Modeling and Mechanical Performance Analysis of Porous Gradient Bone Scaffolds

Modeling and Mechanical Performance Analysis of Porous Gradient Bone Scaffolds | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Modeling and Mechanical Performance Analysis of Porous Gradient Bone Scaffolds Kaixin Lin, Kaihuan Yu, Ning Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4647620/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Currently, personalized adaptive technology using 3D printing scaffold is widely employed in bone tissue repair engineering to aid in healing and restoring large segmental bone defects. Although the scaffold matches the external appearance, its internal tissue structure differs significantly from that of natural bone tissue, and issues of mechanical matching and stress shielding persist after transplantation, impacting patient recovery. Drawing on the tissue structure of natural bone, this study develops a bionic bone scaffold model that replicates the microstructure of natural bone using a noise topology approach. Model samples are created with pore sizes and porosity corresponding to the bone density of various ages. The mechanical properties of bone structures with varying pore sizes and porosities are assessed using finite element simulation analysis software. Mechanical simulation results for bionic bone scaffolds across different ages indicate that the modeling method can adjust the pore size and porosity of the bionic bone structure through voxel parameters, aligning the mechanical characteristics with those of natural bone. This alignment effectively mitigates the stress mismatch between the implant structure and natural tissue post-bone grafting. The hierarchical gradient porous structure and mechanical model of bionic bone scaffold offer valuable insights for the structural design and clinical selection of bone implants. Biological sciences/Biotechnology/Biomaterials Biological sciences/Biotechnology/Biomimetics Noise topology Bone scaffold structure Finite element analysis Bone tissue engineering Bone defect Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction Bone transplantation is the primary method to address bone defects, accounting for one-fourth of all procedures related to bone defects and ranking as the second most common human tissue transplant surgery after blood transfusion [ 1 , 2 ]. Bone defects frequently result from trauma, tumors, infections, metabolic diseases, surgeries, radiation therapy, or functional degeneration, making them a common type of injury in clinical settings. The human skeletal system exhibits a certain degree of recovery and morphological regenerative capability [ 3 , 4 ], where minor bone defects can typically self-heal without external intervention. However, when bone defects exceed a specific size (greater than 2 cm) or when the bone perimeter around the defect exceeds 50%, the self-healing capacity is significantly impaired. This may lead to complications such as non-union, abnormal healing, or pathological fractures [ 5 , 6 ], potentially resulting in lifelong disabilities for the patients. Effectively repairing bone defects, alleviating healing burdens on patients, and shortening postoperative recovery periods are currently the primary focuses of orthopedic research. Bone Tissue Engineering (BTE) was first proposed in 1993 and has since emerged as a rapidly growing research area within tissue engineering. It is regarded as an effective method for addressing the challenges of bone defects [ 7 – 9 ]. Research in BTE has shown that artificial biomimetic bones, which possess characteristics such as bone induction, bone conduction, and bone integration, can effectively promote healing and recovery in the human body [ 10 , 11 ]. Specifically, the bone-conducting properties of scaffolds prevent fibrous capsule formation and facilitate strong bonding with natural bone [ 12 , 13 ]. Their sufficient biocompatibility and bioactivity enhance the adhesion of osteogenic cells to surrounding new bone, thereby alleviating postoperative healing burdens on patients. Moreover, these scaffolds need to mimic the structure, shape, and function of the missing bone segment, featuring optimized geometric shapes and porosity to ensure adequate space for bone regeneration and to support bone membrane development, thereby accurately filling the anatomical structure of the bone defect [ 14 , 15 ]. The interior of bones displays a porous structure, where variations in pore size significantly influence the biological behavior of bone cells. For instance, a pore size of approximately 300 micrometers in trabecular bone is beneficial for bone growth and nutrient exchange within the human tissue environment [ 18 , 19 ]. Furthermore, scaffolds must exhibit sufficient mechanical strength to satisfy the structural demands of tissue substitutes and possess an elastic modulus akin to that of human bone tissue to prevent stress shielding phenomena [ 20 – 22 ]. In recent years, due to limitations in controlling scaffold geometry, pore size, and inter-connectivity using traditional techniques, Additive Manufacturing (AM) has emerged as the preferred method for creating artificial biomimetic bone scaffolds [ 13 , 23 ]. AM technology enables precise control over various attributes of bone scaffolds, such as stiffness, biochemical factors, spatial distribution capabilities, as well as complex or irregular pore shapes and surface morphologiess [ 24 – 26 ]. Additionally, this technology facilitates high-density in vivo interactions by using bioinks containing different cell types and extracellular matrix (ECM) for high-density bioprinting, allowing for the fabrication of large-scale alternative structures for damaged bones [ 27 – 29 ]. AM technology also offers several other benefits, including the ability to process multiple materials incorporating drugs and biomolecules, maintaining structural and shape stability, minimizing material wastage, improving mechanical performance, enhancing cell infiltration, and promoting nutrient circulation, making it an ideal choice in bone tissue engineering. Ashby et al. [ 30 ] proposed a cubic unit cell model for open-cell foam and closed-cell foam, elucidating the relationship between porosity and overall mechanical properties, thereby providing a more rational theoretical basis for scaffold design. Cheah et al. [ 31 – 33 ], considering the manufacturability and spatial geometric characteristics of specific AM technologies, established a library comprising 11 unit types and investigated scaffolds composed of diamond lattices, cubic lattices, truncated octahedra, rhombic dodecahedra, and rhombicuboctahedra to derive analytical relationships between geometric parameters like porosity, scaffold diameter, pore size, and the scaffold's Young's modulus and Poisson's ratio. G. Bini et al. [ 34 ] studied trabecular bone microstructure from a topological perspective, summarizing the concept of topological spatial models for bone tissue microstructure, providing further insights for the design of artificial bone structures. AM technology has become a new trend in preparing artificial biomimetic bone scaffolds in the field of BTE. Based on the requirements of bone tissue engineering for biomimetic bone scaffolds, this study introduces a novel noise topology-based 3D bone scaffold model. The study establishes a porosity pattern classification based on bone density distribution across different age groups and performs mechanical simulations on the resulting bone structure models using finite element software. AM technology ensures that the porous gradient bone scaffold model closely resembles natural bone in terms of shape, structure, porosity, and stress distribution. The layered structure is also better suited to adapt to the distribution of bone tissue membrane layers, cortical bone layers, and trabecular bone layers, from outer to inner layers. At the medical technology level, this approach helps prevent postoperative bone loss due to stress mismatch after bone grafting, ultimately reducing healing pressures on patients and shortening recovery periods. 2. Main Text 2.1 Generation of porous structure using noise topology method The human femoral shaft is cylindrical in structure, with a radial diameter variation rate not exceeding 20%. Based on the layered structure of bone tissue (as shown in Fig. 1 a), it can be divided from the inner to outer layers into four layers: marrow cavity, trabecular bone layer, cortical bone layer, and periosteum layer [ 34 ]. In this study, the bone tissue model is represented as concentric, mutually adhering cylindrical models to streamline the simulation of the bone tissue structure and simplify the model. The thickness ratio of the periosteum, cortical bone, trabecular bone, and marrow cavity layers is set at 1:3:4:5. The overall height of the bone scaffold is established at 14mm, creating an initially simplified, gradient, layered structure. Drawing on human bone sampling results [35,36], and reflecting the radial porosity variations across different age groups (Fig. 1 b), the target porous bone structure model specifies a porosity for the periosteum layer of 10%-15%, cortical bone at 55–60%, and trabecular bone at 75%-80%. Utilizing the noise topology method within Cinema 4D software, specifically through the Proc3Durale plugin, varied porous structures are generated by adjusting various global scales, voxels, thresholds, and selecting diverse noise types. These structures are then categorized based on type and porosity levels, forming a 'Noise Topology Method Sample Classification' table (Fig. 2 a). Subsequent selections of layered bone structures appropriate for various age groups are made from this table. Sample models are printed using a photosensitive resin through a 3D printer (Fig. 2 b), with ZR680 photosensitive resin selected as the printing material, featuring a density of 1.1g/cm 3 . The resulting sample models and data will contribute to the development of an age-specific porosity standard database. The actual sample porosity is compared with the calculated ideal porosity, with an allowable error margin of 5%. 