Preoperative tibial prosthesis positioning method for ankle arthroplasty based on multi-objective optimization

Abstract

This invention discloses a multi-objective optimization-based method for preoperative tibial prosthesis localization in ankle replacement surgery, primarily addressing the problems of poor accuracy and low reliability in existing ankle prosthesis localization methods. The method includes: 1) acquiring and processing medical CT images and prosthesis model data of the affected lower limb, completing prosthesis standard position calibration and establishing a local coordinate system; 2) segmenting bone tissue, extracting three-dimensional models of the tibia, fibula, and talus, and including HU bone mineral density values; 3) standardizing the skeletal model, labeling anatomical landmarks, and constructing an orthogonal standard coordinate system; 4) pre-calculating relevant data of the distal tibial articular surface; 5) generating initial candidate solutions through grid search and constraint filtering; 6) obtaining the Pareto front by combining the NSGA-II-CDP algorithm and constraint dominance principles; 7) recommending the optimal solution and generating a visual model through multi-stage compromise solution filtering and multi-criteria decision-making. This invention can unify anatomical orientation, improve computational efficiency, and achieve accurate and efficient localization.

Description

Technical Field

[0001] This invention belongs to the field of medical image processing technology, and further relates to computer-assisted orthopedic surgery (CAOS) and multi-objective optimization technology. Specifically, it is a method for tibial prosthesis localization before ankle replacement surgery based on multi-objective optimization, which can be used for precise planning, prosthesis position optimization, surgical risk assessment and clinical surgical navigation before ankle replacement surgery. Background Technology

[0002] Prosthetic placement planning is a core task in preoperative planning for joint replacement surgery, aiming to determine the optimal placement and orientation of the prosthetic component within the patient's skeleton using medical image processing and computer-aided techniques. Total Ankle Replacement (TAR), as an important treatment for end-stage ankle disease, places particular emphasis on the placement planning of the tibial prosthetic component. This is because the complex anatomy of the ankle joint involves the coordination of the tibia, fibula, and talus, demanding higher precision in placement and multi-objective balance. Overall, prosthetic placement planning is an important research direction in the digitalization and intelligentization of orthopedic surgery, and it is of great significance for improving clinical practice and enhancing patient outcomes.

[0003] Ankle prosthesis localization primarily relies on traditional manual measurement methods and computer-aided planning software. Traditional methods involve manual measurement based on two-dimensional X-rays or CT slices, combined with the physician's experience to determine the prosthesis position. Computer-aided methods (such as commercial software like TraumaCad and OrthoView) offer digital measurement and template overlay functions, but still essentially depend on manual adjustments. These methods have the following main drawbacks: 1) Insufficient accuracy and strong subjectivity; manual measurement can result in angular errors of 3-5 degrees and positional errors of 2-3 millimeters, leading to significant differences in planning results among different physicians for the same case; 2) Lack of a quantitative comprehensive evaluation system, failing to accurately quantify key indicators such as bone coverage, osteotomy volume, and cortical perforation risk, and lacking a scientific method for weighing conflicting clinical goals; 3) Low search efficiency; prosthesis localization involves a high-dimensional solution space with six degrees of freedom, and manual methods can only explore a limited number of candidate positions, easily overlooking the globally optimal solution; 4) Insufficient decision support capabilities; traditional methods only provide a single solution and cannot demonstrate the trade-offs between different options.

[0004] Currently, researchers in related fields have applied multi-objective optimization algorithms to the spatial positioning and planning of prostheses for major joints such as the knee and hip. However, in the field of ankle joints, which have more complex anatomical structures and biomechanical environments, there is still a significant technological gap. How to systematically optimize and obtain a complete solution containing multiple key static anatomical indicators based on multi-objective optimization algorithms to achieve precise positioning and reliable implantation of ankle joint prostheses is a critical problem that urgently needs to be solved.

[0005] In terms of academic literature, existing research mainly focuses on preoperative imaging measurements and patient-specific instrument procedures for ankle replacement surgery. The core remains limited to improvements in single or a few geometric parameters, emphasizing positioning deviations and alignment accuracy. It lacks comprehensive consideration of key clinical indicators such as osteotomy volume, bone quality, or cortical risk, making a complete assessment difficult. Regarding patent literature, the technical solution with publication number CN120899387A follows a main line of "image segmentation and 3D reconstruction → extraction of key anatomical parameters of the foot and ankle → determination of the prosthesis model and placement posture based on parameters → closed-loop correction through kinematic simulation." Its focus is on the segmentation model structure and simulation parameter tuning process, without jointly optimizing multiple static clinical indicators within the feasible solution space, and without fully considering key boundary conditions such as fibular / medial malleolus safety constraints and distance fields. The technical solution with publication number CN120189226A is based on the statistical shape model (SSM) and CPD registration matching template, and uses random forest to predict the prosthesis model. It focuses on geometric matching and model identification, but does not jointly optimize multiple static clinical indicators in the feasible solution space, nor does it consider the fibular / medial malleolus safety constraints and distance field, and cannot provide a multi-dimensional basis for clinical decision-making.

[0006] In summary, existing technologies have many shortcomings in the field of ankle prosthesis localization, including a lack of comprehensive consideration of multiple key clinical indicators, making it difficult to obtain the globally optimal solution; insufficient consideration of key boundary conditions, resulting in inadequate safety; and the inability to provide multi-dimensional solutions for weighing options, making it difficult to meet personalized clinical needs. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of existing technologies by proposing a multi-objective optimization-based method for preoperative tibial prosthesis localization in ankle replacement surgery. This method solves the technical problems of poor accuracy and low reliability in existing ankle prosthesis localization, which fails to provide multi-dimensional balancing factors for clinical decision-making. This invention integrates medical image processing, computational geometry, and multi-objective optimization technologies. First, a high-precision three-dimensional skeletal model is constructed based on ankle medical images. Then, a hybrid optimization method consisting of coarse-grained grid search, multi-objective evolutionary algorithms, and constraint handling strategies is employed to efficiently explore prosthesis placement schemes in a high-dimensional solution space, balancing conflicting clinical objectives such as force line correction, joint range of motion, bone preservation, and prosthesis stability. Finally, a Pareto-optimal prosthesis localization scheme is output, and a visualized surgical planning report is generated, providing clinicians with intuitive multi-dimensional decision-making support.

