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In tissue engineering and the development of bioartificial organs, one of the fundamental physiological requirements that must be carefully engineered is the adequate delivery of oxygen to living cells. Cells within a three-dimensional tissue construct or encapsulated organoid must receive sufficient oxygen to maintain metabolism, proliferative capacity, and functional stability. A major challenge in this context arises due to the limitations of oxygen transport through static media. Diffusive transport alone becomes insufficient when the cellular layer or tissue construct surpasses a certain critical thickness. In such scenarios, oxygen concentrations can fall precipitously with increasing depth, creating hypoxic or even anoxic zones that can result in cell death and tissue failure. To overcome these limitations, perfusion systems have been developed that actively drive a fluid---typically a plasma-like or oxygen-carrying medium---through the cellular layer. This technique enhances mass transport by combining diffusion with convection, thereby significantly improving oxygen distribution throughout the construct. One such method involves connecting a device between an artery and a vein, allowing arterial pressure to drive the filtrate---usually blood plasma---through a microporous membrane that permits the transport of oxygen and nutrients while blocking blood cells. This convective flow delivers oxygen directly to the embedded cells, circumventing the shortcomings of pure diffusion.