear force value of each outer surface unit and the reference stress value, to simulate bone absorption and deposition. S5. Adaptive Mesh Optimization Driven by Fluid Shear Force: Based on the mechanical field obtained from mechanical analysis, identify regions where elements are added and deleted; monitor and optimize the mesh after element addition and deletion, and regenerate the optimized mesh. S6. Iterative Evolution: Repeat S3-S5 until the preset number of iterations or convergence criteria are reached, so that the skeletal geometry evolves to a relatively stable state under the new mechanical environment.
[0013] Preferably, the automatic identification of the mechanical boundary features in S1 is achieved through geometric feature identification or topological feature identification; during the identification process, the surfaces with the smallest and largest Z-axis coordinates are automatically identified by calculating the boundary box of the geometric model, and are defined as the fixed constraint surface and the load application surface, respectively.
[0014] Preferably, the specific rules for bone remodeling described in S4 are as follows: If the average fluid shear force of the bone outer surface unit is lower than the first threshold, then this surface unit is determined to be a pruned unit to simulate bone resorption caused by stress shielding. If the average fluid shear force of the bone outer surface unit is higher than the second threshold, then this surface unit is determined to be a pruning unit to simulate bone resorption in the high stress area. If the average fluid shear force of the bone outer surface unit is between the first threshold and the second threshold, then this surface unit is determined to be an augmentation unit to simulate bone growth; The first threshold and the second threshold are set based on the reference stress value.
[0015] Preferably, the reference stress value is the median of the fluid shear force values of all participating remodeling nodes; the first threshold is the product of the reference stress value and a low threshold coefficient; and the second threshold is the product of the reference stress value and a high threshold coefficient.
[0016] Preferably, the depth of the augmenting unit is proportional to the difference between the average fluid shear force value and the reference stress value, and is controlled by a reshaping factor; the depth of the augmenting unit does not exceed a preset maximum depth.
[0017] Preferably, the mechanical field in S5 is the fluid shear force on the surface unit node; the identification of the unit addition region is based on the gradient of the mechanical field, and the unit is expanded in the region where the mechanical field value is higher than the preset gradient threshold.
[0018] Preferably, in step S5, after regenerating the optimized mesh, the analysis step and boundary conditions are automatically updated to adapt to the next iteration of analysis.
[0019] Fluid shear stress-driven skeletal structure evolution system, including: The initialization and feature recognition module is used to read the initial geometric model of the skeleton and automatically identify the mechanical boundary features of the model; The boundary condition and exclusion zone setting module is used to apply displacement constraints to a fixed constraint surface and define the elements of that surface as remodeling exclusion zones; The explicit dynamics analysis module is used to perform explicit dynamics analysis on the bone model and output fluid shear force as a mechanical standard for driving bone remodeling. The bone remodeling driving module is used to calculate the average fluid shear force of each surface unit node extracted from the remodeling exclusion area, set the reference stress value, and calculate whether the surface unit needs to be added or removed based on the comparison between the average fluid shear force of each surface unit and the reference stress value, thus simulating bone absorption and deposition. The adaptive mesh optimization module is used to identify regions where elements are added and removed based on the mechanical field obtained from mechanical analysis; it monitors and optimizes the mesh after element addition and removal, and regenerates the optimized mesh. The iterative control module controls the cyclic execution of the initialization and feature recognition module, the boundary condition and exclusion region setting module, the explicit dynamic analysis module, the bone remodeling driving module, and the adaptive mesh optimization module until the preset number of iterations or convergence criteria are reached, so that the bone geometry evolves to a relatively stable state under the new mechanical environment.
[0020] The present invention further protects a computer device, the computer device including a processor and a memory, the memory storing at least one instruction, at least one program, code set or instruction set, the instruction, program, code set or instruction set being loaded and executed by the processor to implement the above-described fluid shear stress driven skeletal structure evolution method.
[0021] The present invention further protects a computer-readable storage medium storing at least one instruction, at least one program, code set, or instruction set, wherein the instruction, program, code set, or instruction set is loaded and executed by a processor to implement the above-described fluid shear stress-driven skeletal structure evolution method.
[0022] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) In terms of driving signal, the present invention directly uses fluid shear stress, which is closer to the real mechanical stimulation perceived by bone cells and the biological mechanism is more accurate.
