Gradient porous-based sacral implant and design process

Abstract

The invention of the gradient porous structured sacral prosthesis and the manufacturing process aims to create an alternative replacement for bone loss in patients who require bone replacement. The gradient porous structured sacral prosthesis consists of an artificial bone fragment, a metal rod, and a set of screws for fixing the fragments. The manufacturing process consists of seven steps: Identifying the position and boundaries of the bone, First-step topology optimization, Second-step topology optimization, Defining the structural pattern and unit cell size, Designing the artificial bone implant, Mechanical performance testing of the implant, and Fabrication of the sacral implant. The devices and processes according to the present invention are clearly sequenced and characterized. Modification or change in the manufacturing sequence or use may reduce the capabilities of the present invention or make it unusable for the purposes of the present invention.

Description

Gradient Porous-Based Sacral Implant and Design Process

[0001] The present invention relates to the field of the artificial sacral bone component with a gradient porous structure and its manufacturing process.

[0002] The treatment of bone tumors and cancer in the pelvic region often necessitates the surgical removal of affected bone tissue to prevent further spread of the disease. In cases where the resected bone plays a critical role in supporting body mass—such as the sacral or iliac bones, which connect the spine to the lower body—this removal results in a severe loss of structural support. Consequently, patients may experience substantial impairments in mobility, including the inability to stand, walk, or perform routine daily activities.

[0003] To address this issue, surgeons currently reconstruct the spinal-pelvic connection using a technique known as the rod and screw system. This method involves inserting screws into both the spine and the ilium, which are then connected using metal rods to bridge the gap created by the resected sacral bone.

[0004] Rod and screw systems can vary depending on the number and placement of screws and rods. For example:

[0005] 1. Four-Rod Reconstruction (FRR) uses a total of 8 screws—4 inserted into the L4 and L5 vertebrae and 4 into the left and right iliac bones—connected by 4 rods.

[0006] 2. Four-Rod Plus Anterior Column Reconstruction (FRACR) involves 11 screws and 5 rods, adding an additional screw at the bottom of the lowest vertebra and two more in the left and right iliac regions, enhancing anterior column support.

[0007] Despite widespread adoption, the rod-and-screw technique presents several limitations and risks that remain topics of ongoing clinical debate:

[0008] 1. Lack of Engineering-Based Planning: The selection of screw and rod dimensions, angles, and locations is typically based on surgical experience rather than engineering analysis. As a result, the load-bearing capacity of the structure is not always optimized. Post-operative studies have shown a high rate of instrument failure, particularly at rod junctions, due to stress concentrations from cyclic body weight loading, ultimately leading to rod breakage or deformation.

[0009] 2. Insufficient Stabilization: The system often fails to adequately control vertical displacement and rotational instability of the spine. This can lead to deformation and, in severe cases, spinal collapse.

[0010] 3. Surgical Complexity: Successful installation of the rod and screw system requires highly skilled and experienced surgeons, which may not always be available, especially in resource-limited settings.

[0011] 4. Poor Osseointegration: The metal rods and screws are typically manufactured from solid metal, which provides minimal surface area for bone ingrowth. This results in limited long-term stability and increases the risk of screw loosening, particularly in elderly patients or those with osteoporosis.

[0012] To overcome these limitations, recent research has focused on addressing these challenges by utilizing advancements in 3D printing technology. This includes the development of sacral implants that replicate the patient’s original sacral anatomy, along with the integration of porous structures at the contact surfaces between the implant and native bone.

[0013] Studies have demonstrated that such implants can significantly reduce stress on the implant compared to conventional rod-and-screw fixation systems, thereby extending the device's service life and lowering the risk of mechanical failure. Additionally, these implants help preserve spinal alignment and allow for a range of motion that more closely resembles natural movement. The use of porous structures further increases the surface area, promoting better attachment and integration of bone cells with the implant. Nonetheless, current research still faces several limitations, including:

[0014] 1. Limited Integration of Porous Structures in Existing Sacral Implant Patents: Although some existing patents incorporate porous structures in sacral implants, these are often confined to limited areas, with the majority of the implant remaining solid—typically made of titanium (Ti6Al4V). Titanium exhibits significantly higher stiffness than natural bone, resulting in a mechanical property mismatch. This disparity induces a phenomenon known as stress shielding, where the surrounding bone experiences reduced mechanical load. Over time, this can result in bone resorption, ultimately compromising the stability of the implant and increasing the risk of screw loosening or pull-out, particularly in osteoporotic or elderly patients.

[0015] 2. Underrepresentation of TPMS Architectures: Existing designs have yet to incorporate triply periodic minimal surface (TPMS) structures—despite their proven effectiveness in mimicking natural bone architecture. TPMS structures offer interconnected porosity, mechanical compatibility, and biological favorability, making them ideal for bone scaffold applications. However, their integration into sacral implants remains unexplored.

[0016] 3. Limited Ability to Mimic Natural Bone’s Graded Porosity Structure: Current artificial bone implants typically feature uniform pore sizes, which do not replicate the heterogeneous porosity of natural bone. In native bone, both pore size and porosity vary by region to serve distinct mechanical and physiological functions. For example, the articular surface of the femur that bears direct load from the hip joint tends to have low porosity and smaller pores to provide strength and support. In contrast, regions further from the load-bearing surface exhibit a gradual increase in porosity and pore size, facilitating nutrient flow and biological integration. This naturally graded structure ensures efficient material usage—no excess mass where it is unnecessary—while maintaining adequate strength and functionality tailored to local mechanical demands.

