## 4 Discussion  
In this manuscript, we carried out a study of how the O\({}_{2}\) mass transfer is affected by the scaffold manufacturing and the flow perfusion culturing parameters in bone tissue engineering scaffolds. The knowledge obtained from the reported results is needed in order to overcome the product-size limitations, which are commonly experienced due to hypoxia and necrosis in the center of large scaffolds. To solve the problem, we used an image-based approach of scanning the true scaffold structures in 3D using a high resolution \(\mu\)CT, and then fed the obtained geometries to our in-house parallelized fluid flow (LBM) and mass transport (rLST) solvers. Two scaffolds commonly used in bone tissue engineering, the salt leached foam and the nonwoven fiber mesh, were used for this study. The O\({}_{2}\) transport results were parametrized as a function of the specific surface area of the scaffold, the flow rate in the bioreactor, and the affinity to consume the molecule by the cells. The main conclusions from our work are that the scaffolds with the higher specific area (i.e., surface area-to-solid volume ratio) result in more frequent molecular collisions with the cells. This increases the chances of the O\({}_{2}\) uptake by them, which results in a higher consumption (i.e., shorter survival times and distances) of the molecules in the scaffold. Furthermore, by increasing the flow rate in the bioreactor, the O\({}_{2}\) transport can be both facilitated (as seen from the shorter survival time in Figure 4) and delivered deeper into the scaffold (as seen from the longer survival distance in Figure 3). Thus, the overall effective O\({}_{2}\) reaction coefficient k\({}_{\text{eff}}\) can be increased by maximizing both the specific surface area of the scaffold and the flowrate through its pores. This is evident from Figure 6.  
Interestingly, the conclusion that an increased flow rate improves the O\({}_{2}\) delivery to the cells has also been reported by [PERSON] et al. [4]. However, increasing it indefinitely is not an option because there is a trade-off with the shear forces exerted on the cells by the flow. Specifically, values in the range of 0.1-25 dynes/cm\({}^{2}\)[36; 37; 38] are generally considered to be beneficial because they mimic the natural  
Figure 7: O\({}_{2}\) survival time as a function of the consumption rate by the cells on the scaffold surface. Data is plotted for salt leached foam and non-woven fiber mesh scaffolds at four different flow rates. microenvironment in bone canaliculi [9; 10] and have been shown to promote tissue regeneration [39; 40; 41; 42]. On the other hand, an excessive shear in the range of 26-54 dynes/cm\({}^{2}\) and higher can cause cell lysing and/or detachment from the scaffold [43; 44]. Therefore, there is some optimal flow rate, which was found to be 45 \(\upmu\)L/min by the [PERSON] et al. study [4]. However, this value is specific to their scaffold-and-cell combination, and it could vary for other alternatives. Therefore, both image-based numerical simulations and cell viability assays are necessary for tuning the optimal conditions for other types of cultures. Whereas, at least the physical understanding provided in our study should be applicable across all scaffold types because they are expressed in terms of the specific surface area. Finally, Figure 7 in our manuscript provides insight into how the O\({}_{2}\) transport depends on its consumption by the cells. In this case, we are not assuming that the cells are O\({}_{2}\)-starved (and as a result take up every oxygen molecule that collides with them). Instead, we vary consumption rate of the O\({}_{2}\) at the scaffold surface in order to measure how this affects its transport in the scaffold. The results reported in this figure allow other researchers to understand the changes in the scaffold's transport microenvironment over time. They also show how the flowrate and specific surface area trends are affected by the cell-specific O\({}_{2}\) consumption rates.