## 1 Introduction  
Incidences of bone disorders constitute a significant economic burden to societies globally. In the United States alone, the total annual cost (direct and indirect) of treating an estimated 126.6 million people affected by musculoskeletal disorders exceeds $213 billion [1]. Moreover, with an increasingly obese and ageing population, this trend is expected to continue further. Unfortunately, according to U.S Department of Health & Human Services, only \(\sim\)10% out of the 115,000 people who needed a lifesaving organ transplant in 2018 have actually received it. This is because despite the overwhelming demand, almost no FDA approved [2] artificial tissue products are commercially available today. A major hurdle standing in the way of producing viable engineered bone is product size limitations. These in turn stem from the inability to deliver sufficient amounts of metabolites (e.g., O2, nutrients, etc.) to the inner pore spaces of scaffolds, given that the cells consume them in large quantities as they build tissue. Among these, O2 plays a critical role in the cell growth and proliferation, and thus its high concentrations have been correlated with both increased cellularity [3] and cell viability [4]. Conversely, a deficiency in O2 can result in a hypoxic cell state, which is commonly associated with decreased metabolic activity and potentially undesirable differentiation behavior [5; 6; 7]. Hence, optimal oxygen transport is important in maintaining tissue function and overall survival within the artificial tissues. For that reason, bone tissue engineering scaffolds are typically cultured in perfusion bioreactors, the idea behind which is to facilitate the mass transfer using flow. However, understanding what scaffold fabrication parameters and flow culturing conditions result in the optimal O2 delivery to the cells is made difficult by the complexity of the pore network architectures in which they reside. This is because most large scaffolds are not transparent enough for microscopy, and it is also difficult to measure the O2 concentrations at different locations within the scaffolds. Furthermore, the O2 uptake rate by the cells changes over time [3]. All these complications make the problem even more difficult to solve manually. For these reasons, computer simulation of the O2 transport and consumption offers itself as a viable alternative for obtaining insight into the microenvironment, which is experienced by the cells seeded on the surfaces of the scaffold pores. Yet, modeling of mass transport (and specifically of O2) within scaffolds is uncommon when compared to flow parameters, such as stimulatory fluid shear stress, permeability, and pressure (see Table 2 in Ref. [8]). Furthermore, Table 1 below summarizes our overview of the few O2 models that we did find in literature. From it, it can be seen that the studies commonly use idealized geometries for the scaffolds (e.g., a homogeneous porous medium) instead of realistic image-based. In reality, however, the scaffold architectures may be inhomogeneous. Moreover, many of the models either do not take into account specificities of bone tissue engineering, such as the need for flow perfusion, which generates a stimulatory shear environment natural to the bone canaliculi [9; 10]. Instead, many models either target tissue engineering in general, or they may be specific to other tissue engineering disciplines; for example, [PERSON] et al. [11] modeled a cardiac scaffold, which is cultured under pulsatile flow (not the case for bone). Finally, few of the models take into account O2 consumption by the cells. And among those that do, the rate is typically assumed to be constant. Thus, we were not able to find a single bone tissue engineering model that accounted for all of the following: the realistic scaffold structure, O2 diffusion, convection, and variable consumption rates.