[0023] (2) In terms of boundary processing, the present invention has the advantages of precision and stability. Through the "fixed boundary exclusion" mechanism, the key boundary is locked to ensure the stability and physiological rationality of long-term iteration.
[0024] (3) In terms of grid strategy, the present invention can be dynamically and intelligently adaptive, using a mechanical field driven adaptive grid, automatically adding or removing cells in key areas and controlling the quality of the control unit in real time, taking into account both accuracy and efficiency.
[0025] (4) In terms of system stability, the present invention has the characteristics of strong robustness. Through the above three innovations, a highly stable and automated closed-loop simulation system is formed, which can complete the long-term prediction of skeletal structure evolution.
[0026] (5) Technical feasibility: By using fluid shear force, which is readily available in explicit dynamics, as the mechanical standard, engineering feasibility and efficiency are achieved while ensuring biological rationality. Attached Figure Description
[0027] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings involved in the embodiments are now briefly described. Obviously, the drawings in the following description are merely illustrative of some embodiments of the present invention. For those skilled in the art, other forms of drawings can be constructed based on these drawings without creative effort.
[0028] Figure 1 This is a network framework diagram of the fluid shear stress-driven skeletal structure evolution method proposed in this invention. Detailed Implementation
[0029] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0030] The fluid shear stress-driven skeletal structure evolution method proposed in this invention will be further described below with reference to the accompanying drawings and relevant examples.
[0031] Example 1: Please see Figure 1 This invention proposes a fluid shear stress-driven method for skeletal structure evolution. Its core lies in using the fluid shear stress on the bone surface as a direct driving signal, and employing a "fixed boundary exclusion" mechanism and a "mechanical field-driven adaptive mesh" technique to achieve a more biologically consistent, computationally stable, and accurate simulation of bone growth and remodeling. Specifically, it includes the following steps: Step 1: Initialization and Feature Recognition: Read the initial geometric model of the skeleton (e.g., a CAD model); automatically identify the mechanical boundary features of the model, especially surfaces requiring fixed constraints (e.g., simulated joint contact surfaces) and load-bearing surfaces. This recognition can be achieved through geometric features (e.g., the extreme locations of the bounding box) or topological features (e.g., surface normals).
[0032] Step 2: Stable boundary condition setting and exclusion zone definition: Create a boundary condition with zero displacement on the fixed-constraint surface; define the elements of the fixed-constraint surface as the remodeling exclusion zone. The surface elements in this zone do not participate in the addition or removal of elements based on mechanical response in all subsequent iterations, thereby ensuring the long-term stability of the boundary conditions and preventing boundary degradation.
[0033] Step 3: Explicit Dynamics Analysis and Fluid Shear Force Extraction: Explicit dynamics analysis was used to perform fluid-structure interaction analysis on the bone model. Compared to implicit methods, explicit methods are better suited to handling nonlinear problems such as contact and large deformations. In the analysis, the fluid shear forces at the surface nodes were specifically requested for output. These forces were used as a driving standard for bone evolution because they directly reflect the shear forces exerted by the fluid on the bone surface on bone cells.
[0034] Step 4: Shear stress-driven bone remodeling: The fluid shear force value of each surface element node (excluding exclusion zone nodes) is extracted from the analysis results; a reference stress value is set (e.g., the median stress of all nodes); remodeling rules are applied based on the relationship between the average fluid shear force value of the surface element and the reference stress. The specific bone remodeling rules are: High-stress absorption: If the average fluid shear force of the surface element is higher than the high threshold (shear_threshold_high * reference stress), the element is deleted (simulating bone absorption); Low-stress absorption: If the average fluid shear force of the surface element is lower than the low threshold (shear_threshold_low * reference stress), the element is deleted (simulating bone absorption due to stress shielding). Moderate-stress deposition: If the average fluid shear force of the surface element is between the high and low thresholds, elements are added outward along the surface normal (simulating bone growth). Finally, the depth of element addition is proportional to the stress difference and controlled by a remodeling factor, while the depth of element addition is limited to a maximum value to ensure numerical stability.