[0017] Based on the information above, it can be concluded that current sacral implant designs can be further developed by mimicking the naturally graded porous architecture of bone. Such a design would allow the porosity to vary continuously throughout the structure and be tailored regionally to match local mechanical and biological requirements. This approach enables the creation of implants that are not only mechanically strong and anatomically compatible but also feature increased porous surface area, enhancing the potential for bone cell ingrowth. Moreover, the internal and external structures can be optimized to achieve lightweight designs while maintaining sufficient strength under various loading conditions, ultimately extending the implant’s functional lifespan and safety.

[0018] To address these goals, this invention proposes a novel design framework for bone implants using a two-scale, two-step topology optimization approach. The first step focuses on shaping the outer geometry to accommodate loading conditions, while the second step refines the internal porous architecture with a gradually varying wall thickness, corresponding to the locally required material density for load-bearing. The final product is manufactured using advanced 3D printing technology. This method significantly enhances the structural efficiency of the implant, providing a more effective and personalized skeletal support solution, including

[0019] 1. Porosity Gradient Design for Mechanical Efficiency: The porous structure of the implant is designed to closely resemble that of natural bone, with a gradual variation in porosity. The core design principle is that the wall thickness of the porous structure varies according to the mechanical load in each region of the implant. In high-load areas, the walls are thicker and porosity is lower to ensure mechanical strength and effective weight-bearing. Conversely, in regions subjected to less force, the walls are thinner and porosity is higher. This results in a lightweight implant that efficiently uses material, enhances load-bearing performance, and reduces the likelihood of material failure.

[0020] 2. Mitigation of Stress Shielding Through Porosity Control: By increasing the porous volume within the implant, the overall stiffness of the titanium structure is reduced, making it more compatible with the mechanical properties of the surrounding bone. This minimizes stress shielding, helping to prevent bone degeneration adjacent to the implant and improving long-term stability.

[0021] 3. Enhanced Osseointegration with TPMS Structures: The implant is fabricated using triply periodic minimal surface (TPMS) structures, which have been proven to be mechanically robust and biologically conducive to bone integration. The TPMS design allows for uniformly distributed porosity throughout the implant, maintaining structural strength while significantly increasing the surface area available for bone cell ingrowth. Compared to other existing patented implants, this results in superior biological fixation and longer implant lifespan.

[0022] 4. Patient-Specific Structural and Biomechanical Optimization: The implant’s geometry—including size, curvature, and screw hole positioning—is custom-calculated to match each patient. Finite Element Analysis (FEA) is used preoperatively to simulate load-bearing conditions, ensuring biomechanical performance and reducing the risk of treatment failure. This also lowers reliance on surgical experience, enhancing predictability and clinical outcomes.

[0023] Anatomically Conforming Fit for Simplified Surgical Installation: The sacral implant is precisely shaped to conform to the patient’s bone surface, with screw holes placed in pre-determined, patient-specific locations. This anatomical fit serves as a reference guide for accurate placement, reducing surgical time, minimizing complexity, and improving the precision of implant installation.

[0024] The gradient porous bone implant described herein presents notable distinctions from currently available devices used in spino-pelvic reconstruction, as outlined below

[0025] 1. Anatomically Contoured Design for Surgical Efficiency: The gradient porous sacral implant developed in this invention is anatomically contoured to fit the local bone structure at the fixation sites. Screw positions are pre-determined based on patient-specific anatomy, allowing for faster surgical procedures compared to conventional implants that rely on manually bent rods and screws assembled in the operating room. This reduces surgical complexity and dependence on individual surgeon experience.

[0026] 2. Unibody Structure for Enhanced Durability: Unlike modular designs commonly found in existing devices, this implant is constructed as a single-piece (unibody) structure, which eliminates mechanical weak points at joints. This design reduces the risk of failure at connection interfaces and enhances the long-term structural integrity of the implant.

[0027] 3. Three-Dimensional Gradient Porosity for Load Optimization and Bone Ingrowth: This implant features functionally graded porosity across all three axes, ensuring higher material density in load-bearing regions and reduced material in less critical areas. For example, the porous walls are thicker near the implant's center, which receives direct load from the spine, and gradually thin toward the edges. This results in an implant that is lightweight yet mechanically optimized, unlike conventional implants that use uniform pore sizes. The full-body porous design also maximizes surface area for osseointegration, providing better biological fixation and long-term stability.

[0028] Superior Mechanical Performance Through Topology Optimization: The implant exhibits superior load-bearing performance compared to commercially available sacral implants. Utilizing a two-scale, two-step topology optimization process, the design effectively accounts for stress distribution and results in a porous structure with significantly reduced internal stress. When compared to the Four-Rod plus Anterior Column Reconstruction (FRACR) system, the gradient porous sacral implant presented in this patent—despite using two fewer screws—maintains lower stress levels. This contributes to a reduced risk of material fatigue, extended service life, and enhanced patient safety.

[0029] The gradient porous bone implant developed in this invention demonstrates the ability to preserve spinal alignment and motion in a manner comparable to the natural sacrum. In simulations evaluating the mechanical behavior of the porous sacral implant, both the vertical displacement and rotational angle in the sagittal plane (which divides the body into left and right halves) of the lowest lumbar vertebra were found to remain within the physiological range of motion observed in healthy spinal anatomy under equivalent loading conditions.