[0008] To achieve the above objectives, the technical solution of the present invention includes the following steps:

[0009] S1. Acquire and process the original medical CT images and prosthesis model data of the affected lower limb; perform standard position calibration on the prosthesis and establish a local coordinate system;

[0010] S2. Perform bone tissue segmentation on CT images, extract three-dimensional models of the tibia, fibula and talus, and segment the models carrying HU bone density values;

[0011] S3. Standardize the extracted three-dimensional skeletal model, including labeling anatomical landmarks and constructing an orthogonal standard coordinate system based on the labeled landmarks, so as to unify the anatomical orientation of different patients, reduce the amount of calculation, and speed up the subsequent processing.

[0012] S4. Pre-calculate search data for the distal articular surface region of the tibia to obtain the distance field, bone mass HU value atlas, binary slice sequence, Z-axis cumulative bone voxel map and anatomical constraint data;

[0013] S5. Perform coarse-grained mesh search and anatomical constraint screening on the distal tibial articular surface region and prosthesis model, comprehensively evaluate multiple performance indicators, and generate a high-quality initial candidate solution set.

[0014] S6. Combining the initial candidate solution set and the multi-objective optimization criterion, the NSGA-II-CDP multi-objective evolution algorithm and the constraint dominance principle are used to obtain the Pareto front containing multiple non-dominated solutions;

[0015] S7. Perform multi-stage compromise solution screening on the Pareto frontier, combine multi-criteria decision-making and diverse strategies to recommend the optimal solution, and generate a three-dimensional visualization model containing detailed trimming parameters.

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] First, this invention eliminates subjective errors from manual measurement by establishing a standardized skeletal coordinate system and employing mathematical optimization methods; its positioning accuracy reaches 0.1 mm, and its angle positioning accuracy reaches 0.1 degrees, both determined by the system's discretization step size and numerical calculation accuracy; simultaneously, the full-space analysis based on the three-dimensional model avoids projection errors from two-dimensional images, and employs rigid body transformation matrices. A unified coordinate system ensures comparability and complete reproducibility of results among different patients.

[0018] Secondly, because this invention establishes a quantitative evaluation system, which includes five core indicators: bone coverage rate Quantify the fit between the prosthesis and the bone (maximize the target); osteotomy volume. Quantify bone tissue resection volume (in mm³, with the goal of minimizing to preserve more healthy bone tissue); bone quality support. Assessment of mechanical support strength based on HU value (maximization of target); risk of cortical perforation. Safety boundary assessment based on distance field (objective minimization); centrality The displacement of the prosthesis relative to the center of the ankle joint is evaluated (target minimization). Each metric has a clear mathematical definition and calculation method, which can be accurately quantified and supports simultaneous optimization of multiple objectives.

[0019] Third, this invention adopts a hybrid strategy of "coarse search + fine optimization", which has efficient global search capabilities. The coarse-grained grid search covers 10,648 discrete candidate poses, with an exploration space coverage of over 95%. The NSGA-II-CDP evolution algorithm performs fine search in the feasible solution space to ensure global convergence. The constraint dominance principle (CDP) effectively handles hard constraints and avoids getting trapped in infeasible regions or local optima.

[0020] Fourth, this invention adopts a layered constraint design, separating anatomical constraints from performance optimization; among them, hard constraints (anatomical safety) include a fibular safety distance ≥3mm and no interference with the medial malleolus, which are used as screening conditions; soft constraints (performance optimization) are five objective functions used as optimization targets in step S6; the distance field cavity filling technology eliminates interference from low-density areas within the bone through morphological filling, and accurately calculates the true distance from the prosthesis to the outer surface of the bone.

[0021] This invention is the first to incorporate five key clinical objectives—bone coverage, osteotomy volume, bone quality support, cortical risk, and centrality—into a unified multi-objective optimization framework, providing a more comprehensive assessment of ankle prosthesis implantation outcomes. Furthermore, by introducing techniques such as a three-dimensional fibular distance field and an adaptive medial malleolar protection zone, it precisely addresses the unique and more complex anatomical constraints of the ankle joint (such as fibular avoidance), significantly improving the clinical safety and feasibility of the planning scheme. Finally, it provides a set of Pareto optimal solutions containing multiple different trade-off strategies, supplemented by a diversity recommendation algorithm, achieving truly personalized decision support. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating the overall implementation of the method of the present invention;

[0023] Figure 2 This is a schematic diagram of the local standard coordinate system of the prosthesis established in this invention;

[0024] Figure 3 This is a template image of the top surface of the binarized prosthesis constructed in this invention;

[0025] Figure 4 These are the three projected views of the prosthesis established in this invention;

[0026] Figure 5 This is a schematic diagram of the skeletal anatomical landmark annotation and coordinate system establishment in this invention.

[0027] Figure 6 This is a sampling sequence diagram of the tibial slice distance field established in this invention;

[0028] Figure 7 This is the sampled bone quality atlas established in this invention;

[0029] Figure 8 This is a slice sampling diagram of the four-degree-of-freedom search space established in this invention;

[0030] Figure 9 This is the initial search pose diagram of the prosthetic skeleton established in this invention;

[0031] Figure 10 This is a flowchart of the NSGA-II-CDP (Non-dominated Sorting Genetic Algorithm II with Constrained Dominance Principle) multi-objective evolutionary optimization algorithm used in this invention;

[0032] Figure 11 This is a 3D visualization of the three final recommended surgical plans output in this embodiment of the invention. Detailed Implementation

[0033] The present invention will now be further described with reference to the accompanying drawings.

[0034] Example 1: Refer to Appendix Figure 1 This invention proposes a multi-objective optimization-based method for preoperative tibial prosthesis localization in ankle replacement surgery. It applies the Non-Dominated Sorting Genetic Algorithm II (NSGA-II-CDP) with constrained dominance principles to the preoperative localization planning of the tibial prosthesis. Simultaneously, it optimizes five clinically relevant objective functions, including bone coverage, osteotomy volume, bone quality support, cortical perforation risk, and centrality. Furthermore, it provides multiple non-dominated optimal solutions through the Pareto front to support personalized decision-making by physicians. The specific implementation steps include the following:

[0035] Step S1: Acquire and process the original medical CT images and prosthesis model data of the affected lower limb; perform standard position calibration on the prosthesis and establish a local coordinate system;

[0036] Step S2: Perform bone tissue segmentation on the CT images, extract the three-dimensional models of the tibia, fibula and talus, and segment the models carrying HU bone density values;

[0037] Step S3: Standardize the extracted 3D skeletal model, including labeling anatomical landmarks and constructing an orthogonal standard coordinate system based on the labeled landmarks, to unify the anatomical orientation of different patients, reduce computational load, and speed up subsequent processing. In this embodiment, the above-mentioned labeling of anatomical landmarks and construction of an orthogonal standard coordinate system based on the labeled landmarks specifically involves labeling four key anatomical landmarks on the tibia model, including the proximal tibial center point. Ankle joint center point Medial malleolus and lateral ankle tip Construct an orthogonal standard coordinate system; where the Z-axis is defined as the direction of the mechanical axis. The Y-axis is defined as the coronal plane normal, and the X-axis is defined as the sagittal plane normal; by constructing the rigid body transformation matrix All 3D model data is converted to a standard coordinate system. The annotation methods for anatomical landmarks include manual annotation, statistical shape models, or deep learning methods.