2.2 Generation of porous gradient bone scaffolds for different age groups Focusing on the age group of 18–36 years for the bone scaffold model (Fig. 3 a), the bone membrane layer is depicted using a Type 2 noise topology pattern at a 30% global scale. The cortical bone layer is modeled with a Type 3 pattern at a 50% global scale, while the trabecular bone layer utilizes a Type 3 pattern at a 30% global scale. These three components are integrated into concentric circular connectors, leaving the marrow layer vacant. The porosity variation curves for the radial bone scaffold structure across different layers are analyzed (Fig. 3 b). The radial porosity change curve for the porous gradient bone scaffold aligns closely with the natural radial porosity change curve observed in individuals aged 18–36 years, demonstrating negligible differences between the two. Based on bone density variation patterns across age groups, styles and porosity formats from noise topological methods were selected from a standard database to develop porous gradient bone scaffold models for three age groups: 18–36, 36–53, and 53+. These models were subsequently compared radially with actual human femoral bones (Fig. 4 ). Figure 4 a displays a solid bone CT image, highlighting a significant decrease in cross-sectional area with age, and an increase in the hollow marrow cavity for fluid circulation. In the 36–53 age group, the radial width is narrower than in the 18–36 age group, and it is narrowest in the 53 + age group, featuring a distinctly porous mesh within the bone structure. This reflects severe bone mass loss in older populations, leading to reduced load-bearing and impact resistance capabilities. Mirroring changes in bone porosity among age groups, this study utilized noise topography samples with varying porosity rates for bone scaffold models tailored to different age groups (Fig. 4 b), effectively creating porous gradient bone structural models for these groups. Figure 4 c shows the comparison curve between the three types of porous gradient bone scaffold models and the natural bone porosity rates for each age group, indicating minimal differences compared to the layered porosity rates of natural bone within the same age demographics. This model accurately represents the radial structure of natural bone tissues across various age groups. 2.3 Three-Dimensional restoration of porous gradient bone scaffold models The porous gradient model created using Cinema 4D features clearly defined layers of periosteum, cortical bone, and trabecular bone due to gradient differentiation, existing independently rather than as a cohesive unit. This separation can cause issues in subsequent simulations, such as inadequate stress transmission, distortion, and inadequate contact. Therefore, it is essential to convert the model into a single, unified solid structure. The three independent models are joined using the software's linking tool to form a cohesive solid structure, and the 'Volume Generation' feature smooths the edge voxels of the connected model (Fig. 5 a). Optimize any minor debris models that fail to form complete connections, eliminate overlapping interference from completed parts, or address isolated fractures. These small debris models can lead to solidification failures of the STL model or adversely affect the mechanical properties of the porous gradient structure. Consequently, Geomagic Wrap software (Geomagic, USA) is utilized to refine non-manifold edges, self-intersections, highly refractive edges, pin-shaped objects, sub-components, narrow channels, and small holes in the three-dimensional model for repair (Fig. 5 b). Figure 5 c displays a sectional comparison before and after the model's connectivity repair, showing a seamless transition at the gradient interfaces and confirming effective integration within the three-dimensional structure. 2.4 Load-bearing and impact simulation analysis of porous gradient bone scaffold models A segment equivalent to one eighth of the porous gradient bone scaffold model is utilized in Ansys simulation software (ANSYS, USA) to conduct a static load-bearing simulation. The material properties are set as follows: density of 1.2×10 − 9 tonne/mm³, elastic modulus of 3883.4 MPa, Poisson's ratio of 0.3, bulk modulus of 3236.2 MPa, and shear modulus of 1493.6 MPa. The mesh is configured for nonlinear mechanics with a unit size of 0.5 mm. The base of the model is fixed for constraints, and a load simulating an adult male standing, weighing 70 kg, is applied from above to perform the bone scaffold load-bearing simulation. Analysis of the resultant load-bearing simulation cloud diagram (Fig. 6 ) reveals that the deformation resistance and equivalent stress of gradient porous bone scaffold models with varied porosities due to age differ, though their deformation patterns remain consistent, exhibiting an inward tilt angle and lesser deformation in the outer layer compared to greater deformation in the inner layer. This occurs because the cortical bone layer is the primary load-bearing layer in human bones, and the main indication of bone loss is the progressive thinning of the periosteal and cortical bone layers, which leads to increased porosity in the cortical bone and its gradual transition to trabecular bone, thereby thickening the trabecular layer. Areas of concentrated stress are identified in Fig. 6 a and d at the junctions between cortical and trabecular bones; environments of high stress can accelerate bone loss, typically starting from the inner side of the cortical bone. The reduction in thickness of the periosteal and cortical bone layers results in increased deformation, while the growing thickness of the inner trabecular bone contributes to this increase. As depicted in Fig. 6 .d-f, the stress distribution in the porous scaffold of a 36-year-old resembles that of an 18-year-old, with a maximum equivalent stress of 37.596 MPa, which is merely 2.5 times that of the latter (14.958 MPa). However, for the age group above 53, the maximum equivalent stress reaches 384.14 MPa, demonstrating a significant decline in the load-bearing capacity of the human skeleton with bone mass loss and reduced bone density. Using the same material parameters as in the load-bearing simulation, with both the top and bottom secured, an impact force of 100N perpendicular to the model's geometry is applied outside the periosteal layer to simulate real-world impacts (Fig. 7 ). The resulting impact cloud map shows that deformation primarily occurs as compression at the point of load, with the extent of deformation decreasing progressively from the outer to the inner layers. The periosteal layer exhibits the most significant deformation, while the trabecular bone layer experiences the least. In the models for the 18–36 and 36–53 age groups, the trabecular bone layer remains unaffected by the deformation (Fig. 7 d, e). However, in the model for individuals over 53 years old, there is considerable impact on the trabecular bone layer (Fig. 7 f), indicating a compromised structural integrity in the periosteal and cortical layers that fails to shield the internal trabecular bone layer and marrow from external impacts. This reflects a significant reduction in the bone's ability to protect the internal structures due to bone mass loss in the periosteal and cortical layers in individuals aged 53 and above. 2.5 Stress shielding simulation analysis of porous gradient bone scaffold models After repairing the porous gradient bone scaffold model with Geomagic Wrap for 3D solid smoothing, the model is transferred to nTopology (nTopology Inc., USA) to generate the complete mesh. It is then imported into Abaqus (Dassault Systemes SE, France) for compression simulation testing. Two concentric cylindrical sections are positioned at the top and bottom of the model to emulate the natural bone sections adjacent to the implanted bone tissue. The materials for the implanted bone tissues are replaced with those of natural bone (periosteal layer Young's modulus of 20000, Poisson's ratio of 0.26; cortical bone layer Young's modulus of 5700, Poisson's ratio of 0.26; trabecular bone layer Young's modulus of 64, Poisson's ratio of 0.29), titanium alloy (Young's modulus of 109000, Poisson's ratio of 0.33), and PEEK (Young's modulus of 3000, Poisson's ratio of 0.33). A load of 700N is applied from above to the natural bone section to simulate the pressure experienced during single-footed human walking. The base of the natural bone section is secured for constraints, facilitating the study of the stress shielding effects exerted by different implants on the human skeletal system (Fig. 8 a). The results of the natural whole bone compression simulation (Fig. 8 c) show that the cortical bone layer bears the majority of the pressure from top to bottom, with the equivalent stress in the cortical bone layer exceeding that in the periosteal layer, and the trabecular bone layer inside almost devoid of stress. In the titanium alloy simulation (Fig. 8 d), a pronounced stress shielding phenomenon is evident throughout the model, with stress concentration around the titanium alloy segment; the equivalent stress in the natural bone segments above and below is significantly lower than in the middle implant part. Prolonged exposure of the human skeletal