Highly porous tissue engineered scaffolds are widely used in bone regeneration research (Roffi et al., 2017; Vidal et al., 2020) to mitigate well-publicized limitations of bone grafting methods, particularly in large bone defects, including recurring failures with non-union rates as high as 21% (Wagels et al., 2013) and complication rates of 50% due to delayed or non-union, 30% from allograft fracture, and 15% from infection (Chang and Weber, 2005). Synthetic bone tissue engineering (BTE) scaffolds attempt to accelerate the body’s natural healing process. To accomplish this, BTE scaffolds must be designed to accommodate several interrelated factors including biocompatibility, structural durability and permeability while providing a favorable environment for bone healing (Montazerian et al., 2017). Scaffolds lack the vasculature of autologous bone, emphasizing the importance of high levels of permeability, which considers porosity, tortuosity, pore size, shape, distribution and interconnectivity, key factors contributing to new bone development (Dias et al., 2012; Henkel et al., 2013), particularly in large defects. Highly interconnected, high porosity structures, within a range of 50%–90% depending on the anatomical location, are required to enable adequate mass transport of nutrients, gases and waste products during rapid bone development (Henkel et al., 2013; Wu et al., 2014). This exchange supports greater cell migration and proliferation through the three-dimensional scaffold, while playing a crucial role in angiogenesis (Klenke et al., 2008).

Calcium phosphate-based materials, such as hydroxyapatite (HAp) and tricalcium phosphate (TCP), are popular for BTE due to their biocompatibility, high levels of bioactivity (osteoconductivity, osteoinductivity and osteointegration), similarities to human bone composition, non-immunogenicity and tunable degradation rates (Hollister, 2005; Tarafder et al., 2013; Wu et al., 2014). However, these apatite scaffolds exhibit relatively low toughness due to their brittleness (Abbas et al., 2021), limiting their functional usefulness in load-bearing cases, especially as high porosity structures.

The structural integrity of BTE scaffolds can be enhanced with innovative topologies like triply periodic minimal surfaces (TPMS), which have proven to be more robust than traditional strut-based topologies (Abueidda et al., 2019; Yuan et al., 2019). They demonstrate relatively high energy absorption (Abueidda et al., 2019), complemented by high surface-to-volume ratios and an interconnected porous structure for optimal cell attachment and migration (Yoo, 2014; Alizadeh-Osgouei et al., 2021). TPMS have the capacity to be adjusted to imitate the structure of bone, thus facilitating bone growth (Alizadeh-Osgouei et al., 2021). 3D printing enables high-precision fabrication of these complex TPMS scaffolds with specific porosities, pore sizes and shapes, permeability, and tortuosity for different mechanics and applications in BTE (Alizadeh-Osgouei et al., 2021). TPMS have been 3D printed in nearly every major 3D printing process. Material extrusion with a thermal build process is most often used due to its low cost and high flexibility (Bruyas et al., 2018; Germain et al., 2018; Alizadeh-Osgouei et al., 2021). In this method a thin filament of thermoplastic is heated above its glass transition temperature and extruded from a print head that moves in three dimensions to form 3D shapes that solidify as the material cools. Robocasting is also very popular for biomimetic, ceramic scaffolds due to its very low cost and non-thermal processing method (Eqtesadi et al., 2016; Restrepo et al., 2017; Roopavath et al., 2019; Peng et al., 2021; Baumer et al., 2023). Powder bed fusion has been used to print numerous types of TPMS scaffolds (Maskery et al., 2018; Jin et al., 2022; Mulhi et al., 2023; Tilton et al., 2023), including Gyroids, in metals like titanium (Yan et al., 2015). Binder jetting has been used to print numerous types of apatite scaffolds (Butscher et al., 2011; Fielding et al., 2012; Tarafder et al., 2013; Nandi et al., 2018; Lv et al., 2019). TPMS scaffolds were also printed using vat photopolymerization (Melchels et al., 2010; Schwentenwein and Homa, 2015; Lee et al., 2021) and in hydroxyapatite- and TCP-photopolymeric slurry using digital light processing (Zeng et al., 2018; Schmidleithner et al., 2019). Recent excellent reviews discuss the advantages and disadvantages of various 3D printing processes in a wide array of materials, topologies and applications (Travitzky et al., 2014; Bose et al., 2018; Peng et al., 2018; Yuan et al., 2019).

