Numerical and experimental evaluation of TPMS Gyroid scaffolds for bone tissue engineering

Finite element modeling of the free boundary effect on gyroid additively manufactured samples

There is a significant need for models that can capture the mechanical behavior of complex porous lattice architectures produced by 3D printing. The free boundary effect is an experimentally observed behavior of lattice architectures including the gyroid triply periodic minimal surface where the number of unit cell repeats has been shown to influence the mechanical performance of the lattice. The purpose of this study is to use finite element modeling to investigate how architecture porosity, unit cell size, and sample size dictate mechanical behavior. Samples with varying porosity and increasing number of unit cells (relative to sample size) were modeled under an axial compressive load to determine the effective modulus. The finite element model captured the free boundary effect and captured experimental trends in the structure's modulus. The findings of this study show that samples with higher porosity are more susceptible to the impact of the free boundary effect and in some samples, the modulus can be 20% smaller in samples with smaller numbers of unit cell repeats within a given sample boundary. The outcomes from this study provide a deeper understanding of the gyroid structure and the implications of design choices including porosity, unit cell size, and overall sample size.

In vitro evaluation of the osteogenic and antimicrobial potential of porous wollastonite scaffolds impregnated with ethanolic extracts of propolis

Context: The development of porous devices using materials modified with various natural agents has become a priority for bone healing processes in the oral and maxillofacial field. There must be a balance between the proliferation of eukaryotic and the inhibition of prokaryotic cells to achieve proper bone health. Infections might inhibit the formation of new alveolar bone during bone graft augmentation. Objective: This study aimed to evaluate the in vitro osteogenic behavior of human bone marrow stem cells and assess the antimicrobial response to 3D-printed porous scaffolds using propolis-modified wollastonite. Methodology: A fractional factorial design of experiments was used to obtain a 3D printing paste for developing scaffolds with a triply periodic minimal surface (TPMS) gyroid geometry based on wollastonite and modified with an ethanolic propolis extract. The antioxidant activity of the extracts was characterized using free radical scavenging methods (DPPH and ABTS). Cell proliferation and osteogenic potential using Human Bone Marrow Stem Cells (bmMSCs) were assessed at different culture time points up to 28 days. MIC and inhibition zones were studied from single strain cultures, and biofilm formation was evaluated on the scaffolds under co-culture conditions. The mechanical strength of the scaffolds was evaluated. Results: Through statistical design of experiments, a paste suitable for printing scaffolds with the desired geometry was obtained. Propolis extracts modifying the TPMS gyroid scaffolds showed favorable cell proliferation and metabolic activity with osteogenic potential after 21 days. Additionally, propolis exhibited antioxidant activity, which may be related to the antimicrobial effectiveness of the scaffolds against S. aureus and S. epidermidis cultures. The mechanical properties of the scaffolds were not affected by propolis impregnation. Conclusion: These results demonstrate that propolis-impregnated porous wollastonite scaffolds might have the potential to stimulate bone repair in maxillofacial tissue engineering applications.

Additively manufactured porous scaffolds by design for treatment of bone defects

There has been increasing attention to produce porous scaffolds that mimic human bone properties for enhancement of tissue ingrowth, regeneration, and integration. Additive manufacturing (AM) technologies, i.e., three dimensional (3D) printing, have played a substantial role in engineering porous scaffolds for clinical applications owing to their high level of design and fabrication flexibility. To this end, this review article attempts to provide a detailed overview on the main design considerations of porous scaffolds such as permeability, adhesion, vascularisation, and interfacial features and their interplay to affect bone regeneration and osseointegration. Physiology of bone regeneration was initially explained that was followed by analysing the impacts of porosity, pore size, permeability and surface chemistry of porous scaffolds on bone regeneration in defects. Importantly, major 3D printing methods employed for fabrication of porous bone substitutes were also discussed. Advancements of MA technologies have allowed for the production of bone scaffolds with complex geometries in polymers, composites and metals with well-tailored architectural, mechanical, and mass transport features. In this way, a particular attention was devoted to reviewing 3D printed scaffolds with triply periodic minimal surface (TPMS) geometries that mimic the hierarchical structure of human bones. In overall, this review enlighten a design pathway to produce patient-specific 3D-printed bone substitutions with high regeneration and osseointegration capacity for repairing large bone defects.