system to low-stress environments may lead to bone loss in this area, diminishing the strength at the interface between natural bone and the titanium alloy implant and increasing the likelihood of secondary surgery. In the PEEK bone segment implant (Fig. 8 e), no significant stress shielding effect is observed compared to the titanium alloy model; the stress distribution on the outer surface is more uniform, indicating that bone implants made from PEEK material can more effectively mitigate stress shielding effects compared to titanium alloy. The porous gradient bone scaffold model (Fig. 8 b), printed with PEEK material, shows that the internal cortical bone part bears most of the pressure from top to bottom, while the trabecular bone part maintains a loose structure with high porosity similar to natural bone and bears minimal load pressure. The periosteal layer does not exhibit significant stress shielding, but a reduction in equivalent stress is noted at the junction between natural bone and the bone scaffold, due to surface irregularities on the porous gradient bone scaffold model, leading to areas of stress concentration in the cortical bone layer. Under the top-down load, these areas are the first to bear pressure. The bone reconstruction effect in the human body demonstrates that bones can effectively increase bone growth and differentiation capabilities when subjected to mechanical stimulation, thereby altering the corresponding structures. The cluster of equivalent stress concentration points on the upper and lower surfaces of the porous gradient bone model can effectively enhance the growth and differentiation of bone cells in the cortical bone region, improving the bone's growth and repair capabilities at that site and hence shortening the recovery time after bone transplant surgery. The fully repaired and well-fitted complete porous gradient biomimetic bone scaffold model is 3D printed using photosensitive resin and compared with slices of natural human bone (Fig. 9 a-c). In Fig. 9 b, a one-eighth section of the 3D printed porous gradient bone scaffold model is produced through slicing. The 3D printed model reveals that the outermost layer exhibits the lowest porosity, while the internal layers display the highest porosity, mimicking the distribution of natural bone tissue. This high porosity enhances the surface area, effectively facilitating the attachment and growth of osteoblasts and osteoclasts on the artificial biomimetic bone scaffold, thus promoting early recovery following bone grafting surgery. Figure 9 d-g illustrate the top view, sectional view, and corresponding SEM images of the model. The porous gradient bone model is constrained by the extrusion precision of 3D printing and does not fully replicate the microstructure of natural bone tissue at the microscopic level. Figure 9 h-m show porous gradient bone models printed with both photosensitive resin and PEEK material. Given its mechanical properties similar to natural bone, PEEK material is more effective in preventing bone loss associated with the bone reconstruction effect during the postoperative recovery period. 3. Conclusion 1. The bone scaffold structure created by the noise topology method achieves a radial gradient of porosity ranging from 10.1-15.4% in the periosteal layer, 33.07-55.38% in the cortical bone layer, and 63.84-73.74% in the trabecular bone layer. The external biomimetic periosteal layer, smoothly repaired, forms a barrier function that prevents soft tissue invasion into the defect area. The internal trabecular bone part, resembling natural trabecular bone beams, enhances the transport of bone cells, nutrients, and bioactive substances. 2. Load and impact simulations have also compared and differentiated bone scaffold structure models across various age groups. As porosity and bone density decrease with age, the bones' load-bearing capacity and impact resistance diminish significantly. Models in individuals over 53 years old lack sufficient impact resistance to protect the internal trabecular bone layer and the enveloping marrow cavity layer from external impacts, indicating that individuals over 50 are more susceptible to osteoporosis-related fractures due to bone loss. 3. Stress shielding simulation analysis reveals that cortical bone in the human skeletal structure predominantly bears downward stress, while the trabecular bone, due to its loose mesh-like structure, bears minimal stress. After implantation, the stress transition phenomenon at the junction between the porous gradient bone scaffold structure and natural bone parts is notably less pronounced than with titanium alloy and PEEK material implants under identical mechanical conditions. Areas of significant stress in the biomimetic bone structure’s cortical bone layer can mitigate bone loss during bone reconstruction, thus decreasing the likelihood of secondary surgeries for patients during later recovery stages. Declarations Funding The project is supported by Natural Science Foundation of Zhejiang Province of China (Grant No. LY22E050001); State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences (LSL-2113); Public Welfare Technology Application Research Project of Jinhua (2023-4-006); Major/Key research plan of the Jinhua Science and Technology Agency (2021-1-075). Author's contribution LKX and LN participated in the design of this research, wrote the text of the research report, and simulated the theme. During the investigation, YKH supplemented the data. All the readers have read this article. Availability of data and materials The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request. References Campana V, Milano G, Pagano E, et al. Bone substitutes in orthopaedic surgery: from basic science to clinical practice[J]. Journal of Materials Science: Materials in Medicine, 2014, 25: 2445-2461. Quarto R, Giannoni P. Bone Tissue Engineering: Past-Present-Future[J].Methods Mol Biol. 2016;1416:21-33. Ana Y. Rioja, Ethan L.H. Daley, Julia C. Habif, Andrew J. Putnam, Jan P. Stegemann.Distributed vasculogenesis from modular agarose-hydroxyapatite-fibrinogen microbeads[J].Acta Biomaterialia,2017,55:144-152. Alain C. Masquelet, Thierry Begue.The Concept of Induced Membrane for Reconstruction of Long Bone Defects[J].Orthopedic Clinics of North America,2010,41(1):27-37. Ramkumar T. Annamalai, Xiaowei Hong, Nicholas G. Schott, Gopinath Tiruchinapally, Benjamin Levi, Jan P. Stegemann,Injectable osteogenic microtissues containing mesenchymal stromal cells conformally fill and repair critical-size defects[J].Biomaterials,2019,208:32-44. Keating JF, Simpson AHRW, Robinson CM. The management of fractures with bone loss[J]. Bone Joint Surg Br. 2005,87-B(2):142-150. Robert Langer,Joseph Vacanti.Advances in tissue engineering[J].Journal of Pediatric Surgery,2016,51:8-12. Hwang, K.-S.; Choi, J.-W.; Kim, J.-H.; Chung, H.Y.; Jin, S.; Shim, J.-H.; Yun, W.-S.; Jeong, C.-M.; Huh, J.-B. Comparative Efficacies of Collagen-Based 3D Printed PCL/PLGA/β-TCP Composite Block Bone Grafts and Biphasic Calcium Phosphate Bone Substitute for Bone Regeneration[J].Materials 2017, 10, 421. Sung Eun Kim,Young-Pil Yun,Kyu-Sik Shim,Hak-Jun Kim,Kyeongsoon Park and Hae-Ryong Song.3D printed alendronate-releasing poly(caprolactone) porous scaffolds enhance osteogenic differentiation and bone formation in rat tibial defects[J].Biomedical Materials,11(5),055005. Beheshtizadeh, N., Asgari, Y., Nasiri, N., Farzin, A., Ghorbani, M., Lotfibakhshaiesh, N., & Azami, M.A network analysis of angiogenesis/osteogenesis-related growth factors in bone tissue engineering based on in-vitro and in-vivo data: A systems biology approach[J].Tissue and Cell,2021,72:101553. Mengna Duan, Sijia Ma, Chunyan Song, Jie Li, Ming Qian,Three-dimensional printing of a β-tricalcium phosphate scaffold with dual bioactivities for bone repair[J].Ceramics International,2021,47(4):4775-4782. Wang,C.,Zhao, Q.and Wang, M.Cryogenic 3D printing for producing hierarchical porous and rhBMP-2-loaded Ca-P/PLLAnanocomposite scaffolds for bone tissue engineering[J].Biofabrication,9(2):025031. Zimmerling, A., Yazdanpanah, Z., Cooper, D.M.L. et al. 3D printing PCL/nHA bone scaffolds: exploring the influence of material synthesis techniques[J]. Biomater Res,2021,25:3. Park,H., Kim, J. S.,Oh, E. J.,Kim,T.J., Kim, H. M.,Shim, J. H., et al.Effects of three-dimensionally printed polycaprolactone/β-tricalcium phosphate scaffold on osteogenic differentiation of adipose tissue-and bone marrow-derived stem cells[J]. Archives Craniofacial Surg,2018,19 (3):181–189. Koons, G.L., Diba, M. & Mikos, A.G.Materials design for bone-tissue engineering[J].Nat Rev Mater 5,2020,584–603. Ku, J., Kim, Y., and Um, I. The retrospective clinical study of the autogenous tooth block bone graft[J].Dent Implant,2015,34:27–34. Giuliani, A., Manescu, A., Mohammadi, S., Mazzoni, S., Piattelli, A., Mangano, F., et al.Quantitative kinetics evaluation of blocks versus granules of biphasic calcium phosphate scaffolds (HA/β-TCP 30/70) by synchrotron radiation x-ray microtomography: A human study[J]. Implant Dent,2016,25(1):6–15. Karageorgiou, V., and Kaplan, D. Porosity of 3D biomaterial scaffolds and osteogenesis[J].Biomaterials,2005,26(27):5474–5491. Rezwan, K., Chen, Q., Blaker, J., and Boccaccini, A. R.Biodegradable and bioactive porous polymer/inorganic composite scaffolds for bone tissue engineering[J].Biomaterials,2006,27(18):3413–3431. Pattanashetti, N. A., Biscaia, S., Moura, C., Mitchell, G. R., and Kariduraganavar, M. Y. (2019). Development ofnovel 3D scaffolds using BioExtruder by the incorporation of silica into polycaprolactone matrix for bone tissue engineering. Mater. Today Commun.21:100651. Fallah, A., Altunbek, M., Bartolo, P., Cooper, G.,Weightman, A., Blunn, G., et