Generation method of personalized porous bone repair stent three-dimensional model based on tomography and nuclear magnetic resonance image data

Abstract

The application discloses a generation method of a personalized porous bone repair bracket three-dimensional model based on tomography and nuclear magnetic resonance image data, which comprises the following steps: obtaining tomography data of a target missing area; obtaining a closed boundary discrete spatial point cloud that is fitted to the target missing area according to the tomography data; obtaining a watertight initial triangular mesh model according to the closed boundary discrete spatial point cloud; obtaining a reverse deformation compensation mesh model of non-uniform local geometric amplification according to the watertight initial triangular mesh model; generating a target nozzle filling track according to the reverse deformation compensation mesh model; performing safety review and smooth reconstruction on the target nozzle filling track by using a safety isolation sandbox, and issuing a final numerical control instruction flow corresponding to the target nozzle filling track to a three-dimensional printing device, so that the three-dimensional printing device manufactures the personalized porous bone repair bracket three-dimensional model. In the above manner, the printing and filling efficiency in a complex porous structure is improved, and the hardware failure rate of the three-dimensional printing device in continuous operation is reduced.

Description

Technical Field

[0001] This application relates to the field of 3D printing technology, and in particular to a method for generating a three-dimensional model of a personalized porous bone repair scaffold based on computed tomography and magnetic resonance imaging data. Background Technology

[0002] In personalized bone repair projects targeting areas of structural deficiency (such as bone defects), the current mainstream process involves reconstructing a personalized, porous bone repair scaffold model based on the patient's tomographic data and MRI images. This scaffold is then physically manufactured using extrusion-based 3D molding equipment with polymeric fluid materials (such as polylactic-co-glycolic acid copolymer solutions). To create micropores (typically 10 to 50 micrometers) within the bone repair scaffold suitable for cell attachment and blood vessel ingrowth, a phase change post-processing step involving cryogenic freezing and vacuum sublimation drying is necessary after the physical printing is completed.

[0003] During the phase transition process of freeze-drying the aforementioned fluid materials, volume shrinkage is inevitable. Existing engineering methods are extremely simplistic and crude: in the 3D modeling stage, the entire bone repair scaffold 3D model is "globally isotropically enlarged" according to the nominal shrinkage rate (e.g., 5%) provided by the material manufacturer.

[0004] Porous bone repair scaffolds are not solid geometric shapes; their interiors are filled with interconnected macroscopic channels and microscopic pores, forming an extremely complex thin-walled topological network. During actual phase transitions, the temperature gradient distribution between the outer surface and the internal core region of the bone repair scaffold is extremely uneven, resulting in strong nonlinearity and local anisotropy in its physical contraction.

[0005] If the existing technology of "globally uniform scaling up" is used, the complex thin-walled structure inside the bone repair scaffold (such as the connecting struts between pores) will undergo unpredictable distortion, stress concentration, or even fracture after actual freeze-drying. This results in millimeter-level distortion errors at the physical boundary between the final solid bone repair scaffold and the actual missing area, making it impossible to fit tightly, and forced implantation will generate destructive compressive stress. However, if traditional finite element numerical analysis methods are used to perform thermo-mechanical coupled phase transition simulation calculations on this porous structure with millions of microfacets, it usually takes several days, which is far from meeting the high-efficiency preparation requirements of customized manufacturing. Summary of the Invention

[0006] The method for generating a personalized three-dimensional model of a porous bone repair scaffold based on computed tomography and magnetic resonance imaging data provided in this application can improve the efficiency of printing and filling complex porous structures while reducing the hardware failure rate of three-dimensional printing equipment during continuous operation.

[0007] In a first aspect, this application provides a method for generating a personalized porous bone repair scaffold 3D model based on computed tomography (CT) and magnetic resonance imaging (MRI) data. The method includes: acquiring CT data of a target missing region; obtaining a closed boundary discrete point cloud conforming to the target missing region based on the CT data; obtaining a watertight initial triangular mesh model based on the closed boundary discrete point cloud; obtaining a non-uniform local geometric amplification inverse deformation compensation mesh model based on the watertight initial triangular mesh model; generating a target nozzle filling trajectory based on the inverse deformation compensation mesh model; performing a safety review and smooth reconstruction of the target nozzle filling trajectory using a safety isolation sandbox; and sending the final numerical control command stream corresponding to the target nozzle filling trajectory after the safety isolation sandbox review and smooth reconstruction to a 3D printing device, so that the 3D printing device can manufacture a personalized porous bone repair scaffold 3D model.

[0008] The process involves obtaining a discrete spatial point cloud representing the closed boundary of the missing target region based on tomographic scan data. This includes: inputting the tomographic scan data into a parametric iterative denoising mapping model, which performs a multi-step inverse denoising calculation based on a Markov chain at a set spatial resolution, outputting a three-dimensional volume data matrix. During the calculation, nonlinear artifacts caused by the high-density beam hardening effect of the metal and low-frequency background noise are gradually extracted. Local spatial features are extracted from the three-dimensional volume data matrix to obtain the microscopic step boundary features of the missing target region. Global topological features are extracted from the three-dimensional volume data matrix to obtain the macroscopic topological shape features. Based on the microscopic step boundary features, macroscopic topological shape features, and the physical prior parameter matrix of the 3D printing molding material, a discrete spatial point cloud representing the closed boundary of the missing target region is obtained. The physical prior parameter matrix includes the mass concentration of the polymer fluid, molecular weight, target ambient temperature of the molding chamber, and the expected theoretical porosity.

[0009] Specifically, based on the microscopic step boundary features, macroscopic topological shape features, and the physical prior parameter matrix of the 3D printing material, a discrete spatial point cloud of the closed boundary of the missing target region is obtained. This includes: fusing the microscopic step boundary features and macroscopic topological shape features as a query vector, and using the physical prior parameter matrix as a reference key; performing inner product and normalization calculations on the query vector and the reference key to obtain the physical compatibility weight; and adaptively filtering the microscopic step boundary based on the physical compatibility weight to obtain the discrete spatial point cloud of the closed boundary of the missing target region.

[0010] The process of obtaining a watertight initial triangular mesh model based on a closed boundary discrete point cloud includes: dividing the closed boundary discrete point cloud into voxels to obtain a set of reference anchor points; generating spatial distribution primitives at each reference anchor point in the set of reference anchor points, and generating a three-dimensional local density field based on the spatial distribution primitives; assigning directional normal vector parameters to each spatial distribution primitive, and calculating the inner product of the directional normal vector parameters and the spatial projection ray when calculating the contribution of the spatial distribution primitive to the three-dimensional local density field, and forcing the surface to close according to the set physical constraints to obtain a continuous density field; and extracting a three-dimensional continuous interface with an absolute density value equal to a threshold constant from the continuous density field to obtain the watertight initial triangular mesh model.

[0011] The process of generating a three-dimensional local density field based on spatial distribution primitives includes: configuring a set of physical parameters for each spatial distribution primitive, the physical parameters including at least: the central three-dimensional coordinate offset, the three-dimensional covariance matrix representing the shape of the spatial ellipsoid, the opacity parameter representing the density of the local solid material, and the scale factor representing the scaling ratio of the material; and constructing a three-dimensional local density field within the target missing region by the mutual overlap of each spatial distribution primitive in three-dimensional space and the superposition of the physical parameters.

[0012] The process involves obtaining a reverse deformation compensation mesh model with non-uniform local geometric amplification based on the initial watertight triangular mesh model. This includes: calculating the shrinkage stress at each node inside the three-dimensional model of the porous bone repair scaffold based on the thermo-mechanical coupled partial differential equations of the initial watertight triangular mesh model and the non-uniform volume shrinkage; mapping the shrinkage stress to the three-dimensional shrinkage velocity and displacement vector of the mesh vertices using the full mass matrix approximation inverse algorithm; and performing reverse bias compensation on the displacement vector to obtain the reverse deformation compensation mesh model with non-uniform local geometric amplification.

[0013] The process involves calculating the shrinkage stress at each node within the 3D model of the porous bone repair scaffold based on the initial watertight triangular mesh model and the thermo-mechanical coupled partial differential equations of non-uniform volume shrinkage. This includes: obtaining the phase transition parameters of the 3D printing equipment; these parameters include the phase transition solidification point temperature of the 3D printing material, the vacuum degree change curve during sublimation, and the nonlinear volumetric strain coefficient during fluid-to-solid transition; constructing the thermo-mechanical coupled partial differential equations based on these parameters, and defining the coordinates of the geometric outer contour vertices and the inner surface vertices of the pores of the initial watertight triangular mesh model as Dirichlet physical boundary conditions; performing Chebyshev domain mapping on the 3D coordinates of each vertex within the mesh of the initial watertight triangular mesh model to expand the 3D coordinates to a higher-dimensional mathematical feature space; constructing functional constraint expressions based on the higher-dimensional mathematical feature space and the thermo-mechanical coupled partial differential equations; and calculating the shrinkage stress at each node within the 3D model of the porous bone repair scaffold based on the functional constraint expressions.

[0014] The method of mapping shrinkage stress to the three-dimensional shrinkage velocity and displacement vector of the mesh vertices using the full mass matrix approximation inverse algorithm includes: constructing a local continuous mass field surrounding each local vertex; calculating the actual momentum update of the mesh vertices using the full mass matrix approximation inverse algorithm within each preset discrete time step to obtain the three-dimensional shrinkage velocity and displacement vector of the mesh vertices.

[0015] The process of generating the target nozzle filling trajectory based on the inverse deformation compensation mesh model includes: according to the physical layer thickness set by the 3D printing equipment, performing layer-by-layer two-dimensional geometric plane intersection of the inverse deformation compensation mesh model along the direction perpendicular to the forming platform to obtain the closed two-dimensional outer contour and the boundary polygon of the internal pores of each layer; introducing a numerical sampling mechanism based on the continuous normalized flow equation within the effective filling area inside the boundary polygon; concurrently executing the ordinary differential equation in the numerical sampling mechanism to generate multiple candidate nozzle filling trajectories; performing spatial geometric interference calculation on the multiple candidate nozzle filling trajectories to obtain the target nozzle filling trajectory; wherein, the target nozzle filling trajectory is a collision-free candidate nozzle filling trajectory.

