Plenary Speaker 2

From Nonlinear PDEs to Bioartificial Organs: Mathematics of Fluid–Poroelastic Interaction

The design of implantable bioartificial organs presents a rich class of mathematical problems in which incompressible fluid flow, deformable porous media, membrane mechanics, and the transport and consumption of biological solutes are strongly coupled across multiple spatial scales. Motivated by the development of an implantable bioartificial pancreas that could function without immunosuppressant therapy, this talk will focus on the modeling, analysis, and numerical simulation of fluid–poroelastic structure interaction (FPSI) involving multilayered poroelastic media.

At the macroscale, blood flow is modeled by the time-dependent incompressible Navier–Stokes equations and is coupled to a multilayered Biot-type poroelastic structure representing semipermeable nanopore membranes and a cell-containing hydrogel. The resulting moving-boundary problem combines geometric and constitutive nonlinearities, incompressibility constraints, and the interaction of distinct dissipative mechanisms. I will present a constructive well-posedness theory for this nonlinear system, including the first existence result for finite-energy weak solutions coupling the time-dependent Navier–Stokes equations with Biot-type multilayered poroelasticity. Particular attention will be devoted to the novel analytical ideas required to control the moving geometry, obtain uniform energy estimates, establish compactness, and pass to the limit in the nonlinear coupling terms.

I will then describe a multiscale computational framework that couples the FPSI model to nonlinear advection–reaction–diffusion equations governing oxygen transport and cellular consumption. At the microscale, Smoothed Particle Hydrodynamics and encoder–decoder convolutional neural networks are used to connect the fine architecture of the hydrogel to effective macroscale quantities, including a spatially dependent permeability tensor. Numerical simulations reveal how scaffold geometry, permeability, and blood-flow conditions influence oxygen delivery and cell viability. I will conclude by showing how these mathematical and computational results informed the design of a second-generation implantable bioartificial pancreas.

This work is joint with S. Roy, Y. Wang, M. Bukač, J. Kuan, J. Webster, L. Bociu, and B. Muha.