Three-dimensional printed exoskeletons and orthoses for the upper limb-A systematic review

This systematic review aims to assess and summarize the current landscape in exoskeletons and orthotic solutions developed for upper limb medical assistance, which are partly or fully produced using 3-dimensional printing technologies and contain at least the elbow or the shoulder joints. The initial search was conducted on Web of Science, PubMed, and IEEEXplore, resulting in 92 papers, which were reduced to 72 after removal of duplicates. From the application of the inclusion and exclusion criteria and selection questionnaire, 33 papers were included in the review, being divided according to the analyzed joints. The analysis of the selected papers allowed for the identification of different solutions that vary in terms of their target application, actuation type, 3-dimensional printing techniques, and material selection, among others. The results show that there has been far more research on the elbow joint than on the shoulder joint, which can be explained by the relative complexity of the latter. Moreover, the findings of this study also indicate that there is still a gap between the research conducted on these devices and their practical use in real-world conditions. Based on current trends, it is anticipated that the future of 3-dimensional printed exoskeletons will revolve around the use of flexible and high-performance materials, coupled with actuated devices. These advances have the potential to replace the conventional fabrication methods of exoskeletons with technologies based on additive manufacturing.

Osseointegration of functionally graded Ti6Al4V porous implants: Histology of the pore network

The additive manufacturing of titanium into porous geometries offers a means to generate low-stiffness endosseous implants with a greater surface area available for osseointegration. In this work, selective laser melting was used to produce gyroid-based scaffolds with a uniform pore size of 300 μm or functionally graded pore size from 600 μm to 300 μm. Initial in vitro assessment with Saos-2 cells showed favourable cell proliferation at pore sizes of 300 and 600 μm. Following implantation into rabbit tibiae, early histological observations at four weeks indicated some residual inflammation alongside neovessel infiltration into the scaffold interior and some early apposition of mineralized bone tissue. At twelve weeks, both scaffolds were filled with a mixture of adipocyte-rich marrow, micro-capillaries, and mineralized bone tissue. X-ray microcomputed tomography showed a higher bone volume fraction (BV/TV) and percentage of bone-implant contact (BIC) in the implants with 300 μm pores than in the functionally graded specimens. In functionally graded specimens, localized BV/TV measurement was observed to be higher in the innermost region containing smaller pores (estimated at 300-400 μm) than in larger pores at the implant exterior. The unit cell topology of the porous implant was also observed to guide the direction of bone ingrowth by conducting along the implant struts. These results suggest that in vivo experimentation is necessary alongside parametric optimization of functionally graded porous implants to predict short-term and long-term bone apposition.

Development of Bioactive Scaffolds for Orthopedic Applications by Designing Additively Manufactured Titanium Porous Structures: A Critical Review

We overview recent findings achieved in the field of model-driven development of additively manufactured porous materials for the development of a new generation of bioactive implants for orthopedic applications. Porous structures produced from biocompatible titanium alloys using selective laser melting can present a promising material to design scaffolds with regulated mechanical properties and with the capacity to be loaded with pharmaceutical products. Adjusting pore geometry, one could control elastic modulus and strength/fatigue properties of the engineered structures to be compatible with bone tissues, thus preventing the stress shield effect when replacing a diseased bone fragment. Adsorption of medicals by internal spaces would make it possible to emit the antibiotic and anti-tumor agents into surrounding tissues. The developed internal porosity and surface roughness can provide the desired vascularization and osteointegration. We critically analyze the recent advances in the field featuring model design approaches, virtual testing of the designed structures, capabilities of additive printing of porous structures, biomedical issues of the engineered scaffolds, and so on. Special attention is paid to highlighting the actual problems in the field and the ways of their solutions.