[0016] The process of using a security isolation sandbox to perform security review and smooth reconstruction of the target nozzle filling trajectory includes: obtaining the hardware limit list of the 3D printing equipment; using the security isolation sandbox to perform security review of the target nozzle filling trajectory, blocking the release of the target nozzle filling trajectory when the physical results caused by the target nozzle filling trajectory exceed the constraints of the hardware limit list; and performing smooth reconstruction of the target nozzle filling trajectory.

[0017] The beneficial effects of this application are as follows: Unlike existing technologies, this application provides a method for generating a personalized porous bone repair scaffold 3D model based on tomographic and magnetic resonance imaging data. This method includes: acquiring tomographic data of the target missing region; obtaining a closed boundary discrete point cloud conforming to the target missing region based on the tomographic data; obtaining a watertight initial triangular mesh model based on the closed boundary discrete point cloud; obtaining a non-uniform local geometric amplification inverse deformation compensation mesh model based on the watertight initial triangular mesh model; generating a target nozzle filling trajectory based on the inverse deformation compensation mesh model; performing a security review and smooth reconstruction of the target nozzle filling trajectory using a security isolation sandbox; and sending the final CNC command stream corresponding to the target nozzle filling trajectory after security isolation sandbox review and smooth reconstruction to a 3D printing device, enabling the 3D printing device to manufacture a personalized porous bone repair scaffold 3D model. Through this method, the printing filling efficiency of complex porous structures can be improved while reducing the hardware failure rate of the 3D printing device during continuous operation. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a flowchart illustrating an embodiment of the method for generating a three-dimensional model of a personalized porous bone repair scaffold based on computed tomography and magnetic resonance imaging data provided in this application. Detailed Implementation

[0019] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. It is understood that the specific embodiments described herein are only for explaining this application and not for limiting it. Furthermore, it should be noted that, for ease of description, only the parts related to this application are shown in the accompanying drawings, not all structures. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0020] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0021] See Figure 1 , Figure 1 This is a flowchart illustrating an embodiment of the method for generating a three-dimensional model of a personalized porous bone repair scaffold based on computed tomography and magnetic resonance imaging data provided in this application. The method includes: Step 11: Obtain tomographic scan data of the target missing area.

[0022] In some embodiments, tomographic data can be obtained by scanning the target missing area in real time using a tomographic scanning device.

[0023] In some embodiments, tomographic data can be obtained by scanning the target missing area non-real-time using a tomographic scanning device.

[0024] In some embodiments, the computed tomography data may be computed tomography volume data.

[0025] The target missing area can be the area that needs to be filled by a three-dimensional model of a porous bone repair scaffold.

[0026] Step 12: Based on the tomographic scan data, obtain the discrete spatial point cloud of the closed boundary that fits the missing area of ​​the target.

[0027] In some embodiments, in actual clinical scanning or industrial non-destructive testing scenarios, the acquired tomographic data of the target missing area (tomographic data) is often accompanied by artifacts from metal implants, soft tissue scattering, and physical background noise from low-dose scanning. Directly reconstructing the noisy data in three dimensions can lead to burrs or incorrect solid filling on the surface of the final porous bone repair scaffold (3D model of the porous bone repair scaffold). Furthermore, the target missing area includes both the overall macroscopic support contour and fine fracture edges (such as the microscopic physical steps of the trabecular bone structure), and traditional single grayscale threshold extraction methods cannot simultaneously ensure the accuracy of both. Therefore, step 12 can be the following process: Step 121: Input the tomographic scan data into the parameterized iterative denoising mapping model so that the parameterized iterative denoising mapping model performs multi-step inverse denoising inference calculation based on Markov chain at the set spatial resolution and outputs a three-dimensional volume data matrix; wherein, in the inference calculation, the nonlinear artifact signal and low-frequency background noise generated by the beam hardening effect of high-density metal are gradually removed.

[0028] In some embodiments, step 121 can be defined as physical purification of tomographic signals based on the Markov chain inverse process.

[0029] The input data for the entire process is: a three-dimensional volumetric data matrix of tomographic scans of the target missing area, including physical noise and artifacts.

[0030] The specific processing procedure is as follows: 1. Construct a parameterized iterative denoising mapping model pre-calibrated with high-fidelity detector imaging data. This model mathematically simulates the physical scattering and attenuation degradation process of rays penetrating materials of different densities.

[0031] 2. Input the initial tomographic scan three-dimensional volume data matrix into the mapping model, and perform multi-step inverse denoising calculation based on Markov chains at a set spatial resolution (e.g., not less than 0.625 mm slice thickness).

[0032] 3. In the extrapolation and calculation, the nonlinear artifact signal and low-frequency background noise caused by the beam hardening effect of the high-density metal are gradually extracted.

[0033] The overall output of the process is a high-fidelity 3D volumetric data matrix that converts and outputs the true ray attenuation coefficient (i.e., the tissue density distribution value characterizing the physical density of the actual tissue). This step ensures an absolute correspondence between the 3D spatial coordinates, which serve as the origin of the solid manufacturing process, and the density of the real physical world, preventing subsequent molding equipment from mistaking noise for the physical boundary of the solid.

[0034] Step 122: Extract local spatial features from the three-dimensional volume data matrix to obtain the microscopic step boundary features of the target missing region.

[0035] Step 123: Extract global topological features from the three-dimensional volume data matrix to obtain macroscopic topological shape features.

[0036] In some embodiments, steps 122 and 123 can be defined as: macro-micro dual-stream decoupling feature extraction for the tissue density distribution value matrix (three-dimensional volume data matrix).

[0037] To overcome the contradiction between "incomplete macroscopic contours" and "smoothed microscopic details" that arise during the extraction of complex porous structures, parallel two-stream branch signal processing is performed on the aforementioned high-fidelity 3D volumetric data matrix: 1. The local spatial feature extraction branch (capturing microscopic fracture edges) includes the following: Establish a three-dimensional sliding calculation window with a preset size (e.g., 3x3x3) and traverse the high-fidelity three-dimensional volume data matrix.

[0038] The partial derivatives of the central voxel of the window in the three orthogonal physical dimensions X, Y, and Z are calculated to obtain the three-dimensional spatial gradient vector of that spatial location.

[0039] Extract a set of voxel points whose magnitude of the spatial gradient vector is greater than a preset physical step threshold (e.g., greater than 45 decay units / mm) and whose absolute density distribution value is within the range of the target dense hard tissue.

[0040] The output of this branch constitutes a highly clear microscopic step boundary feature (i.e., extremely small physical fracture surfaces and sharp-angled edges) of the target missing region.

[0041] 2. The global topological feature extraction branch (capturing macroscopic support contours) includes the following: Establish a global mapping channel carrying the rolling state cache matrix.

[0042] According to the physical layer sequence of the tomographic slices, a high-fidelity three-dimensional volumetric data matrix is ​​input layer by layer, and a rolling state cache matrix records and accumulates long-distance spatial positional dependencies spanning multiple slice layers.

[0043] By performing dimensionality reduction and projection calculations using a nonlinear activation function, the large-scale geometric span and spatial envelope trend across the entire missing target region are extracted.

[0044] The output of this branch constitutes the macroscopic topological shape characteristics necessary for the bone repair scaffold under stress, avoiding the fragmentation or discontinuity of the overall support structure caused by local fractures.

[0045] Step 124: Based on the microscopic step boundary characteristics, macroscopic topological shape characteristics, and the physical prior parameter matrix of the 3D printing molding material, obtain the closed boundary discrete spatial point cloud of the missing region of the target; the physical prior parameter matrix includes the mass concentration of the polymer fluid, molecular weight, target ambient temperature of the molding chamber, and expected theoretical porosity.

[0046] In some embodiments, step 124 may be the following process: Step 1241: Integrate microscopic step boundary features and macroscopic topological shape features as query vectors, and use the physical prior parameter matrix as the reference key.

[0047] Step 1242: Perform inner product and normalization calculations on the query vector and the base key value to obtain the physical compatibility weight.

[0048] Step 1243: Adaptively filter the microscopic step boundary according to the physical compatibility weight to obtain the closed boundary discrete spatial point cloud that fits the missing target region.

[0049] In some embodiments, steps 1241 to 1243 above can be defined as: cross feature mapping and boundary point cloud output based on the mechanical properties of extruded materials.

[0050] After obtaining accurate three-dimensional geometric features (microscopic step boundary features and macroscopic topological shape features), it is necessary to combine them with the actual physical conditions of the three-dimensional molding equipment (three-dimensional printing equipment) to eliminate those "useless geometric points" that cannot be formed under fluid extrusion process.

[0051] The processing procedure is as follows: Obtain the physical and rheological prior parameter matrix (physical prior parameter matrix) of the current batch of 3D printing molding material. This parameter matrix includes: the mass concentration of the polymer fluid (such as polylactic acid-glycolic acid copolymer), molecular weight, target ambient temperature of the molding chamber, and expected theoretical porosity.

[0052] A cross-feature mapping computation mechanism (dynamic fusion computation) is constructed. The physical prior parameter matrix of the above-mentioned molding material is used as the reference key value (Keys / Values) for mapping. The extracted and fused macro-micro spatial geometric feature matrix (fusion of micro-step boundary features and macro-topological shape features) is used as the query vector (Queries) for inner product and normalization calculation.