[0035] Step 5: Mechanical field-driven adaptive mesh optimization: Based on the mechanical field obtained from the current analysis (such as fluid shear force), the regions that need to add elements (high gradient regions) and delete elements (low gradient regions) are identified; the surface elements in the high gradient regions are expanded to regenerate hexahedral element meshes; this step ensures sufficient computational accuracy in mechanically critical regions while optimizing overall computational resources.
[0036] Step 6: Iterative evolution: Repeat steps 3 to 5 to form a closed-loop feedback system of "analysis → reshaping → mesh update and optimization → reanalysis"; after a preset number of iterations, the geometry of the skeleton will evolve into a structure that reaches a relatively stable state under the new mechanical environment.
[0037] The specific implementation of the above key steps is as follows: 1. Feature recognition and boundary setting: This corresponds to the "Identify Original Features" and "Set Boundary Conditions" methods in the program.
[0038] The program automatically identifies the surfaces with the smallest and largest Z coordinates by calculating the bounding box of the model, and uses them as the fixed surface and the load surface, respectively. Nodes on the fixed face are explicitly marked by creating a node set named BottomNodes_NoRemodeling. These nodes are completely excluded in subsequent remodeling.
[0039] 2. Explicit dynamic analysis and surface force extraction: This corresponds to the "Create Display Analysis Step" method.
[0040] Create an ExplicitDynamicsStep and set the field output request, specifically requiring the output of the fluid shear force CSHEARMAG. This field variable is the basis for calculating the bone evolution threshold.
[0041] 3. Shear stress-driven bone remodeling: This corresponds to the "Perform bone reconstruction simulation" method.
[0042] Read the fluid shear force CSHARMAG of the surface nodes from the ODB results file; skip the nodes in the BottomNodes_NoRemodeling set; calculate the average fluid shear force for the surface elements involved in the remodeling; use the median of the fluid shear forces of all surface elements as the reference stress reference_shear; apply the following rules to determine which surface elements are added and which are removed: (reference_shear = np.median(filtered_shear_values); formation_threshold = reference_shear * self.parameters['formation_threshold']; resorption_threshold = reference_shear * self.parameters['resorption_threshold']); add and remove elements according to the outward normal of the surface elements to update the mesh.
[0043] 4. Adaptive mesh optimization: This corresponds to the methods of "identifying bone formation / bone resorption areas" and "adaptive mesh control".
[0044] Based on the average fluid shear force of surface elements, high-gradient regions (elements with average fluid shear force higher than a threshold) and low-gradient regions are identified; for surface elements in high-gradient regions, an element addition operation is performed, calling the create_hex8_element method to create a new hexahedral mesh on the outer surface of the target element; after regenerating the mesh, the analysis step and boundary conditions are automatically updated to prepare for the next iteration.
[0045] 5. Iterative control: The main loop controls the entire iteration process until the preset maximum number of iterations is reached. Each iteration outputs detailed calculation status and results for easy monitoring and debugging.
[0046] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.
Claims
1. A method of fluid shear stress driven skeletal structure evolution, characterized by, The method comprises the following steps: S1, initialization and feature recognition: reading an initial geometric model of a bone, and automatically recognizing mechanical boundary features of the model, including a fixed constraint surface and a load application surface; S2, stable boundary condition setting and exclusion zone definition: applying displacement constraints on the fixed constraint surface, and defining the cells of the surface as remodeling exclusion areas, which are not involved in cell addition and deletion in subsequent iterations; S3, explicit dynamics analysis and fluid shear stress extraction: performing fluid-structure coupling analysis on the bone model using explicit dynamics analysis method, and outputting fluid shear stress as a basic parameter for driving bone remodeling threshold; S4, bone remodeling driven by shear stress: based on the fluid shear stress extracted in S3, calculating the average fluid shear stress of each external surface cell except the remodeling exclusion area, setting a reference stress value, and calculating whether the external surface cell needs to add or delete cells along its surface normal according to the comparison relationship between the average fluid shear stress of each external surface cell and the reference stress value, to simulate bone absorption and deposition; S5, adaptive mesh optimization driven by shear stress: based on the fluid shear stress value obtained by mechanical analysis, identifying the cell addition area and the cell deletion area; monitoring and optimizing the deletion of cells to ensure the quality of the cells; S6, iterative evolution: repeating S3-S5 until a preset number of iterations or a convergence criterion is reached, so that the bone geometry evolves to a relatively stable state in the new mechanical environment.