A novel artificial vertebral implant with Gyroid porous structures for reducing the subsidence and mechanical failure rate after vertebral body replacement

BACKGROUND

Prosthesis subsidence and mechanical failure were considered significant threats after vertebral body replacement during the long-term follow-up. Therefore, improving and optimizing the structure of vertebral substitutes for exceptional performance has become a pivotal challenge in spinal reconstruction.

METHODS

The study aimed to develop a novel artificial vertebral implant (AVI) with triply periodic minimal surface Gyroid porous structures to enhance the safety and stability of prostheses. The biomechanical performance of AVIs under different loading conditions was analyzed using the finite element method. These implants were fabricated using selective laser melting technology and evaluated through static compression and subsidence experiments.

RESULTS

The results demonstrated that the peak stress in the Gyroid porous AVI was consistently lower than that in the traditional porous AVI under all loading conditions, with a maximum reduction of 73.4%. Additionally, it effectively reduced peak stress at the bone-implant interface of the vertebrae. Static compression experiments demonstrated that the Gyroid porous AVI was about 1.63 times to traditional porous AVI in terms of the maximum compression load, indicating that Gyroid porous AVI could meet the safety requirement. Furthermore, static subsidence experiments revealed that the subsidence tendency of Gyroid porous AVI in polyurethane foam (simulated cancellous bone) was approximately 15.7% lower than that of traditional porous AVI.

CONCLUSIONS

The Gyroid porous AVI exhibited higher compressive strength and lower subsidence tendency than the strut-based traditional porous AVI, indicating it may be a promising substitute for spinal reconstruction.

In silico assessment of the bone regeneration potential of complex porous scaffolds

Mechanical environment plays a crucial role in regulating bone regeneration in bone defects. Assessing the mechanobiological behavior of patient-specific orthopedic scaffolds in-silico could help guide optimal scaffold designs, as well as intra- and post-operative strategies to enhance bone regeneration and improve implant longevity. Additively manufactured porous scaffolds, and specifically triply periodic minimal surfaces (TPMS), have shown promising structural properties to act as bone substitutes, yet their ability to induce mechanobiologially-driven bone regeneration has not been elucidated. The aim of this study is to i) explore the bone regeneration potential of TPMS scaffolds made of different stiffness biocompatible materials, to ii) analyze the influence of pre-seeding the scaffolds and increasing the post-operative resting period, and to iii) assess the influence of patient-specific parameters, such as age and mechanosensitivity, on outcomes. To perform this study, an in silico model of a goat tibia is used. The bone ingrowth within the scaffold pores was simulated with a mechano-driven model of bone regeneration. Results showed that the scaffold's architectural properties affect cellular diffusion and strain distribution, resulting in variations in the regenerated bone volume and distribution. The softer material improved the bone ingrowth. An initial resting period improved the bone ingrowth but not enough to reach the scaffold's core. However, this was achieved with the implantation of a pre-seeded scaffold. Physiological parameters like age and health of the patient also influence the bone regeneration outcome, though to a lesser extent than the scaffold design. This analysis demonstrates the importance of the scaffold's geometry and its material, and highlights the potential of using mechanobiological patient-specific models in the design process for bone substitutes.

Chitosan Hydrogel as Tissue Engineering Scaffolds for Vascular Regeneration Applications

Chitosan hydrogels have a wide range of applications in tissue engineering scaffolds, mainly due to the advantages of their chemical and physical properties. This review focuses on the application of chitosan hydrogels in tissue engineering scaffolds for vascular regeneration. We have mainly introduced these following aspects: advantages and progress of chitosan hydrogels in vascular regeneration hydrogels and the modification of chitosan hydrogels to improve the application in vascular regeneration. Finally, this paper discusses the prospects of chitosan hydrogels for vascular regeneration.