al.3D printed scaffold design for bone defects with improved mechanical and biological properties[J].Journal of the Mechanical Behavior of Biomedical Materials,2022,134:105418-----10.1016/j.jmbbm.2022.105418 Huber, F., Vollmer,D., Vinke, J.,Riedel, B.,Zankovic, S., Schmal, H., etal.Influence of 3D printing parameters on the mechanical stability ofPCL scaffolds and the proliferation behavior of bone cells[J].Materials,2022,15(6):2091. Liu, Y., Wang, R., Chen, S., Xu, Z., Wang, Q., Yuan, P., et al. Heparan sulfate loaded polycaprolactone-hydroxyapatite scaffolds with 3D printing for bone defect repair[J].International Journal of Biological Macromolecules,2020,148:153–162. Konopnicki, S., Sharaf, B., Resnick, C., Patenaude, A., Pogal-Sussman, T., Hwang, K.G., et al.Tissue-engineered bone with 3-dimensionally printed β-tricalcium phosphate and polycaprolactone scaffolds and early implantation: An in vivo pilot study in a porcine mandible model[J].Journal of Oral and Maxillofacial Surgery,2015,73(5):1016. Wang, W., Caetano, G., Ambler, W., Blaker, J., Frade, M., Mandal, P., et al.Enhancing the hydrophilicity and cell attachment of 3D printed PCL/graphene scaffolds for bone tissue engineering[J]. Materials,2016,9(12):992. Du, X., Wei, D., Huang, L., Zhu, M., Zhang, Y., and Zhu, Y.3D printing of mesoporous bioactive glass/silk fibroin composite scaffolds for bone tissue engineering[J].Materials Science and Engineering:C,2019,103:109731. Russmueller, G., Liska, R., Stampfl, J., Heller, C., Mautner, A., Macfelda, K., et al.3D printable biophotopolymers for in vivo bone regeneration[J]. Materials,2015,8(6):3685–3700. Celikkin, N., Mastrogiacomo, S., Dou, W., Heerschap, A., Oosterwijk, E.,Walboomers, X. F., et al.In vitro and in vivo assessment of a 3D printable gelatin methacrylate hydrogel for bone regeneration applications[J].Jourmal of Biomedical Materials Research,2022,110:2133–2145. Chen, S., Shi, Y., Zhang, X., and Ma, J. Evaluation of BMP-2 and VEGF loaded 3D printed hydroxyapatite composite scaffolds with enhanced osteogenic capacity in vitro and in vivo[J]. Materials Science and Engineering:C,2020,112:110893. Ashby, M.F., Medalist, R.F.M. The mechanical properties of cellular solids[J]. Metall Trans A,1983,14:1755–1769. Cheah, C., Chua, C., Leong, K. et al. Development of a Tissue Engineering Scaffold Structure Library for Rapid Prototyping. Part 1: Investigation and Classification[J].The International Journal of Advanced Manufacturing Technology,2003,21:291–301. Cheah, C., Chua, C., Leong, K. et al. Development of a Tissue Engineering Scaffold Structure Library for Rapid Prototyping. Part 2: Investigation and Classification[J].The International Journal of Advanced Manufacturing Technology,2003,21:291–301. R. Hedayati, M. Sadighi, M. Mohammadi-Aghdam, A.A. Zadpoor,Mechanics of additively manufactured porous biomaterials based on the rhombicuboctahedron unit cell[J].Journal of the Mechanical Behavior of Biomedical Materials,2016,53:272-294. G. Bini, F. Bini, R. Bedini, A. Marinozzi, F. Marinozzi,A topological look at human trabecular bone tissue[J].Mathematical Biosciences,2017,288:159-165. Huawei Qu, Zhenyu Han, Zhigang Chen, Lan Tang, Chongjian Gao, Kaizheng Liu, Haobo Pan, Hongya Fu, Changshun Ruan. Fractal Design Boosts Extrusion-Based 3D Printing of Bone-Mimicking Radial-Gradient Scaffolds. Research. 2021;2021. M.K.H. Malo, D. Rohrbach, H. Isaksson, J. Töyräs, J.S. Jurvelin, I.S. Tamminen, H. Kröger, K. Raum,Longitudinal elastic properties and porosity of cortical bone tissue vary with age in human proximal femur[J].Bone,2013,53(2):451-458. Ding M, Dalstra M, Danielsen CC, Kabel J, Hvid I, Linde F. Age variations in the properties of human tibial trabecular bone[J].The Bone&Joint Journal,1997,79-B(6):995-1002. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4647620","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":329492985,"identity":"b89f6f18-92db-4341-b350-f18fde310d7f","order_by":0,"name":"Kaixin Lin","email":"","orcid":"","institution":"Zhejiang Normal University","correspondingAuthor":false,"prefix":"","firstName":"Kaixin","middleName":"","lastName":"Lin","suffix":""},{"id":329492986,"identity":"6544c74d-a18e-4a5d-bdff-01cb8e51766e","order_by":1,"name":"Kaihuan Yu","email":"","orcid":"","institution":"chinese academy of sciences","correspondingAuthor":false,"prefix":"","firstName":"Kaihuan","middleName":"","lastName":"Yu","suffix":""},{"id":329492987,"identity":"cb2ad3a2-aeae-45f6-aee8-082a45f829b7","order_by":2,"name":"Ning Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsElEQVRIie3OMQrCMBiG4T8EMhVdIwpe4e8u9ioJgUyCjh0zSCe7B/QSbh0jXYMeoEt6Bhe76eScbIJ55++BDyCX+8FmQPsg6g0QE0sYMI3B6yRS4GI89gnH2NIgSvOo6PmEMHUxZOVEkN1AycUjaX0M4cKh9AMjdoeUNFFEGi6be5FCFHyI4ylEMxReIbH6cGtjyJzvn+Or3lalVdcwxZBvpQFwKQBgnTbP5XK5f+oNJzAz0Ycn9+YAAAAASUVORK5CYII=","orcid":"","institution":"Zhejiang Normal University","correspondingAuthor":true,"prefix":"","firstName":"Ning","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2024-06-27 10:02:49","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4647620/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4647620/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":60945386,"identity":"890ce235-22da-4d05-8c2c-5c7fd15020b5","added_by":"auto","created_at":"2024-07-23 22:24:43","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":38008,"visible":true,"origin":"","legend":"\u003cp\u003ea) Schematic diagram of gradient structural layering. b) Curve of age-dependent porosity variation across different layers.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4647620/v1/4fd04e962c748b446b9a909c.jpg"},{"id":60945614,"identity":"2fb60a72-04d9-41e5-8587-1a30564de46a","added_by":"auto","created_at":"2024-07-23 22:32:43","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":45037,"visible":true,"origin":"","legend":"\u003cp\u003ea) Classification of noise topology method samples. b) Bone samples of varying porosities obtained through 3D printing.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4647620/v1/efeedfec37a2f9e74a6556d1.jpg"},{"id":60944212,"identity":"6a6406cc-47a5-4bf6-ac9b-11b23ef5b587","added_by":"auto","created_at":"2024-07-23 22:08:43","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":39258,"visible":true,"origin":"","legend":"\u003cp\u003ea) Schematic diagram of porous gradient bone scaffold structure generation. b) Porosity variation curves across different levels\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4647620/v1/20615d689c9bfa63ccb2fbe4.jpg"},{"id":60944214,"identity":"109e5188-95b2-4f09-9f9b-29844bdbbe6d","added_by":"auto","created_at":"2024-07-23 22:08:43","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":53579,"visible":true,"origin":"","legend":"\u003cp\u003ea) Radial CT images of femurs across different age ranges. b) Porous gradient bone scaffold models across different age ranges with partial magnifications. c) Curves showing radial porosity rate variations between natural and modeled structures across different age ranges.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4647620/v1/e910f1b991fe8eb742365f62.jpg"},{"id":60944949,"identity":"14018e13-5d6d-4d1d-9cb9-9a312d7f6486","added_by":"auto","created_at":"2024-07-23 22:16:43","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":47951,"visible":true,"origin":"","legend":"\u003cp\u003ea) Schematic diagram of the model's layered connection. b) Schematic diagram of the model's smooth repair. c) Comparison of the model before and after repair.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4647620/v1/68766ea3ecdce794ac889d8b.jpg"},{"id":60944217,"identity":"f9e31d55-5e65-4f91-a550-049b16d87b9d","added_by":"auto","created_at":"2024-07-23 22:08:43","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":75431,"visible":true,"origin":"","legend":"\u003cp\u003ea) Deformation cloud map for bone structure, ages 18-36. b) Deformation cloud map for bone structure, ages 36-53. c) Deformation cloud map for bone structure, ages 53+. d) Deformation cloud map for bone structure, ages 18-36. e) Deformation cloud map for bone structure, ages 36-53. f) Deformation cloud map for bone structure, ages 53+. g) Deformation curve of the porous gradient bone scaffold model. h) Equivalent stress cloud map of the porous gradient bone scaffold model.\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4647620/v1/2e94c5097d282b8fdd52c906.jpg"},{"id":60945388,"identity":"d32cb02b-1aab-460e-b9a8-f860085ddc4a","added_by":"auto","created_at":"2024-07-23 22:24:43","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":75789,"visible":true,"origin":"","legend":"\u003cp\u003ea) Impact cloud map for bone models aged 18-36. b) Impact cloud map for bone models aged 36-53. c) Impact cloud map for bone models aged 53+. d) Cross-sectional impact cloud map for bone models aged 18-36. e) Cross-sectional impact cloud map for bone models aged 36-53. f) Cross-sectional impact cloud map for bone models aged 53+. g) Impact stress distribution cloud map for bone models aged 18-36. h) Impact stress distribution cloud map for bone models aged 36-53. i) Impact stress distribution cloud map for bone models aged 53+.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4647620/v1/02eae21a0bbbdfe97744f36d.jpg"},{"id":60944220,"identity":"27740579-7b8b-4988-8ef7-59e90d24ed31","added_by":"auto","created_at":"2024-07-23 22:08:43","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":66692,"visible":true,"origin":"","legend":"\u003cp\u003ea) Schematic diagram of compression simulation. b) Compression simulation results of the porous gradient bone scaffold model. c) Compression simulation results of natural bone. d) Compression simulation results of titanium alloy. e) Compression simulation results of PEEK bone segment.