Collaborative Research: Mechanistic modeling of cell encapsulation

Cell encapsulation is a biologically inspired technology that isolates live cells from the hostile environment. This is done by packaging the cells in a scaffold, which is encapsulated in a semi-permeable isolating membrane. The packaged cells are connected to the host’s vasculature via a tube (anastomosis graft) transporting oxygen and nutrients rich blood to the cells.

The semi-permeable encapsulating membrane, located at the interface between the blood flow in the graft and the cell scaffold, is designed to block the host’s immune cells from attacking the transplanted cells, while allowing passage of oxygen and nutrients to the cells. A major challenge in cell encapsulation is sufficient oxygen and nutrients supply to maintain the long-term viability of cells.

The main goal of this project is to develop a comprehensive multi-scale and multi-physics mathematical and computational framework modeling cell encapsulation. Using this framework, The PIs will address the long-term viability of encapsulated cells by (1) studying how hydrogel architecture and elasticity affect oxygen and nutrients supply to the cells, and by (2) exploring design of ultrafiltrate channels within the hydrogel to maximize oxygen and nutrients supply to the cells.

The concept of cell encapsulation is highly relevant for bioartificial organs design and for controlled delivery of biological therapeutics. This interdisciplinary project will provide mentoring of undergraduate and graduate students at the interface between mathematics and biology. A new graduate course at Texas Tech will be introduced to train students in the state-or-the-art mathematical methods developed in this project.

To promote participation of women in STEM, a series of Summer Workshops for High School girls will be organized at the UC Berkeley Mathematics Department with scientific visits to the UCSF Biodesign Laboratory.

The goal of this project is to develop a comprehensive multi-scale, multi-physics mathematical and computational model of cell encapsulation for bioartificial organs design. At the macro-scale, two sets of time-dependent coupled models will be developed and analyzed: (1) a fluid-structure interaction (FSI) model between the Stokes/Navier-Stokes equations and the Biot membrane equations coupled to the nonlinear Biot poroelastic medium equations, and (2) a set of coupled nonlinear advection-reaction-diffusion equations defined on moving domains describing oxygen concentration in the encapsulated organ.

Two partitioned schemes will be developed to solve the FSI problem and the coupled advection-reaction-diffusion problems. The numerical schemes will be designed to deal with the novel coupling conditions holding across a Biot poroelastic membrane interface, defined on a “mixed’’ 2D/3D domain. Stability analysis and convergence tests will be performed.

To capture the impact of micro-scale hydrogel architecture on local hydraulic conductivity, Smoothed Particle Hydrodynamics (SPH) simulations will be used. The results of the SPH simulations will provide synthetic data for the Encoder-Decoder Convolution Neural Networks training (offline) to produce macro-scale parameters, such as the hydrogel permeability tensor, needed in macro-scale simulations.

Validation and parameter estimation will be provided by the experiments at the UCSF Biodesign Laboratory. The results from this research will advance the knowledge in mathematical FSI involving poroelastic media and in coupled nonlinear advection-reaction-diffusion systems on moving domains. The outcomes of the findings will advance the knowledge in cell encapsulation for bioartificial organ design and in controlled delivery of biological therapeutics.

This proposal is jointly funded by the Mathematical Biology Program of the Division of Mathematical Science (DMS), the Fluid Dynamics Program and the Engineering of Biomedical Systems (EBMS) Program, both in the Chemical, Bioengineering, Environmental, and Transport Systems (CBET) Division, Directorate for Engineering.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.