Stress shielding aware bone reconstruction assessment method, apparatus, device, and storage medium

Abstract

The embodiment of the application discloses a kind of bone reconstruction evaluation method, device, equipment and storage medium considering stress shielding, by regarding bone reconstruction process as optimization process, the density of each reconstruction field unit is defined as bone density, and is simultaneously optimization design variable, the function of stress of reconstruction field unit is target function, constraint function includes external load constraint, energy constraint, volume fraction constraint, stress shielding effect is realized by filtering function processing in optimization process, the above-mentioned method can better simulate the bone density distribution under the influence of stress shielding effect in postoperative bone reconstruction process, can better carry out preoperative evaluation.

Description

Technical Field

[0001] This invention relates to the field of biomechanics, and more particularly to a method, apparatus, device, and storage medium for assessing bone remodeling that takes stress shielding into account. Background Technology

[0002] Clinically, spinal fusion is a primary treatment for spinal diseases, and interbody fusion devices are widely used in cervical and lumbar spine fusion surgeries. Evaluating bone remodeling after interbody fusion is a necessary preoperative assessment. Bone remodeling refers to the physiological behavior of bone tissue morphology and density changing in response to alterations in the biomechanical environment. Postoperative bone remodeling requires bone tissue to withstand a certain level of stress. Wolff's Law states the relationship between bone growth and the stress environment: higher stress promotes bone growth, while lower stress fails to promote growth and leads to bone resorption.

[0003] Computational bone reconstruction is one of the important methods for preoperative assessment of bone reconstruction. It refers to using the finite element method or other computational methods to assess the postoperative bone stress state for a given surgical plan (selection and location of the interbody fusion cage, etc.) in order to confirm whether the bone can be reconstructed as expected.

[0004] Current calculation methods do not consider stress shielding. Stress shielding refers to the phenomenon where, during bone reconstruction, the stiffer implant (interbody fusion cage) and the less stiff bone tissue share the external load. Under consistent strain boundaries, the stress borne by the bone tissue is significantly less than that borne by the implant. Ignoring stress shielding in calculations leads to a higher calculated stress on the bone tissue than would actually be under stress shielding, causing the calculation results to deviate from reality and rendering preoperative assessments invalid. Summary of the Invention

[0005] Based on this, it is necessary to propose a bone reconstruction method, device, computing equipment, and storage medium that considers stress shielding to address the above problems, so as to more realistically simulate the growth prediction of bone tissue and effectively evaluate the preoperative effect of bone reconstruction.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for assessing bone remodeling that takes stress shielding into account, the method comprising:

[0008] A computational model is established, comprising a structure and boundary conditions. The structure includes a reconstruction domain, undesignable bone, an implant, and initial reconstructed bone disposed within the reconstruction domain, the initial reconstructed bone growing within the reconstruction domain. The boundary conditions include external loads acting on the undesignable bone and the positional relationship between the implant and the undesignable bone. The computational model is meshed to obtain cells and nodes, wherein the cells involved in the reconstruction domain are reconstruction domain cells, and the number of reconstruction domain cells is n.

[0009] Formulate an optimization problem, wherein the design variables of the optimization problem are ρ=(ρ1,…,ρ e …,ρ n ) T , where ρ e ρ represents the relative density of the e-th reconstruction domain unit, which physically represents the bone density within the bone reconstruction region. min <ρ e ≤1, ρ min Given a minimum density; the objective function of the optimization problem formulation is the stress σ of each of the reconstructed domain elements. e The function I = I(σ) e The constraints include external load constraints, energy constraints, and volume fraction constraints.

[0010] After solving the optimization problem formulation, and in at least one of the solution steps, the updated design variable ρ is further filtered. The filtering process involves: when the stress σ of one or more of the reconstructed domain elements... e When the stress is less than the given stress limit, the relative density of the reconstructed domain element is multiplied by a filtering function less than 1;

[0011] After completing the formulation of the optimization problem, the reconstructed bone after growth is obtained according to the updated design variable ρ. The reconstructed bone after growth is set in the reconstruction domain to obtain the updated calculation model. The updated calculation model is used to calculate the stress distribution field of the reconstructed bone after growth. The stress distribution field is statistically analyzed to obtain the bone reconstruction evaluation result.

[0012] Another technical solution involves an optimized apparatus for a bone remodeling assessment method considering stress shielding, the apparatus comprising:

[0013] A computational model building module is used to build a computational model, which includes a structure and boundary conditions. The structure includes a reconstruction domain, undesignable bone, an implant, and initial reconstructed bone set within the reconstruction domain, wherein the initial reconstructed bone grows within the reconstruction domain. The boundary conditions include external loads acting on the undesignable bone and the positional relationship between the implant and the undesignable bone. The computational model is meshed to obtain cells and nodes, wherein the cells involved in the reconstruction domain are reconstruction domain cells, and the number of reconstruction domain cells is n.