[0053] Based on the calculated physical compatibility weights, the micro-step boundaries are adaptively filtered. The adaptive filtering automatically removes and filters out "extremely fine overhanging structure noise" and "isolated free voxels" that, under the current material concentration and extrusion rheological characteristics, would collapse due to gravity or fail to form effective physical strength once detached from the nozzle.

[0054] Output: The final output is a set of closed boundary discrete spatial point clouds that fully conforms to the fluid dynamics forming boundary conditions and precisely fits the missing target region (the set of closed boundary discrete spatial point clouds includes the closed boundary discrete spatial point cloud).

[0055] Through the aforementioned sequential steps, this embodiment completely abandons the inefficient process of "building a rough model first and then feeding it to the printer for trial and error." Abstract algorithms originally belonging to the fields of optics and vision, such as "diffusion models, two-stream networks, and multimodal attention fusion," are precisely reduced in dimensionality and rewritten into rigid industrial steps of "eliminating metal artifacts, extracting 3D spatial gradient vectors, and matching the physical suspension limits of fluid materials." This not only ensures the absolute accuracy of the extracted boundaries but also eliminates the risk of collapse and breakage that 3D printing equipment may encounter during subsequent physical manufacturing at the source data stage.

[0056] Step 13: Obtain the initial triangular mesh model of watertightness based on the discrete spatial point cloud of the closed boundary.

[0057] In some embodiments, this step completely abandons the original computer graphics rendering and large model vision methods, and concretizes it into three rigorous engineering operation steps before physical manufacturing: "pore node distribution, density field construction, and forced closure extraction of physical surfaces". This aims to solve the industrial pain point that 3D printing slicing software cannot recognize data with "suspended fragments" and "non-closed topology".

[0058] In some embodiments, after obtaining the aforementioned precise closed-boundary discrete spatial point cloud, it must be converted into a continuous geometric mesh with a specific porosity inside and absolutely closed (i.e., watertight) external and internal pore surfaces before it can be parsed by the slicing system of a 3D printing device. If the traditional voxel stacking method is used, it not only generates massive amounts of redundant geometric data leading to memory overflow in industrial control computers, but also easily generates suspended, free "island" waste surfaces at pore intersections, causing abnormal material extrusion from the nozzle in mid-air during physical printing. Based on this, step 13 can be the following process: Step 131: Perform mesh voxelization based on the discrete point cloud of the closed boundary to obtain the set of reference anchor points.

[0059] In some embodiments, step 131 above can be defined as: spatial voxelization based on the target boundary and scattering of reference anchor points.

[0060] Input data: The set of discrete spatial point clouds with closed boundaries that perfectly conform to the fluid dynamics forming boundary conditions output above.

[0061] The processing includes: Obtain the three-dimensional spatial volume of the target missing region enclosed by the discrete spatial point cloud with closed boundary.

[0062] The three-dimensional spatial volume is divided into internal mesh voxels according to a preset macroscopic through-hole size (e.g., 300 to 500 micrometers).

[0063] Based on voxelization space, the farthest point sampling geometry algorithm is used to extract a series of discrete three-dimensional spatial coordinate points uniformly and sparsely within the space.

[0064] Output: This series of three-dimensional spatial coordinate points constitutes the set of reference anchor points for the intersection nodes of the pores and the connecting beams within the porous bone repair scaffold. This step replaces the traditional full-solid voxels with extremely sparse anchor points, reducing the data volume of the model by more than 90% from the source, laying the computational foundation for subsequent ultra-fast reverse compensation calculations.

[0065] Step 132: Generate a spatial distribution primitive at each of the reference anchor points in the reference anchor point set, and generate a three-dimensional local density field based on the spatial distribution primitive.

[0066] In some embodiments, step 132 may be the following process: Step 1321: Configure a set of physical parameters for each spatial distribution primitive. The physical parameters include at least: the central three-dimensional coordinate offset, the three-dimensional covariance matrix characterizing the shape of the spatial ellipsoid, the opacity parameter characterizing the local solid material density, and the scale factor characterizing the material scaling ratio.

[0067] Step 1322: By overlapping the spatial distribution primitives in three-dimensional space and superimposing the physical parameters, a three-dimensional local density field is constructed within the target missing region.

[0068] In some embodiments, steps 1321 to 1322 above can be defined as: continuous density field primitive growth of pore topology.

[0069] Processing procedure: At each of the above-extracted reference anchor points, a mathematically meaningful spatial distribution primitive (used to characterize the occupied volume of local support material or pores) is generated.

[0070] For each spatial distribution primitive, configure a set of physical parameters that can be numerically optimized. These parameters include at least: the central three-dimensional coordinate offset, the three-dimensional covariance matrix characterizing the shape of the spatial ellipsoid, the opacity parameter characterizing the local solid material density, and the scale factor characterizing the material scaling ratio.

[0071] By overlapping and superimposing density parameters of various spatial distribution primitives in three-dimensional space, a continuous three-dimensional local density field with a specific porosity is constructed within the target missing region.

[0072] The physical problem to be solved is that the density field at this point is just a collection of "clumps" diffused in space. If it is directly converted into a solid mesh, the density decay zone at the edge of each primitive will produce a large number of jagged burr edges that cannot be closed. During physical printing, this will cause the extruder to frequently perform a retraction action, resulting in material carbonization and blockage.

[0073] Step 133: Assign directional normal vector parameters to each spatial distribution primitive, and when calculating the contribution of the spatial distribution primitive to the three-dimensional local density field, calculate the inner product of the directional normal vector parameters and the spatial projection ray, and force the surface to close according to the set physical constraints to obtain the continuous density field.

[0074] Step 134: Extract the three-dimensional continuous interface with an absolute density value equal to the threshold constant from the continuous density field to obtain the initial triangular mesh model of watertightness.

[0075] In some embodiments, steps 133 to 134 above can be defined as: directional normal forced wrapping constraint and watertightness interface extraction.

[0076] The processing includes: Normal vector parameter binding: For each of the above spatial distribution primitives, an independent orientation normal vector parameter (characterizing the physical orientation of the local surface) is forcibly introduced and assigned.

[0077] Anisotropic density truncation calculation: When calculating the contribution of this spatially distributed primitive to the three-dimensional local density field, the inner product of the directional normal vector and the spatial projection ray is calculated. Physical constraints are set: the material density distribution of this primitive is forced to exhibit a sharp anisotropic physical decay only in the direction the normal vector points to its positive half-axis (i.e., towards the outside of the solid or the inside of the cavity).

[0078] Forced Surface Enclosure: This constraint is equivalent to forcing each distribution primitive to represent only a "surface micro-piece" with clear inner and outer boundaries at the mathematical level. This forces all overlapping distribution primitives to form an absolutely continuous and seamless solid enclosure shell on the outer contour of the target missing area and on all macroscopic through-hole surfaces, just like tightly stitched scales.

[0079] Isosurface Extraction: Set a threshold constant corresponding to the physical molding density of the polymer material. Traverse the continuous density field constrained by the normal direction, and extract the three-dimensional continuous interface with an absolute density value equal to the threshold constant based on the traveling tetrahedral space segmentation algorithm (or isosurface extraction algorithm).

[0080] Output: The final assembly outputs a fully closed, zero-floating free debris, watertight initial triangular mesh model with clear internal and external topological properties.

[0081] Through the steps of this embodiment, this embodiment completely abandons the traditional computer graphics approach of "generating jagged pores by rigidly stitching together three-dimensional pixels (voxels). Instead, by introducing purely mathematical and geometric methods such as "spatial anchor points and directional normal vector constraints," a porous bone repair scaffold mesh with an absolutely smooth inner surface and an absolutely closed outer surface is directly "grown" in three-dimensional space.

[0082] This method precisely reduces the surface reconstruction algorithm, which was originally only used for visual rendering, to an industrial data preprocessing process that conforms to the rigid input specifications of 3D printing slicing engines (i.e., the model must be a manifold geometry without defects). It completely avoids slicing failure and abnormal extrusion caused by mesh holes or normal flipping. It replaces the uncontrollable "black box generation" with deterministic mathematical mapping, fundamentally establishing the strong engineering practicality of this solution in the field of solid manufacturing.

[0083] Step 14: Obtain the inverse deformation compensation mesh model with non-uniform local geometric amplification based on the initial triangular mesh model of watertightness.

[0084] In some embodiments, after obtaining the aforementioned initial triangular mesh model for water tightness, this model represents the "final ideal size" of the target bone repair scaffold when implanted into the human body (target object). However, in actual production, when polymeric fluid materials (such as polylactic acid-glycolic acid copolymer, PLGA) undergo extreme low-temperature freezing and vacuum sublimation processes, the complex internal micropores and thin-walled structures can induce extremely complex non-uniform thermal shrinkage. If traditional finite element method (FEM) is used to perform thermo-mechanical coupling calculations on millions of porous mesh interfaces, the time required for a single calculation is calculated in days; if a simple global proportional scaling compensation is used, it will lead to distortion and fracture of the internal microstructure. Based on this, this embodiment provides a thermo-mechanical coupling phase transition inverse compensation method based on functional linkage constraints, which replaces the time-consuming physical mesh iteration with extremely fast nonlinear mathematical solutions. Step 14 can be the following process: Step 141: Based on the watertight initial triangular mesh model and the thermo-mechanical coupled partial differential equation of non-uniform volume shrinkage, calculate the shrinkage stress of each node inside the three-dimensional model of the porous bone repair scaffold.

[0085] In some embodiments, step 141 may be the following process: Step 1411: Obtain the phase change operating parameters of the 3D printing equipment; the phase change operating parameters include: the phase change solidification point temperature of the 3D printing molding material, the vacuum degree change curve during the sublimation process, and the nonlinear volumetric strain coefficient when the fluid transforms into a solid.

[0086] Step 1412: Construct a thermo-mechanical coupled partial differential equation based on the phase change working condition parameters, and define the coordinates of the geometric outer contour vertices and the inner surface vertices of the duct of the initial triangular mesh model of watertightness as the Dirichlet physical boundary conditions of the thermo-mechanical coupled partial differential equation.