[0030] When compared with multiple existing patent applications, this invention exhibits significant technical differences. For example, in U.S. Patent Application No. US20200171437A1, although triply periodic minimal surface (TPMS) structures are employed, they are used primarily for mass transfer applications such as distillation and mixing, rather than for orthopedic load-bearing applications. In contrast, the TPMS design in this invention has been developed specifically to optimize load distribution, while also accounting for fluid flow through interconnected porous networks. The resulting TPMS structure is not only mechanically functional but also permeable, with a graded porosity distribution tailored to orthopedic needs. These differences in design intent, structural integration, and functional gradation make the present invention fundamentally distinct. Moreover, the approach employed here requires advance planning and specialized knowledge, making it non-obvious to a person skilled in the art.

[0031] Similarly, U.S. Patent Application No. US20200023584A1 describes the use of continuously functionally graded three-dimensional structures, which aligns in concept with the present invention. However, the invention presented here is uniquely tailored for biomedical applications, particularly for use within the human body. It considers realistic load-bearing characteristics of human bone, including integration with screw and rod fixation systems. Furthermore, the referenced patent focuses on 3D structures within composite materials, while the present invention utilizes a two-scale, two-step topology optimization process to simultaneously design both the external geometry and internal architecture of a fully integrated metallic implant. It is therefore evident that this invention draws upon multidisciplinary expertise, encompassing engineering, biomechanics, and human anatomy, to achieve functionality and differentiation that go beyond the scope of existing disclosures. Merely reading the content of the referenced patents would not enable a practitioner of ordinary skill to conceive or replicate the novel features of this invention without specific domain knowledge and intentional design methodology.

[0032] These and other purposes and characteristics of the present invention will become clearer when considered in conjunction with the accompanying drawings and the best possible description of the invention which will be described below.

[0033] This invention aims to solve the problem of determining the screw drilling position for the creation of Sacrum and ilium replacement structures and reduce the possibility of device damage after long-term treatment by designing the structure based on considering the force of the artificial bone to be consistent with the necessity of daily force bearing, together with designing the porous structure within the workpiece to be suitable for bone cell growth to determine the precise drilling position, reduce the surgical time, significantly increase the efficiency of the force bearing of the artificial bone, as well as promote the growth of bone cells in the artificial bone, help create biological adhesion between the artificial bone and the surrounding bone, and increase the strength of the artificial bone in the long term.

[0034] The nature of this invention is to consist of parts of devices that have been constructed and a process for constructing those devices, which the invention requires to have all the devices assembled together in order to be able to perform according to the inventor's intentions.

[0035] The sacral prosthesis with a gradual porous structure according to the present invention comprises an artificial bone component, metal rods, and a set of fixation screws, wherein the sacral implant (5) is designed as a unibody structure shaped to resemble the human sacrum. The implant includes ten threaded cylindrical holes for screw fixation, distributed as follows: 1 to 3 holes on the left and 1 to 3 holes on the right for attachment to the iliac wings (6); 2 holes on the superior surface for fixation to the L5 vertebra (7); and 2 holes on the posterior side for fixation to the L4 vertebra (8) using connecting rods and screws. The implant supports the installation of up to 12 screws and 2 rods for secure fixation to the L4 vertebra.

[0036] In one aspect, the threaded cylindrical holes have a wall thickness of 2 to 5 millimeters and an inner diameter of 1 to 10 millimeters.

[0037] In one aspect, the screw set for iliac wing fixation (6) includes 1 to 3 lateral screw pairs, each with a diameter of 1 to 10 millimeters, a length of 30 to 60 millimeters, and an inter-screw spacing of 10 to 25 millimeters. The screw set for L5 fixation (7) includes 1 pair of screws with a spacing of 15 to 25 millimeters, inserted vertically upward from the bottom of the sacral implant into the L5 vertebra. Each screw has a diameter of 1 to 10 millimeters and a length of 30 to 60 millimeters. The screw and rod set for L4 fixation (8) includes 1 screw pair, spaced 20 to 30 millimeters apart, comprising screws inserted into the posterior side of the sacral implant (11) and connected to screws inserted into the L4 vertebra (9) using a metal rod (10). Each screw has a diameter of 1 to 10 millimeters and a length of 30 to 60 millimeters, and each rod has a diameter of 1 to 10 millimeters and a length of 40 to 60 millimeters.

[0038] In another aspect, the metal rods may be composed of aluminum, titanium, or other biocompatible bone substitute materials suitable for implantation in the human body.

[0039] This invention incorporates a manufacturing process as follows:

[0040] a. Identifying the position and boundaries of the bone.

[0041] b. First-step topology optimization.

[0042] c. Second-step topology optimization.

[0043] d. Defining the structural pattern and unit cell size.

[0044] e. Designing the artificial bone implant.

[0045] f. Mechanical performance testing of the implant.

[0046] g. Fabrication of the sacral implant.

[0047] This method is characterized by the following:

[0048] In the first topology optimization step, the objective is to define the external shape of the implant according to anticipated loading conditions, resulting in a solid structure as the initial output, which is then used in the next optimization step. In the second topology optimization step, the goal is to assign localized density distributions throughout the structure. This data is subsequently used to define the internal geometry, including the wall thickness and unit cell size of the porous structure. These features are designed to vary gradually, enabling the creation of a triply periodic minimal surface (TPMS) lattice architecture that replaces the solid core produced in the first step.