[0014] The optimization problem formulation module, wherein the optimization problem formulation model is used to form the optimization problem formulation, and the design variables of the optimization problem formulation are ρ=(ρ1,…,ρ e …,ρ n ) T , where ρ e ρ represents the relative density of the e-th reconstruction domain unit, which physically represents the bone density within the bone reconstruction region. min <ρ e ≤1, ρ min Given a minimum density; the objective function of the optimization problem formulation is the stress σ of each of the reconstructed domain elements. e The function I = I(σ) e The constraints include external load constraints, energy constraints, and volume fraction constraints.

[0015] A filtering module is configured to perform filtering on the updated design variable ρ after at least one solution step in solving the formulation of the optimization problem. The filtering process involves: when the stress σ of one or more of the reconstructed domain elements... e When the stress is less than the given stress limit, the relative density of the reconstructed domain element is multiplied by a filtering function less than 1;

[0016] The bone reconstruction result evaluation module is used to evaluate the bone reconstruction results. The evaluation process is as follows: after solving the optimization problem formula, the reconstructed bone after growth is obtained according to the updated design variable ρ. The reconstructed bone after growth is set in the reconstruction domain to obtain the updated calculation model. The updated calculation model is used to calculate the stress distribution field of the reconstructed bone after growth. The stress distribution field is statistically analyzed to obtain the bone reconstruction evaluation result.

[0017] Another technical solution includes a computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the method described above.

[0018] Another technical solution is a computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the steps of the method described above.

[0019] Implementing the embodiments of the present invention will have the following beneficial effects:

[0020] This invention employs a density-based topology optimization method to simulate the bone reconstruction process. The density of each reconstruction domain unit is used as the design variable, and the stress function of the reconstruction domain unit is used as the objective function. The constraint functions include external load constraints, energy constraints, and volume fraction constraints. A stress criterion is introduced into this method, treating the stress shielding effect as a filtering function in the optimization process to consider the impact of stress shielding on the bone reconstruction process. The above method can better simulate the situation in the bone reconstruction process where the stress borne by the less stiff bone tissue is much less than that borne by the more stiff implant, thus enabling better preoperative assessment. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] in:

[0023] Figure 1 This is a flowchart of a bone reconstruction assessment method considering stress shielding according to a specific embodiment of the present invention;

[0024] Figure 2 This is a schematic diagram illustrating the relationship between the magnitude of stress on bone tissue and changes in bone mass in the theory of bone mass regulation system.

[0025] Figure 3 This is a two-dimensional computational model in one example of the present invention;

[0026] Figure 4 This is the initial state of Example 1 of this invention;

[0027] Figure 5 This is a contour plot of the stress range of 0 to 2 MPa in Example 1 of this invention;

[0028] Figure 6 This is a contour plot of the stress range of 2 to 20 MPa in Example 1 of this invention;

[0029] Figure 7 This is the initial state of Example 2 of this invention;

[0030] Figure 8 This is a contour plot of the stress range of 0 to 2 MPa in Example 2 of this invention;

[0031] Figure 9 This is a contour plot of the stress range of 2 to 20 MPa in Example 2 of this invention;

[0032] Figure 10 This is the initial state of Example 3 of this invention;

[0033] Figure 11 This is a contour plot of the stress range of 0 to 2 MPa in Example 3 of this invention;

[0034] Figure 12 This is a contour plot of the stress range of 2 to 20 MPa in Example 3 of this invention;

[0035] Figure 13 This is the initial state of Example 4 of this invention;

[0036] Figure 14 This is a contour plot of the stress range of 0 to 2 MPa in Example 4 of this invention;

[0037] Figure 15 This is a contour plot of the stress range of 2 to 20 MPa in Example 4 of this invention;

[0038] Figure 16 This is the initial state of Example 5 of this invention;

[0039] Figure 17 This is a contour plot of the stress range of 0 to 2 MPa in Example 5 of this invention;

[0040] Figure 18 This is a contour plot of the stress range of 2 to 20 MPa in Example 5 of this invention;

[0041] Figure 19 This is a structural block diagram of an optimized device for a bone reconstruction assessment method considering stress shielding according to a specific embodiment of the present invention.

[0042] Figure 20 A structural block diagram of a computer device for a bone reconstruction assessment method considering stress shielding according to a specific embodiment of the present invention. Detailed Implementation

[0043] 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.