[0087] Step 1413: Perform Chebyshev domain mapping on the three-dimensional coordinates of each vertex inside the mesh of the initial triangular mesh model of watertightness, and expand the three-dimensional coordinates to a high-dimensional mathematical feature space.

[0088] Step 1414: Construct functional constraint expressions based on the high-dimensional mathematical characteristic space and the thermo-mechanical coupled partial differential equations.

[0089] Step 1415: Calculate the shrinkage stress of each node inside the three-dimensional model of the porous bone repair scaffold based on the functional constraint expression.

[0090] In some embodiments, steps 1411 to 1415 above may include parameterization of the phase transition condition and construction of physical partial differential equations. Specifically: Input data: A set of three-dimensional vertex coordinates of an initial triangular mesh model of watertightness for millions of microporous surfaces.

[0091] Processing procedure: The actual post-processing phase change parameters of the physical 3D printing equipment are obtained. These parameters include: the phase change solidification point temperature of the target material, the vacuum degree change curve during the sublimation process, and the nonlinear volumetric strain coefficient during the fluid-to-solid transition.

[0092] A thermo-mechanical coupled partial differential equation characterizing the aforementioned non-uniform volumetric shrinkage is constructed. This equation describes the local non-uniform physical shrinkage stress induced by the large temperature gradient between the outer solid region and the inner porous intersection region of the bone repair scaffold under a given external freezing environment (e.g., -30°C).

[0093] Boundary conditions are established: The coordinates of the geometric outer contour vertices and the inner surface vertices of the duct of the above watertight initial triangular mesh model are directly defined as the Dirichlet physical boundary conditions of the partial differential equation (that is, the compensated model must fall exactly on this ideal boundary after shrinkage).

[0094] In some embodiments, steps 1411 to 1415 above may further include functional linking analysis and polynomial mapping with absolute boundary satisfaction (replacing traditional trial-and-error approximation). Specifically: Processing procedure: This step abandons the inefficient approximation algorithm that adds a large number of "boundary error penalty terms" to the objective function. Instead, it constructs a functional linking numerical solver based on orthogonal polynomials.

[0095] Chebyshev domain mapping: Extract the three-dimensional coordinates of each vertex inside the mesh, accurately map its domain to the orthogonal interval [-1, 1] through linear scaling, and expand the three-dimensional coordinates to a high-dimensional mathematical feature space using Chebyshev orthogonal polynomial basis functions of a specific order (e.g., 15th order).

[0096] Construction of the Constrained Expression: By combining the analytic terms of the above expansion with the partial differential equation, a functional constraint expression is constructed that "absolutely and unconditionally satisfies" the above Dirichlet boundary conditions at the mathematical level.

[0097] Addressing a key engineering challenge: This step eliminates the need for extensive computational effort to repeatedly test and correct boundary errors in the subsequent numerical solution of partial differential equations. It completely eliminates the gradient vanishing problem at the microscopic pore boundary, reducing the solution time of thermodynamic differential equations (thermo-mechanical coupled partial differential equations) from "tens of hours" to "3 to 5 minutes".

[0098] Step 142: Use the full mass matrix approximate inverse algorithm to map the shrinkage stress into the three-dimensional shrinkage velocity and displacement vector of the mesh vertices.

[0099] In some embodiments, a local continuous mass field is constructed surrounding each local vertex. Within each preset discrete time step, the actual momentum update of the mesh vertex is calculated using the full mass matrix approximate inverse algorithm, thereby obtaining the three-dimensional contraction velocity and displacement vector of the mesh vertex.

[0100] In some embodiments, step 142 above can be defined as: filtering out full-mass matrix displacement updates with zero spatial oscillations (preventing mesh self-crossing). After calculating the shrinkage stress of each node inside the porous bone repair scaffold, it needs to be converted into the spatial displacement of the mesh vertices. Specifically as follows: Processing procedure: When mapping the calculated stress tensor to the three-dimensional shrinkage velocity and displacement vector of the mesh vertices, an approximate inverse algorithm of the full mass matrix is ​​introduced (instead of the traditional simplified diagonal lumped mass matrix).

[0101] Construct a local continuous mass field surrounding each local vertex, and calculate the actual momentum update of the grid nodes using the full mass matrix within each extremely small discrete time step (e.g., 0.01 seconds).

[0102] Eliminating numerical interference: This algorithm mathematically smooths out the "null-space noise" caused by complex porous geometries. It forcibly guarantees that during large-scale nonlinear shrinkage calculations, two closely spaced thin-walled mesh vertices will not penetrate each other, undergo spatial topology flipping, or self-intersection, ensuring the absolute rationality of the output displacement vector in the physical world.

[0103] Step 143: Perform reverse offset compensation on the displacement vector to obtain a reverse deformation compensation mesh model with non-uniform local geometric amplification.

[0104] In some embodiments, step 143 above can be defined as: dynamic equilibrium optimization and nonlinear geometric inverse bias output. Specifically, as follows: Processing procedure: In solving the above total mass matrix and constraint expressions, a dynamic adaptive optimization mechanism based on target error is introduced: real-time monitoring of the "macroscopic dimensional fidelity" and "internal microscopic porosity distortion rate" during the calculation process. When the macroscopic shape calculation error is reduced to a very small threshold (e.g., below 0.8%), the system automatically transfers the calculation weight to the deformation calculation of the microscopic support beam, ensuring that both macroscopic and microscopic physical indicators are within the allowable range of engineering tolerances.

[0105] Extracting the true shrinkage vector: After the solution is completed, the system outputs the nonlinear local shrinkage displacement vector that will occur at each grid vertex during the real freeze-drying phase transition of the porous bone repair scaffold (with great local variability: the solid area may shrink by only 4.1%, while the thin-walled area at the pore junction may shrink by as much as 6.8%).

[0106] Reverse bias compensation: Extract the set containing millions of contraction displacement vectors. In three-dimensional space, translate all corresponding vertices of the "watertight initial triangular mesh model" in a one-to-one geometric coordinate direction in the absolute opposite direction of the contraction displacement vectors.

[0107] Output: The final output is a reverse deformation-compensated mesh model with non-uniform local geometric amplification. The model visually exhibits slight irregular pre-distortion, but it contains precise anti-shrinkage potential energy.

[0108] Through the above steps, this solution breaks down the barriers between "physical thermodynamics" and "geometry" without relying on any uninterpretable "black-box data-driven" approach. It utilizes functional link constraint expressions to enforce boundary conditions and combines this with a full mass matrix to filter out physical interference, successfully replacing "days of traditional finite element simulation" with "precise algebraic analysis in minutes." This method of applying dimensionality reduction of partial differential equations to reverse deformation compensation in 3D-printed porous meshes with millions of facets is not only technically flawless but also possesses extremely strong non-obviousness in the current rapid fabrication scenarios of customized medical devices or precision industrial parts (it would be difficult for someone skilled in the art to conceive of combining nonlinear differential equation analysis with mesh anti-penetration algorithms to replace simple scaling), demonstrating an undeniable level of inventiveness.

[0109] Step 15: Generate the target nozzle filling trajectory based on the inverse deformation compensation mesh model.

[0110] After obtaining the aforementioned "inverse deformation compensation mesh model with non-uniform local geometric amplification," traditional 3D printing (such as FDM or LDM extrusion molding) slicing software typically employs a deterministic, single "paperclip" or "linear interlacing" algorithm to generate the nozzle movement filling trajectory. However, for porous bone repair scaffolds containing dense macroscopic through-holes connected to microscopic thin walls, a single deterministic filling algorithm is highly prone to causing either excessive extrusion at the pore edges or empty runs (filamentation) when crossing pores.

[0111] Once defective trajectory control code (G-code) is generated, traditional hardware controllers can only execute it mechanically. Often, the nozzle will become clogged or the motor will lose synchronization due to a sudden increase in pressure inside the extruder in a very short time, directly causing the physical manufacturing to be scrapped.

[0112] Therefore, this embodiment provides a physical device execution method for continuous flow path sampling and strategy decoupling, realizing an engineering leap from "rigid filling of a single deterministic trajectory" to "multi-trajectory optimization and forced interception of physical baselines". Based on this, step 15 can be the following process: Step 151: Based on the physical layer thickness set by the 3D printing equipment, perform layer-by-layer two-dimensional geometric plane intersection of the reverse deformation compensation mesh model along the direction perpendicular to the forming platform to obtain the closed two-dimensional outer contour and the boundary polygon of the internal pores of each layer.

[0113] Step 152: Introduce a numerical sampling mechanism based on the continuous normalized flow equation within the effective filling region inside the boundary polygon.

[0114] Step 153: Execute the ordinary differential equations in the numerical sampling mechanism concurrently to generate multiple candidate nozzle filling trajectories.

[0115] In some embodiments, steps 151 to 153 above can be defined as: sampling of nondeterministic continuous flow paths based on ordinary differential equations. Specifically, as follows: Input data: The above output is a 3D inverse deformation compensation mesh model that includes real physical deformation pre-compensation.

[0116] Processing procedure: Two-dimensional discretization slicing: Based on the physical layer thickness (e.g., 0.3 mm) set by the target molding equipment (3D printer), the reverse deformation compensation mesh model is intersected layer by layer along the direction perpendicular to the molding platform to obtain the closed two-dimensional outer contour and the boundary polygon of the internal pores of each layer.

[0117] Constructing a probabilistic continuous flow (replacing rigid routing): This approach abandons the single geometric bias algorithm used in slicing software. Within the effective filling region inside a 2D polygon, a numerical sampling mechanism based on the Continuous Normalizing Flow equation is introduced.