[0049] In one aspect, in the first optimization step, the volume fraction applied during the first topology optimization step falls within the range of 0.1 to 0.9.

[0050] In one aspect, in the first topology optimization step, the volume of the implant may deviate from the actual volume of the natural sacrum by no more than 30 percent.

[0051] In one form of use, the steps must be performed in sequence only to achieve the intended use of the present invention.

[0052] The following drawings form part of the present specification and are included to demonstrate certain aspects of the present invention further. The present invention may be better understood by reference to one or more of these drawings in combination with the detailed description of specific embodiments presented herein.Fig.1

[0053] shows a schematic representation of the coccyx and sacral bones.

[0054] shows a schematic illustration of the appearance of the sacroiliac and sacral ossicles with a graduated porous structure implant, combined with a metal rod and screws, and the bone replacement is placed.

[0055] shows a schematic illustration of the appearance of the sacral prosthesis with a gradient porous structure when combined with a metal rod and fixation screws.

[0056] shows a schematic image of the artificial sacral bone with a gradient porous structure.

[0057] shows the coordinates of the placement of the metal brackets and screws.

[0058] shows the pattern of tumor development in the coccyx and the method of resecting the tumor fragments that caused damage.

[0059] shows the design process of the gradient porous sacral prosthesis.

[0060] shows the contact surface where the original sacral bone attaches to the femoral head and the location where the screws are drilled.

[0061] shows a comparative image of the stress distribution of a four-rod reconstruction (FRR), a four-rod plus anterior column reconstruction (FRACR) and a gradient porous coccygeal prosthesis when subjected to three daily life loads: standing, stair climbing, and stair descending.

[0062] shows the decreasing trend of the average stress on the metal rod of the porous gradient sacral prosthesis compared to the metal rod brace in a simulated daily load.

[0063] shows the design process of the artificial sacral bone with a gradient porous structure.

[0064] The following disclosure provides a detailed description of the invention, exemplified through a design case and supported by reference drawings. Identical elements in the drawings are marked with consistent reference numbers for clarity. However, it should be understood that these drawings serve illustrative purposes only and do not limit the scope of the invention, which is defined by the appended claims.

[0065] The invention pertains to a gradient porous-based sacral implant, specifically designed to overcome the drawbacks of conventional spinal-pelvic fixation systems. The objective of the invention is to provide a sacral implant capable of effectively supporting the spine and transferring forces from the upper to the lower body while promoting long-term biological integration and reducing mechanical failure.

[0066] The implant incorporates an internal gradient porous structure, engineered to mimic the mechanical behavior of natural bone. This structure improves stress distribution within the implant and reduces the stress shielding effect, a phenomenon that often leads to degeneration of the surrounding bone due to non-physiological load transfer. By enhancing osseointegration—the biological bonding between bone and implant—the invention significantly increases the long-term stability of the implant and reduces the risk of loosening, breakage, or failure.

[0067] The design of the implant is achieved through a two-step topology optimization process:

[0068] 1. External Shape Optimization: The first topology optimization is used to define the external geometry of the implant, based on biomechanical loading conditions derived from the patient's anatomy.

[0069] 2. Internal Structure Optimization: The second topology optimization focuses on generating a local relative density field, which is then used to design the porous internal architecture (i.e., lattice structures) with varying wall thickness, pore size, and distribution, resulting in a gradient porous configuration.

[0070] This design method can be adapted to various anatomical regions depending on the type and location of the bone resection. The system is highly customizable to accommodate specific patient requirements, anatomical limitations, and disease progression.

[0071] As illustrated in Figures 6A–6D, sacral tumors can be classified into various types based on their location:

[0072] Midline Sacral Tumors: Include mid-sacral, high sacral, and total sacrectomy types (Figures 6A–6C).

[0073] Eccentric Sacral Tumors: Involve lateral or asymmetric tumors affecting both the sacrum and iliac bones (Figure 6D).

[0074] According to Fourney et al. (Fourney DR, et al. J Neurosurg Spine, 2005), treatment approaches vary depending on tumor classification. For midline tumors, only the sacral bone is typically removed (Figures 6E–6G), whereas eccentric tumors require resection of both sacral and iliac regions (Figure 6H). Therefore, the proposed implant is applicable to both types of resections—replacing just the sacrum or both the sacrum and iliac bone as needed.

[0075] The full workflow of the implant design process is illustrated inand consists of the following steps:

[0076] 1. 3D Reconstruction (16): CT scan data of the patient is processed to create a 3D anatomical model, which helps identify the affected area and plan the resection.

[0077] 2. Boundary Definition (17): Based on the tumor location and surgical plan, the boundaries for implant design are established.

[0078] 3. First Topology Optimization (18): Performed using the Solid Isotropic Material with Penalization (SIMP) method to define the outer geometry of the implant, ensuring structural stability under physiological loads.

[0079] 4. Second Topology Optimization (19): Generates a density field, which is used to define the gradient porous internal structure.

[0080] 5. Gradient Porous Design (20): The lattice architecture is designed based on the density field, with attention to pore size, distribution, and wall thickness to ensure mechanical compatibility and biological integration.

[0081] 6. Gradient Porous-based Sacral Implant Design (21): The sacral implant is designed by incorporating the data from the 2-step topology optimization and the defined porous properties of the lattice structure.