The Effect of Tortuosity on Permeability of Porous Scaffold

In designing porous scaffolds, permeability is essential to consider as a function of cell migration and bone tissue regeneration. Good permeability has been achieved by mimicking the complexity of natural cancellous bone. In this study, a porous scaffold was developed according to the morphological indices of cancellous bone (porosity, specific surface area, thickness, and tortuosity). The computational fluid dynamics method analyzes the fluid flow through the scaffold. The permeability values of natural cancellous bone and three types of scaffolds (cubic, octahedron pillar, and Schoen's gyroid) were compared. The results showed that the permeability of the Negative Schwarz Primitive (NSP) scaffold model was similar to that of natural cancellous bone, which was in the range of 2.0 × 10^-11 m² to 4.0 × 10^-10 m². In addition, it was observed that the tortuosity parameter significantly affected the scaffold's permeability and shear stress values. The tortuosity value of the NSP scaffold was in the range of 1.5-2.8. Therefore, tortuosity can be manipulated by changing the curvature of the surface scaffold radius to obtain a superior bone tissue engineering construction supporting cell migration and tissue regeneration. This parameter should be considered when making new scaffolds, such as our NSP. Such efforts will produce a scaffold architecturally and functionally close to the natural cancellous bone, as demonstrated in this study.

PCL strut-like scaffolds appear superior to gyroid in terms of bone regeneration within a long bone large defect: An in silico study

The treatment of large bone defects represents a major clinical challenge. 3D printed scaffolds appear as a promising strategy to support bone defect regeneration. The 3D design of such scaffolds impacts the healing path and thus defect regeneration potential. Among others, scaffold architecture has been shown to influence the healing outcome. Gyroid architecture, characterized by a zero mean surface curvature, has been discussed as a promising scaffold design for bone regeneration. However, whether gyroid scaffolds are favourable for bone regeneration in large bone defects over traditional strut-like architecture scaffolds remains unknown. Therefore, the aim of this study was to investigate whether gyroid scaffolds present advantages over more traditional strut-like scaffolds in terms of their bone regeneration potential. Validated bone defect regeneration principles were applied in an in silico modeling approach that allows to predict bone formation in defect regeneration. Towards this aim, the mechano-biological bone regeneration principles were adapted to allow simulating bone regeneration within both gyroid and strut-like scaffolds. We found that the large surface curvatures of the gyroid scaffold led to a slower tissue formation dynamic and conclusively reduced bone regeneration. The initial claim, that an overall reduced zero mean surface curvature would enhance bone formation, could not be confirmed. The here presented approach illustrates the potential of in silico tools to evaluate in pre-clinical studies scaffold designs and eventually lead to optimized architectures of 3D printed implants for bone regeneration.

Deformation of implant retaining screws-Study with stereoscopic microscopy and microCT

BACKGROUND

The prosthetic screw fixes the prostheses to the implants. Upon osteointegration, the untightening of the prosthetic screw is the most common problem in oral rehabilitation with implants.

OBJECTIVE

To study the deformation of the implant retaining hexagonal screw head.

METHODS

This investigation used two methods for evaluating the screw head's area of deformation (mm² ): a stereoscopic microscopy and micro computed tomography (microCT). For stereoscopic microscopy, 16 titanium alloy (T) and 16 titanium gold-plated alloy (G) screws of the Zimmer Biomet™ brand were used, divided into eight groups: group 0 (control group), groups T1 and G1 (screws tightened 10 times to 20 Ncm), the groups T2 and G2 (screws tightened 20 times to 20 Ncm) and the groups T3 and G3 (screws tightened 10 times to 30 Ncm). In the study with microCT, one screw was randomly chosen from each of the groups described above to perform the scanning by microCT.

RESULTS

When comparing the type of screw material using stereoscopic microscopy, no statistically significant differences were found (p > 0.05). Contrarily, different number of successive grips and different torque value showed statistically significant differences in the head section of the retaining screws (p < 0.05). The observation by microCT showed the torque applied is crucial to the head deformation in titanium screws. In gold-plated screws the successive tightening appears to be pivotal.

CONCLUSION

Titanium and gold screws tend to behave similarly. By increasing the tightening cycles and the torque values of protocols greater levels of deformations can be expected. In general, microCT data showed better results for gold-plated titanium alloy.

CLINICAL SIGNIFICANCE

To control severe screw head deformation and the impossibility of untightening the implant's restoration, clinicians should avoid extreme torque values and prevent surpassing 10 tightening cycles.