[0038] Step S4: Perform pre-calculation of search data for the distal tibial articular surface region to obtain the distance field, bone mass HU value atlas, binary slice sequence, Z-axis cumulative bone voxel map, and anatomical constraint data. Specifically, the pre-calculation includes: a binary template B generated by orthogonal projection of the prosthesis top surface; and a distance field sequence obtained by calculating the two-dimensional Euclidean distance transformation of equidistant tibial slices along the Z-axis after filling with morphological holes. Three-dimensional bone quality atlas based on HU value Bone matrix image obtained by summing along the Z-axis for querying osteotomy volume. 3D distance field of the fibula And a protective mask for the medial malleolus elliptical cylinder generated based on the tibial diameter ratio method. .

[0039] In this embodiment, the above-mentioned three-dimensional distance field of the fibula This is used to quickly determine whether the distance between the prosthesis and the fibula remains within a safe range. Specifically, it is obtained by loading fibular segmentation data and calculating a three-dimensional Euclidean distance transformation on the fibular model in a standard coordinate system, where each voxel value represents the nearest distance from that point to the fibular surface. The medial malleolus elliptical cylinder protective mask marks the medial malleolus protection area where the prosthesis cannot be invaded. This protection area is specifically determined according to the following method: at the center point of the ankle joint... Obtain a cross-section of the tibia from above and measure the anteroposterior diameter of this section. and inner and outer diameters Calculate the anteroposterior radius of the medial malleolus ellipse based on the ratio of the medial malleolus size to the tibial diameter. and inner and outer radii ; with the tip of the medial malleolus An elliptical cylindrical mask is generated along the positive Z-axis with the bottom center as the center. .

[0040] Step S5: Perform coarse-grained mesh search and anatomical constraint screening on the distal tibial articular surface region and prosthesis model, comprehensively evaluate multiple performance indicators, and generate a high-quality initial candidate solution set.

[0041] Step S6: Combining the initial candidate solution set and the multi-objective optimization criterion, the NSGA-II-CDP multi-objective evolution algorithm and the constraint dominance principle are used to obtain the Pareto front containing multiple non-dominated solutions.

[0042] In this embodiment, steps S5 and S6 constitute a hierarchical hybrid optimization, including: simplifying six degrees of freedom to four degrees of freedom ( , , , The coarse-grained grid search reduces the search space and improves efficiency; the feasible pose selection is based on the dual anatomical constraints of the fibular safety distance and the medial malleolus protection area to ensure the safety of prosthesis implantation; the selected feasible poses are used as the initial population, and the NSGA-II-CDP multi-objective evolutionary algorithm is used for fine optimization to obtain the Pareto front solution.

[0043] The aforementioned multi-objective optimization criterion includes defining five objective functions and minimizing them uniformly, achieving optimization through Pareto dominance sorting; wherein the five objective functions are defined as: the negative ratio of the intersection area of ​​the prosthesis mask and the tibial slice. osteotomy volume The mean HU value for the covered area is negative. Risk of cortical perforation Center offset .

[0044] Step S7: Perform multi-stage compromise solution screening on the Pareto front, combine multi-criteria decision-making and diversity strategies to recommend the optimal solution, and generate a three-dimensional visualization model containing detailed truncation parameters. In this embodiment, the optimal solution mentioned in this step is specifically achieved through a three-stage filtering process: hard thresholding of bone coverage → soft thresholding → descending truncation. TOPSIS / VIKOR / WSM, using clinical preference weight vectors, are introduced to perform multi-criteria decision scoring on the non-dominated solutions of the Pareto front. Then, based on diversity strategy clustering, a diversity recommendation is made using a greedy strategy that maximizes the minimum distance among high-scoring candidate solutions, combined with clinical experience and mechanical simulation. The aforementioned three-stage filtering process of hard thresholding of bone coverage → soft thresholding → descending truncation specifically includes: setting a hard threshold for bone coverage, selecting solutions that meet the conditions from the Pareto solutions to enter the candidate pool; if the hard threshold screening result is empty, lowering the threshold and setting a soft threshold for re-screening; if the soft threshold still has no solutions, sorting by bone coverage in descending order, selecting at least 3 solutions to enter the candidate pool.

[0045] Example 2: The overall implementation steps of the pre-operative tibial prosthesis localization method for ankle replacement proposed in this example are the same as in Example 1. The implementation process of the pre-calculation of search data in step S4 will now be described in further detail:

[0046] The above pre-calculation process is carried out in the standard skeletal coordinate system to ensure consistency with the coordinates used in subsequent search and evaluation. Specifically, it includes:

[0047] Step B1: Generate a two-dimensional template based on the contact surface of the prosthesis osteotomy. In the local standard coordinate system of the prosthesis, the main contact plane is identified with the top surface normal as a reference; the geometry of the top surface of the prosthesis is orthogonally projected along this normal, and a binary template is obtained by discretization at a resolution of 0.4 mm / pixel. The template size is automatically determined based on the prosthesis projection range (typically 64×64 to 128×128 pixels) for subsequent rapid two-dimensional evaluation.

[0048] Step B2: Slice the tibia model along the Z-axis (the mechanical axis of the standard skeletal coordinate system) at 0.5mm intervals to generate a two-dimensional binary image sequence. Using the center point of the ankle joint as the origin of the Z-axis (Z=0mm), a slice sequence with a Z-coordinate range of [0, 30]mm is generated along the positive direction of the Z-axis (from distal to proximal), covering the distal tibial osteotomy and prosthesis implantation area 30mm above the ankle joint. It should be noted that this pre-calculated range is larger than the search range defined in subsequent step S5 (e.g., [2, 15]mm) to provide sufficient data redundancy for the refined evolutionary optimization in step S6, ensuring that the algorithm does not make errors due to missing data when exploring the search boundary, and also providing more comprehensive contextual information for future algorithm expansion and visualization. In this typical embodiment, a total of 61 slices are generated ( Each slice is a binary image, with a pixel value of 1 representing tibial tissue and a pixel value of 0 representing the background.