[0082] 7. Mechanical Evaluation (22): Finite element analysis is used to verify structural performance, including stress distribution, maximum stresses, vertical displacement, and rotational angles. These must remain within clinically acceptable limits.

[0083] 8. Iterative Redesign (22 to 19): If performance criteria are not met, the implant volume or topology parameters are adjusted and re-evaluated until requirements are satisfied.

[0084] 9. Manufacturing (23): Once approved, the implant is fabricated using 3D-printing technology, enabling high-resolution construction of complex porous structures.

[0085] Topology optimization is a computational technique used to improve the structural efficiency of a design by removing non-load-bearing material. It produces an optimized structure that can withstand prescribed loads with minimal weight. The process requires setting objectives and constraints, including boundary conditions and a volume fraction, which defines how much material should be retained.

[0086] Objective

[0087] While is the minimum compliance is the relative density is the global displacement is the global stiffness matrix is the number of elements is the element relative density is the penalization power is the element displacement vector is the element stiffness matrix

[0088] Volume fraction

[0089] While is the volume fraction is the material volume is the design domain

[0090] In the topology optimization process, the design domain is discretized into finite elements through a process called meshing. The resolution of the resulting topology is determined by the mesh size; smaller mesh sizes allow for more detailed calculation, while larger meshes yield coarser results.

[0091] Once the mesh is generated, a load-bearing simulation is performed based on defined boundary conditions. This simulation calculates the force distribution across each element. The output of this simulation is a local relative density value assigned to each element, representing the material distribution required to support the applied loads. The relative density ranges between 0 and 1, where:

[0092] A relative density of 0 indicates that the element does not carry any load and thus requires no material.

[0093] A relative density of 1 signifies that the element experiences maximum load and must be fully solid.

[0094] Historically, due to limitations in manufacturing technologies, it was only feasible to fabricate structures with binary densities, either fully solid (1) or completely void (0). To address this, the Solid Isotropic Material with Penalization (SIMP) method was introduced. SIMP applies a penalization power to convert intermediate relative density values (between 0 and 1) toward discrete 0 or 1 values, thereby producing a manufacturable binary structure.

[0095] According to the theory, the local Young’s modulus of each element is a function of its relative density. As the density changes, so does the stiffness of the element. The SIMP method expresses this relationship using the following equation:

[0096] Solid isotropic material with penalization (SIMP)

[0097] While is the Young’s modulus of the element is the local relative density of the element is the penalization power is the Young’ modulus of the design domain

[0098] However, with the advent of advanced additive manufacturing techniques, it is now possible to fabricate components with continuous density gradients, enabling a more accurate realization of the theoretical topology optimization results.

[0099] 2-Step Topology Optimization Design

[0100] The design of the gradient porous-based sacral implant is achieved through a two-step topology optimization process: one for determining the external geometry and the other for defining the internal porous structure. These processes ensure that the implant offers optimal mechanical performance while maintaining biocompatibility and manufacturability.

[0101] First topology optimization: External shape driven topology optimization

[0102] The first step (18) involves determining the external geometry of the implant using Solid Isotropic Material with Penalization (SIMP)-based topology optimization. This step aims to produce a solid structure with a binary material distribution, where the local relative density for each element is either 0 (void) or 1 (solid).

[0103] A geometric design domain is created, and a fine mesh is applied to allow for smooth transitions and precise control of the structure. Finer meshes lead to better convergence of relative density values toward binary solutions and produce smoother, more manufacturable surfaces—ideal for defining external shapes.

[0104] The volume fraction is set between 0.1 and 0.9, selected to approximate the original volume of the patient's sacral bone, as determined from CT scans of the sacrum and pelvis. The final solid volume resulting from this optimization should not deviate more than 30% from the actual anatomical volume.

[0105] Second topology optimization: Internal feature driven topology optimization

[0106] After defining the external shape, the second topology optimization (19) is performed to determine the local relative density distribution within the implant. This data will be used to design the internal porous lattice structure, specifically the characteristics such as wall thickness, pore size, and lattice unit cell size.

[0107] The solid body generated from the first optimization serves as the design domain for this step.

[0108] The result is a density field, representing continuous local relative densities (ranging from 0 to 1) across the domain. Unlike the first step, no penalization is applied, and intermediate density values are used directly to guide the lattice structure.

[0109] The internal porous structure is modeled using Triply Periodic Minimal Surface (TPMS) structures. The lattice wall thickness and unit cell size are computed to match the target local relative densities using the following relationship, adapted from Poltue et al. (Poltue, T., Karuna, C., Khrueaduangkham, S., Seehanam, S. and Promoppatum, P., 2021. Design exploration of 3D-printed triply periodic minimal surface scaffolds for bone implants. International Journal of Mechanical Sciences, 211, p.106762.)

[0110]

[0111] While is the local relative density is the wall thickness of the lattice structure is the constant for the relationship with the relative density is the unit cell size

[0112]

[0113] The gradient transition of the porous structure is influenced by the mesh size used in the second topology optimization. The mesh size in this step is selected based on the unit cell size of the lattice structure and the target pore diameter. According to the findings, a coarse mesh results in a gradual transition of relative density across the structure, which is desirable for generating smooth and continuous porous gradients. In contrast, a fine mesh may cause abrupt changes in relative density—such as sudden shifts from 0 to 1—leading to sharp transitions in the porous architecture. Therefore, a coarse mesh is preferred for the second topology optimization to ensure smooth variation in porosity, which is in contrast to the first topology optimization, where a fine mesh is necessary to achieve precise and well-defined external geometry.