Development of an architecture-property model for triply periodic minimal surface structures and validation using material extrusion additive manufacturing with polyetheretherketone (PEEK)

Additively manufactured structures designed from triply periodic minimal surfaces (TPMSs) have been receiving attention for their potential uses in the medical, aerospace, and automobile industries. Understanding how these complex geometries can be designed to achieve particular architectural and mechanical properties is essential for tuning their function to certain applications. In this study, we created design tools for visualizing the interplay between TPMS design parameters and resulting architecture and aimed to validate a model of the relationship between structure architecture and Young's modulus. A custom MATLAB script was written to analyze structural properties for families of Schoen gyroid and Schwarz diamond structures, and a numerical homogenization scheme was performed to predict the effective Young's moduli of the structures based on their architecture. Our modeling methods were validated experimentally with polyetheretherketone (PEEK) structures created using material extrusion additive manufacturing. The architectural characteristics of the structures were determined using micro-computed tomography, and compression testing was performed to determine yield strength and Young's modulus. Two different initial build orientations were tested to determine the behavior both perpendicular and parallel to the layer deposition direction (referred to as z-direction and xy-direction, respectively). The z-direction Young's modulus ranged from 289.7 to 557.5 MPa and yield strength ranged from 10.12 to 20.3 MPa. For the xy-direction, Young's modulus ranged from 133.8 to 416.4 MPa and yield strength ranged from 3.8 to 12.2 MPa. For each initial build orientation, the mechanical properties were found to decrease with increasing porosity, and failure occurred due to both strut bending and interlayer debonding. The mechanical properties predicted by the modeling agreed with the values found for z-direction samples (difference 2-11%) but less so for xy-direction samples (difference 27-62%) due to weak interlayer bonding and print path irregularities. Ultimately, the findings presented here provide better understanding of the range of properties achievable for additive manufacturing of PEEK and encouraging results for a TPMS architecture-property model.

A Critical Review on the Design, Manufacturing and Assessment of the Bone Scaffold for Large Bone Defects

In recent years, bone tissue engineering has emerged as a promising solution for large bone defects. Additionally, the emergence and development of the smart metamaterial, the advanced optimization algorithm, the advanced manufacturing technique, etc. have largely changed the way how the bone scaffold is designed, manufactured and assessed. Therefore, the aim of the present study was to give an up-to-date review on the design, manufacturing and assessment of the bone scaffold for large bone defects. The following parts are thoroughly reviewed: 1) the design of the microstructure of the bone scaffold, 2) the application of the metamaterial in the design of bone scaffold, 3) the optimization of the microstructure of the bone scaffold, 4) the advanced manufacturing of the bone scaffold, 5) the techniques for assessing the performance of bone scaffolds.

Application of Computational Method in Designing a Unit Cell of Bone Tissue Engineering Scaffold: A Review

The design of a scaffold of bone tissue engineering plays an important role in ensuring cell viability and cell growth. Therefore, it is a necessity to produce an ideal scaffold by predicting and simulating the properties of the scaffold. Hence, the computational method should be adopted since it has a huge potential to be used in the implementation of the scaffold of bone tissue engineering. To explore the field of computational method in the area of bone tissue engineering, this paper provides an overview of the usage of a computational method in designing a unit cell of bone tissue engineering scaffold. In order to design a unit cell of the scaffold, we discussed two categories of unit cells that can be used to design a feasible scaffold, which are non-parametric and parametric designs. These designs were later described and being categorised into multiple types according to their characteristics, such as circular structures and Triply Periodic Minimal Surface (TPMS) structures. The advantages and disadvantages of these designs were discussed. Moreover, this paper also represents some software that was used in simulating and designing the bone tissue scaffold. The challenges and future work recommendations had also been included in this paper.