[0044] like Figure 1 As shown, this invention provides a bone reconstruction method considering stress shielding. This method can be applied to both terminals and servers; this embodiment illustrates its application to a terminal. The bone reconstruction method considering stress shielding specifically includes the following steps:

[0045] S1: Establish a computational model.

[0046] A computational model is established based on the surgical plan. The computational model includes structure and boundaries. The structural part of the model includes a reconstruction domain, undesignable bone, an implant, and initial reconstructed bone placed within the reconstruction domain, which grows within the domain. The boundary conditions of the computational model include external loads acting on the undesignable bone, which mainly simulate the stress conditions of the undesignable bone, and the positional relationship between the implant and the undesignable bone, which mainly refers to the location where the implant will be placed in the surgical plan. The purpose of this invention is to predict the bone reconstruction after the implant is placed into the undesignable bone according to the surgical plan.

[0047] In the above scheme, the initial reconstructed bone adopts a randomized initial design scheme to simulate intraoperative bone fragment filling. In this specific embodiment, the implant refers to the intervertebral fusion cage, and the undesignable bone refers to the vertebrae located above and below the intervertebral fusion cage, respectively. According to the surgical plan, the intervertebral fusion cage is implanted between the two vertebrae.

[0048] In one specific embodiment, the undesignable skeleton is obtained from radiographic images.

[0049] In a preferred embodiment, the undesignable skeleton is obtained from imaging images via the following process:

[0050] S101. Read the color information in the imaging image and convert it into a grayscale image. The grayscale image includes pixels with different grayscale values, and adjacent pixels of the same grayscale value form a pixel block.

[0051] S102. Compare the gray values ​​of adjacent pixel blocks in the grayscale image. If the difference in gray values ​​between adjacent pixel blocks is less than a given segmentation threshold, merge the adjacent pixel blocks. The gray value of the merged pixel block is the average of the merged adjacent pixel blocks. Repeat until the size of the pixel block exceeds a given size threshold or there are no more pixel blocks that can be merged, forming a physical model of an undesignable skeleton composed of pixel blocks. This merging operation can greatly reduce the number of pixel blocks, simplify the calculation model, and improve computational efficiency.

[0052] S103. Mesh the physical model of the undesignable skeleton composed of pixel blocks formed in the previous step. Use the proportional boundary element method to mesh the pixel block, generating a proportional boundary element mesh for each pixel block. That is, generate a proportional boundary element subdomain for each pixel block. The proportional center of the subdomain is set at the geometric center of the corresponding pixel block. If there are dangling nodes, add new nodes, modify the connectivity information, and generate the corresponding boundary line units.

[0053] In this specific embodiment, the implant is used as the boundary. When dividing the reconstruction domain into grids, the reconstruction domain can be divided into grids according to any existing technology. The unit involved in the reconstruction domain is the reconstruction domain unit, and the number of reconstruction domain units is n.

[0054] S2: Formulate the optimization problem.

[0055] The optimization problem of bone reconstruction considering stress shielding is formulated as follows:

[0056] Find the design variable ρ = (ρ1, ..., ρ n ) T ,u

[0057] Make the objective function Minimum

[0058] Constraints:

[0059] K(ρ)u=f,

[0060]

[0061]

[0062] ρ min ≤ρ e ≤1

[0063] In the formula, n is the number of reconstruction domain units, ρ e ρ is the density of the e-th reconstruction domain unit, which physically represents the bone density within the bone reconstruction region and is an optimization design variable. min It is the minimum density of a given reconstruction domain element, when the reconstruction domain element density is below ρ. min At that time, delete the reconstructed domain element; u is the nodal displacement vector associated with ρ. It is a function of a certain stress in the e-th reconstruction domain element. In this specific embodiment, it is chosen as the Mises stress. In the two-dimensional case, p is a given positive parameter; K is the global stiffness matrix; and f is the external load vector. In the constraints, the constraint function C(ρ) is the strain energy function, limited by an upper limit on strain energy. V is a volume fraction function, limited by the upper limit of volume. v eIt is the volume of the e-th reconstruction domain unit.

[0064] S3: Solving the above optimization formula, during the solution process, after solving at least one of the solution steps, the updated design variable ρ is also filtered. The filtering process is as follows: when the stress σ of one or more reconstructed domain elements... e When the stress is less than the given stress limit, the relative density of the reconstructed domain element is multiplied by a filter function less than 1.

[0065] In one specific embodiment, the cell density update employs a Heaviside filtering function. That is, after obtaining the updated cell density by solving the optimization formula, the following function is used to filter the updated cell density again.