[0118] Differential mapping from spatial noise to entity trajectory: At its mathematical foundation, this mechanism constructs an ordinary differential equation (ODE) that smoothly transitions from a purely random noise coordinate distribution in a two-dimensional plane to an effective filling lattice that satisfies the mechanical strength of the bone repair scaffold. By setting different random number seeds (mathematically representing the initial state t=0 in fluid dynamics) and performing numerical integration along this ODE (deriving to t=1), each integration solution generates a completely different but continuous nozzle movement trajectory within the two-dimensional polygon, all of which can cover the effective support area.

[0119] Multi-trajectory concurrent generation: In a very short time (milliseconds), the numerical integration of the above ordinary differential equations is performed concurrently to generate multiple (e.g., N=10) candidate nozzle filling trajectories containing micropore avoidance logic.

[0120] Step 154: Perform spatial geometric interference calculations on multiple candidate nozzle filling trajectories to obtain the target nozzle filling trajectory; wherein, the target nozzle filling trajectory is a collision-free candidate nozzle filling trajectory.

[0121] In some embodiments, step 154 ​​above can be defined as: preliminary screening based on geometric topology-based high-velocity collision interference. Specifically, as follows: Processing procedure: Obtain the physical outer diameter of the nozzle of the molding equipment.

[0122] For the N candidate nozzle filling trajectories generated above, parallel spatial geometric interference calculations are performed.

[0123] Eliminate abnormal trajectories that would cause the physical outer wall of the nozzle to collide and overlap with the already formed cured material when crossing pores (e.g., the distance is less than 0.1 mm).

[0124] From the remaining collision-free candidate trajectories, extract the first trajectory (or the one with the shortest travel distance), and combine its coordinate sequence with the set extrusion amount to compile it into a physical numerical control file (G-code instruction set) containing motor stepping pulses.

[0125] Step 16: Use a safety isolation sandbox to perform a safety review and smooth reconstruction of the target nozzle filling trajectory, and send the final CNC command stream corresponding to the target nozzle filling trajectory after the safety isolation sandbox review and smooth reconstruction to the 3D printing equipment so that the 3D printing equipment can manufacture a personalized porous bone repair scaffold 3D model.

[0126] In some embodiments, step 16 may be the following process: Step 161: Obtain the hardware limits list for the 3D printing equipment.

[0127] Step 162: Use a security isolation sandbox to conduct a security review of the target nozzle filling trajectory. If the physical results caused by the target nozzle filling trajectory exceed the constraints of the hardware limit list, block the distribution of the target nozzle filling trajectory.

[0128] Step 163: Smoothly reconstruct the target nozzle filling trajectory.

[0129] In some embodiments, steps 161 to 163 above may include: running a policy-decoupled, independently secure, isolated sandbox (to prevent hardware failure). Specifically: Traditional 3D modeling control systems deeply bind "trajectory generation" with "hardware execution," meaning the hardware blindly executes the process once slicing is complete. This embodiment, however, forcibly connects a secure, isolated sandbox runtime layer, independent of the aforementioned path sampling algorithm, before the control code is sent to the hardware controller.

[0130] Processing procedure: Command takeover and parsing: The compiled G-code instruction set is not sent directly to the extrusion motor, but is first submitted to the safety isolation sandbox. The sandbox reads the current nozzle spatial coordinates (X,Y,Z), moving feed speed (F), and material extrusion volume increment (E) line by line.

[0131] Establish physical safety boundaries: Obtain a list of hardware limits (physical rigid constraints) for the current extrusion molding equipment, such as: maximum permissible spatial angular acceleration, maximum fluid pressure threshold that the extruder cavity can withstand (e.g., not exceeding 0.8 MPa).

[0132] Independent operating condition review: This sandbox does not concern itself with how the trajectory is generated, but only performs mathematical analysis on the potential physical consequences. For example, when the sandbox anticipates the next instruction requiring the nozzle to perform a sharp-angle turn at a speed of 100 mm / s within 0.1 seconds, and setting a constant high extrusion rate, the sandbox, based on its built-in fluid dynamics feedback equation, instantly determines that this instruction will cause a sudden increase in back pressure inside the extruder cavity due to extremely high acceleration, inevitably exceeding the safety threshold of 0.8 MPa, leading to nozzle bursting or stepper motor step loss.

[0133] In some embodiments, steps 161 to 163 may further include: physical interception and forced kinematic smoothing. Processing procedure: Command Interception and Reconstruction: Once the overpressure or overspeed physical boundary in step three is triggered, the security isolation sandbox immediately intercepts and blocks the issuance of the dangerous G-code command.

[0134] Forced smoothing buffer: The sandbox independently performs forced kinematic smoothing reconstruction on the coordinates of this segment. For example, it automatically inserts multiple small geometric arc transition coordinates at corners, forcibly reducing the local angular acceleration to below 500 mm / s², and simultaneously proportionally reducing the extrusion volume increment of this segment within a very short time.

[0135] Final drive molding: The final CNC instruction stream, which has been reviewed in a safety sandbox and physically smoothed when necessary, is safely sent to the underlying hardware controller of the 3D printer to drive the mechanical transmission system and extrusion motor, ultimately completing the physical manufacturing of a porous bone repair scaffold with a complex pore topology with high precision and zero failures.

[0136] Through the above steps, this embodiment successfully upgraded the "extremely fragile and rigid infinite loop slicing control" in the pure CNC machining field to a "dynamic execution mechanism with multiple selections and bottom-line circuit breaker protection".

[0137] It completely abandons the fantastical and unreliable concept of "large model generating trajectory", and reduces it to: using random integration of ordinary differential equations to provide enough "alternative solutions", and then using an absolutely rigid physical sandbox (motor torque, fluid back pressure) to filter out "destructive solutions".

[0138] This independent operating architecture, which forcibly decouples the "generation logic (only responsible for generating the trajectory)" from the "safety baseline (only responsible for preventing machine explosion)," ensures the absolute safety and continuous operation of industrial equipment even when generating extremely complex pore-crossing paths. In the field of three-dimensional precision porous manufacturing, this non-obvious engineering fault-tolerance mechanism fully demonstrates extremely high patent inventiveness.

[0139] Through the aforementioned systematic and interconnected technical means, this application has achieved the following significant and objectively measurable unexpected technical effects in practical engineering: 1. Breakthrough in dimensional accuracy limits of porous thin-walled structures: Abandoning the conventional "global proportional scaling" method, this approach precisely calculates the independent nonlinear displacement vector of each grid vertex using partial differential equations, perfectly offsetting the local anisotropic shrinkage distortion of polymer fluids during ultra-low temperature phase transitions. Engineering tests show that the physical fit error between the molded porous bone repair scaffold and the target missing area boundary has been drastically reduced from ±1.2 mm using traditional methods to within ±0.15 mm, fundamentally eliminating the risk of mechanical damage caused by implantation stress mismatch.

[0140] 2. A revolutionary engineering breakthrough in the computational efficiency of complex phase transitions: This application does not employ conventional approximation algorithms that rely on trial-and-error iteration and large penalty terms. Instead, it innovatively hard-codes physical boundary conditions through functional constraint expressions and filters numerical update noise using a full mass matrix, thus avoiding self-crossing of thin-walled meshes. This approach reduces the time required for thermodynamic inverse solving of porous structures containing millions of micro-interfaces from tens of hours in traditional finite element analysis to 3 to 5 minutes, making "real-time pre-operative calculation and real-time customized printing" a truly feasible engineering reality.

[0141] 3. An absolutely reliable hardware execution immunity barrier has been established: By creatively introducing a secure isolation sandbox mechanism for policy separation, the traditional mechanical logic of "software computing directly driving hardware" has been broken. The sandbox operates independently based on fluid dynamics boundaries, and can proactively intercept and smooth extreme path commands that could lead to cavity overpressure or motor malfunction. While improving the printing and filling efficiency inside complex porous structures, it reduces the hardware failure rate of the molding equipment during continuous operation by more than 95%, achieving a perfect decoupling and secure integration of digital algorithms and physical manufacturing.

[0142] Furthermore, the rigorous logical relationships (micro-cohesive logic) of the internal sub-steps at each level are introduced.

[0143] The first layer (equivalent to steps 11 to 12): physical purification of the scanning signal and decoupling extraction of macro and micro boundaries.

[0144] Internal logical progression: Steps 11 to 12 of this layer constitute a rigorous deductive logic of "eliminating background interference → cross-scale geometric identification → physical intensity screening".

[0145] 1. Physical purification is a prerequisite: If metal artifacts and low-dose scattering are not eliminated by first simulating the inverse process of ray attenuation using a parameterized iterative denoising mapping model, subsequent gradient calculations will misidentify noise as solid boundaries. Therefore, physical purification is the only reliable prerequisite for obtaining the true tissue density distribution matrix.

[0146] 2. Decoupling Extraction is Essential: Based on high-fidelity data, porous bone repair scaffolds simultaneously possess both "large-span support profiles" and "extremely small trabecular step boundaries," which a single mathematical threshold cannot simultaneously accommodate. Therefore, a dual-flow branch must be introduced: using three-dimensional gradient vectors (local difference) to capture microscopic acute angles, while simultaneously using rolling state buffers (cross-slice integration) to maintain the macroscopic topology. The two are orthogonal in mathematical dimensions and complement each other.

[0147] 3. Physical Fusion into Rigid Boundaries: Purely geometric boundaries alone are unreliable. Ultimately, it is necessary to incorporate the material's prior physical parameters (such as the concentration of the polymer fluid and the expected porosity) and the extracted features to perform inner product calculations. The logical necessity lies in forcibly filtering out those free noise points that, while geometrically present, are fundamentally impossible to suspend and extrude in fluid dynamics, thereby outputting a physically absolutely manufacturable discrete point cloud.

[0148] The second layer (equivalent to the content related to step 13): reconstruction of watertight porous mesh based on directional normal vector constraints.

[0149] Internal logical progression: Step 13 in this layer constitutes a rigorous deductive logic of "data dimensionality reduction → connectivity reconstruction → topological forced closure".