Numerical-experimental analysis of the permeability-porosity relationship in triply periodic minimal surfaces scaffolds

Bone Tissue Engineering has been focusing on improving the current methods for bone repair, being the use of scaffolds presented as an upgrade to traditional surgery techniques. Scaffolds are artificially porous matrices, meant to promote cell seeding and proliferation, being these properties influenced by the permeability of the structure. This work employed experimental pressure drop tests and Computational Fluid Dynamics models to assess permeability (and fluid streamlines) within different triply periodic minimal surfaces scaffold geometries (Schwarz D, Gyroid and Schwarz P). The pressure outputs from the computational analysis presented a good correlation with the experimental results, with R² equal to 0.903; they have also shown that a lower porosity may not mean a lower permeability if the geometry is altered, such as the difference between 60% porous Gyroid scaffolds (8.1*10^-9 mm²) and 70% porous Schwarz D scaffolds (7.1*10^-9 mm²). Fluid streamlines revealed how the Gyroid geometries are the most appropriate design for most bone tissue engineering applications, due to their consistent fluid permeation, followed by Schwarz D. The Schwarz P geometries have shown flat streamlines and significant variation of the permeability with the porosity (an increase of 10% in their porosity lead to an increase in the permeability from 5.1*10^-9 mm² to 11.7*10^-9 mm²), which would imply a poor environment for cell seeding and proliferation.

Relationship between the morphological, mechanical and permeability properties of porous bone scaffolds and the underlying microstructure

Bone scaffolds are widely used as one of the main bone substitute materials. However, many bone scaffold microstructure topologies exist and it is still unclear which topology to use when designing scaffold for a specific application. The aim of the present study was to reveal the mechanism of the microstructure-driven performance of bone scaffold and thus to provide guideline on scaffold design. Finite element (FE) models of five TPMS (Diamond, Gyroid, Schwarz P, Fischer-Koch S and F-RD) and three traditional (Cube, FD-Cube and Octa) scaffolds were generated. The effective compressive and shear moduli of scaffolds were calculated from the mechanical analysis using the FE unit cell models with the periodic boundary condition. The scaffold permeability was calculated from the computational fluid dynamics (CFD) analysis using the 4×4×4 FE models. It is revealed that the surface-to-volume ratio of the Fischer-Koch S-based scaffold is the highest among the scaffolds investigated. The mechanical analysis revealed that the bending deformation dominated structures (e.g., the Diamond, the Gyroid, the Schwarz P) have higher effective shear moduli. The stretching deformation dominated structures (e.g., the Schwarz P, the Cube) have higher effective compressive moduli. For all the scaffolds, when the same amount of change in scaffold porosity is made, the corresponding change in the scaffold relative shear modulus is larger than that in the relative compressive modulus. The CFD analysis revealed that the structures with the simple and straight pores (e.g., Cube) have higher permeability than the structures with the complex pores (e.g., Fischer-Koch S). The main contribution of the present study is that the relationship between scaffold properties and the underlying microstructure is systematically investigated and thus some guidelines on the design of bone scaffolds are provided, for example, in the scenario where a high surface-to-volume ratio is required, it is suggested to use the Fischer-Koch S based scaffold.

Porous Scaffold Design for Additive Manufacturing in Orthopedics: A Review

With the increasing application of orthopedic scaffolds, a dramatically increasing number of requirements for scaffolds are precise. The porous structure has been a fundamental design in the bone tissue engineering or orthopedic clinics because of its low Young's modulus, high compressive strength, and abundant cell accommodation space. The porous structure manufactured by additive manufacturing (AM) technology has controllable pore size, pore shape, and porosity. The single unit can be designed and arrayed with AM, which brings controllable pore characteristics and mechanical properties. This paper presents the current status of porous designs in AM technology. The porous structures are stated from the cellular structure and the whole structure. In the aspect of the cellular structure, non-parametric design and parametric design are discussed here according to whether the algorithm generates the structure or not. The non-parametric design comprises the diamond, the body-centered cubic, and the polyhedral structure, etc. The Voronoi, the Triply Periodic Minimal Surface, and other parametric designs are mainly discussed in parametric design. In the discussion of cellular structures, we emphasize the design, and the resulting biomechanical and biological effects caused by designs. In the aspect of the whole structure, the recent experimental researches are reviewed on uniform design, layered gradient design, and layered gradient design based on topological optimization, etc. These parts are summarized because of the development of technology and the demand for mechanics or bone growth. Finally, the challenges faced by the porous designs and prospects of porous structure in orthopedics are proposed in this paper.