[0066]

[0067] in

[0068]

[0069] In the formula, H is the Heaviside filtering function. is the density of the reconstructed domain elements after filtering; ∈ and γ are control parameters that control the degree of regularization to ensure the nonsingularity of the overall stiffness matrix K; σ It is the minimum effective growth stress.

[0070] refer to Figure 2 The bone mass regulation system theory, based on the relationship between the magnitude of stress on bone tissue and changes in bone mass, roughly divides bone remodeling theory into four states:

[0071] 1. When the stress on bone tissue is less than 2 MPa, it is considered to be in a disused state. At this time, the rate of bone resorption exceeds the rate of bone formation, resulting in a reduction in bone mass. In this specific embodiment, the minimum effective growth stress is... σ =2MPa.

[0072] 2. When the stress on bone tissue is between 2 MPa and 20 MPa, it is in an adaptive remodeling state. At this time, mechanical stimulation activates bone remodeling activity, causing the rate of bone formation to increase and reach its peak, which offsets the effect of bone resorption and keeps the local bone mass stable.

[0073] 3 When the stress on bone tissue is between 20 MPa and 60 MPa, it is considered a moderate overload state. At this time, bone remodeling has reached its peak, but it is still unable to meet the requirements of adapting to the load environment. Therefore, bone remodeling becomes active, and a large amount of bone is formed through lamellar bone drift.

[0074] 4. When the stress on bone tissue is between 60 MPa and 120 MPa, it is considered a pathological overload state. At this time, a large amount of woven bone appears to form bone more quickly, while stress exceeding this range will lead to fracture.

[0075] In existing technologies, the minimum effective growth stress is not considered. σ The impact of σ < 2MPa on the calculation process. This leads to a situation where, in a certain optimization step, there is unused bone tissue (σ < 2MPa) within the reconstruction domain, but in subsequent calculations, this type of tissue still participates in the analysis, without reflecting its absorbed state. Such simulation calculations are unconvincing, rendering the preoperative assessment invalid.

[0076] In this invention, the Heaviside filtering function is used to interpolate the updated cell density obtained in the optimization step, and the influence of the minimum effective growth stress is introduced. The bone reconstruction effect is evaluated under the consideration of stress shielding.

[0077] In one specific embodiment, the proportional boundary element method is used for subsequent solution. During this process, the displacement field of the subdomain boundary is obtained by the following equation.

[0078]

[0079] Where u b is the subdomain boundary displacement vector, and p is the equivalent nodal force of the subdomain. It is the stiffness matrix, determined by the following expression:

[0080]

[0081] Where Q and Φ are determined by the following linear eigenvalue problem:

[0082]

[0083] Φ=[φ1,φ2,…,φ n ]

[0084] Q = [q1, q2, ..., q n ]

[0085] Where n is the number of units and λ is the eigenvalue.

[0086] in

[0087]

[0088]

[0089]

[0090] Where B1 and B2 are strain matrices, see Equation 11 of Xing W, Song C, Tin-Loi FA scaled boundary finite element based node-to-node scheme for 2D frictional contact problems[J]. Computer Methods in Applied Mechanics and Engineering, 2018, 333(MAY1):114-146, J is the Jacobian matrix of the divided elements, and D is the elasticity matrix of the e-th element. e Determined by the following formula:

[0091]

[0092] Where D0 is the elasticity matrix of solid bone tissue. It is the cell density after filtering the e-th reconstruction domain cell.

[0093] After obtaining the displacement on the boundary of the subdomain, the expression for the displacement of the radial line from the scale center of the subdomain to the boundary node is:

[0094]

[0095] Where c = Φ -1 u b , where φ i c is the i-th column vector of Φ. i It is the i-th component of c.

[0096] The displacement and stress fields of the entire subdomain are calculated using the following interpolation formulas.

[0097] u(ξ,η)=N u (η)u(ξ)

[0098]

[0099] Where N u (η) is the interpolation function, and (ξ,η) are the scale boundary coordinates of the current subdomain.

[0100] In one specific embodiment, the SIMP method (Solid Isotropic Material Penalty Method) is used to solve the optimization formula. In the SIMP method, sensitivity analysis is required; the sensitivity of the objective function I to the design variables is...