[0049] Step B3: For each slice Calculate the two-dimensional Euclidean distance transform (EDT) to obtain the range field. Each pixel value represents the Euclidean distance from that point to the outer contour of the bone. Before calculating the distance field, the binary slices are morphologically filled with holes (binary_fill_holes) to fill the low-density areas inside the bone (cancellous bone holes, medullary cavities) as the foreground, ensuring that the distance field is calculated only from the outer contour of the bone, rather than from the edges of the internal holes. This accurately reflects the shortest distance from any point inside the bone to the outer surface, which is crucial for subsequent determination of whether the prosthesis has perforated the cortical bone. The distance field is calculated using a fast Euclidean distance transform algorithm (based on scipy.ndimage).

[0050] Step B4: Extract bone quality information corresponding to the slice sequence from the segmentation file carrying HU values ​​(e.g., tibia_masked.nrrd) and construct a three-dimensional bone quality atlas. The NRRD format file is generated and exported from the segmentation process, and contains HU value information from both the segmentation mask and the original CT scan. The Z-axis range of the bone quality atlas is consistent with the slice sequence ([0, 30] mm, 61 slices), and the XY plane resolution is consistent with the original CT scan. According to the Hounsfield Units (HU) standard, different HU value ranges correspond to tissues of different densities. In this invention, areas with HU values ​​greater than 300 are marked as good cancellous bone, and areas with HU values ​​greater than 700 are marked as cortical bone. This atlas is used to evaluate the bone quality support of the prosthesis-covered area. In the multi-objective optimization in step S6, bone density and mechanical strength are evaluated by querying the mean HU value of the prosthesis-covered area.

[0051] Step B5, fibular distance field calculation: Load fibular segmentation data (e.g., fibula_masked.nrrd), calculate the three-dimensional Euclidean distance transformation of the fibular model in the standard coordinate system, and obtain the fibular distance field. Each voxel value represents the nearest distance (in millimeters) from that point to the fibular surface. This distance field is used to quickly determine whether the prosthesis maintains a sufficient safe distance from the fibula.

[0052] Step B6, Generation of Medial Malleolus Protection Area: The medial malleolus elliptical cylinder protection area is determined based on the tibial diameter ratio method. The specific steps are: (1) At the center point of the ankle joint (1) Obtain the tibial cross section at 10 mm above (Z-axis of standard coordinate system); (2) Measure the anteroposterior diameter of this cross section. and inner and outer diameters (3) According to anatomical statistical studies, there is a proportional relationship between the size of the medial malleolus and the diameter of the tibia. This invention uses this relationship to calculate the radius of the medial malleolus ellipse: mm (front and back radius) mm (inner and outer radii), where 0.32 is the medial malleolus-tibia diameter ratio coefficient used in this invention, and 1.0 mm is the safety boundary; (4) with the medial malleolus apex An elliptical cylindrical mask with a height of 20mm is generated along the positive Z-axis (upwards) with the bottom center as the center. The mask marks the non-invasive medial malleolar protection area.

[0053] Example 3: The overall implementation steps of the preoperative tibial prosthesis localization method for ankle replacement proposed in this example are the same as in Example 1. The implementation process of the coarse-grained mesh search and constraint filtering in step S5 will now be described in further detail:

[0054] Step C1: Define the four-degree-of-freedom search space: The pose of the prosthesis is determined by three translation parameters. and single rotation parameter Description. Since a standard skeletal coordinate system has been established in step S3 and the Z-axis is the mechanical axis of the tibia, to ensure force transmission, the upper surface of the prosthesis remains perpendicular to the Z-axis. Rotation around the X and Y axes is disabled, allowing only rotation around the Z-axis. The search range is set as: translation. millimeters Millimeters (from the center of the ankle joint upwards); rotation The search range covers the reasonable placement area for the vast majority of cases, while balancing computational efficiency and solution space coverage.

[0055] Step C2: Perform grid search using a discretized step size: translation step size millimeters, rotation step The step size is an engineering trade-off between ensuring a sufficiently good initial solution and controlling computation time. Depending on the set search range and step size, the candidate solution space includes... A discrete pose.

[0056] Step C3: For each candidate pose Anatomical constraint testing was performed: (1) Detection of fibular safety distance: the voxel occupied by the prosthesis in the fibular distance field was calculated. minimum value ,like If the distance is less than 3 mm, it violates fibular restraint. A distance of 3 mm is a generally accepted clinical safety standard in orthopedic surgery to avoid impact or compression between the implant and adjacent bone structures; (2) Medial malleolus interference detection: to determine whether the voxel occupied by the prosthesis is in contact with the medial malleolus elliptical cylinder mask. There is overlap, and if any overlap exists, the medial malleolus constraint is violated. The pose is considered anatomically feasible only if both constraints are satisfied.

[0057] Step C4, adopting a hierarchical screening strategy: (1) Fast bounding box detection: pre-screening based on the bounding boxes of the prosthesis and the constraint region; (2) Precise voxel detection: voxel-level constraint verification of the candidate poses that have passed the pre-screening. Vectorized computation and spatial index optimization techniques are used to improve computational efficiency. Depending on the individual differences in the patient's anatomical structure, the number of feasible solutions that satisfy the anatomical constraints will vary.

[0058] Example 4: The overall implementation steps of the preoperative tibial prosthesis localization method for ankle replacement proposed in this example are the same as in Example 1. Now, for the NSGA-II-CDP multi-objective evolution optimization process described in step S6, specific parameter settings are given in detail:

[0059] Step D1: Set evolutionary algorithm parameters: population size Maximum iteration algebra Crossover probability Probability of mutation Cross-distribution index Variation distribution index These parameters are the classic recommended configuration for the NSGA-II algorithm, which is widely used in the field of multi-objective optimization and can effectively balance the convergence of the algorithm with the diversity of the solution set.

[0060] Step D2: Define five optimization objective functions: Maximize bone coverage. Minimize osteotomy volume Maximize bone quality support Minimize the risk of cortical perforation Optimize centrality .

[0061] Step D3: Use fast non-dominated sorting to divide candidate solutions into different levels and calculate the crowding distance. We select solutions with low non-dominant levels and large crowding distances to construct the initial population.

[0062] Step D4: Perform evolutionary iteration: Generate offspring through binary tournament selection, simulated binary crossover (SBX), and polynomial mutation; merge parent and offspring populations; and select the optimal offspring. Individuals form the next generation. This process is repeated until convergence or the maximum number of generations is reached.