Among the many TPMS topologies, Gyroid and Fischer-Koch S (FKS) are particularly well suited for bone regeneration scaffolds (Abou-Ali et al., 2019; Lu et al., 2020). Computational simulations have led to hypotheses that some topologies may be better suited than others in particular bone regeneration applications. For example, finite-element analysis of different TPMS topologies (Lu et al., 2020) suggest that FKS topology may be better suited to remediate a cortical diaphyseal bone defect because its high strength, low permeability, and isotropic behavior (Lu et al., 2019) better mimics dense cortical bone than other TPMS, such as Gyroids. It was similarly proposed that Gyroid scaffolds might be better suited to procedures where high anisotropy and permeability are preferable to better match the properties of cancellous bone. Gyroid TPMS have been widely studied in many forms (Restrepo et al., 2017; Bose et al., 2018; Peng et al., 2018; Abueidda et al., 2019). FKS, on the other hand, is relatively unexplored beyond computer simulations. Tools for creating G-code for printing FKS and other non-Gyroid TPMS are emerging (Baumer et al., 2023), but most are proprietary software that is bundled with expensive 3D printers. To the best of our knowledge, no one has fabricated ceramic FKS scaffolds and experimentally compared them to ceramic gyroid scaffolds. In this paper, we design and 3D print ceramic FKS scaffolds and compare key physical properties to an equivalent gyroid scaffold in the context of BTE.

Structural characterization of each topology confirmed that robocasting produced TPMS HAp scaffolds with parameters in the nominal range for BTE in large bone defects. In terms of the optimal scaffold parameters, the critical need to balance mechanical and osteogenic properties is dependent on the material and application. In 2021, Blazquez-Carmona et al. optimized HAp scaffolds specifically for regenerating load bearing defects and provided the key insight that since these in vivo procedures are stabilized by metal fixation, like intramedullary nails or fixation plates, the mechanical loads required by the scaffolds significantly change (Blázquez-Carmona et al., 2021). Mechanical testing of critical defect repairs in cadaveric canine limbs have shown that the bending stiffness of the bone stabilized by an external plate did not significantly change when the scaffold was removed (Schneiderhan, 2022). This suggests that metal fixation plays a crucial role in supporting substantial loads in large bone defects, potentially enabling scaffolds to be tailored for the lower end of the bone’s strength spectrum. Considering the demonstrated benefits of higher porosity scaffolds for bone growth (Karageorgiou and Kaplan, 2005), it is preferable to pursue the highest porosity structure that fulfills the necessary mechanical failure criteria while closely mirroring the stiffness of the targeted tissue (Sturm et al., 2010). With mechanical and porosity objectives established, it is essential to recognize the impact of other design factors, such as interconnected pore size, on bone growth. While pore size studies may yield differing outcomes between in vitro and in vivo settings, there exists a widely acknowledged minimum optimum of 300 µm for scaffold design (Henkel et al., 2013; Zadpoor, 2015). Balancing pore size against factors like permeability and surface area adds complexity to the optimization process. The optimization by Blazquez-Carmona et al. recommended parameters of 59.3% porosity, 5.768 mm⁻¹ specific surface area, and 360 µm pore size for their rectilinear HAp scaffolds in a large defect. Comparing optimizations proves challenging due to the diverse topologies and interrelated factors involved (Bahraminasab, 2020). Thus, considering all requirements, the TPMS scaffolds in this report were crafted with the aim of striking a balance. They were designed at the highest achievable porosity (∼70%) and pore size (∼1 mm), predicted to sustain the lower range of trabecular bone strength, as indicated by prior studies (Isaacson et al., 2022), while maintaining a specific surface area of approximately 5.7 mm⁻¹. The as-sintered scaffold porosity, pore size and specific surface area values varied by topology in this report (74.00%, 1.212 mm, and 5.796 mm⁻¹ for FKS and 68.49%, 1.039 mm, and 5.514 mm⁻¹ for Gyroid), but they were considered good fidelity for direct comparison. Moreover, a comparison of a single high porosity design for each topology is valid in this case because trends in scaffold strength and permeability are dominated more by differences in topology than small variations (±5%) in porosity (Lu et al., 2020). Some manufacturing defects did occur, such as ooze on the exterior faces and layer gaps (Figure 1), which are believed to have caused the deviations from the as-designed 70% porosity. These gaps appear on X-Y planes consistently throughout the scaffold’s depth and are visible in sliced models in Cura prior to printing. Hence, they are attributed to interpolation of road width not the printing process. Resolution in robocasting is limited by nozzle diameter which was set to the smallest size (0.413 mm) that permitted consistent viscous extrusion of a slurry with a high solid content required to maximize mechanical strength. Since the nozzle size was fixed, and therefore the wall thickness was fixed, the FKS and Gyroid could not be reliably produced with precisely the same structural parameters because porosity, pore size, and surface area are highly interrelated. Further challenges in robocasting TPMS ceramics have been elaborated on in prior work (Baumer et al., 2023). These gaps probably reduce mechanical strength, especially in the X-Y direction, where the missing material would strengthen bonding in the internal substructure. Furthermore, these gaps increase permeability by creating additional flow paths, thereby reducing tortuosity.