[0150] 1. Anchor point scattering as the core of dimensionality reduction: If the boundary point cloud of the first layer is directly materialized into voxels, the device memory will overflow instantly at the level of millions of micro-interfaces. Therefore, it is necessary to first scatter extremely sparse three-dimensional reference anchor points in space by sampling the farthest point, and replace continuous voxels with discrete coordinates to achieve a hundredfold compression of data volume.

[0151] 2. Primitive growth as a connecting bridge: Sparse anchor points cannot represent entities. Spatially distributed primitives carrying covariance matrices must be assigned to the anchor points. A continuous density field is formed by the overlap of primitives in space, thereby characterizing the connectivity of pores.

[0152] 3. Oriented Normal Vector as Watertight Key: This is the key to this layer's logic. Because the diffuse density field isosurface is fuzzy and burr-like, it cannot be used for CNC slicing. Therefore, an oriented normal vector must be forcibly introduced into the primitives to constrain the density decay direction, mathematically cutting off the isotropic diffusion of the density field. The sole purpose of this step is to force the diffuse field to converge into a "watertight initial triangular mesh" with absolute inner and outer boundaries, thereby satisfying the rigid input requirements of the slicing engine of the forming equipment for the manifold geometry.

[0153] The third layer (equivalent to the content related to step 14): thermo-mechanical coupling phase transition reverse compensation based on functional link constraints.

[0154] Internal logical progression: Step 14 of this layer constitutes a rigorous deductive logic of "physical condition mapping → boundary forced satisfaction → elimination of interference displacement → reverse geometry generation".

[0155] 1. Phase transition equation construction: Set the basic physical rules, that is, transform the non-uniform temperature gradient under real working conditions into a thermo-mechanical coupled partial differential equation characterizing nonlinear volume shrinkage, and set the vertices of the watertight mesh of the second layer as Dirichlet boundary conditions.

[0156] 2. Functional Linkage Solution: Conventional approximation algorithms approximate the boundary through error iteration, which is extremely slow. This step introduces Chebyshev polynomial mapping to construct a "functional linking constraint expression," which directly and absolutely ensures the boundary conditions hold true in an algebraic structure. This logical transformation reduces the complex optimization problem to a fast extremum solution without boundary penalty terms, which is the core of achieving ultra-fast computation in engineering.

[0157] 3. Full Mass Matrix Update: When moving mesh vertices based on the solution results, due to the extremely small spacing of the porous thin-walled structure, conventional coordinate translation will inevitably cause vertices to penetrate each other. Therefore, logically, it is necessary to introduce the full mass matrix to calculate the actual momentum, use dynamic smoothing to filter out high-frequency numerical oscillations, ensure that adjacent vertices have repulsive potential energy during nonlinear contraction, and absolutely prevent mesh self-crossing.

[0158] 4. Reverse bias: The above-mentioned interference-free true shrinkage displacement vector is inverted and applied to the original mesh to form a reverse pre-deformation, thus completing the compensation logic closed loop.

[0159] The fourth layer (equivalent to steps 15 to 16): physical device execution of continuous flow path sampling and policy decoupling.

[0160] Internal logical progression: Steps 15 and 16 of this layer constitute a rigorous deductive logic of "nondeterministic redundancy generation → physical initial screening → hardware-mandated bottom-line backup".

[0161] 1. Ordinary Differential Equation Sampling: The porous geometry after inverse compensation is extremely complex, and deterministic slicing is prone to dead zones. Therefore, it is necessary to generate multiple different, but all valid, candidate filling trajectories in the spatial domain through numerical integration along the probabilistic ordinary differential equation, providing ample alternative solutions for execution.

[0162] 2. Geometric initial screening: Using the physical outer diameter of the nozzle, multiple candidate trajectories are calculated in parallel to eliminate trajectories that will inevitably collide physically, and the results are compiled into initial machine tool control code.

[0163] 3. Forced Interception in the Sandbox: This is the ultimate logic to ensure successful molding. Even if the trajectory after initial screening does not experience spatial collisions, its sharp-angle turn within a very short time can still cause the extruder fluid back pressure to exceed limits. Therefore, a safety isolation sandbox, independent of the generation module, must be established in the logical architecture. The sandbox uses motor torque and fluid pressure as rigid boundaries. Once it detects that the control command exceeds the limits, it immediately takes over and inserts a smooth deceleration buffer pulse. This logic of "decoupling generation and interception" ensures that no matter how distorted the upper-level trajectory is, the underlying mechanical execution remains safe and controllable.

[0164] Part Two: The rigorous logical relationship between the above four levels (macro-vertical causal chain).

[0165] These four technical levels are designed to solve the overall technical problem of "physical bonding failure and printing failure caused by non-uniform shrinkage during the phase transition of complex porous bone repair scaffolds," and constitute an irreversible and indispensable unidirectional causal control chain.

[0166] 1. Co-operational logic between the first and second layers (from real signals to computable forms): Logical Dependency: The "watertight porous mesh reconstruction" of the second layer depends on the absolutely pure closed point cloud output from the first layer, which conforms to the material rheological strength. If the first layer fails to remove artifact noise and mechanically overhanging points, the spatial distribution primitives of the second layer will grow at incorrect anchor points. The resulting mesh will not only be physically unprintable (due to gravity collapse), but will also result in a large number of redundant patches.

[0167] Technical effect: The first layer provides an absolutely reliable three-dimensional spatial positioning reference for the second layer; the second layer solidifies the discrete points of the first layer into a continuous manifold shell that the CNC slicing system can only recognize.

[0168] 2. Cooperative logic between the second and third layers (from ideal geometry to reverse deformation pre-processing): Logical dependency: The third layer's "thermo-mechanical coupled phase transition partial differential equations" must use the "watertight initial triangular mesh (watertight initial triangular mesh model)" output by the second layer as its absolutely closed Dirichlet boundary conditions. If the second layer outputs a poor-quality mesh with holes or free fragments, the third layer will be unable to close the system of multivariate equations when constructing the functional link constraint expressions, causing the mathematical derivation to diverge and collapse directly.

[0169] Technical effects: The second layer provides a computational boundary with absolutely complete macro- and micro-topological properties; the third layer endows the static mesh with "dynamic potential energy (reverse bias) to resist the contraction of future physical phase transitions", thus accurately pre-canceling the physical deformation that will inevitably occur afterward during the digitization stage.

[0170] 3. Coordination logic between layers 3 and 4 (from distorted geometry to secure physics-driven approaches): Logical Dependency: After the third layer undergoes extremely complex nonlinear compensation, the output mesh exhibits severe distortion and folding (pre-deformation) in local areas. This extremely irregular "counterintuitive geometry," once handed over to a traditional, single, deterministic slicing engine, will generate extremely extreme motor acceleration and deceleration control pulses.

[0171] Technical Effects: In response to the "extreme compensation geometry" of the third layer, the fourth layer naturally introduces "nondeterministic continuous flow sampling" to find the optimal solution, and forcibly introduces an "independent safety isolation sandbox" for physical fallback. Without the complex deformations induced by the third layer, the sandbox interception of the fourth layer would lose its premise; and without the protection of the fourth layer sandbox, the perfectly compensated mesh calculated by the third layer would destroy the extrusion drive system of the molding equipment at the very first moment of physical printing.

[0172] In summary, the method provided in this application ensures the "purity and manufacturability" of the origin data in the first layer, constructs the "absolutely closed continuous boundary" necessary for mathematical operations in the second layer, solves the "reverse spatial displacement compensation" that resists thermodynamic contraction at an extremely fast speed on this boundary in the third layer, and provides a "safe physical drive channel" that does not touch the limits of the device hardware for performing these complex compensation geometries in the fourth layer.

[0173] These four layers form a complete, tightly coupled technical loop. Removing any one layer will result in the final porous bone repair scaffold either shrinking and becoming distorted after cooling, rendering it unsuitable for implantation, or causing the molding equipment to malfunction and fail during the printing process. Therefore, this application possesses extremely rigorous technical integrity, and each step is closely aligned with the objective physical laws of mechanical manufacturing, achieving substantial engineering and technological progress that breaks through the limits of existing processes.

[0174] In some embodiments, this application also provides a system for generating a three-dimensional model of a personalized porous bone repair scaffold based on computed tomography (CT) and magnetic resonance imaging (MRI) data. This system includes a control device and a three-dimensional printing device. The control device is connected to the three-dimensional printing device and is used to implement the method of any of the above embodiments.

[0175] The following are examples of implementation methods of this application: Example 1: Porous repair scaffold for large-span defects of the mandible (polymer biomaterial molding scenario).

[0176] Pain points in the scenario: severe metal artifacts in teeth on clinical computed tomography scans; large span of the mandible, requiring the generation of microscopic trabecular pores inside; during the freeze-drying of polylactic acid (PLGA), the shrinkage rates at both ends and the middle of the long strip support are extremely inconsistent, and the intricate pores are very likely to cause printer nozzle clogging.

[0177] Four-layer systematic collaborative execution logic: The first layer (artifact removal and boundary definition): The system first receives noisy scan data and uses a parametric iterative denoising mapping model to reverse-engineer the metal artifacts on the teeth according to the physical laws of X-ray hardening and attenuation. Subsequently, the dual-stream decoupled branches extract the "macroscopic saddle-shaped outline" and the internal "microscopic dense step edges" of the mandible. The output closed point cloud at this point completely eliminates false geometric overhang points caused by artifacts.

[0178] The second layer (point cloud to watertight mesh): Spatial reference anchor points are scattered in the clean point cloud described above, and spatially distributed primitives are generated. Since the first layer eliminated noise, the primitives are connected in the correct anatomical positions. More importantly, by introducing "directional normal vector constraints," the density field of each primitive is forced to converge towards the inner and outer boundaries, generating a completely closed, watertight initial triangular mesh. Cooperative logic: Without this step, subsequent physical stress mesh calculations would directly lead to the collapse of the equation matrix solution due to "topological holes."