\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4647620/v1/cabb471e5b09a208b93e1423.jpg"},{"id":60944953,"identity":"0f5cf6a0-f11b-4802-93c9-d1b91da1ed4e","added_by":"auto","created_at":"2024-07-23 22:16:43","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":41208,"visible":true,"origin":"","legend":"\u003cp\u003e3D printed physical model of the porous gradient bone scaffold.\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4647620/v1/c59cca681f4a70aa167c7790.jpg"},{"id":63991332,"identity":"14c7737e-48a1-44a4-91c5-d45f67e57eac","added_by":"auto","created_at":"2024-09-04 15:29:52","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":857190,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4647620/v1/0b1132b1-f384-4d59-8605-9112bf198ffd.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Modeling and Mechanical Performance Analysis of Porous Gradient Bone Scaffolds","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eBone transplantation is the primary method to address bone defects, accounting for one-fourth of all procedures related to bone defects and ranking as the second most common human tissue transplant surgery after blood transfusion [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Bone defects frequently result from trauma, tumors, infections, metabolic diseases, surgeries, radiation therapy, or functional degeneration, making them a common type of injury in clinical settings. The human skeletal system exhibits a certain degree of recovery and morphological regenerative capability [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], where minor bone defects can typically self-heal without external intervention. However, when bone defects exceed a specific size (greater than 2 cm) or when the bone perimeter around the defect exceeds 50%, the self-healing capacity is significantly impaired. This may lead to complications such as non-union, abnormal healing, or pathological fractures [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], potentially resulting in lifelong disabilities for the patients. Effectively repairing bone defects, alleviating healing burdens on patients, and shortening postoperative recovery periods are currently the primary focuses of orthopedic research.\u003c/p\u003e \u003cp\u003eBone Tissue Engineering (BTE) was first proposed in 1993 and has since emerged as a rapidly growing research area within tissue engineering. It is regarded as an effective method for addressing the challenges of bone defects [\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Research in BTE has shown that artificial biomimetic bones, which possess characteristics such as bone induction, bone conduction, and bone integration, can effectively promote healing and recovery in the human body [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Specifically, the bone-conducting properties of scaffolds prevent fibrous capsule formation and facilitate strong bonding with natural bone [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Their sufficient biocompatibility and bioactivity enhance the adhesion of osteogenic cells to surrounding new bone, thereby alleviating postoperative healing burdens on patients. Moreover, these scaffolds need to mimic the structure, shape, and function of the missing bone segment, featuring optimized geometric shapes and porosity to ensure adequate space for bone regeneration and to support bone membrane development, thereby accurately filling the anatomical structure of the bone defect [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. The interior of bones displays a porous structure, where variations in pore size significantly influence the biological behavior of bone cells. For instance, a pore size of approximately 300 micrometers in trabecular bone is beneficial for bone growth and nutrient exchange within the human tissue environment [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Furthermore, scaffolds must exhibit sufficient mechanical strength to satisfy the structural demands of tissue substitutes and possess an elastic modulus akin to that of human bone tissue to prevent stress shielding phenomena [\u003cspan additionalcitationids=\"CR21\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn recent years, due to limitations in controlling scaffold geometry, pore size, and inter-connectivity using traditional techniques, Additive Manufacturing (AM) has emerged as the preferred method for creating artificial biomimetic bone scaffolds [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. AM technology enables precise control over various attributes of bone scaffolds, such as stiffness, biochemical factors, spatial distribution capabilities, as well as complex or irregular pore shapes and surface morphologiess [\u003cspan additionalcitationids=\"CR25\" citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. Additionally, this technology facilitates high-density in vivo interactions by using bioinks containing different cell types and extracellular matrix (ECM) for high-density bioprinting, allowing for the fabrication of large-scale alternative structures for damaged bones [\u003cspan additionalcitationids=\"CR28\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. AM technology also offers several other benefits, including the ability to process multiple materials incorporating drugs and biomolecules, maintaining structural and shape stability, minimizing material wastage, improving mechanical performance, enhancing cell infiltration, and promoting nutrient circulation, making it an ideal choice in bone tissue engineering. Ashby et al. [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] proposed a cubic unit cell model for open-cell foam and closed-cell foam, elucidating the relationship between porosity and overall mechanical properties, thereby providing a more rational theoretical basis for scaffold design. Cheah et al. [\u003cspan additionalcitationids=\"CR32\" citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], considering the manufacturability and spatial geometric characteristics of specific AM technologies, established a library comprising 11 unit types and investigated scaffolds composed of diamond lattices, cubic lattices, truncated octahedra, rhombic dodecahedra, and rhombicuboctahedra to derive analytical relationships between geometric parameters like porosity, scaffold diameter, pore size, and the scaffold's Young's modulus and Poisson's ratio. G. Bini et al. [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] studied trabecular bone microstructure from a topological perspective, summarizing the concept of topological spatial models for bone tissue microstructure, providing further insights for the design of artificial bone structures. AM technology has become a new trend in preparing artificial biomimetic bone scaffolds in the field of BTE.\u003c/p\u003e \u003cp\u003eBased on the requirements of bone tissue engineering for biomimetic bone scaffolds, this study introduces a novel noise topology-based 3D bone scaffold model. The study establishes a porosity pattern classification based on bone density distribution across different age groups and performs mechanical simulations on the resulting bone structure models using finite element software. AM technology ensures that the porous gradient bone scaffold model closely resembles natural bone in terms of shape, structure, porosity, and stress distribution. The layered structure is also better suited to adapt to the distribution of bone tissue membrane layers, cortical bone layers, and trabecular bone layers, from outer to inner layers. At the medical technology level, this approach helps prevent postoperative bone loss due to stress mismatch after bone grafting, ultimately reducing healing pressures on patients and shortening recovery periods.\u003c/p\u003e"},{"header":"2. Main Text","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Generation of porous structure using noise topology method\u003c/h2\u003e \u003cp\u003eThe human femoral shaft is cylindrical in structure, with a radial diameter variation rate not exceeding 20%. Based on the layered structure of bone tissue (as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea), it can be divided from the inner to outer layers into four layers: marrow cavity, trabecular bone layer, cortical bone layer, and periosteum layer [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. In this study, the bone tissue model is represented as concentric, mutually adhering cylindrical models to streamline the simulation of the bone tissue structure and simplify the model. The thickness ratio of the periosteum, cortical bone, trabecular bone, and marrow cavity layers is set at 1:3:4:5. The overall height of the bone scaffold is established at 14mm, creating an initially simplified, gradient, layered structure. Drawing on human bone sampling results [35,36], and reflecting the radial porosity variations across different age groups (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb), the target porous bone structure model specifies a porosity for the periosteum layer of 10%-15%, cortical bone at 55\u0026ndash;60%, and trabecular bone at 75%-80%.