On the Tortuosity of TPMS Scaffolds for Tissue Engineering

Recently, bone tissue engineering (TE) has seen new developments, with triply periodic minimal surfaces (TPMSs) being used to develop new porosity-controlled scaffolds to interface new tissue growth. The process of choosing the best geometry to a specific application still lacks research, so the goal for this work is to propose a new method of scaffold selection, based on assessing the tortuosity inside these symmetric TPMS-based structures. Additionally, computer fluid dynamic (CFD) simulations were conducted to validate this method. The comparison between tortuosity and CFD outputs suggests that an analysis of the tortuosity could be used as an early indicator of the scaffold’s viability for specific applications, favouring scaffolds with more intricate and curvature-dependent streamlines.

The anisotropic elastic behavior of the widely-used triply-periodic minimal surface based scaffolds

The Triple Periodic Minimal Surface (TPMS) has emerged as a new approach for producing open cell porous scaffolds for biomedical applications. However, different from the traditional scaffolds, the TPMS scaffolds always exhibit anisotropic elastic behaviors and consequently the simple mechanical testing is not capable to provide a full characterization of their mechanical behaviors. Additionally, it is still unclear if the TPMS scaffolds possess the similar anisotropic behaviors as the natural bones. The aim of the present study was to analyze the anisotropic elastic behaviors of TPMS based scaffolds using the numerical homogenization method and the analytical analysis approach. Five widely-used TPMS scaffold topologies (Diamond, Gyroid, Fischer-Koch S, Schwarz P and F-RD) were investigated. The independent elastic constants were determined from the analytical analysis and then, the values for these independent constants were determined using the finite element (FE) unit cell models of the scaffolds combined with the periodic boundary condition. The analytical analysis revealed that the Diamond, Gyroid and Fischer-Koch S topologies are threefold rotational symmetric and consequently have seven independent elastic constants. The Schwarz P and F-RD topologies are cubic symmetric and have three independent elastic constants. The FE analysis showed that the Diamond, Gyroid and Fischer-Koch S based scaffolds have only three non-zero independent elastic constants, implying the cubic symmetric property of these scaffolds. All the independent elastic constants decreased quadratically with the increase of scaffold porosity. The absolute difference between the Zener anisotropic factor and one increased the most for the Gyroid based scaffold, while the value for the Fischer-Koch S based scaffold increased the least. The present study revealed that all the five TPMS scaffolds possess cubic symmetry, limiting their anisotropic behaviors. The information on the Zener anisotropic factor and the relationship between the scaffold elastic constants and the porosity can facilitate the selection and design of scaffolds in biomedicine and relevant fields.

Permeability versus Design in TPMS Scaffolds

Scaffolds for bone tissue engineering are porous structures that serve as support for cellular growth and, therefore, new tissue formation. The present work assessed the influence of the porous architecture of triply periodic minimal surface (TPMS) scaffolds on their macroscopic permeability behavior, combining numerical and experimental methods. The TPMS scaffolds considered were Schwartz D, Schwartz P, and Gyroid, which have been previously studied for bone tissue engineering, with 70% porosity. On the experimental side, these scaffolds were produced by MultiJet 3D printing and tested for fluid passage to calculate their permeability through Darcy’s Law. On the numerical side, finite element (FE) models of the scaffolds were simulated on ABAQUS^® for fluid passage under compression to assess potential fluid concentration spots. The outcomes revealed that the design of the unit cell had a noticeable effect on both calculated permeability and FE computed fluid flow velocity, regardless of the identical porosity, with the Gyroid scaffold having higher permeability and the Schwartz P a lower probability of fluid trapping. Schwartz D had the worst outcomes in both testing modalities, so these scaffolds would most likely be the last choice for promoting cell differentiation onto bone cells. Gyroid and Schwartz P would be up for selection depending on the application and targeted bone tissue.