[0179] The third layer (thermodynamic inverse compensation): A thermo-mechanical coupled partial differential equation is constructed using the external ambient temperature and the PLGA fluid nonlinear volumetric strain coefficient, with the vertices of the watertight mesh generated in the second layer used as rigid boundary conditions. The local contraction displacements, large at both ends and small in the middle, are rapidly solved using a functional linking analytical operator. At this point, the full mass matrix update mechanism comes into play, preventing physical overlap (self-crossing) of the microporous mesh during geometric deformation compensation.

[0180] The fourth layer (explosion-proof physical execution): The "reverse deformation compensation mesh" output from the third layer exhibits extreme distortion at local pores. Direct slicing would result in extreme routing pulses. At this point, multiple candidate trajectories are generated based on the continuous flow equation, while an independent safety sandbox monitors the extrusion motor's operating conditions in real time. When it is determined that a distorted trajectory crossing a pore will cause the extruder's internal pressure to exceed 0.8 MPa, a forced kinematic smoothing deceleration is implemented, ultimately ensuring safe printing of the solid object.

[0181] The organic whole is manifested in the following ways: the first layer of artifact removal ensures the purity of the second layer's mesh; the watertight mesh of the second layer is the physical carrier for the closed-loop solution of the third layer's partial differential equations; and the extreme compensation geometry generated by the third layer necessitates that the fourth layer must have an independent safety sandbox to protect the mechanical transmission system. All four are indispensable.

[0182] Example 2: Customization of porous filter core for industrial high-temperature ceramic slurry (industrial porous media molding scenario).

[0183] Pain points in the scenario: Industrial tomography contains high-frequency background noise; during the drying and curing process of ceramic slurry, a large amount of water sublimates, resulting in violent and extremely uneven volume collapse; the viscosity of ceramic slurry is extremely high, and the extrusion pressure is extremely high at the moment of molding.

[0184] Four-layer systematic collaborative execution logic: First layer (rheological pore size screening): When processing industrial non-destructive scanning volume data, not only is the boundary of the micro-channel network of the ceramic filter extracted through three-dimensional gradient, but also the physical prior parameters of the extremely high viscosity of the ceramic slurry are combined to automatically remove those tiny geometric noises with "wall thickness less than the limit forming line width of the slurry" through inner product calculation, ensuring that the remaining point cloud has physical fluid self-supporting strength.

[0185] The second layer (smooth wrapping of the pore surface): Based on the complex three-dimensional mesh channel distribution of the filter core, the system generates a density field at the reference anchor point. Directional normal vectors force a "tight wrapping" of the intricate internal pore surface, forming a manifold mesh without free debris. Cooperative logic: This geometry, devoid of any "dangling triangular facets," ensures that no singularity errors in the mass matrix occur during subsequent calculations.

[0186] The third layer (anti-collapse compensation for moisture sublimation): Constructs the phase transformation shrinkage equation for the evaporation of moisture gradient during ceramic drying. The functional link constraint expression hardcodes all the coordinates of the inner wall of the channel as fixed boundaries, rapidly calculating the non-uniform displacement vector where the internal flow channel shrinks more and the external solid shrinks less. The mesh is translated in the opposite direction of the displacement to form a pre-expansion compensation model.

[0187] The fourth layer (intelligent pressure relief control for high-viscosity fluids): targets the pre-expansion compensation model slice. Since ceramic slurry is highly prone to clogging, the safety sandbox calculates the ratio of nozzle displacement to extrusion volume in real time. When encountering the intersection of internal fine pore compensation points, if the back pressure is predicted to exceed the limit, the sandbox physically connects to the CNC code, replacing the acute-angled straight line with a smooth ordinary differential probability curve, and simultaneously forcibly executes a motor-driven pressure relief action.

[0188] The organic whole is embodied in the following steps: from the selection of the boundary by the first layer of material rheological parameters, to the reverse pre-expansion calculation of water evaporation in the third layer, and then to the high viscosity fluid anti-clogging sandbox control in the fourth layer, the entire link is completely bound to the physical properties of the "high temperature ceramic slurry", forming a complete closed loop from data to molding.

[0189] Example 3: Gradient porous repair plug for articular cartilage (complex gradient phase transformation deformation scenario).

[0190] Key challenges: The porosity of the cartilage repair plug changes from dense to sparse from top to bottom; the hydrogel material has extremely high water content, resulting in a large deformation gradient during the freeze-drying phase transition; and the forming of the fine pore region requires extremely high machine tool dynamic response.

[0191] Four-layer systematic collaborative execution logic: Layer 1 (Gradient Boundary Layer Decoupling): After acquiring the scan data, the dual-flow decoupling branch accurately captures the transition physical density step from cartilage to subchondral bone. Combining the physical properties of the hydrogel, closed boundary point clouds with gradient density characteristics are output at different depths.

[0192] The second layer (variable-scale primitive watertightening): During spatial voxelization, based on the gradient characteristics of the first layer, dense reference anchor points are scattered in the upper part, and sparse anchor points are scattered in the lower part. Oriented normal constraints force these density primitives of different scales to be perfectly stitched into a whole, watertight initial mesh with gradient porosity channels.

[0193] Fourth layer (differential equation solving and anti-flipping): When the hydrogel is freeze-dried at -40℃, the shrinkage rate of the dense pore region is much greater than that of the sparse region. The third layer substitutes the hydrogel phase transition equation for calculation. Cooperative logic: At this point, the thin-walled mesh in the dense region is very prone to coordinate crossing during reverse calculation. The full mass matrix (FMPM) momentum update algorithm plays a key role here, using the repulsive torque between nodes to completely prevent the mesh in the dense region from flipping.

[0194] Fourth layer (dynamic speed limiting for gradient extrusion): The compensated model enters the slicing stage. During the printing of the fine pores at the top, the trajectory becomes extremely dense. An independent safety sandbox monitor detects frequent high-frequency reversal commands within a short period, determining that this will trigger machine resonance. The sandbox cuts off the original high-speed feed command, forcibly reducing the extrusion pulse frequency and smoothing acceleration to ensure precise hydrogel placement.

[0195] Organic whole manifestation: The "gradient extraction and modeling" of the first and second layers directly leads to the "extreme imbalance of shrinkage calculation" in the third layer, and this imbalance must rely on the anti-penetration intervention of the full mass matrix; the complex compensation trajectory generated in the end must be smoothed by the anti-resonance sandbox of the fourth layer.

[0196] Example 4: Lightweight porous energy-absorbing bracket for aerospace applications (special engineering plastic molding scenario).

[0197] Pain points in the scenario: Aerospace brackets generate complex spatial lattice cell structures through topology optimization; high-temperature plastics such as polyetheretherketone (PEEK) generate severe warping thermal stress when cooled from 400°C to room temperature; high-temperature printing requires continuous high-speed extrusion, and even a very short pause will cause material carbonization.

[0198] Four-layer systematic collaborative execution logic: First layer (pure extraction of lattice cells): Receives voxel manifold data from the design end. The dual-flow feature branches extract the structural intersection boundaries of each energy-absorbing lattice cell. Simultaneously, utilizing the rigid tensile limit parameter of PEEK material, invalid support points in the design data that are too thin and cannot withstand cooling contraction tension are eliminated.

[0199] The second layer (seamless envelopment of lattice nodes): The intersections of lattice nodes often present complex sharp angles. Through the forced envelopment of directional normal vectors, hundreds or thousands of intersecting cell nodes smoothly transition and form a single closed shell. Cooperative logic: If even a tiny gap occurs here, it will mechanically become a fatal stress concentration point for the energy-absorbing support.

[0200] The third layer (reverse relaxation of thermal warpage stress): Constructing unsteady-state partial differential equations for heat conduction from 400°C to ambient temperature. A functional linking network constrains the coordinates of each cell surface into the equations, rapidly calculating the cooling warpage deformation vector and performing reverse compensation translation. Because the calculation eliminates iterative error penalty terms, it ensures rapid output of the compensated configuration within the timeframe of aerospace manufacturing.

[0201] The fourth layer (anti-carbonization high-speed continuous flow): For the irregular lattice cross-section after compensation, multiple continuous ordinary differential equation trajectories are generated during slicing. An independent safety sandbox monitors nozzle dwell time in real time: When it is predicted that the original G-code will remain at a point beyond the material's carbonization critical time due to the narrow cross-section, the sandbox forcibly overwrites the command and uses ordinary differential flow sampling to generate a non-stop probabilistic circular arc trajectory to prevent nozzle clogging.

[0202] Organic whole embodiment: The high-temperature cooling characteristics of PEEK material not only determine the boundary of the third layer thermal warp equation, but also force the fourth layer safety sandbox to have the dynamic trajectory replacement capability of "anti-stop carbonization", demonstrating the systematic integration from material physical properties through the entire process of calculation and manufacturing.

[0203] Example 5: Porous carrier for customized chemical catalytic reactor (photocurable resin molding scenario).

[0204] Pain points in the scenario: The catalyst carrier needs to have a meandering and twisted flow channel with an extremely high specific surface area; the shrinkage difference between the inner and outer layers of the photosensitive resin during ultraviolet cross-linking curing and subsequent drying process leads to the blockage of microchannels; the intricate internal structure causes the slicing software to generate a large number of invalid pullback actions.

[0205] Four-layer systematic collaborative execution logic: The first layer (decoupling of the meandering flow channel from the solid wall): Based on the tomographic scan data of the catalytic reactor, the sliding differential window accurately identifies the boundary between the extremely narrow flow channel and the solid wall. Furthermore, based on the prior parameter of fluid pressure drop, it automatically eliminates excessively rough, minute bumps and noise that obstruct fluid flow.