[0063] Example 5: The overall implementation steps of the preoperative tibial prosthesis localization method for ankle replacement proposed in this example are the same as in Example 1. The specific parameter settings for the implementation process of the compromise solution selection in step S7 are described in detail below:

[0064] Step E1, Coverage-First Three-Stage Filtering: From the Pareto front (containing 15-30 non-dominated solutions) output in Step S6, first apply a hard threshold for bone coverage. 95% of high-quality candidate solutions are selected; if no satisfactory solution is found, the threshold is lowered to 90% (soft threshold); if no solution is found, the top 40% of solutions, with a minimum of 3 solutions, are selected in descending order of coverage to form a high-coverage candidate pool.

[0065] Step E2, Multi-criteria Decision Scoring: Within the high-coverage candidate pool, one of the following multi-criteria decision-making methods is employed: TOPSIS (Topology for Ideal Solutions), VIKOR (Compromise Ranking), or WSM (Weighted Sum Method). For the five objective functions defined in Step S6, a clinical preference weight vector (coverage 0.30, osteotomy amount 0.25, bone quality support 0.20, cortical perforation risk 0.15, centrality 0.10) is introduced in this step to perform a weighted comprehensive score, calculating the overall superiority or inferiority of each candidate solution.

[0066] Step E3, Diverse Recommendations: Among the top 12 candidate solutions, Euclidean distance is calculated in the normalized target space, and a greedy selection strategy based on maximizing the minimum distance is adopted to select three significantly different solutions. This ensures that the recommended solutions are complementary in dimensions such as coverage, osteotomy volume, centrality, and cortical risk, providing clinicians with diverse choices.

[0067] Step E4, Surgical Parameter Output: Generate a complete surgical planning report for each recommended plan, including precise prosthesis placement parameters (center coordinates accurate to 0.1mm, osteotomy height accurate to 0.5mm based on pre-calculated slice intervals, rotation angle accurate to 0.1 degrees), evaluation values ​​of each objective function, constraint satisfaction status, risk warnings, and a 3D visualization model.

[0068] Example 6: The overall implementation steps of the preoperative tibial prosthesis positioning method for ankle replacement proposed in this example are the same as in Example 1. Please refer to the appendix for details. Figure 1-11 The overall implementation process of the present invention is further described in detail with specific examples.

[0069] Step 1: Data Acquisition and Preprocessing

[0070] In this embodiment, the patient's ankle joint CT scan data was first acquired. The CT scan parameters were set as follows: slice thickness 1.0 mm, reconstruction interval 0.5 mm, and the scan range should extend distally from above the tibial plateau, at least including the talus.

[0071] In this embodiment, 3D Slicer software is used to manually segment CT images. Specifically, after importing CT data in DICOM format, a threshold segmentation tool is used to set the HU value range [150, 3000] for initial segmentation. Then, the boundaries are finely adjusted using region growing and manual editing tools to finally extract the three-dimensional models of the tibia, fibula, and talus. The segmentation results are uniformly exported in NRRD format, which contains both the segmentation mask and the HU value information of the original CT scan in a single file (saved files such as tibia_masked.nrrd, fibula_masked.nrrd, etc.), thus simplifying data management. Simultaneously, a standard tibial prosthesis three-dimensional model (e.g., STL / PLY) is loaded to complete unit and direction consistency verification, establish a local standard coordinate system, and generate a two-dimensional template.

[0072] The establishment of the local standard coordinate system for the tibial prosthesis component follows these principles: the top surface of the prosthesis (the overall area in contact with the osteotomy surface) is defined as the "top surface," and its principal geometric normal is defined as the top surface normal; the front surface of the prosthesis (the direction observed by the surgeon) is defined as the "front surface," and its outer surface normal is defined as the front surface normal; the outer surface normal, orthogonal to the front surface and forming a right-handed coordinate system, is defined as the side surface normal. Using these three mutually orthogonal normal vectors, a local standard coordinate system (top / front / side) is constructed, and when aligned with the bone standard coordinate system, the top surface normal is aligned with the Z-axis, the front surface normal with the X-axis, and the side surface normal with the Y-axis. The parameters of the tibial prosthesis component are: length approximately 40 mm, width approximately 30 mm, and height approximately 15 mm.

[0073] To facilitate reproduction, the operational rules for "establishing the local coordinate system of the prosthesis" are given: This embodiment automatically determines the main orientation of the prosthesis through geometric analysis. Specifically: the principal plane region of the top surface of the prosthesis is identified, and its normal vector is defined as the Z-axis (top surface normal); the Y-axis (side normal) is determined based on the symmetry analysis of the prosthesis geometry; the X-axis (front normal) is obtained through cross product, ensuring that a right-handed coordinate system is formed. For template generation: the geometry of the top surface of the prosthesis is projected onto a plane perpendicular to the top surface normal, and a binary template is generated by discretization at a resolution of 0.4 mm / pixel. The template size is automatically determined based on the prosthesis projection range (typical values ​​are 64×64 to 128×128 pixels). For example... Figure 2 As shown in the figure, this diagram is a schematic diagram of the establishment of the local standard coordinate system of the prosthesis (multi-view display). It marks the top surface normal, frontal normal and side normal, and indicates the right-handed coordinate system relationship and the alignment direction with the standard coordinate system of the skeleton (top surface normal → Z, frontal normal → X, side normal → Y).

[0074] like Figure 3 The image shown is a two-dimensional template of a prosthesis. The diagram illustrates the binarization process, showing a sampling grid of 0.4 mm / pixel and an example of the generated binary template. Figure 4 These are the three projected views of the prosthesis.

[0075] Step 2: Skeletal Standardization and Coordinate System Establishment

[0076] Four key anatomical landmarks were marked on the 3D skeletal model. In this embodiment, manual marking was performed using the point annotation function provided by medical imaging software (such as 3D Slicer), specifically defined as follows: the center point of the proximal tibia. The center of the tibial plateau is located using a 3D view, and the midpoint between its two intercondylar spines is taken; the center point of the ankle joint is also considered. In the tibiotalar joint region, the midpoint between the medial malleolus of the distal tibia and the lateral malleolus of the distal fibula is located; the medial malleolus apex is also considered. and lateral ankle tip Then, locate the most distal protruding points of the medial and lateral malleoli in the coronal view, respectively.

[0077] To improve reproducibility and automation, this embodiment imports anatomical landmarks from a 3D Slicer Markups annotation file. This file contains coordinateSystem set to "LPS", coordinateUnits set to "mm", and... , , , , Five points. Among them, the center point of the ankle joint. In this embodiment, the prosthetic STL model may be stored in the LPS (left-back-top) coordinate system, and converted to the RAS (right-front-top) coordinate system as needed during processing to unify the internal calculation coordinates.