[0101]

[0102] Where is the derivative vector of the Mises stress with respect to each stress component, in the two-dimensional case,

[0103]

[0104] The accompanying field displacement w is calculated by the following formula:

[0105] Kw = f ad

[0106] in

[0107]

[0108] S4: After completing the formulation of the optimization problem, the reconstructed bone after growth is obtained according to the updated design variable ρ. The reconstructed bone after growth is set in the reconstruction domain to obtain the updated calculation model. The updated calculation model is used to calculate the stress distribution field of the reconstructed bone after growth. The stress distribution field is statistically analyzed to obtain the bone reconstruction evaluation result.

[0109] The following five case studies, all employing interbody fusion, demonstrate the beneficial effects of this invention.

[0110] The calculation model is as follows Figure 3 The two-dimensional model shown in the image has the upper black area representing the upper vertebral body 1 and the lower black area representing the lower vertebral body 2. Both the upper and lower vertebral bodies are non-designable skeletal structures. The connection between the upper and lower vertebral bodies represents the cross-section of the intervertebral fusion device 3. The calculated model dimensions are 45mm × 64.7428mm. The magnitude and direction of the external load are as follows. Figure 3 As shown, F1 = 900N simulates the pressure exerted on the upper vertebral body by the upper intervertebral disc, and F2 = 45N simulates the pressure exerted on the vertebral body by the vertebral arch.

[0111] The material parameters, excluding those of the interbody fusion device, are shown in Table 1.

[0112] Table 1 Material Parameters

[0113]

[0114] The comparison of the examples is performed in two dimensions.

[0115] First, the effect of stress shielding was analyzed using a PEEK interbody fusion cage with an elastic modulus of 3600 MPa. The calculation results are shown in the figure. Example 1 shows the estimation of bone reconstruction effect without considering stress shielding. Example 2 shows the estimation of bone reconstruction effect considering stress shielding.

[0116] Figure 4 This is the initial state of Example 1. The random patterns in the upper and lower vertebral bodies are simulated by randomly initializing the intraoperative bone fragments. Figure 5 This is the contour plot of the stress range in Example 1, which is between 0 and 2 MPa. Figure 6This is a contour plot of the stress range of 2 to 20 MPa in Example 1.

[0117] Figure 7 This is the initial state of Example 2. The random patterns in the upper and lower vertebral bodies are simulated by randomly initializing the intraoperative bone fragments. Figure 8 This is the contour plot of the stress range in Example 2, which is between 0 and 2 MPa. Figure 9 This is a contour plot of the stress range of 2 to 20 MPa in Example 2.

[0118] The calculation results for the two examples can also be obtained from Table 2.

[0119] Table 2 shows the calculation results for Examples 1 and 2.

[0120]

[0121] contrast Figure 5 and Figure 8 As shown in Table 2, the proportion of bone remodeling in the 0–2 MPa range in Example 1 is 82.99%, which is greater than the 61.66% proportion in Example 2. Since the 0–2 MPa range is the absorption stage, this indicates that Example 1 will show more bone resorption without considering stress shielding.

[0122] contrast Figure 6 and Figure 9 As shown in Table 2, the proportion of bone reconstruction in the 2–20 MPa range in Example 1 is 16.55%, which is less than the 38.20% proportion in Example 2. Since the 2–20 MPa range is the adaptation reconstruction stage, this indicates that, without considering stress shielding, Example 1 will exhibit less bone adaptation reconstruction.

[0123] Compare again Figure 6 and Figure 9 , Figure 6 The medium-to-high stress components (>2MPa) are mostly distributed near high-rigidity structures such as the upper and lower vertebral bodies and interbody fusion cages, and tend to be located inside the interbody fusion cages. Figure 9 In the middle, the distribution of high-stress components (>2MPa) is much larger than... Figure 6 The bone remodeling was uniform and well distributed both inside and outside the interbody fusion cage. Clearly, Example 2, which considered stress shielding, more accurately estimated the postoperative bone remodeling status.

[0124] Secondly, the impact of different materials used in interbody fusion cages on postoperative bone reconstruction under stress shielding conditions was considered. Example 3 used a material similar to trabecular bone with an elastic modulus of 150 MPa; Example 4 used a porous material similar to cortical bone with an elastic modulus of 12000 MPa; and Example 5 used a titanium alloy with an elastic modulus of 110000 MPa. The simulation results are shown in Table 3.

[0125] Table 3 shows the calculation results for Examples 3 to 5.

[0126]

[0127]

[0128] Figure 10 This is the initial state of example 3. The random patterns in the upper and lower vertebral bodies are simulated by randomly initializing the intraoperative bone fragments. Figure 11 This is the contour plot of the stress range in Example 3, which is between 0 and 2 MPa. Figure 12 This is a contour plot of the stress range of 2 to 20 MPa in Example 3.

