The work reported here has been motivated by the design of lab-grown organs, such as a bioartificial pancreas. The design of lab-grown organs relies on using biocompatible materials, typically poroelastic hydrogels, to generate scaffolds to support seeded cells of different organs.  Additionally, to prevent the patient's own immune cells from attacking the transplanted organ, the hydrogel containing seeded cells is encapsulated between two semi-permeable, nano-pore size membranes/plates and connected to the patient's vascular system via a tube (anastomosis graft). The semi-permeable membranes are designed to prevent the patient's own immune cells from attacking the transplant, while permitting oxygen and nutrients carrying blood plasma (Newtonian fluid) to reach the cells for long-term cell viability.  A key challenge is to design a hydrogel with ``roadways'' for blood plasma to carry oxygen and nutrients to the transplanted cells.

We present a complex, multi-scale model, and a first well-posedness result in the area of fluid-poroelastic structure interaction (FPSI) with multi-layered structures modeling organ encapsulation. We show global existence of a weak solution to a FPSI problem between the flow of an incompressible, viscous fluid, modeled by the time-dependent Stokes equations, and a multi-layered poroelastic medium consisting of a thin poroelastic plate and a thick poroelastic medium modeled by a Biot model. Numerical simulations of the underlying problem showing optimal design of a bioartificial pancreas, will be presented. This is a joint work with bioengineer Shuvo Roy (UCSF), and mathematicians Yifan Wang (UCI), Lorena Bociu (NCSU), Boris Muha (University of Zagreb), and Justin Webster (University of Maryland, Baltimore County).