Flow-induced shear stresses have been found to be a stimulatory factor in pre-osteoblastic cells seeded in 3D porous scaffolds and cultured under continuous flow perfusion. However, due to the complex internal structure of the scaffolds, whole scaffold calculations of the local shear forces are computationally-intensive. Instead, representative volume elements (RVEs), which are obtained by extracting smaller portions of the scaffold, are commonly used in literature without a numerical accuracy standard. Hence, the goal of this study is to examine how closely the whole scaffold simulations are approximated by the two types of boundary conditions used to enable the RVEs: "wall boundary condition" (WBC) and "periodic boundary condition" (PBC). To that end, Lattice-Boltzmann Method fluid dynamics simulations were used to model the surface shear stresses in 3D scaffold reconstructions, obtained from high resolution microcomputed tomography images. It was found that despite the RVEs being sufficiently larger than 6 times the scaffold pore size (which is the only accuracy guideline found in literature), the stresses were still significantly under-predicted by both types of boundary conditions: between 20 and 80% average error, depending on the scaffold's porosity. Moreover, it was found that the error grew with higher porosity. This is likely due to the small pores dominating the flow field, and thereby negating the effects of the unrealistic boundary conditions, when the scaffold porosity is small. Finally, it was found that the PBC was always more accurate and computationally efficient than the WBC. Therefore, it is the recommended type of RVE. Overall, this work provides a previously-unavailable guidance to researchers regarding the best choice of boundary conditions for RVE simulations.
Incidences of bone disorders constitute a significant economic burden to societies globally. In the United States alone, over $213 billion is the total annual cost (direct and indirect) of treating the estimated 126.6 million people affected by musculoskeletal disorders. [1] Unfortunately, with an increasingly obese and ageing population, this trend is expected to continue further. Current approaches for replacing the damaged bone tissues include the use of bone grafts (i.e., autografts or allografts). However, these methods have several shortcomings, limited availability and risk of disease transmission. [2][3][4] To address those disadvantages, bone tissue engineering has emerged as an alternative regenerative strategy.
In bone tissue engineering, a combination of osteo-inductive biological factors, mesenchymal stem cells obtained from patients’ own bone marrow and porous biodegradable scaffolds are used. Typically, the process involves seeding the cells within the 3-D scaffolds, followed by culturing under flow in perfusion bioreactors. The flow is a necessary part of the culture, because the stimulatory shear that it imposes on the stem cells mimics the natural microenvironment in bone canaliculi. [5,6] Moreover, it has been shown to promote tissue regeneration. [7][8][9][10] Thus, the applied shear stresses should be within the physiological range required for stimulation: 0.1 -25 dynes/cm 2 , [11][12][13] because excessive shear of 26-54 dynes/cm 2 can cause cell lysing and/or detachment from the scaffold. [14,15] Therefore, the ability to predict the shear stress distribution in different scaffold microarchitectures can provide insight into whether or not a particular scaffold design will promote tissue growth. Moreover, when used in conjunction with the latest advances in 3D microfabrication technologies, such predictive capabilities can be used to create optimized scaffold geometries. Unfortunately, however, the complex internal structure of the porous scaffolds makes estimation of the required shear stresses via experimental or analytical techniques impractical. Hence, computational fluid dynamics models, based on either idealized pore geometries [6,8,[16][17][18][19][20] or actual scaffold images, [12,[21][22][23][24][25][26][27][28][29][30][31][32][33] are commonly utilized.
The latter is the more realistic approach since it is based on the actual microscopic pore structures, which are typically obtained via a 3D scanning technique such as micro-computed tomography (µCT). Yet, due to the computationally intensive nature of the scaffold reconstructions resulting from such high-resolution imaging, researchers are forced to resort to implementing approximations. [12,[21][22][23][24][25][26][27][28][29][30][31][32][33] For example, rectangular “representative volume elements” (RVE) are cut from whole scaffolds and implemented in conjunction with various boundary conditions along the artificially created periphery. Two common types of boundary conditions that are typically implemented for this purpose are the “wall boundary condition” (WBC) [8,12,19,21,22,26,27,[29][30][31][32][33] and the “periodic boundary condition” (PBC). [18,20,[23][24][25]28] In the former case, the RVE is surrounded by solid walls in the non-flow directions, while the latter is an application of periodicity in all three dimensions.
Although these approaches save on computation time, it is not obvious how accurate the resulting shear stresses are, or which of the two boundary conditions yields the better results. Consequently, the RVE approach is commonly questioned by journal reviewers, as no standards or guidance regarding their use exist. We have found only one publication that investigated the accuracy of the RVE-WBC, as compared to the whole scaffold simulation. [21] Here, a guideline was provided stating that for scaffolds with a homogenous pore distribution the domain size should be at least 6 times the average pore size. However, this suggestion was made based on average wall stresses only, while in reality the spatial distribution of the stresses is also important to tissue growth. For example, the cells within the scaffold migrate around in a nonrandom manner, are therefore more likely to experience stresses at some preferred locations. Furthermore, only scaffolds prepared using the same fabrication technique were studied, though two different materials were used in their manufacturing. Nonetheless, the scaffold’s structure depends more on the fabrication method than it does on the material. [23,24,34] Moreover, just a single scaffold sample was used for each type of the material. Hence, a more thorough investigation of the RVEs’ accuracy is warranted, especially given that no PBC studies were found at all. Therefore, in this work we set out to quantify how the two relevant boundary conditions compare against each other, when applied to scaffolds manufactured using different fabrication methods, and for a large num
This content is AI-processed based on open access ArXiv data.