The comparative properties of FKS and Gyroid scaffolds were in good agreement with current literature, and the performance of both topologies mimicked the low range of trabecular long bones. FKS scaffolds were shown to be significantly stronger and absorb more energy than Gyroid scaffolds in both normal and transverse compression, but no significant differences could be found between their moduli. In flow testing, FKS scaffolds were shown to be significantly less permeable than Gyroids scaffolds in the Darcian regime. Ravichander et al. (2022) showed that FKS scaffolds with a linear porosity gradient manufactured using metal powder bed fusion (PBF) had higher compressive strength, Young’s modulus, and energy absorption than Gyroids. Zou et al. (2022) manufactured TPMS scaffolds using titanium PBF to show that FKS had a stiffer elastic modulus, greater compressive strength, and lower permeability than Lu et al. (2020) demonstrated that FKS and Gyroid had similar compressive moduli when simulated using FEA and tested using titanium PBF across a range of porosities. In the same report, CFD calculations using both Darcy’s law and Kozeny-Carman’s relation revealed that FKS had the lowest permeability of all structures tested (including Gyroid), leading them to the conclusion that FKS may be the most favorable in scenarios where nutrient is not limiting, e.g., in bone fusion. Kapfer et al. (2011) predicted using FEA that Gyroids have a larger Young’s Modulus, but that FKS is more isotropic. Asbai-Ghoudan et al. (2021) showed that FKS had lower permeability than Gyroid across a range of pore sizes and porosities. Lu and their team also predicted FKS to be more isotropic than Gyroid using FEA, and consequently, they proposed that FKS might be better for compact bone scaffolds, while Gyroid might be better for trabecular bone scaffolds (Lu et al., 2019). Our ceramic results are in good agreement with the trends seen between FKS and Gyroid in simulations and metal-based experiments. This current study demonstrates that the compressive strength of robocast FKS and Gyroid scaffolds (1–2 MPa) were in the low range of human cancellous bone in uniaxial compression (0.898–29.20 MPa) (Rincón-Kohli and Zysset, 2009), and that their permeabilities (1.01 × 10⁻⁹ m² to 2.18 × 10⁻⁹ m²) were similar to trabecular bone (0.4–11 × 10⁻⁹ m²) and to other scaffold literature (Grimm and Williams, 1997; Montazerian et al., 2017). Moreover, in normal compression, both topologies showed relatively high reliability (>86%) across all failure modes at the targeted 1 MPa threshold. In addition to strength and permeability, the ability of scaffolds to match the anisotropy and modulus of surrounding tissues is important for bone growth (Henkel et al., 2013), but the variability of these metrics in this report were too high to draw significant conclusions. Unlike compressive strength, the stiffness of scaffolds in this report (40–70 MPa) failed to compare to the elastic modulus range for trabecular bone (105–1,310 MPa) (Rincón-Kohli and Zysset, 2009). The prevalence of quasi-brittle behavior in nearly half of all scaffolds reduced the moduli by extending the region of strain. While this may offer advantages in terms of energy absorption and robustness, it diminished the stiffness of the constructs and introduced notable variability. These findings suggest that Gyroid and FKS HAp scaffolds may both be well suited for use in large bone defects, and that robocasting enables the structural and mechanical properties to be tuned for this specific application. FKS scaffolds show greater promise than Gyroid in mimicking natural trabecular bone strength in a high porosity ceramic due to their higher reliability in multiple loading directions. In designing BTE scaffolds, FKS scaffolds may indeed be better suited to applications of dense bone than Gyroids where strength is prioritized over permeability, as suggested by Lu et al. (2019) in earlier simulations.