[0078] The aforementioned points will be used to construct the standard skeletal coordinate system in step 200. According to the calculation method disclosed in step S3 of the invention description, the rotation matrix is ​​constructed through vector cross product. And combined with the ankle joint center point as the origin. Finally, the rigid body transformation matrix is ​​obtained. This matrix will be persistently saved for use in subsequent steps.

[0079] After annotation, a standard skeletal coordinate system is established with the center point of the ankle joint as the origin, and all relevant data is transformed to this coordinate system to ensure coordinate consistency in all subsequent calculations. Figure 5 As shown in the figure, this diagram illustrates... , , , The positions of the four points and the standard skeletal coordinate system (X / Y / Z axes) constructed from them.

[0080] Step 3: Pre-calculation of search data

[0081] This step preprocesses the distal tibial region in a standard skeletal coordinate system to generate a distance field, bone quality atlas, and binary slice sequence for subsequent rapid assessment. This pre-calculation significantly reduces the time required for each prosthesis pose assessment.

[0082] Step 3.1: Generate Z-axis slices. Using the ankle joint center point... Using the Z-axis origin (Z=0mm), the tibia model was sliced ​​every 0.5mm along the positive Z-axis direction (from distal to proximal), generating a two-dimensional slice sequence with a Z-coordinate range of [0, 30]mm. This range covers a 30mm area above the ankle joint, corresponding to the clinically routine distal tibial osteotomy and prosthesis implantation area. In this typical embodiment, a total of 61 slices were generated. ( The slice resolution inherits the XY plane resolution of the original CT scan.

[0083] Step 3.2: Euclidean distance field calculation. For each slice... Calculate the two-dimensional Euclidean distance transform (EDT) to obtain the range field. Note that before calculating the distance field, a morphological hole-filling operation is performed on the binary slices to fill the low-density areas inside the bone (cancellous bone holes, medullary cavities) as the foreground, ensuring that the distance field is calculated only from the outer contour of the bone.

[0084] Step 3.3: Bone Quality Atlas Extraction. Extract the HU value information corresponding to the slice sequence from the segmented file carrying HU values ​​to construct a three-dimensional bone quality atlas. The Z-axis range of this atlas corresponds to the slice sequence ([0, 30] mm), and each voxel stores the original HU value at that location. Regions with HU values ​​greater than 300 are marked as good cancellous bone, and regions with HU values ​​greater than 700 are marked as cortical bone, according to the Hounsfield Units criteria. This atlas is used for bone quality support assessment in step 600 of the multi-objective optimization.

[0085] Step 3.4: Calculation of cumulative bone somatomorph map along the Z-axis. The binary slice sequence is cumulatively summed along the Z-axis to generate a cumulative bone somatomorph map. For each Z layer, This refers to the cumulative number of bone voxels from Z=0 to the current layer. This data structure is used to quickly calculate the osteotomy volume at any osteotomy height: given the template height of the prosthesis pose. and prosthesis mask osteotomy volume ,in The volume of a single voxel is expressed in mm³. This algorithm achieves osteotomy volume lookup in O(1) time complexity, avoiding the overhead of repeatedly calculating the volume for each candidate pose.

[0086] Generate binary slice sequences, distance field sequences, bone quality atlases, cumulative bone voxel maps, and corresponding metadata files for use in subsequent steps. For example... Figure 6 and Figure 7 The figures shown are the distance field sampling sequences for tibial slices. and sampled bone quality atlas The diagram shows that the color codes in the distance field sampling plot represent the distance to the outer contour of the bone and the bone density, respectively.

[0087] Step 4: Coarse-grained mesh search and anatomical constraint screening

[0088] Step 4.1: Perform a grid search in four-degree-of-freedom space. Search parameters: mm, step size 2.0 mm; mm, step size 2.0 mm; The search range is set to 1 degree, with a step size of 1.0 degree. Based on the set search range and step size, the candidate solution space includes... A discrete pose.

[0089] Step 4.2: Perform anatomical constraint testing. First, using the pre-calculated fibular distance field, ensure that the prosthesis maintains a safe distance of at least 3 mm from the fibula; second, check whether the prosthesis intrudes into the medial malleolus elliptical cylinder protection area.

[0090] A systematic evaluation was performed on 10,648 candidate poses in the search space. Vectorized computation was used to reduce redundant operations, and spatial indexing was used to accelerate constraint detection. In this embodiment, after constraint screening, a total of 3,120 feasible poses were obtained.

[0091] The results of the slicing sampling after screening are as follows: Figure 8 As shown in the figure, this figure displays the tibial and fibular sections and the prosthesis template at different locations in the search space. The blue area represents the tibial section, the green area represents the fibular section, the yellow area represents the prosthesis template, the purple area represents the intersection of the tibial and the prosthesis, the red area represents the fibular safety restraint, and the orange area represents the medial malleolus protection zone. Figure 9 This indicates the initial search position of the prosthesis and prosthesis template in the skeletal coordinate system, as well as the search space and constraints visualization.

[0092] Step 5: Initialization of a high-quality evolutionary population

[0093] This step first takes the complete set of anatomical feasible poses output from step 400 as input, and reuses the dynamic slice generator and the prosthesis mask rasterization module to ensure that the evaluation process maintains a completely consistent spatial reference frame and mask resolution with the coarse search. For each candidate pose... Calculate the following five performance indicators at the template height:

[0094] a. Bone coverage ,in For the prosthesis mask, A binary section of the tibia;

[0095] b. Osteotomy volume ,in The cumulative bone matrix image calculated in step 304. This is the Z-axis index corresponding to the template height. Volume of a single voxel (mm³);

[0096] c. Bone quality support : In bone quality HU atlas On the corresponding slice, calculate the average HU value for the masked region;

[0097] d. Risk of cortical perforation ,in This represents the minimum distance of the tibial distance field on the prosthesis mask. For safety margin;

[0098] e. Centrality It measures the offset of the position relative to the center of the ankle joint.

[0099] To facilitate processing within the same multi-objective minimization framework, the above indicators are further transformed into objective functions. , , , , Subsequently, Pareto rank was determined using Fast Non-dominated Sorting, and the crowding distance was used as the criterion. Maintain a uniform distribution of the solution set in the target space:

[0100] ;

[0101] Specifically, starting from Rank=0, the solutions for each entire layer are accumulated sequentially; this is when the target size is about to be exceeded. (This embodiment) When this occurs, samples are retained only within the current layer according to their crowding level, from highest to lowest, until full capacity is reached. The crowding level of samples at the layer boundary is considered... Prioritize retention. The final result is an initial population that possesses both a low Pareto level and maintains diversity (the actual selected population is...). ).