[0114] The purpose of the second topology optimization is to tailor the implant’s local Young’s modulus to closely match that of the surrounding bone tissue, thereby minimizing the risk of stress shielding and promoting healthy load transfer and bone remodeling.

[0115] To design the gradient internal porous structure through the second topology optimization, specific criteria must be considered for defining the unit cell size of the lattice. These include:

[0116] Pore diameter within the range of 100 to 1000 microns, which is considered optimal for promoting osseointegration between the implant and surrounding bone tissue.

[0117] Relative density values ranging from 0.1 to 0.9, selected based on manufacturing feasibility and the resolution limits of current 3D-printing technologies.

[0118] The relationships among the key design parameters—wall thickness, unit cell size, pore diameter, and relative density—are governed by the following equations:

[0119] Pore diameter

[0120] While is the pore diameter is the constant for the relationship with the pore diameter

[0121]

[0122] Relative density

[0123] While is the vector of minimum relative densities

[0124] The volume fraction for the second topology optimization is set within the range of 0.1 to 0.9. The optimal value is determined based on performance evaluation through mechanical simulation using finite element analysis (FEA). This simulation models the loading conditions acting on the gradient porous-based sacral implant when integrated with the surrounding bone structures. The goal is to ensure that:

[0125] Vertical displacement and rotational angles of the spine remain within physiological limits of natural spinal movement.

[0126] Stress distribution across the implant is uniform, minimizing stress concentrations that could lead to mechanical failure.

[0127] By validating these criteria, the design ensures both structural integrity and biomechanical compatibility, reducing the risk of implant loosening or fracture over time.

[0128] Mechanical evaluation of the sacral implant

[0129] The 3D models of the sacrum and pelvis (16), along with the gradient porous-based sacral implant (21) obtained from the preceding design stages, are used for mechanical evaluation (22). This evaluation assesses the implant’s ability to withstand physiological loading and maintain spinal stability, based on analysis of vertical deformation and rotation angle of the spine.

[0130] The simulation is conducted using .STL files, representing both anatomical and implant geometries, to simulate daily activity loading conditions, such as a two-legged standing posture. The boundary conditions, loading magnitudes, and locations are referenced from Cheng et al. (Cheng L, Yu Y, Zhu R, Lv H, Jia Y, Zeng Z, Chen B, Ding Z. Structural stability of different reconstruction techniques following total sacrectomy: a biomechanical study. Clinical Biomechanics, 2011 Dec 1;26(10):977–981).

[0131] To validate the simulation accuracy, results obtained from the inventors’ analysis are compared with those published by Cheng et al., showing consistent outcome values and thereby confirming the validity of the simulation method used in this invention.

[0132] The performance criteria are as follows:

[0133] The sacral implant, when subjected to vertical loading and torque, must withstand the applied forces without mechanical failure.

[0134] The maximum stress within the implant must remain below 10–15% of the yield strength of Grade 5 titanium (Ti-6Al-4V), to minimize risks of plastic deformation, fatigue failure, or fracture.

[0135] The implant must maintain the biomechanical integrity of the spinal column, particularly preserving spinal mobility within the range of natural physiological motion.

[0136] This is assessed by analyzing the vertical displacement and rotation angle in the sagittal plane of the L5 vertebra under body weight loading in a standing posture. The displacement and angular motion must fall within the range of:

[0137] 0.2 – 0.4 mm vertical displacement

[0138] 0 – 2.8 degrees rotation angle

[0139] These acceptable ranges are also referenced from Cheng et al. (2011).

[0140] If the gradient porous-based sacral implant fails to meet any of the above criteria, the design process must return to the second topology optimization step (19) to refine the relative density distribution and improve structural performance. Only after passing all mechanical and biomechanical validation criteria should the implant proceed to manufacturing, using the Laser Powder Bed Fusion (LPBF) process.

[0141] Example Characteristics of the Gradient Porous-Based Sacral Implant

[0142] The gradient porous-based sacral implant, designed as a replacement for the sacrum (1), comprises three primary components:

[0143] 1. The sacral implant (5)

[0144] 2. A screw set for fixation with the ilium (6)

[0145] 3. A metal rod and screw set for fixation with the vertebrae (7, 8)

[0146] These components work together to provide structural support, load transfer, and stable fixation between the spine and pelvis. The detailed characteristics are as follows:

[0147] 1. Sacral Implant (5)

[0148] Constructed as a unibody structure, primarily composed of a porous lattice, with localized solid threaded regions for fixation (see).

[0149] Threaded cylinders for screw fixation have:

[0150] - Wall thickness: 2–5 mm

[0151] - Outer diameter: 1–10 mm

[0152] Side fixation holes for the ilium (2):

[0153] - Located bilaterally (left and right sides)

[0154] - Number of holes: 2–6

[0155] Midline fixation holes for attachment to the L5 vertebra (3):

[0156] - Located centrally

[0157] - Number of holes: 2

[0158] Posterior fixation holes for securing to L4 vertebra via rods and screws:

[0159] - Number of holes: 2

[0160] - Positioned at the back of the implant for rod connection

[0161] 2. Screw Set for Ilium Fixation (6)

[0162] Includes 1–3 pairs of screws for securing the sacral implant to the iliac bones.