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eUtilizing the noise topology method within Cinema 4D software, specifically through the Proc3Durale plugin, varied porous structures are generated by adjusting various global scales, voxels, thresholds, and selecting diverse noise types. These structures are then categorized based on type and porosity levels, forming a 'Noise Topology Method Sample Classification' table (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea). Subsequent selections of layered bone structures appropriate for various age groups are made from this table. Sample models are printed using a photosensitive resin through a 3D printer (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb), with ZR680 photosensitive resin selected as the printing material, featuring a density of 1.1g/cm\u003csup\u003e3\u003c/sup\u003e. The resulting sample models and data will contribute to the development of an age-specific porosity standard database. The actual sample porosity is compared with the calculated ideal porosity, with an allowable error margin of 5%.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Generation of porous gradient bone scaffolds for different age groups\u003c/h2\u003e \u003cp\u003eFocusing on the age group of 18\u0026ndash;36 years for the bone scaffold model (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea), the bone membrane layer is depicted using a Type 2 noise topology pattern at a 30% global scale. The cortical bone layer is modeled with a Type 3 pattern at a 50% global scale, while the trabecular bone layer utilizes a Type 3 pattern at a 30% global scale. These three components are integrated into concentric circular connectors, leaving the marrow layer vacant. The porosity variation curves for the radial bone scaffold structure across different layers are analyzed (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). The radial porosity change curve for the porous gradient bone scaffold aligns closely with the natural radial porosity change curve observed in individuals aged 18\u0026ndash;36 years, demonstrating negligible differences between the two.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eBased on bone density variation patterns across age groups, styles and porosity formats from noise topological methods were selected from a standard database to develop porous gradient bone scaffold models for three age groups: 18\u0026ndash;36, 36\u0026ndash;53, and 53+. These models were subsequently compared radially with actual human femoral bones (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea displays a solid bone CT image, highlighting a significant decrease in cross-sectional area with age, and an increase in the hollow marrow cavity for fluid circulation. In the 36\u0026ndash;53 age group, the radial width is narrower than in the 18\u0026ndash;36 age group, and it is narrowest in the 53\u0026thinsp;+\u0026thinsp;age group, featuring a distinctly porous mesh within the bone structure. This reflects severe bone mass loss in older populations, leading to reduced load-bearing and impact resistance capabilities. Mirroring changes in bone porosity among age groups, this study utilized noise topography samples with varying porosity rates for bone scaffold models tailored to different age groups (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb), effectively creating porous gradient bone structural models for these groups. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec shows the comparison curve between the three types of porous gradient bone scaffold models and the natural bone porosity rates for each age group, indicating minimal differences compared to the layered porosity rates of natural bone within the same age demographics. This model accurately represents the radial structure of natural bone tissues across various age groups.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Three-Dimensional restoration of porous gradient bone scaffold models\u003c/h2\u003e \u003cp\u003eThe porous gradient model created using Cinema 4D features clearly defined layers of periosteum, cortical bone, and trabecular bone due to gradient differentiation, existing independently rather than as a cohesive unit. This separation can cause issues in subsequent simulations, such as inadequate stress transmission, distortion, and inadequate contact. Therefore, it is essential to convert the model into a single, unified solid structure. The three independent models are joined using the software's linking tool to form a cohesive solid structure, and the 'Volume Generation' feature smooths the edge voxels of the connected model (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea). Optimize any minor debris models that fail to form complete connections, eliminate overlapping interference from completed parts, or address isolated fractures. These small debris models can lead to solidification failures of the STL model or adversely affect the mechanical properties of the porous gradient structure. Consequently, Geomagic Wrap software (Geomagic, USA) is utilized to refine non-manifold edges, self-intersections, highly refractive edges, pin-shaped objects, sub-components, narrow channels, and small holes in the three-dimensional model for repair (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb). Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec displays a sectional comparison before and after the model's connectivity repair, showing a seamless transition at the gradient interfaces and confirming effective integration within the three-dimensional structure.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Load-bearing and impact simulation analysis of porous gradient bone scaffold models\u003c/h2\u003e \u003cp\u003eA segment equivalent to one eighth of the porous gradient bone scaffold model is utilized in Ansys simulation software (ANSYS, USA) to conduct a static load-bearing simulation. The material properties are set as follows: density of 1.2\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e tonne/mm\u0026sup3;, elastic modulus of 3883.4 MPa, Poisson's ratio of 0.3, bulk modulus of 3236.2 MPa, and shear modulus of 1493.6 MPa. The mesh is configured for nonlinear mechanics with a unit size of 0.5 mm. The base of the model is fixed for constraints, and a load simulating an adult male standing, weighing 70 kg, is applied from above to perform the bone scaffold load-bearing simulation. Analysis of the resultant load-bearing simulation cloud diagram (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) reveals that the deformation resistance and equivalent stress of gradient porous bone scaffold models with varied porosities due to age differ, though their deformation patterns remain consistent, exhibiting an inward tilt angle and lesser deformation in the outer layer compared to greater deformation in the inner layer. This occurs because the cortical bone layer is the primary load-bearing layer in human bones, and the main indication of bone loss is the progressive thinning of the periosteal and cortical bone layers, which leads to increased porosity in the cortical bone and its gradual transition to trabecular bone, thereby thickening the trabecular layer. Areas of concentrated stress are identified in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea and d at the junctions between cortical and trabecular bones; environments of high stress can accelerate bone loss, typically starting from the inner side of the cortical bone. The reduction in thickness of the periosteal and cortical bone layers results in increased deformation, while the growing thickness of the inner trabecular bone contributes to this increase. As depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.d-f, the stress distribution in the porous scaffold of a 36-year-old resembles that of an 18-year-old, with a maximum equivalent stress of 37.596 MPa, which is merely 2.5 times that of the latter (14.958 MPa). However, for the age group above 53, the maximum equivalent stress reaches 384.14 MPa, demonstrating a significant decline in the load-bearing capacity of the human skeleton with bone mass loss and reduced bone density.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eUsing the same material parameters as in the load-bearing simulation, with both the top and bottom secured, an impact force of 100N perpendicular to the model's geometry is applied outside the periosteal layer to simulate real-world impacts (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). The resulting impact cloud map shows that deformation primarily occurs as compression at the point of load, with the extent of deformation decreasing progressively from the outer to the inner layers. The periosteal layer exhibits the most significant deformation, while the trabecular bone layer experiences the least. In the models for the 18\u0026ndash;36 and 36\u0026ndash;53 age groups, the trabecular bone layer remains unaffected by the deformation (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ed, e). However, in the model for individuals over 53 years old, there is considerable impact on the trabecular bone layer (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ef), indicating a compromised structural integrity in the periosteal and cortical layers that fails to shield the internal trabecular bone layer and marrow from external impacts. This reflects a significant reduction in the bone's ability to protect the internal structures due to bone mass loss in the periosteal and cortical layers in individuals aged 53 and above.