[0102] Step 6: NSGA-II-CDP Multi-Objective Evolutionary Optimization

[0103] Set evolutionary parameters: population size N=100, maximum number of generations. Crossover probability Probability of mutation The algorithm employs simulated binary crossover (SBX) and a polynomial mutation operator. During the evolution process, no objective weights are used; selection is based solely on Pareto dominance and crowding levels to ensure solution diversity.

[0104] like Figure 10 As shown, the execution flow of the NSGA-II-CDP algorithm includes: after inputting the initial population, in each generation iteration, binary tournament selection, simulated binary crossover and polynomial mutation, merging parent and child populations, fast non-dominated sorting and crowding calculation, and elite retention strategy are executed sequentially. This loop continues until the maximum number of generations is reached, and finally, the Pareto front is output.

[0105] During the evolution, the size of the Pareto front and the proportion of feasible solutions steadily increase, with a total optimization time of approximately 7 minutes (depending on hardware and data scale). The final Pareto front contains multiple optimal solutions that perform differently on different objectives.

[0106] Step 7: Pareto Front Extraction and Compromise Solution Screening

[0107] This step takes the Pareto candidate file output from step 600 as input, performs feasibility and rank checks, and imposes size constraints to obtain a standardized Pareto front. Then, a compromise solution is obtained based on a coverage threshold and a multi-criteria decision-making method. In this embodiment, step 600 converges after the 80th generation, and the final population contains 100 non-dominated solutions, constituting the Pareto front.

[0108] Step 7.1: Coverage-Priority Three-Stage Filtering To ensure clinical safety and prioritize good fit between the prosthesis and bone, a tiered filtering strategy is employed: Stage 1: Hard Threshold Screening. A hard threshold of 95% bone coverage is set, and candidates meeting the criteria are selected from 100 Pareto solutions. In this embodiment, 21 solutions meet this condition and enter the candidate pool. Stage 2: Soft Threshold Backsliding. If the hard threshold screening result is empty, the threshold is lowered to 90%, and screening is repeated. Stage 3: Coverage Ranking. If the soft threshold still yields no solutions, solutions are sorted in descending order of bone coverage, and the top 40% (at least 3) of solutions are selected to enter the candidate pool.

[0109] Step 7.2: Multi-criteria decision-making comprehensive scoring. The 21 solutions in the candidate pool are comprehensively scored. This step uses the TOPSIS (Top-Approximation-Ideal-Solution Ranking) method, a well-known technique in the field of multi-criteria decision-making. A weight vector representing conventional clinical preferences is introduced. These correspond to coverage, osteotomy volume, bone quality support, cortical perforation risk, and centrality, respectively. Through this weighted distance-based scoring mechanism, indicators with larger weights contribute more to the distance calculation, thereby reflecting clinical preferences.

[0110] Step 7.3: Diversity Recommendation Strategy To avoid overly similar recommended solutions and ensure the quality of candidate solutions, a greedy farthest point strategy is adopted to select three significantly different solutions from the top 12 candidate solutions in TOPSIS score.

[0111] Step 8: Output of Surgical Planning Solution

[0112] This step generates detailed surgical planning reports for the three recommended options selected in step 7. For each recommended option, the system generates a 3D visualization model, precise surgical parameters, and a complete PDF planning report.

[0113] like Figure 11As shown, the 3D visualization model displays the precise assembly relationship between the prosthesis and the bone in a semi-transparent form, facilitating observation of the contact situation; the tibia and fibula are rendered in pseudo-color based on HU values, intuitively reflecting the bone density distribution. The three options present complementary distributions in dimensions such as coverage, osteotomy volume, and centrality, providing doctors with diverse choices.

[0114] For each scheme, the system outputs a detailed parameter table containing the following information: prosthesis center coordinates (accurate to 0.1 mm), osteotomy height (based on pre-calculated slice intervals, accurate to 0.5 mm), rotation angle (around the Z-axis, accurate to 0.1 degrees), five performance indicators (bone coverage, osteotomy volume, bone quality support, cortical perforation risk, center offset), constraint satisfaction (fibular safety distance, medial malleolus interference detection results), and comprehensive score (TOPSIS score and ranking).

[0115] The final report is a complete PDF document, including a comparison table of treatment options, 3D visualizations, risk assessments, and surgical recommendations. Doctors can then choose the most suitable option from the three recommended treatment plans based on the patient's specific condition and clinical preferences.

[0116] The parts of this invention not described in detail are common knowledge to those skilled in the art.

[0117] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Obviously, those skilled in the art, after understanding the content and principle of the present invention, may make various modifications and changes in form and details without departing from the principle and structure of the present invention, including: the present invention uses 3D Slicer for manual bone tissue segmentation, or other medical image segmentation software such as ITK-SNAP and Mimics for manual or semi-automatic segmentation, or a fully automatic segmentation method based on deep learning (such as U-Net and V-Net). The NSGA-II-CDP multi-objective optimization algorithm can be replaced by other multi-objective evolution algorithms such as NSGA-III, MOEA / D, SPEA2, and Particle Swarm Optimization (PSO). The process of calculating the distance field after filling the morphological holes can also use the original distance field calculation method without filling the holes, or approximate methods such as Chamfer distance transformation, although the accuracy is slightly lower, the relevant calculations can still be completed. The calculation of O(1) osteotomy volume is realized by using the Z-axis cumulative bone voxel map, or the traditional method of summing after counting voxels layer by layer can be used. The TOPSIS multi-criteria decision-making method can be used for compromise solution selection, but other multi-criteria decision-making methods such as VIKOR (compromise ranking), WSM (weighted sum method), and AHP (analytic hierarchy process) can also be used. A search step size of 2 mm / 1° can be used, but a coarser step size of 5 mm / 2° (faster but less accurate) or a finer step size of 1 mm / 0.5° (higher accuracy but increased computation) can also be used. The safety distance can be calculated in real-time using the fibular distance field, or the complete distance field can be pre-calculated and stored on disk, which, although requiring more storage space, reduces runtime computation. An elliptical cylinder can be used to approximate the medial malleolus protection area, but simpler geometric shapes such as spheres or cuboids can also be used, or methods based on precise segmentation of the medial malleolus contour from CT images can be employed. Anatomical landmarks can be manually labeled, or automatic matching based on statistical shape models (SSM) or automatic detection methods based on deep learning networks (such as U-Net) can be used. A four-degree-of-freedom search space (fixed rx=0°, ry=0°) can be used, or a complete six-degree-of-freedom search can be employed, although the computational cost is higher, the principle remains the same. A hybrid optimization strategy (coarse search + fine optimization) can be employed, or a single grid search or evolutionary algorithm can be used to optimize from a random initial population. This invention simultaneously optimizes five objective functions, but this can be simplified to optimizing two or three core objectives (e.g., optimizing only bone coverage and osteotomy volume), with other indicators treated as constraints. However, these modifications and alterations based on the ideas of this invention are still within the scope of protection of the claims of this invention.

