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Next generation bioreactors are being developed to generate multiple human cell-based tissue analogs within the same fluidic system, to better recapitulate the complexity and interconnection of human physiology [1, 2]. The effective development of these devices requires a solid understanding of their interconnected fluidics, to predict the transport of nutrients and waste through the constructs and improve the design accordingly. In this work, we focus on a specific model of bioreactor, with multiple input/outputs, aimed at generating osteochondral constructs, i.e., a biphasic construct in which one side is cartilaginous in nature, while the other is osseous. We next develop a general computational approach to model the microfluidics of a multi-chamber, interconnected system that may be applied to human-on-chip devices. This objective requires overcoming several challenges at the level of computational modeling. The main one consists of addressing the multi-physics nature of the problem that combines free flow in channels with hindered flow in porous media. Fluid dynamics is also coupled with advection-diffusion-reaction equations that model the transport of biomolecules throughout the system and their interaction with living tissues and C constructs. Ultimately, we aim at providing a predictive approach useful for the general organ-on-chip community. To this end, we have developed a lumped parameter approach that allows us to analyze the behavior of multi-unit bioreactor systems with modest computational effort, provided that the behavior of a single unit can be fully characterized.