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.

Scaffolds are used in diverse tissue engineering applications as hosts for cell proliferation and extracellular matrix formation. One of the most used tissue engineering materials is collagen, which is well known to be a natural biomaterial, also frequently used as cell substrate, given its natural abundance and intrinsic biocompatibility. This study aims to evaluate how the macroscopic biomechanical stimuli applied on a construct made of polycaprolactone scaffold embedded in a collagen substrate translate into microscopic stimuli at the cell level. Eight poro-hyperelastic finite element models of 3D printed hybrid scaffolds from the same batch were created, along with an equivalent model of the idealized geometry of that scaffold. When applying an 8% confined compression at the macroscopic level, local fluid flow of up to 20 m/s and octahedral strain levels mostly under 20% were calculated in the collagen substrate. Conversely unconfined compression induced fluid flow of up to 10 m/s and octahedral strain from 10 to 35%. No relevant differences were found amongst the scaffold-specific models. Following the mechanoregulation theory based on Prendergast et al. (J Biomech 30:539–548, 1997. 10.1016/S0021-9290(96)00140-6), those results suggest that mainly cartilage or fibrous tissue formation would be expected to occur under unconfined or confined compression, respectively. This in silico study helps to quantify the microscopic stimuli that are present within the collagen substrate and that will affect cell response under in vitro bioreactor mechanical stimulation or even after implantation.

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The triply periodic minimal surfaces (TPMS) methodology is explored to design porosity and curvature‐controlled tissue engineering (TE) scaffolds. This work combines mechanical testing and finite element (FE) simulation to characterize TPMS scaffolds micromechanical behavior, i.e., to estimate the response at the cell level to the macromechanical properties of different geometries (Schwartz D, Gyroid, and Schwartz P, with 60%, 70%, and 80% porosity, identified from SD60 to SP80) and testing conditions (6%, 8%, and 10% ramp compression, during 10, 20, and 30 s). Mechanical tests with ten 3D printed samples per model obtain Young Modulus levels from 0.048 GPa (SD80) to 0.267 GPa (SD60) and yield stresses from 0.495 MPa (SP80) to 5.226 MPa (SD60), being these associated with trabecular bone. FE simulations identify strain rate as the major influencer for cell response, as the probabilities for bone formation increase from 23.18% (SD) to 29.81% (SP) when increasing the compression period from 10 to 30 s. Additionally, compression beyond 6% causes excessive rates of cell death. SD and SG models have more consistent cell adhesion paths than SP ones, but superior stiffness of SD scaffolds induces higher cell death probabilities. Thus, SG scaffolds would be a better choice for most TE applications.

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The loaded disk culture system is an intervertebral disk (IVD)-oriented bioreactor developed by the VU Medical Center (VUmc, Amsterdam, The Netherlands), which has the capacity of maintaining up to 12 IVDs in culture, for approximately 3 weeks after extraction. Using this system, eight goat IVDs were provided with the essential nutrients and submitted to compression tests without losing their biomechanical and physiological properties, for 22 days. Based on previous reports (Paul et al., 2012, 2013; Detiger et al., 2013), four of these IVDs were kept in physiological condition (control) and the other four were previously injected with chondroitinase ABC (CABC), in order to promote degenerative disk disease (DDD). The loading profile intercalated 16 h of activity loading with 8 h of loading recovery to express the standard circadian variations. The displacement behavior of these eight IVDs along the first 2 days of the experiment was numerically reproduced, using an IVD osmo-poro-hyper-viscoelastic and fiber-reinforced finite element (FE) model. The simulations were run on a custom FE solver (Castro et al., 2014). The analysis of the experimental results allowed concluding that the effect of the CABC injection was only significant in two of the four IVDs. The four control IVDs showed no signs of degeneration, as expected. In what concerns to the numerical simulations, the IVD FE model was able to reproduce the generic behavior of the two groups of goat IVDs (control and injected). However, some discrepancies were still noticed on the comparison between the injected IVDs and the numerical simulations, namely on the recovery periods. This may be justified by the complexity of the pathways for DDD, associated with the multiplicity of physiological responses to each direct or indirect stimulus. Nevertheless, one could conclude that ligaments, muscles, and IVD covering membranes could be added to the FE model, in order to improve its accuracy and properly describe the recovery periods.

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