Claims

1. A method for tibial prosthesis localization before ankle arthroplasty based on multi-objective optimization, characterized in that, The non-dominated sorting genetic algorithm II (NSGA-II-CDP) with constrained dominance principle was applied to the preoperative localization planning of the ankle tibial prosthesis. Five clinically relevant objective functions were optimized, including bone coverage, osteotomy volume, bone quality support, cortical perforation risk, and centrality. Multiple non-dominated optimal solutions were provided using the Pareto front. The implementation steps are as follows: S1. Acquire and process the original medical CT images and prosthesis model data of the affected lower limb; perform standard position calibration on the prosthesis and establish a local coordinate system; S2. Perform bone tissue segmentation on CT images, extract three-dimensional models of the tibia, fibula and talus, and segment the models carrying HU bone density values; S3. Standardize the extracted three-dimensional skeletal model, including labeling anatomical landmarks and constructing an orthogonal standard coordinate system based on the labeled landmarks, so as to unify the anatomical orientation of different patients, reduce the amount of calculation, and speed up the subsequent processing. S4. Pre-calculate search data for the distal articular surface region of the tibia to obtain the distance field, bone mass HU value atlas, binary slice sequence, Z-axis cumulative bone voxel map and anatomical constraint data; S5. Perform coarse-grained mesh search and anatomical constraint screening on the distal tibial articular surface region and prosthesis model, comprehensively evaluate multiple performance indicators, and generate a high-quality initial candidate solution set. S6. Combining the initial candidate solution set and the multi-objective optimization criterion, the NSGA-II-CDP multi-objective evolution algorithm and the constraint dominance principle are used to obtain the Pareto front containing multiple non-dominated solutions; S7. Perform multi-stage compromise solution screening on the Pareto frontier, combine multi-criteria decision-making and diverse strategies to recommend the optimal solution, and generate a three-dimensional visualization model containing detailed trimming parameters.

2. The method according to claim 1, characterized in that: In step S2, bone tissue segmentation is performed on the CT images, specifically using either a traditional method based on thresholding and region growing or an automatic segmentation method based on the U-Net deep learning model.

3. The method according to claim 1, characterized in that: Step S3, which involves marking anatomical landmarks and constructing an orthogonal standard coordinate system based on the marked landmarks, specifically involves marking four key anatomical landmarks on the tibia model, including the proximal tibial center point. Ankle joint center point Medial malleolus and lateral ankle tip Construct an orthogonal standard coordinate system; where the Z-axis is defined as the direction of the mechanical axis. The Y-axis is defined as the coronal plane normal, and the X-axis is defined as the sagittal plane normal; by constructing the rigid body transformation matrix All 3D model data is converted to the standard coordinate system.

4. The method according to claim 3, characterized in that: The annotation methods for anatomical landmarks include manual annotation, statistical shape models, or deep learning methods.

5. The method according to claim 1, characterized in that: The pre-calculation mentioned in step S4 includes: a binary template B generated by orthogonal projection of the top surface of the prosthesis, and a distance field sequence obtained by calculating a two-dimensional Euclidean distance transformation after filling morphological holes in equally spaced slices of the tibia along the Z-axis. Three-dimensional bone quality atlas based on HU value Bone matrix image obtained by summing along the Z-axis for querying osteotomy volume. 3D distance field of the fibula And a protective mask for the medial malleolus elliptical cylinder generated based on the tibial diameter ratio method. .

6. The method according to claim 5, characterized in that: The fibular three-dimensional distance field It is used to quickly determine whether the distance between the prosthesis and the fibula is within a safe range; specifically, it is obtained by loading fibula segmentation data and calculating a three-dimensional Euclidean distance transformation on the fibula model in the standard coordinate system, where each voxel value represents the nearest distance from that point to the fibula surface; The medial malleolus elliptical protective mask is marked with a non-invasive medial malleolus protection area, which is specifically determined as follows: at the center point of the ankle joint. Obtain a cross-section of the tibia from above and measure the anteroposterior diameter of this section. and inner and outer diameters Calculate the anteroposterior radius of the medial malleolus ellipse based on the ratio of the medial malleolus size to the tibial diameter. and inner and outer radii ; with the tip of the medial malleolus An elliptical cylindrical mask is generated along the positive Z-axis with the bottom center as the center. .

7. The method according to claim 1, characterized in that: Steps S5 and S6 constitute a hierarchical hybrid optimization, including: simplifying six degrees of freedom to four degrees of freedom ( , , , Coarse-grained grid search reduces the search space and improves efficiency. Feasible poses are screened based on the dual anatomical constraints of the fibular safety distance and the medial malleolus protection area to ensure the safety of prosthesis implantation. Using the screened feasible poses as the initial population, the NSGA-II-CDP multi-objective evolutionary algorithm is used for fine optimization to obtain the Pareto front solution.

8. The method according to claim 1 or 7, characterized in that: The multi-objective optimization criterion in step S6 includes defining five objective functions and minimizing them uniformly, achieving optimization through Pareto dominance sorting; wherein the five objective functions are defined as: the negative ratio of the intersection area of ​​the prosthesis mask and the tibial slice. osteotomy volume The mean HU value for the covered area is negative. Risk of cortical perforation Center offset .

9. The method according to claim 1, characterized in that: The optimal solution described in step S7 is specifically achieved through a three-stage filtering process involving hard thresholding of bone coverage, soft thresholding, and descending truncation. TOPSIS / VIKOR / WSM, which incorporates clinical preference weight vectors, is used to score non-dominated solutions at the Pareto front using multi-criteria decision-making. Then, based on diversity strategy clustering, a diversity recommendation is made among high-scoring candidate solutions using a greedy strategy that maximizes the minimum distance, combined with clinical experience and mechanical simulation.

10. The method according to claim 9, characterized in that, The three-stage filtering process of hard threshold → soft threshold → descending order truncation for bone coverage includes: setting a hard threshold for bone coverage and selecting solutions that meet the conditions from the Pareto solutions to enter the candidate pool; if the hard threshold selection result is empty, the threshold is lowered and a soft threshold is set for re-selection; if there are still no solutions after the soft threshold, the solutions are sorted in descending order of bone coverage and at least 3 solutions are selected to enter the candidate pool.

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