In order to analyze the performance and reliability of robocast TPMS scaffolds, it was necessary to define a more robust method for determining mechanical properties to accurately characterize the mixture of brittle and quasi-brittle behavior (Figure 4). Traditional methods, such as the ASTM standard for advanced dense ceramics (ASTM C28 Committee, 2024), describe a model for “isotropic, homogeneous, and continuous behavior” which does not describe the porous HAp scaffolds tested. Unlike conventional elastic modulus analysis, stiffness calculations in this study presented a non-trivial challenge due to quasi-brittle failure. Morgan and Keaveny (2001) showed that moduli varied significantly based on the strain range chosen for bone tissue and that non-linear behavior existed even at small strains. They recommended that a second order polynomial fit be used in the region from 0%–0.2% strain for a more robust stiffness definition, but the addition of this parameter makes comparison with scaffold literature and different behavior types more difficult. To capture the diverse scaffold behavior in the current study and to compare with more classical definitions of elastic modulus, a linear fit from 0%–0.5% strain was selected for the initial modulus because it generally showed the lowest standard deviation across all sample groups. Limiting the linear fit region to an excessively small range results in high variation due to local failures, which can create a non-sensical approximation, such as seen in the quasi-brittle behavior of Figure 4B. These early local failures could have resulted from protrusions on outer scaffold surfaces due to improper sanding, but they could not be differentiated from internal local failures which are implicit in the scaffold fabrication process. As a result, no outliers were rejected, and the same rule for initial modulus was applied to all samples. It is important to note that this initial modulus does not represent the overall load-bearing capacity of the cellular scaffold due to failures and possible self-reinforcement (Isaacson et al., 2022) of internal struts, which result in multiple linear regions on the stress-strain curve before ultimate compressive strength is reached. For this reason, “ultimate” modulus was defined to represent the pre-failure stiffness of the scaffold to better characterize the functional performance of the construct in a large bone defect. Innovations in fabricating high porosity TPMS ceramics are needed to reduce variability, shrink the gap between initial and ultimate moduli, and mitigate local failures for higher performance. Despite these shortcomings, this report shows that robocast ceramics are candidates for further study in potential for aiding large bone defect repair.

The combination of brittle and quasi-brittle failures highlighted in this report raises inquiries regarding the performance of TPMS scaffolds as ceramics. Meille et al. discovered that beyond a critical porosity threshold of approximately 50%, the compressive behavior of gelcast alumina scaffolds underwent a notable transition (Meille et al., 2012). Instead of exhibiting brittle failure characterized by a linear region and abrupt collapse, the scaffolds adopted a more cellular-like fracture mode, marked by localized drops. They attributed this shift to the fact that highly porous, cellular ceramics tend to fail through individual walls rather than the propagation of cracks between isolated pores. It was additionally observed that the thickness of the wall, intricately linked to the ratio of porosity to pore size, wields considerable influence over the failure patterns, with mechanics describable through Weibull theory. Similarly, Genet et al. (2013) observed a comparable phenomenon in their rectilinear robocast HAp scaffolds. They noted that non-critical rods led to local failures, which they identified as instances of quasi-brittle behavior, analogous to cellular failure. They demonstrated a direct correlation between the Weibull coefficients and the diameter of the rod to elucidate failure behavior. Interestingly, FKS and Gyroid scaffolds in the current study exhibited this cellular/quasi-brittle behavior approximately half of the time, and the distinct failure modes did not show a clear correlation with the scaffold topology. This suggests the possible existence of a “critical” inflection point at a porosity level of 70% for this specific material and fabrication method. The Weibull theory effectively captured the failure behavior of these scaffolds across various regimes, as evidenced by high coefficients of determination. It is postulated that, even with the utilization of advanced TPMS topologies, the fracture mechanics of ceramics at high porosities remain predominantly governed by material properties and the volume of solid walls or struts.