[0163] Screw specifications:

[0164] - Diameter: 1–10 mm

[0165] - Length: 30–60 mm

[0166] Spacing between screws: 10–25 mm (center-to-center)

[0167] 3. Metal Rod and Screw Set for Spinal Fixation (7, 8)

[0168] Screw dimensions:

[0169] - Diameter: 1–10 mm

[0170] - Length: 30–60 mm

[0171] Rod dimensions:

[0172] - Diameter: 1–10 mm

[0173] - Length: 40–60 mm

[0174] Fixation with L5 Vertebra (7):

[0175] Comprises 1 pair of screws, inserted upward from the bottom of the implant into the L5 vertebra.

[0176] Spacing between screws: 15–25 mm

[0177] Fixation with L4 Vertebra (8):

[0178] Consists of 1 pair of screws and rods

[0179] Screws are inserted posteriorly from the back of the sacral implant (11).

[0180] Metal rods (11) connect the sacral implant to the screws inserted into the L4 vertebra (9).

[0181] Rod distance: 20–30 mm

[0182] The Design

[0183] The gradient porous-based sacral implant is developed using a 2-step topology optimization process, with a design example illustrated in, corresponding to a midline sacral resection of the total sacrectomy type, as depicted in Figures 6C and 6G.

[0184] The design process begins with the generation of a 3D model from the patient’s CT scan. The damaged sacrum (1) is digitally removed and replaced with a rectangular design domain, having a width and length of 100–160 mm, and a height of 50–100 mm.

[0185] To ensure proper fixation and integration, the design domain includes intersecting volumes (2–30 mm) with adjacent bone structures at the original sacrum-ilium interfaces, creating a contact surface for mechanical and biological stability. In the design example, a rectangular box of 135 × 130 × 75 mm was used, intersecting the superior surface (top of the box) with the L5 vertebra by 5 mm, and laterally intersecting with the iliac bones by 10 mm on both sides (see Figure 7A).

[0186] Next, Boolean subtraction was used to remove the intersected volumes from the rectangular design box. This processed volume was then used for the positioning of screws and rods required for fixation with the spine and pelvis.

[0187] To accurately define the design domain for the topology optimization process, the volumes of the spinal fixation screws and rods were subtracted from the implant body. These subtracted volumes represent the actual spaces occupied by the implants’ hardware and ensure that actual volume of the material is used for the optimization.

[0188] Meanwhile, the screw set for ilium fixation was retained (union) with the implant body, as these elements are physically integrated with the implant and serve as mechanical anchorage points. Although the screws and rods were not included in the relative density calculations, their geometries were used to define the boundary conditions applied during the topology optimization, such as load input points and constraint surfaces. This configuration is illustrated in Figure 7B.

[0189] The first topology optimization was conducted to determine the external shape of the sacral implant using a finite element analysis (FEA) program. The implant design volume was discretized through meshing, with a mesh size ranging from 1 – 15 mm, allowing the stress distribution within each region of the volume to be accurately evaluated at varying resolutions. The material properties of the implant, assumed to be Ti-6Al-4V (Grade 5 titanium) were assigned, and boundary conditions simulating bipedal standing posture were applied. A vertical load of 400 – 600 N was imposed on the superior surface of the implant where it contacts the L5 vertebra, while the lateral surfaces corresponding to the screw fixation points with the ilium were fully constrained in all degrees of freedom. A volume fraction constraint of 0.1 – 0.9 was defined, which controlled the amount of material retained in the optimized structure relative to the original design. The optimization then analyzed the internal stress distribution and produced a density field, a spatial map assigning each mesh element a local relative density between 0 (void) and 1 (solid), based on its load-bearing requirement. Using the Solid Isotropic Material with Penalization (SIMP) method, intermediate density values between 0 and 1 were driven toward binary values of 0 or 1, resulting in a manufacturable solid implant geometry. The final optimized solid structure from this step is shown in Figure 7C.

[0190] The solid body obtained from the first topology optimization is then used as the design domain for the second topology optimization, which focuses on determining the porous structure distribution within the implant. This second optimization follows a similar methodology to the first but differs in two key parameters: mesh size and volume fraction.

[0191] The mesh size in this step plays a crucial role in defining the characteristics of the porous architecture. A fine mesh results in a more uniform relative density, which translates into a consistent pore structure throughout the implant. In contrast, a coarse mesh allows for a gradual variation in local relative densities, enabling the formation of a gradient porous structure that better mimics the natural variation in bone properties. This gradient distribution corresponds to the density field generated from the second topology optimization, as illustrated in Figure 7D.

[0192] The resulting density field is then used to guide the design of the internal lattice architecture, particularly by adjusting the wall thickness of the porous structures in accordance with the local relative density values. During post-processing, threaded cylindrical holes are added for screw installation, and fine features that exceed 3D printing limitations are removed to ensure manufacturability. The final, fully optimized gradient porous-based sacral implant is shown in Figure 7E.