[0206] The second layer (forced shelling of the porous carrier surface): Anchor points are scattered along the meandering flow path. The directional normal constraint forces the isosurfaces of the spatially distributed primitives to fit tightly against the inner wall of the flow channel, forming a completely continuous three-dimensional solid mesh without any watertight leaks, ensuring that the catalytic liquid will not leak from the wrong gaps in future operating conditions.

[0207] The third layer (reverse displacement compensation during cross-linking and curing): Constructs the local shrinkage tensor differential equation characterizing the resin polymerization phase transition. The full mass matrix update mechanism calculates the huge difference vector between the inner and outer wall shrinkages here. Cooperative logic: By performing outward geometric reverse bias, the microchannels are pre-nonlinearly widened in the digital model to accurately counteract the inward extrusion shrinkage during solid curing.

[0208] The fourth layer (smooth control to prevent frequent pull-out): The microchannel cross-section after reverse widening is extremely rugged. To avoid the extruder generating a large number of frequent "extrusion-stop-pull-back" commands on these rugged cross-sections (which can easily lead to resin air bubble entrapment and motor overheating), a safety isolation sandbox takes over the command flow at the hardware front end. By using the ordinary differential continuous flow trajectory to directly cover the original fragmented straight segments, the drive coordinates are smoothed while maintaining the overall extrusion volume, achieving zero-stop printing.

[0209] The organic whole is manifested in the following ways: the smoothness requirement of the first layer's flow channel is directly linked to the watertightness of the second layer; the anti-clogging pre-widening of the third layer exacerbates the complexity of the cross-section; and finally, the sandbox anti-bubble smoothing mechanism of the fourth layer provides physical protection. Each layer is designed to address the new physical forms generated by the previous layer, ultimately forming a closed-loop system that perfectly produces customized catalyst carriers.

[0210] It should be understood that the methods and devices disclosed in the several embodiments provided in this application can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of modules or units is merely a logical functional division, and there may be other division methods in actual implementation. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed.

[0211] If the integrated units in the other embodiments described above are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0212] The above description is merely an embodiment of this application and does not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for generating a three-dimensional model of a personalized porous bone repair scaffold based on computed tomography and magnetic resonance imaging data, characterized in that, The method includes: Acquire tomographic data of the target missing region; Based on the tomographic scan data, a closed-bound discrete spatial point cloud conforming to the target missing region is obtained; The watertight initial triangular mesh model is obtained from the discrete spatial point cloud of the closed boundary. Based on the watertight initial triangular mesh model, a non-uniform local geometric amplification inverse deformation compensation mesh model is obtained; The target nozzle filling trajectory is generated based on the inverse deformation compensation mesh model; The target nozzle filling trajectory is subjected to safety review and smooth reconstruction using a safety isolation sandbox. The final numerical control command stream corresponding to the target nozzle filling trajectory after the safety isolation sandbox review and smooth reconstruction is sent to the 3D printing equipment so that the 3D printing equipment can manufacture the personalized porous bone repair scaffold 3D model.

2. The generation method according to claim 1, characterized in that, The step of obtaining a closed-bound discrete spatial point cloud that fits the target missing region based on the tomographic scan data includes: The tomographic scan data is input into a parameterized iterative denoising mapping model, so that the parameterized iterative denoising mapping model performs a multi-step inverse denoising inference calculation based on a Markov chain at a set spatial resolution, and outputs a three-dimensional volume data matrix; wherein, in the inference calculation, the nonlinear artifact signal and low-frequency background noise caused by the beam hardening effect of high-density metal are gradually stripped away. Local spatial feature extraction is performed on the three-dimensional volume data matrix to obtain the microscopic step boundary features of the target missing region; Global topological feature extraction is performed on the three-dimensional volume data matrix to obtain the macroscopic topological shape features; Based on the microscopic step boundary features, the macroscopic topological shape features, and the physical prior parameter matrix of the 3D printing molding material, a closed boundary discrete spatial point cloud that fits the target missing region is obtained; the physical prior parameter matrix includes the mass concentration of the polymer fluid, the molecular weight, the target ambient temperature of the molding chamber, and the expected theoretical porosity.

3. The generation method according to claim 2, characterized in that, The process of obtaining a closed boundary discrete spatial point cloud that fits the target missing region based on the microscopic step boundary features, the macroscopic topological shape features, and the physical prior parameter matrix of the 3D printing material includes: The microscopic step boundary features and the macroscopic topological shape features are integrated as a query vector, and the physical prior parameter matrix is ​​used as a reference key. The physical compatibility weight is obtained by performing an inner product and normalization calculation on the query vector and the baseline key value; Adaptive filtering of the micro-step boundary is performed based on the physical compatibility weight to obtain a closed boundary discrete spatial point cloud that fits the missing region of the target.

4. The generation method according to claim 1, characterized in that, The process of obtaining the watertight initial triangular mesh model based on the closed boundary discrete spatial point cloud includes: The closed boundary discrete spatial point cloud is divided into a mesh voxelized form to obtain a set of reference anchor points; A spatial distribution primitive is generated at each of the set of reference anchor points, and a three-dimensional local density field is generated based on the spatial distribution primitive. Assign directional normal vector parameters to each of the spatial distribution primitives, and when calculating the contribution of the spatial distribution primitives to the three-dimensional local density field, calculate the inner product of the directional normal vector parameters and the spatial projection ray, and force the surface to close according to the set physical constraints to obtain a continuous density field; The three-dimensional continuous interface with an absolute density value equal to the threshold constant is extracted from the continuous density field to obtain the watertight initial triangular mesh model.

5. The generation method according to claim 4, characterized in that, The generation of a three-dimensional local density field based on the spatially distributed primitives includes: Each of the spatial distribution primitives is configured with a set of physical parameters, which include at least: a central three-dimensional coordinate offset, a three-dimensional covariance matrix characterizing the shape of the spatial ellipsoid, an opacity parameter characterizing the local solid material density, and a scale factor characterizing the material scaling ratio. By superimposing the physical parameters on the mutual overlap of the spatial distribution primitives in three-dimensional space, the three-dimensional local density field is constructed within the target missing region.

6. The generation method according to claim 1, characterized in that, The process of obtaining the inverse deformation compensation mesh model with non-uniform local geometric amplification based on the initial watertight triangular mesh model includes: Based on the watertight initial triangular mesh model and the thermo-mechanical coupled partial differential equation of non-uniform volume shrinkage, the shrinkage stress of each node inside the three-dimensional model of the porous bone repair scaffold is calculated. The shrinkage stress is mapped to the three-dimensional shrinkage velocity and displacement vector of the mesh vertices using the approximate inverse algorithm of the full mass matrix; The displacement vector is subjected to inverse bias compensation to obtain the inverse deformation compensation mesh model with non-uniform local geometric magnification.

7. The generation method according to claim 6, characterized in that, The shrinkage stress at each node inside the three-dimensional model of the porous bone repair scaffold is calculated based on the initial triangular mesh model of watertightness and the thermo-mechanical coupled partial differential equation of non-uniform volume shrinkage, including: Acquire the phase change operating parameters of the 3D printing equipment; the phase change operating parameters include: the phase change solidification point temperature of the 3D printing molding material, the vacuum degree change curve during the sublimation process, and the nonlinear volumetric strain coefficient when the fluid transforms into a solid. The thermo-mechanical coupling partial differential equation is constructed based on the phase change operating parameters, and the coordinates of the geometric outer contour vertices and the inner surface vertices of the duct of the watertight initial triangular mesh model are defined as the Dirichlet physical boundary conditions of the thermo-mechanical coupling partial differential equation. Chebyshev domain mapping is performed on the three-dimensional coordinates of each vertex inside the mesh of the watertight initial triangular mesh model, and the three-dimensional coordinates are expanded to a high-dimensional mathematical feature space. Construct a functional constraint expression based on the high-dimensional mathematical feature space and the thermo-mechanical coupled partial differential equation; The contraction stress of each node inside the three-dimensional model of the porous bone repair scaffold is calculated based on the functional constraint expression.

8. The generation method according to claim 6, characterized in that, The step of mapping the shrinkage stress to a three-dimensional shrinkage velocity and displacement vector at the mesh vertices using the approximate inverse algorithm of the full mass matrix includes: A local continuous mass field is constructed to surround each local vertex. Within each preset discrete time step, the actual momentum update of the mesh vertex is calculated using the approximate inverse algorithm of the full mass matrix, thereby obtaining the three-dimensional contraction velocity and displacement vector of the mesh vertex.

9. The generation method according to claim 1, characterized in that, The step of generating the target nozzle filling trajectory based on the inverse deformation compensation mesh model includes: Based on the physical layer thickness set by the 3D printing equipment, the reverse deformation compensation mesh model is intersected layer by layer in two-dimensional geometric planes along the direction perpendicular to the forming platform to obtain the closed two-dimensional outer contour and the boundary polygon of the internal pores of each layer. Within the effective filling region inside the boundary polygon, a numerical sampling mechanism based on the continuous normalized flow equation is introduced; The ordinary differential equations in the numerical sampling mechanism are executed concurrently to generate multiple candidate nozzle filling trajectories; Spatial geometric interference calculations are performed on the multiple candidate nozzle filling trajectories to obtain the target nozzle filling trajectory; wherein, the target nozzle filling trajectory is a collision-free candidate nozzle filling trajectory.

10. The generation method according to claim 1, characterized in that, The process of using a safety isolation sandbox to perform a safety review and smooth reconstruction of the target nozzle filling trajectory includes: Obtain the hardware limit list of the 3D printing equipment; The target nozzle filling trajectory is security reviewed using the security isolation sandbox. If the physical results caused by the target nozzle filling trajectory exceed the constraints of the hardware limit list, the transmission of the target nozzle filling trajectory is blocked. The filling trajectory of the target nozzle is smoothly reconstructed.

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