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Stress shielding simulation analysis of porous gradient bone scaffold models\u003c/h2\u003e \u003cp\u003eAfter repairing the porous gradient bone scaffold model with Geomagic Wrap for 3D solid smoothing, the model is transferred to nTopology (nTopology Inc., USA) to generate the complete mesh. It is then imported into Abaqus (Dassault Systemes SE, France) for compression simulation testing. Two concentric cylindrical sections are positioned at the top and bottom of the model to emulate the natural bone sections adjacent to the implanted bone tissue. The materials for the implanted bone tissues are replaced with those of natural bone (periosteal layer Young's modulus of 20000, Poisson's ratio of 0.26; cortical bone layer Young's modulus of 5700, Poisson's ratio of 0.26; trabecular bone layer Young's modulus of 64, Poisson's ratio of 0.29), titanium alloy (Young's modulus of 109000, Poisson's ratio of 0.33), and PEEK (Young's modulus of 3000, Poisson's ratio of 0.33). A load of 700N is applied from above to the natural bone section to simulate the pressure experienced during single-footed human walking. The base of the natural bone section is secured for constraints, facilitating the study of the stress shielding effects exerted by different implants on the human skeletal system (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe results of the natural whole bone compression simulation (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ec) show that the cortical bone layer bears the majority of the pressure from top to bottom, with the equivalent stress in the cortical bone layer exceeding that in the periosteal layer, and the trabecular bone layer inside almost devoid of stress. In the titanium alloy simulation (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ed), a pronounced stress shielding phenomenon is evident throughout the model, with stress concentration around the titanium alloy segment; the equivalent stress in the natural bone segments above and below is significantly lower than in the middle implant part. Prolonged exposure of the human skeletal system to low-stress environments may lead to bone loss in this area, diminishing the strength at the interface between natural bone and the titanium alloy implant and increasing the likelihood of secondary surgery. In the PEEK bone segment implant (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ee), no significant stress shielding effect is observed compared to the titanium alloy model; the stress distribution on the outer surface is more uniform, indicating that bone implants made from PEEK material can more effectively mitigate stress shielding effects compared to titanium alloy. The porous gradient bone scaffold model (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb), printed with PEEK material, shows that the internal cortical bone part bears most of the pressure from top to bottom, while the trabecular bone part maintains a loose structure with high porosity similar to natural bone and bears minimal load pressure. The periosteal layer does not exhibit significant stress shielding, but a reduction in equivalent stress is noted at the junction between natural bone and the bone scaffold, due to surface irregularities on the porous gradient bone scaffold model, leading to areas of stress concentration in the cortical bone layer. Under the top-down load, these areas are the first to bear pressure. The bone reconstruction effect in the human body demonstrates that bones can effectively increase bone growth and differentiation capabilities when subjected to mechanical stimulation, thereby altering the corresponding structures. The cluster of equivalent stress concentration points on the upper and lower surfaces of the porous gradient bone model can effectively enhance the growth and differentiation of bone cells in the cortical bone region, improving the bone's growth and repair capabilities at that site and hence shortening the recovery time after bone transplant surgery.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe fully repaired and well-fitted complete porous gradient biomimetic bone scaffold model is 3D printed using photosensitive resin and compared with slices of natural human bone (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ea-c). In Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eb, a one-eighth section of the 3D printed porous gradient bone scaffold model is produced through slicing. The 3D printed model reveals that the outermost layer exhibits the lowest porosity, while the internal layers display the highest porosity, mimicking the distribution of natural bone tissue. This high porosity enhances the surface area, effectively facilitating the attachment and growth of osteoblasts and osteoclasts on the artificial biomimetic bone scaffold, thus promoting early recovery following bone grafting surgery. Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ed-g illustrate the top view, sectional view, and corresponding SEM images of the model. The porous gradient bone model is constrained by the extrusion precision of 3D printing and does not fully replicate the microstructure of natural bone tissue at the microscopic level. Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eh-m show porous gradient bone models printed with both photosensitive resin and PEEK material. Given its mechanical properties similar to natural bone, PEEK material is more effective in preventing bone loss associated with the bone reconstruction effect during the postoperative recovery period.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Conclusion","content":"\u003cp\u003e1. The bone scaffold structure created by the noise topology method achieves a radial gradient of porosity ranging from 10.1-15.4% in the periosteal layer, 33.07-55.38% in the cortical bone layer, and 63.84-73.74% in the trabecular bone layer. The external biomimetic periosteal layer, smoothly repaired, forms a barrier function that prevents soft tissue invasion into the defect area. The internal trabecular bone part, resembling natural trabecular bone beams, enhances the transport of bone cells, nutrients, and bioactive substances.\u003c/p\u003e\n\u003cp\u003e2. Load and impact simulations have\u0026nbsp;also compared and differentiated bone scaffold structure models across various age groups. As porosity and bone density decrease with age, the bones\u0026apos; load-bearing capacity and impact resistance diminish significantly. Models in individuals over 53 years old lack sufficient impact resistance to protect the internal trabecular bone layer and the enveloping marrow cavity layer from external impacts, indicating that individuals over 50 are more susceptible to osteoporosis-related fractures due to bone loss.\u003c/p\u003e\n\u003cp\u003e3. Stress shielding simulation analysis reveals that cortical bone in the human skeletal structure predominantly bears downward stress, while the trabecular bone, due to its loose mesh-like structure, bears minimal stress. After implantation, the stress transition phenomenon at the junction between the porous gradient bone scaffold structure and natural bone parts is notably less pronounced than with titanium alloy and PEEK material implants under identical mechanical conditions. Areas of significant stress in the biomimetic bone structure\u0026rsquo;s cortical bone layer can mitigate bone loss during bone reconstruction, thus decreasing the likelihood of secondary surgeries for patients during later recovery stages.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe project is supported by Natural Science Foundation of Zhejiang Province of China (Grant No. LY22E050001); State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences (LSL-2113); Public Welfare Technology Application Research Project of Jinhua (2023-4-006); Major/Key research plan of the Jinhua Science and Technology Agency (2021-1-075).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor's contribution\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eLKX and LN participated in the design of this research, wrote the text of the research report, and simulated the theme. During the investigation, YKH supplemented the data. All the readers have read this article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eCampana V, Milano G, Pagano E, et al. Bone substitutes in orthopaedic surgery: from basic science to clinical practice[J]. Journal of Materials Science: Materials in Medicine, 2014, 25: 2445-2461. \u003c/li\u003e\n\u003cli\u003eQuarto R, Giannoni P. Bone Tissue Engineering: Past-Present-Future[J].Methods Mol Biol. 2016;1416:21-33.\u003c/li\u003e\n\u003cli\u003eAna Y. Rioja, Ethan L.H. Daley, Julia C. Habif, Andrew J. Putnam, Jan P. Stegemann.Distributed vasculogenesis from modular agarose-hydroxyapatite-fibrinogen microbeads[J].Acta Biomaterialia,2017,55:144-152.\u003c/li\u003e\n\u003cli\u003eAlain C. Masquelet, Thierry Begue.The Concept of Induced Membrane for Reconstruction of Long Bone Defects[J].Orthopedic Clinics of North America,2010,41(1):27-37.\u003c/li\u003e\n\u003cli\u003eRamkumar T. Annamalai, Xiaowei Hong, Nicholas G. Schott, Gopinath Tiruchinapally, Benjamin Levi, Jan P. Stegemann,Injectable osteogenic microtissues containing mesenchymal stromal cells conformally fill and repair critical-size defects[J].Biomaterials,2019,208:32-44.\u003c/li\u003e\n\u003cli\u003eKeating JF, Simpson AHRW, Robinson CM. The management of fractures with bone loss[J]. Bone Joint Surg Br. 2005,87-B(2):142-150.\u003c/li\u003e\n\u003cli\u003eRobert Langer,Joseph Vacanti.Advances in tissue engineering[J].Journal of Pediatric Surgery,2016,51:8-12.\u003c/li\u003e\n\u003cli\u003eHwang, K.-S.; Choi, J.-W.; Kim, J.-H.; Chung, H.Y.; Jin, S.; Shim, J.-H.; Yun, W.-S.; Jeong, C.-M.; Huh, J.-B. Comparative Efficacies of Collagen-Based 3D Printed PCL/PLGA/\u0026beta;-TCP Composite Block Bone Grafts and Biphasic Calcium Phosphate Bone Substitute for Bone Regeneration[J].Materials 2017, 10, 421.\u003c/li\u003e\n\u003cli\u003eSung Eun Kim,Young-Pil Yun,Kyu-Sik Shim,Hak-Jun Kim,Kyeongsoon Park and Hae-Ryong Song.3D printed alendronate-releasing poly(caprolactone) porous scaffolds enhance osteogenic differentiation and bone formation in rat tibial defects[J].Biomedical Materials,11(5),055005.