2. The fluid shear stress driven skeletal structure evolution method of claim 1, wherein, The automatic recognition of the mechanical boundary features in S1 is realized by geometric feature recognition or topological feature recognition; In the identification process, the bounding box of the geometric model is calculated to automatically identify the surfaces with the minimum and maximum Z-axis coordinates, which are defined as the fixed constraint surface and the load application surface, respectively.
3. The fluid shear stress driven skeletal structure evolution method of claim 1, wherein, The specific rules for bone remodeling in S4 are as follows: If the average fluid shear stress of the bone external surface cell is lower than the first threshold value, it is determined that this surface cell is a deletion cell, simulating bone absorption caused by stress shielding; If the average fluid shear stress of the bone external surface cell is higher than the second threshold value, it is determined that this surface cell is a deletion cell, simulating bone absorption in high stress areas; If the average fluid shear stress of the bone external surface cell is between the first threshold value and the second threshold value, it is determined that this surface cell is an addition cell, simulating bone growth; Wherein, the first threshold value and the second threshold value are set based on the reference stress value.
4. The fluid shear stress driven skeletal structure evolution method of claim 3, wherein, The reference stress value is the median of the fluid shear stress values of all participating remodeling nodes; the first threshold value is the product of the reference stress value and a low threshold coefficient; The second threshold value is the product of the reference stress value and a high threshold coefficient.
5. The fluid shear stress driven skeletal structure evolution method according to claim 3 or 4, characterized in that, The depth of the addition cell is proportional to the difference between the average fluid shear stress value and the reference stress value, and is controlled by a remodeling factor; the depth of the addition cell does not exceed the preset maximum depth.
6. The fluid shear stress driven skeletal structure evolution method of claim 1, wherein, The mechanical field in S5 is the fluid shear stress on the nodes of the surface cells; the identification of the cell addition area is based on the gradient of the mechanical field, and the cell expansion is performed on the area where the mechanical field value is higher than the preset gradient threshold.
7. The fluid shear stress driven skeletal structure evolution method of claim 6, wherein, After the optimized mesh is regenerated in S5, the analysis step and the boundary conditions are automatically updated to adapt to the next iteration analysis.
8. A fluid shear stress driven skeletal architecture evolution system applying the method according to any one of claims 1 to 7, characterized in that, It comprises: The initialization and feature recognition module is configured to read an initial geometric model of a bone and automatically recognize mechanical boundary features of the model. The boundary condition and exclusion zone setting module is configured to apply displacement constraints on a fixed constraint surface and define cells of the surface as remodeling exclusion zones. The explicit dynamics analysis module is configured to perform explicit dynamics analysis on the bone model and output fluid shear stress as a mechanical criterion for driving bone remodeling. The bone remodeling driving module is configured to calculate average fluid shear stress of each surface cell except the remodeling exclusion zones based on fluid shear stress of extracted surface cell nodes, set a reference stress value, and calculate whether each surface cell is a cell to be added or a cell to be deleted based on a comparison between the average fluid shear stress of the surface cell and the reference stress value, so as to simulate bone absorption and deposition. The adaptive mesh optimization module is configured to identify cell addition zones and cell deletion zones based on a mechanical field obtained through mechanical analysis. The adaptive mesh optimization module is configured to identify cell addition zones and cell deletion zones based on a mechanical field obtained through mechanical analysis. The iteration control module is configured to control cyclic execution of the initialization and feature recognition module, the boundary condition and exclusion zone setting module, the explicit dynamics analysis module, the bone remodeling driving module, and the adaptive mesh optimization module until a preset iteration number or a convergence criterion is reached, so that the bone geometric structure evolves to a relatively stable state in a new mechanical environment.
9. A computer device, comprising: The computer device includes a processor and a memory, and the memory stores at least one instruction, at least one program, a code set, or an instruction set, which are loaded and executed by the processor to implement the fluid shear stress driven bone structure evolution method according to any one of claims 1-7.
10. A computer-readable storage medium, characterized in that, The computer readable storage medium stores at least one instruction, at least one program, a code set, or an instruction set, which are loaded and executed by the processor to implement the fluid shear stress driven bone structure evolution method according to any one of claims 1-7.