[0129] Figure 13 This is the initial state of example 4. The random patterns in the upper and lower vertebral bodies are simulated by randomly initializing the intraoperative bone fragments. Figure 14 This is the contour plot of the stress range in Example 4, which is between 0 and 2 MPa. Figure 15 This is a contour plot of the stress range of 2 to 20 MPa in Example 4.

[0130] Figure 16 This is the initial state of example 5. The random patterns in the upper and lower vertebral bodies are simulated by randomly initializing the intraoperative bone fragments. Figure 17 This is the contour plot of the stress range in Example 5, which is between 0 and 2 MPa. Figure 18 This is a contour plot of the stress range of 2 to 20 MPa in Example 5.

[0131] A comparison of examples 3-5 reveals that in example 5, the titanium alloy skeleton bore excessive load, resulting in the vast majority (93.38%) of the reconstructed area being unusable, leading to an unsatisfactory bone reconstruction process. This indicates that high-stiffness interbody fusion cages are detrimental to bone reconstruction. Conversely, excessively low-stiffness interbody fusion cages are also unfavorable for bone reconstruction. For instance, in example 3, the proportion of bone tissue in the moderate and pathological overloaded areas was significantly higher than in examples 4 and 5, which also hinders bone reconstruction. Therefore, this set of comparative examples demonstrates that the stiffness selection of the interbody fusion cage is related to the bone reconstruction effect, necessitating the selection of an interbody fusion cage with appropriate stiffness.

[0132] The present invention also provides an optimized apparatus for a bone remodeling assessment method that takes into account stress shielding, such as... Figure 19As shown, the optimization device for the bone reconstruction assessment method considering stress shielding provided in this embodiment can execute the bone reconstruction assessment method considering stress shielding provided in any embodiment of the present invention, and has the corresponding functional modules and beneficial effects for executing the method. The optimization device includes: a calculation model establishment module 100, an optimization problem formulation module 200, a filtering processing module 300, and a bone reconstruction result evaluation module 400.

[0133] Specifically, the computational model building module 100 is used to build a computational model, which includes a structure and boundary conditions. The structure includes a reconstruction domain, undesignable bone, implants, and initial reconstructed bone set within the reconstruction domain, which grows within the reconstruction domain. The boundary conditions include external loads acting on the undesignable bone and the positional relationship between the implants and the undesignable bone. The computational model is meshed to obtain elements and nodes, wherein the elements involved in the reconstruction domain are reconstruction domain elements, and the number of reconstruction domain elements is n.

[0134] The optimization problem formulation module 200 is used to generate the optimization problem formulation. The design variables of the optimization problem formulation are ρ = (ρ1, ..., ρ2). e …,ρ n ) T , where ρ e Let ρ be the relative density of the e-th reconstruction domain unit, which physically represents the bone density within the bone reconstruction region. min <ρ e ≤1, ρ min Given the minimum density; the objective function of the optimization problem formulation is the stress σ of each reconstructed domain element. e The function I = I(σ) e The constraints include external load constraints, energy constraints, and volume fraction constraints.

[0135] The filtering module 300 is used to further filter the updated design variable ρ after at least one solution step in solving the formulation of the optimization problem. The filtering process is as follows: when the stress σ of one or more reconstructed domain elements... e When the stress is less than the given stress limit, the relative density of the reconstructed domain element is multiplied by a filter function less than 1.

[0136] The bone reconstruction result evaluation module 400 is used to evaluate the bone reconstruction results. The evaluation process is as follows: after completing the formulation of the optimization problem, the reconstructed bone after growth is obtained according to the updated design variable ρ. The reconstructed bone after growth is set in the reconstruction domain to obtain the updated calculation model. The updated calculation model is used to calculate the stress distribution field of the reconstructed bone after growth. The stress distribution field is statistically analyzed to obtain the bone reconstruction evaluation result.

[0137] The present invention also provides a computer device for a bone remodeling assessment method that takes into account stress shielding, with reference to Figure 20 The diagram illustrates the internal structure of a computer in one embodiment. This computer can specifically be a terminal or a server. Figure 20 As shown, the computer includes a processor, memory, and a network interface connected via a system bus. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and may also store a computer program. When executed by the processor, this computer program enables the processor to implement an optimization method for thin-walled stiffened structures. The internal memory may also store a computer program, which, when executed by the processor, enables the processor to implement the optimization method for thin-walled stiffened structures. Those skilled in the art will understand that… Figure 20 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer to which the present application is applied. A specific computer may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0138] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the following steps:

[0139] S1: Establish a computational model, which includes structure and boundary conditions. The structure includes a reconstruction domain, undesignable bone, implants, and initial reconstructed bone set within the reconstruction domain, which grows within the reconstruction domain. Boundary conditions include external loads acting on the undesignable bone and the positional relationship between the implants and the undesignable bone. Mesh the computational model to obtain elements and nodes. The elements involved in the reconstruction domain are called reconstruction domain elements, and the number of reconstruction domain elements is n.