\u003c/li\u003e\n\u003cli\u003eBeheshtizadeh, N., Asgari, Y., Nasiri, N., Farzin, A., Ghorbani, M., Lotfibakhshaiesh, N., \u0026amp; Azami, M.A network analysis of angiogenesis/osteogenesis-related growth factors in bone tissue engineering based on in-vitro and in-vivo data: A systems biology approach[J].Tissue and Cell,2021,72:101553.\u003c/li\u003e\n\u003cli\u003eMengna Duan, Sijia Ma, Chunyan Song, Jie Li, Ming Qian,Three-dimensional printing of a \u0026beta;-tricalcium phosphate scaffold with dual bioactivities for bone repair[J].Ceramics International,2021,47(4):4775-4782.\u003c/li\u003e\n\u003cli\u003eWang,C.,Zhao, Q.and Wang, M.Cryogenic 3D printing for producing hierarchical porous and rhBMP-2-loaded Ca-P/PLLAnanocomposite scaffolds for bone tissue engineering[J].Biofabrication,9(2):025031.\u003c/li\u003e\n\u003cli\u003eZimmerling, A., Yazdanpanah, Z., Cooper, D.M.L. et al. 3D printing PCL/nHA bone scaffolds: exploring the influence of material synthesis techniques[J]. Biomater Res,2021,25:3.\u003c/li\u003e\n\u003cli\u003ePark,H., Kim, J. S.,Oh, E. J.,Kim,T.J., Kim, H. M.,Shim, J. H., et al.Effects of three-dimensionally printed polycaprolactone/\u0026beta;-tricalcium phosphate scaffold on osteogenic differentiation of adipose tissue-and bone marrow-derived stem cells[J]. Archives Craniofacial Surg,2018,19 (3):181\u0026ndash;189.\u003c/li\u003e\n\u003cli\u003eKoons, G.L., Diba, M. \u0026amp; Mikos, A.G.Materials design for bone-tissue engineering[J].Nat Rev Mater 5,2020,584\u0026ndash;603.\u003c/li\u003e\n\u003cli\u003eKu, J., Kim, Y., and Um, I. The retrospective clinical study of the autogenous tooth block bone graft[J].Dent Implant,2015,34:27\u0026ndash;34.\u003c/li\u003e\n\u003cli\u003eGiuliani, A., Manescu, A., Mohammadi, S., Mazzoni, S., Piattelli, A., Mangano, F., et al.Quantitative kinetics evaluation of blocks versus granules of biphasic calcium phosphate scaffolds (HA/\u0026beta;-TCP 30/70) by synchrotron radiation x-ray microtomography: A human study[J]. Implant Dent,2016,25(1):6\u0026ndash;15.\u003c/li\u003e\n\u003cli\u003eKarageorgiou, V., and Kaplan, D. Porosity of 3D biomaterial scaffolds and osteogenesis[J].Biomaterials,2005,26(27):5474\u0026ndash;5491.\u003c/li\u003e\n\u003cli\u003eRezwan, K., Chen, Q., Blaker, J., and Boccaccini, A. R.Biodegradable and bioactive porous polymer/inorganic composite scaffolds for bone tissue engineering[J].Biomaterials,2006,27(18):3413\u0026ndash;3431.\u003c/li\u003e\n\u003cli\u003ePattanashetti, N. A., Biscaia, S., Moura, C., Mitchell, G. R., and Kariduraganavar, M. Y. (2019). Development ofnovel 3D scaffolds using BioExtruder by the incorporation of silica into polycaprolactone matrix for bone tissue engineering. Mater. Today Commun.21:100651.\u003c/li\u003e\n\u003cli\u003eFallah, A., Altunbek, M., Bartolo, P., Cooper, G.,Weightman, A., Blunn, G., et al.3D printed scaffold design for bone defects with improved mechanical and biological properties[J].Journal of the Mechanical Behavior of Biomedical Materials,2022,134:105418-----10.1016/j.jmbbm.2022.105418\u003c/li\u003e\n\u003cli\u003eHuber, F., Vollmer,D., Vinke, J.,Riedel, B.,Zankovic, S., Schmal, H., etal.Influence of 3D printing parameters on the mechanical stability ofPCL scaffolds and the proliferation behavior of bone cells[J].Materials,2022,15(6):2091.\u003c/li\u003e\n\u003cli\u003eLiu, Y., Wang, R., Chen, S., Xu, Z., Wang, Q., Yuan, P., et al. Heparan sulfate loaded polycaprolactone-hydroxyapatite scaffolds with 3D printing for bone defect repair[J].International Journal of Biological Macromolecules,2020,148:153\u0026ndash;162.\u003c/li\u003e\n\u003cli\u003eKonopnicki, S., Sharaf, B., Resnick, C., Patenaude, A., Pogal-Sussman, T., Hwang, K.G., et al.Tissue-engineered bone with 3-dimensionally printed \u0026beta;-tricalcium phosphate and polycaprolactone scaffolds and early implantation: An in vivo pilot study in a porcine mandible model[J].Journal of Oral and Maxillofacial Surgery,2015,73(5):1016.\u003c/li\u003e\n\u003cli\u003eWang, W., Caetano, G., Ambler, W., Blaker, J., Frade, M., Mandal, P., et al.Enhancing the hydrophilicity and cell attachment of 3D printed PCL/graphene scaffolds for bone tissue engineering[J]. Materials,2016,9(12):992.\u003c/li\u003e\n\u003cli\u003eDu, X., Wei, D., Huang, L., Zhu, M., Zhang, Y., and Zhu, Y.3D printing of mesoporous bioactive glass/silk fibroin composite scaffolds for bone tissue engineering[J].Materials Science and Engineering:C,2019,103:109731.\u003c/li\u003e\n\u003cli\u003eRussmueller, G., Liska, R., Stampfl, J., Heller, C., Mautner, A., Macfelda, K., et al.3D printable biophotopolymers for in vivo bone regeneration[J]. Materials,2015,8(6):3685\u0026ndash;3700.\u003c/li\u003e\n\u003cli\u003eCelikkin, N., Mastrogiacomo, S., Dou, W., Heerschap, A., Oosterwijk, E.,Walboomers, X. F., et al.In vitro and in vivo assessment of a 3D printable gelatin methacrylate hydrogel for bone regeneration applications[J].Jourmal of Biomedical Materials Research,2022,110:2133\u0026ndash;2145.\u003c/li\u003e\n\u003cli\u003eChen, S., Shi, Y., Zhang, X., and Ma, J. Evaluation of BMP-2 and VEGF loaded 3D printed hydroxyapatite composite scaffolds with enhanced osteogenic capacity in vitro and in vivo[J]. Materials Science and Engineering:C,2020,112:110893.\u003c/li\u003e\n\u003cli\u003eAshby, M.F., Medalist, R.F.M. The mechanical properties of cellular solids[J]. Metall Trans A,1983,14:1755\u0026ndash;1769.\u003c/li\u003e\n\u003cli\u003eCheah, C., Chua, C., Leong, K. et al. Development of a Tissue Engineering Scaffold Structure Library for Rapid Prototyping. Part 1: Investigation and Classification[J].The International Journal of Advanced Manufacturing Technology,2003,21:291\u0026ndash;301.\u003c/li\u003e\n\u003cli\u003eCheah, C., Chua, C., Leong, K. et al. Development of a Tissue Engineering Scaffold Structure Library for Rapid Prototyping. Part 2: Investigation and Classification[J].The International Journal of Advanced Manufacturing Technology,2003,21:291\u0026ndash;301.\u003c/li\u003e\n\u003cli\u003eR. Hedayati, M. Sadighi, M. Mohammadi-Aghdam, A.A. Zadpoor,Mechanics of additively manufactured porous biomaterials based on the rhombicuboctahedron unit cell[J].Journal of the Mechanical Behavior of Biomedical Materials,2016,53:272-294.\u003c/li\u003e\n\u003cli\u003eG. Bini, F. Bini, R. Bedini, A. Marinozzi, F. Marinozzi,A topological look at human trabecular bone tissue[J].Mathematical Biosciences,2017,288:159-165.\u003c/li\u003e\n\u003cli\u003eHuawei Qu, Zhenyu Han, Zhigang Chen, Lan Tang, Chongjian Gao, Kaizheng Liu, Haobo Pan, Hongya Fu, Changshun Ruan. Fractal Design Boosts Extrusion-Based 3D Printing of Bone-Mimicking Radial-Gradient Scaffolds. Research. 2021;2021.\u003c/li\u003e\n\u003cli\u003eM.K.H. Malo, D. Rohrbach, H. Isaksson, J. T\u0026ouml;yr\u0026auml;s, J.S. Jurvelin, I.S. Tamminen, H. Kr\u0026ouml;ger, K. Raum,Longitudinal elastic properties and porosity of cortical bone tissue vary with age in human proximal femur[J].Bone,2013,53(2):451-458.\u003c/li\u003e\n\u003cli\u003eDing M, Dalstra M, Danielsen CC, Kabel J, Hvid I, Linde F. Age variations in the properties of human tibial trabecular bone[J].The Bone\u0026amp;Joint Journal,1997,79-B(6):995-1002.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Noise topology, Bone scaffold structure, Finite element analysis, Bone tissue engineering, Bone defect","lastPublishedDoi":"10.21203/rs.3.rs-4647620/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4647620/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCurrently, personalized adaptive technology using 3D printing scaffold is widely employed in bone tissue repair engineering to aid in healing and restoring large segmental bone defects. Although the scaffold matches the external appearance, its internal tissue structure differs significantly from that of natural bone tissue, and issues of mechanical matching and stress shielding persist after transplantation, impacting patient recovery. Drawing on the tissue structure of natural bone, this study develops a bionic bone scaffold model that replicates the microstructure of natural bone using a noise topology approach. Model samples are created with pore sizes and porosity corresponding to the bone density of various ages. The mechanical properties of bone structures with varying pore sizes and porosities are assessed using finite element simulation analysis software. Mechanical simulation results for bionic bone scaffolds across different ages indicate that the modeling method can adjust the pore size and porosity of the bionic bone structure through voxel parameters, aligning the mechanical characteristics with those of natural bone. This alignment effectively mitigates the stress mismatch between the implant structure and natural tissue post-bone grafting. The hierarchical gradient porous structure and mechanical model of bionic bone scaffold offer valuable insights for the structural design and clinical selection of bone implants.\u003c/p\u003e","manuscriptTitle":"Modeling and Mechanical Performance Analysis of Porous Gradient Bone Scaffolds","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-23 22:08:38","doi":"10.21203/rs.3.rs-4647620/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ec51d08e-7d0f-4f6b-8373-b1c2458a6aac","owner":[],"postedDate":"July 23rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":34881830,"name":"Biological sciences/Biotechnology/Biomaterials"},{"id":34881831,"name":"Biological sciences/Biotechnology/Biomimetics"}],"tags":[],"updatedAt":"2024-09-04T15:21:45+00:00","versionOfRecord":[],"versionCreatedAt":"2024-07-23 22:08:38","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4647620","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4647620","identity":"rs-4647620","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}