[0193] References component numbers

[0194] No. 1 Sacrum

[0195] No. 2 Ilium

[0196] No. 3 L5 vertebra

[0197] No. 4 L4 vertebra

[0198] No. 5 Sacral implant

[0199] No. 6 Screw set for fixation with pelvic

[0200] No. 7 Screw set for fixation with L5 vertebra

[0201] No. 8 Screw and rod set for fixation with L4 vertebra

[0202] No. 9 Screws inserted into the L4 vertebra

[0203] No. 10 Spinal rods

[0204] No. 11 Screws inserted into the posterior of the sacral implant

[0205] No. 12 Tumor

[0206] No. 13 Initial geometric design volume

[0207] No. 14 Original sacrum interfaces

[0208] No. 15 Screw and rod installation positions

[0209] No. 16 CT Three-dimensional modeling from CT image data

[0210] No. 17 Defining design boundary

[0211] No. 18 First topology optimization

[0212] No. 19 Second topology optimization

[0213] No. 20 Lattice structure design

[0214] No. 21 Gradient porous-based sacral implant design

[0215] No. 22 Mechanical performance evaluation

[0216] No. 23 Manufacturing with 3D-printing technology

[0217] Although the present invention has been described in detail and illustrated through the attached figures and examples, it should be understood that modifications, adaptations, or variations may be made by persons skilled in the art without departing from the scope and spirit of the invention. Such changes are considered to be within the general knowledge and capabilities of practitioners in relevant technical fields.

[0218] This patent includes any implementations or configurations not explicitly mentioned in the claims, but which nonetheless achieve substantially similar functions or results as those disclosed and claimed herein.BEST MODE OF THE INVENTION

[0219] Best mode or preferred embodiment of the invention is as provided in the description of the invention.

Claims

1.A gradient porous sacral implant and its method of manufacture, comprising an artificial bone component, metal rods, and a set of fixation screws, wherein the sacral implant (5) is designed as a unibody structure shaped to resemble the human sacrum. The implant includes ten threaded cylindrical holes for screw fixation, distributed as follows: 1 to 3 holes on the left and 1 to 3 holes on the right for attachment to the iliac wings (6); 2 holes on the superior surface for fixation to the L5 vertebra (7); and 2 holes on the posterior side for fixation to the L4 vertebra (8) using connecting rods and screws. The implant supports the installation of up to 12 screws and 2 rods for secure fixation to the L4 vertebra.2.The gradient porous sacral implant according to claim 1, wherein the threaded cylindrical holes have a wall thickness of 2 to 5 millimeters and an inner diameter of 1 to 10 millimeters.3.The gradient porous sacral implant according to claim 1, wherein the screw set for iliac wing fixation (6) includes 1 to 3 lateral screw pairs, each with a diameter of 1 to 10 millimeters, length of 30 to 60 millimeters, and inter-screw spacing of 10 to 25 millimeters.4.The gradient porous sacral implant according to claim 1, wherein the screw set for L5 fixation (7) includes 1 pair of screws with a spacing of 15 to 25 millimeters, inserted vertically upward from the bottom of the sacral implant into the L5 vertebra, each screw having a diameter of 1 to 10 millimeters and a length of 30 to 60 millimeters.5.The gradient porous sacral implant according to claim 1, wherein the screw and rod set for L4 fixation (8) includes 1 screw pair, spaced 20 to 30 millimeters apart, comprising screws inserted into the posterior side of the sacral implant (11), connected to screws inserted into the L4 vertebra (9) using a metal rod (10). Each screw has a diameter of 1 to 10 millimeters and a length of 30 to 60 millimeters, and each rod has a diameter of 1 to 10 millimeters and a length of 40 to 60 millimeters.6.The gradient porous sacral implant according to claim 1, wherein the metal rods may be composed of aluminum, titanium, or other biocompatible bone substitute materials suitable for implantation in the human body.7.The gradient porous sacral implant according to claim 1, wherein the invention is applicable for producing replacement components for the sacrum alone, or for the sacrum in combination with the iliac wings.8.The gradient porous sacral implant according to claim 1, wherein the entire implant (5) is porous, except for the threaded cylindrical zones, which remain solid.9.The gradient porous sacral implant and its method of manufacture comprise the following seven sequential steps:a. Identifying the position and boundaries of the bone.b. First-step topology optimization.c. Second-step topology optimization.d. Defining the structural pattern and unit cell size.e. Designing the artificial bone implant.f. Mechanical performance testing of the implant.g. Fabrication of the sacral implant.This method is characterized by the following:In the first topology optimization step, the objective is to define the external shape of the implant according to anticipated loading conditions, resulting in a solid structure as the initial output, which is then used in the next optimization step.In the second topology optimization step, the goal is to assign localized density distributions throughout the structure. This data is subsequently used to define the internal geometry, including the wall thickness and unit cell size of the porous structure. These features are designed to vary gradually, enabling the creation of a triply periodic minimal surface (TPMS) lattice architecture that replaces the solid core produced in the first step.10.The gradient porous sacral implant and its method of manufacture according to claim 8, wherein the volume fraction applied during the first topology optimization step falls within the range of 0.1 to 0.9.11.The gradient porous sacral implant and its method of manufacture according to claim 8, wherein during the first topology optimization step, the volume of the implant may deviate from the actual volume of the natural sacrum by no more than 30 percent.12.The gradient porous sacral implant and its method of manufacture according to claim 8, wherein the process described is specifically intended for the fabrication of replacement components for either the sacrum alone, or the sacrum in combination with the iliac wings.13.The gradient porous sacral implant and its method of manufacture according to claim 8, wherein the step of defining the structural pattern and unit cell size incorporates a combination of various porous architecture concepts.

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