## 3 Results  
As previously discussed, efficient delivery of O\({}_{2}\) is vital to the cell survival in the 3D bone tissue engineering scaffolds. Yet, choosing the optimal scaffold manufacturing parameters and the culturing flow conditions is non-trivial, due to the complex transport phenomena occurring in the pore networks of the engineered tissue constructs. For this reason, we have performed image-based simulation of the fluid flow and of the O\({}_{2}\) transport that occur within two common types of bone tissue engineering PLLA scaffolds: the salt-leached foam and the non-woven fiber mesh. Their geometries were varied by controlling the amount and the size of the leached salt grains for the former, and the fiber diameter for the latter. In order to compare the scaffolds on the same scale, here the results are plotted as a function of the \"specific surface area\"--defined as the ratio of surface area to total volume (as opposed to just solid volume). Furthermore, in order to analyze how the transport of O\({}_{2}\) is affected by the rate at which it is consumed by the cells, we considered different probabilities with which its molecules can react upon colliding with the scaffold walls. Specifically, we examined the condition of a uniform coverage of the scaffold surfaces with O\({}_{2}\)-starved cells in Figures 3-6, while Figure 7 considers the case of the cells not starved for O\({}_{2}\). Namely, the former corresponds to an infinite surface reaction rate (i.e., instantaneous consumption of every O\({}_{2}\) molecule that collides with a scaffold wall). It should be treated as a limiting case scenario, which allows for a comparison of different scaffold structures on an equivalent basis. Figure 3 is a plot of the O\({}_{2}\) \"survival distance\" in the stream-wise direction (the X-direction), as a function of the scaffold structure and the cell-culture media perfusion flow rate. The survival distance is defined as the distance that the rLST markers (representing the O\({}_{2}\) molecules) travel on average, until they are \"consumed\" via a collision with a scaffold wall. From this figure, it is apparent that the survival distance in the stream-wise direction increases as the flow rate goes up. This is consistent with the Taylor-Aris dispersion theory, which states that the effective diffusivity in the stream-wise direction should increase with the square of the Peclet number [20,34]:  
\[Pe_{m}=Re*Sc \tag{2}\]  
where Re is the Reynolds number and Sc is the Schmidt Number. Its physical meaning is the ratio of the transport by advection to transport by diffusion. In this study, Sc is fixed for an O\({}_{2}\) molecule in an aqueous cell culture media at T = 37 \({}^{\circ}\)C, as was discussed in the methods section. Hence, according to Equation (2), the Peclet number will increase proportionally with the value of Re, which depends on the velocity of the fluid. This leads to a higher effective diffusivity of the solute in the stream-wise direction, and thus, the O\({}_{2}\) can make it further into the scaffold before it is fully consumed by the cells. Another trend that is apparent from Figure 3 is that the survival distance of O\({}_{2}\) is also inversely proportional to the specific surface area of the scaffold. This makes sense, because the O\({}_{2}\) molecules have a smaller chance to collide with the scaffold's surface when it has less area exposed. Furthermore, Figure 3 shows that the foam scaffolds have a lower specific surface area than the fiber ones. This leads to noticeably longer survival distances of O\({}_{2}\) in the foam scaffolds. Overall, the result demonstrates that it is plausible to modify the scaffold's geometry in order to increase the efficiency of the O\({}_{2}\) transport within its structure.