[0140] S2: Formulate the optimization problem statement. The design variables of the optimization problem statement are ρ=(ρ1,…,ρ…). e …,ρ n ) T , where ρ e Let ρ be the relative density of the e-th reconstruction domain unit, which physically represents the bone density within the bone reconstruction region. min <ρ e ≤1, ρ min Given the minimum density; the objective function of the optimization problem formulation is the stress σ of each reconstructed domain element. e The function I = I(σ) e The constraints include external load constraints, energy constraints, and volume fraction constraints.

[0141] S3: Solve the optimization problem formulation. After at least one solution step, the updated design variable ρ is filtered. The filtering process is as follows: when the stress σ of one or more reconstructed domain elements... e When the stress is less than the given stress limit, the relative density of the reconstructed domain element is multiplied by a filter function less than 1.

[0142] S4: After completing the formulation of the optimization problem, obtain the reconstructed bone after growth based on the updated design variable ρ, set the reconstructed bone in the reconstruction domain, obtain the updated calculation model, calculate the stress distribution field of the reconstructed bone after growth, statistically analyze the stress distribution field, and obtain the bone reconstruction evaluation result.

[0143] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the following steps:

[0144] S1: Establish a computational model, which includes structure and boundary conditions. The structure includes a reconstruction domain, undesignable bone, implants, and initial reconstructed bone set within the reconstruction domain, which grows within the reconstruction domain. Boundary conditions include external loads acting on the undesignable bone and the positional relationship between the implants and the undesignable bone. Mesh the computational model to obtain elements and nodes. The elements involved in the reconstruction domain are called reconstruction domain elements, and the number of reconstruction domain elements is n.

[0145] S2: Formulate the optimization problem statement. The design variables of the optimization problem statement are ρ=(ρ1,…,ρ…). e …,ρ n ) T , where ρ e Let ρ be the relative density of the e-th reconstruction domain unit, which physically represents the bone density within the bone reconstruction region. min <ρ e ≤1, ρ min Given the minimum density; the objective function of the optimization problem formulation is the stress σ of each reconstructed domain element. e The function I = I(σ) e The constraints include external load constraints, energy constraints, and volume fraction constraints.

[0146] S3: Solve the optimization problem formulation. After at least one solution step, the updated design variable ρ is filtered. The filtering process is as follows: when the stress σ of one or more reconstructed domain elements... e When the stress is less than the given stress limit, the relative density of the reconstructed domain element is multiplied by a filter function less than 1.

[0147] S4: After completing the formulation of the optimization problem, obtain the reconstructed bone after growth based on the updated design variable ρ, set the reconstructed bone in the reconstruction domain, obtain the updated calculation model, calculate the stress distribution field of the reconstructed bone after growth, statistically analyze the stress distribution field, and obtain the bone reconstruction evaluation result.

[0148] 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 may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may 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 RAMbus dynamic RAM (RDRAM), etc.

[0149] 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.

[0150] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for assessing bone remodeling considering stress shielding, characterized in that, The method includes: A computational model is established, comprising a structure and boundary conditions. The structure includes a reconstruction domain, undesignable bone, an implant, and initial reconstructed bone grown within the reconstruction domain. The boundary conditions include external loads acting on the undesignable bone and the positional relationship between the implant and the undesignable bone. The computational model is meshed to obtain elements and nodes, wherein the elements involved in the reconstruction domain are reconstruction domain elements, and the number of reconstruction domain elements is [number missing]. indivual; Formulate an optimization problem, wherein the design variables of the optimization problem formulation are: ,in For the first The relative density of each reconstructed domain unit, physically representing the bone density within the bone reconstruction region. , Given a minimum density; the objective function of the optimization problem formulation is the stress of each of the reconstructed domain elements. function The constraints include external load constraints, energy constraints, and volume fraction constraints. Solving the formulation of the optimization problem, after at least one solution step, further updating the design variables... The filtering process is performed when the stress of one or more of the reconstructed domain elements is... When the stress is less than the given stress limit, the relative density of the reconstructed domain element is multiplied by a filtering function less than 1; After completing the formulation of the optimization problem, based on the updated design variables... The reconstructed bone after growth is obtained, and the reconstructed bone after growth is placed in the reconstruction domain to obtain the updated calculation model. The updated calculation model is used to calculate the stress distribution field of the reconstructed bone after growth, and the stress distribution field is statistically analyzed to obtain the bone reconstruction evaluation result.