To better understand the behavior of cellular ceramics, it is critical to examine their failure modes. SEM imagery showed (unsurprisingly) that most cracks initiated at the interfacial boundary of roads. It is hypothesized that the layer-wise photocuring process prevented homogeneity among roads due to variance in parameters like wall thickness. Corrugated walls resulting from the viscous extrusion process (Baumer et al., 2023) created thinner walls between roads and therefore stress concentrations. Not only are these road boundaries thinner, but it is predicted that the curing varied as well. Ideally, a photocast road is mostly cured during deposition, enough to bridge open pores, and is then continuously cured by subsequent exposure passes. This can result in inconsistent curing between upper and lower regions of a road and between successive roads, which was not part of this study. It is hypothesized that this resulted in interfacial defects during sintering because stresses caused by thermal gradients and variance in shrinkage dissipated through these discontinuities. Cracks tended to propagate along grains rather than through them as they follow natural crack propagation pathways. From the relatively small size of HAp grains (87 nm), there was little fracture resistance, and SEM images did not reveal significant crack deviation. Such crack propagation behavior leads to a hypothesis that initial localized failure (Figure 4B) should immediately lead to overall failure of the scaffold, but this is not always the case. The scaffolds generally failed along shear planes near the support points of suspended sections of the scaffold (Figure 7A). Due to the lattice-like nature of FKS and Gyroid structures, opportunities for the isolating the failure of non-critical rods arose where cracks extended through the entirety of a scaffold section yet the section remained in contact with the previously connected structure (Figure 7B), similar to behavior observed in prior work (Isaacson et al., 2022). As these sections of roads fail and are shifted in the direction of the load force, they can become lodged against still-intact sections of the scaffold, thereby reinforcing the strut’s integrity. Comprehending this self-reinforcing behavior is pivotal for the progress of TPMS ceramics, given their distinct failure characteristics compared to existing simulations and metal-based experiments.

It follows from these observations that all scaffolds of both topologies were weaker transversally due to the alignment of road boundaries and direction of applied loads. It is evident that anisotropy primarily resulted from layer-wise fabrication which made topological effects insignificant. The more irregular cross sections of FKS scaffolds (Baumer et al., 2023) may have contributed to their increased strength in a ceramic because cracks required more deflection to become catastrophic, and opportunities for self-reinforcement were greater. Previous work in our lab has shown similar self-reinforcing behavior in Gyroid HAp scaffolds at various porosities (Isaacson et al., 2022). One key observation in both studies is a slightly negative correlation between compressive strength and the propensity for local failures. Generally speaking, stronger scaffolds failed catastrophically whereas comparatively weaker scaffolds showed quasi-brittle behavior as described by the small differences in reliability in Table 2. This makes intuitive sense; Quasi-brittle behavior necessitates the initial failure of weaker walls or layers, a phenomenon likely attributable to manufacturing defects that serve as sites for crack initiation. Preventing the formation of the microcracks that cause early failure has been discussed for quite some time (Lankford et al., 1998). While methods developed to model this failure in comparatively geometrically simple scaffolds have previously been investigated (Genet et al., 2013; Gross et al., 2019), modeling of more complex TPMS ceramic structures is limited. Due to the comparatively young age of additive manufacturing, empirical evaluation centered on road size of ceramic scaffolds has only relatively recently begun (Sabree et al., 2015; Thiraux et al., 2022).

In this study, FKS and Gyroid scaffolds were photocast in HAp to compare experimental properties for their use in BTE. Bone regeneration scaffolds face a pivotal design challenge in striking a balance between strength and permeability, with potential enhancements attainable through the utilization of TPMS structures. We presented the initial elastic modulus of these structures to enable more classical comparisons with other structures and materials and in addition we argue that current methods do not adequately characterize the unique quasi-brittle behavior of TPMS ceramics. We therefore propose that ultimate modulus may be a better predictor of performance in large bone defects. Results revealed that both topologies could achieve the lower ends of the strength and permeability ranges akin to trabecular long bone, with high reliability. However, FKS exhibited notable strength advantages with only a minor compromise in permeability, compared to Gyroid scaffolds. In the context of designing BTE scaffolds, FKS structures appear to be better suited than Gyroids for further study in applications prioritizing denser bone and strength over permeability, echoing insights from earlier simulations (Lu et al., 2019). The TPMS ceramics examined in this report displayed quasi-brittle failure modes effectively described by Weibull distributions. Notably, this cellular failure mode remained consistent across different topologies and has been observed in prior studies utilizing rectilinear and gas-forming methods (Meille et al., 2012; Genet et al., 2013). This suggests that material properties and strut thickness predominantly govern ceramic failure at high porosities. The occurrence of localized failures poses a significant obstacle in accurately mimicking the elastic modulus of bone using cellular ceramics. As bone tissue engineering advances for high porosity ceramics, FKS emerges once more with promising results among the TPMS options, reinforcing its potential for applications demanding both strength and structural integrity.