2. The method according to claim 1, characterized in that, The objective function is: The external load constraint is The energy constraint is a strain energy function. ， The volume fraction constraint is as follows: In the formula, To and The relevant nodal displacement vectors, Given an upper limit for strain energy, It is a given upper limit for volume fraction; It is the first The stress function of each of the reconstructed domain elements ; It is a given positive parameter; It is the overall stiffness matrix. It is the external load vector; It is the first The volume of each of the reconstructed domain units.

3. The method according to claim 2, characterized in that, The filtering function is the Heaviside filtering function: The updated design variables Perform filtration In the formula, It is the first The relative density of the reconstructed domain units, It is the first The filtered relative density of each of the reconstructed domain units and It is a control parameter that controls the degree of regularization. It is the minimum effective growth stress.

4. The method according to claim 1, characterized in that, The physical model of the undesignable skeleton was obtained from radiographic images.

5. The method according to claim 4, characterized in that, The steps for obtaining the physical model of the undesignable skeleton from imaging images are as follows: S101. Read the color information in the imaging image, convert the color information into a grayscale image, the grayscale image includes pixels with different grayscale values, and group adjacent pixels of the same grayscale value into pixel blocks; S102. Compare the gray values ​​of each adjacent pixel block. If the difference in gray values ​​between adjacent pixel blocks is less than a given division threshold, merge the adjacent pixel blocks. The gray value of the merged pixel block is the average of the gray values ​​of the merged adjacent pixel blocks. Repeat until the size of the pixel block exceeds a given size threshold or there are no more pixel blocks that can be merged, forming a physical model of the undesignable skeleton composed of pixel blocks.

6. The method according to claim 5, characterized in that, The physical model of the undesignable skeleton is meshed using the proportional boundary element method, and a proportional boundary element subdomain is generated for each pixel block. The proportional center of the subdomain is set at the geometric center of the corresponding pixel block.

7. The method according to claim 5, characterized in that, The optimization problem is solved using the solid isotropic material penalty method, and the sensitivity used in the solution process is: in For the first The stress function of each of the reconstructed domain elements , for The derivative vectors of each stress component, in the two-dimensional case, , and These are the stress components in the two-dimensional case. For the first The associated field displacement of each reconstructed domain element, and the overall associated field. Calculated by the following formula: in in and It is the strain matrix, the first... The elastic matrix of each of the reconstructed domain units Determined by the following formula: in It is the elastic matrix of solid bone tissue. It is the first Cell density after filtering of individual cells These are the scale boundary coordinates of the current subdomain. The number of units These are the eigenvalues.

8. An optimized apparatus for a bone remodeling assessment method considering stress shielding, characterized in that, The device includes: A computational model building module is used to build a computational model, which includes a structure and boundary conditions. The structure includes a reconstruction domain, undesignable bone, an implant, and initial reconstructed bone placed within the reconstruction domain, the initial reconstructed bone growing within the reconstruction domain. The boundary conditions include external loads acting on the undesignable bone and the positional relationship between the implant and the undesignable bone. The computational model is meshed to obtain cells and nodes, wherein the cells involved in the reconstruction domain are reconstruction domain cells, and the number of reconstruction domain cells is [number missing]. indivual; The optimization problem formulation module is used to generate an optimization problem formulation, and the design variables of the optimization problem formulation are... ,in For the first The relative density of the reconstructed domain units, , Given a minimum density; the objective function of the optimization problem formulation is the stress of each of the reconstructed domain elements. function The constraints include external load constraints, energy constraints, and volume fraction constraints. A filtering module is configured to, after at least one solution step of solving the formulation of the optimization problem, further update the design variables. The filtering process is performed when the stress of one or more of the reconstructed domain elements is... When the stress is less than the given stress limit, the relative density of the reconstructed domain element is multiplied by a filtering function less than 1; A bone reconstruction result evaluation module is used to evaluate the bone reconstruction results. The evaluation process involves: after solving the optimization problem, evaluating the results based on the updated design variables. The reconstructed bone after growth is obtained, and the reconstructed bone after growth is placed in the reconstruction domain to obtain the updated calculation model. The updated calculation model is used to calculate the stress distribution field of the reconstructed bone after growth, and the stress distribution field is statistically analyzed to obtain the bone reconstruction evaluation result.

9. A computer device comprising a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the method as claimed in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the steps of the method as claimed in any one of claims 1 to 7.

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