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We present a multi-scale mathematical model and a novel numerical solver to study blood plasma flow and oxygen concentration in a prototype model of an implantable Bioartificial Pancreas (iBAP) that operates under arteriovenous pressure differential without the need for immunosuppressive therapy. The iBAP design consists of a poroelastic cell scaffold containing the healthy transplanted cells, encapsulated between two semi-permeable nano-pore size membranes to prevent the patient’s own immune cells from attacking the transplant. The device is connected to the patient’s vascular system via an anastomosis graft bringing oxygen and nutrients to the transplanted cells of which oxygen is the limiting factor for long-term viability. Mathematically, we propose a (nolinear) fluid–poroelastic structure interaction model to describe the flow of blood plasma through the scaffold containing the cells, and a set of (nonlinear) advection–reaction–diffusion equations defined on moving domains to study oxygen supply to the cells. These macro-scale models are solved using finite element method based solvers. One of the novelties of this work is the design of a novel second-order accurate fluid–poroelastic structure interaction solver, for which we prove that it is unconditionally stable. At the micro/nano-scale, Smoothed Particle Hydrodynamics (SPH) simulations are used to capture the micro/nano-structure (architecture) of cell scaffolds and obtain macro-scale parameters, such as hydraulic conductivity/permeability, from the micro-scale scaffold-specific architecture. To avoid expensive micro-scale simulations based on SPH simulations for every new scaffold architecture, we use Encoder–Decoder Convolution Neural Networks. Based on our numerical simulations, we propose improvements in the current prototype design. For example, we show that highly elastic scaffolds have a higher capacity for oxygen transfer, which is an important finding considering that scaffold elasticity can be controlled during their fabrication, and that elastic scaffolds improve cell viability. The mathematical and computational approaches developed in this work provide a benchmark tool for computational analysis of not only iBAP, but also, more generally, of cell encapsulation strategies used in the design of devices for cell therapy and bio-artificial organs.
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Parallel Implementation of a PETSc-Based Framework for the General Curvilinear Coastal Ocean Model
The General Curvilinear Coastal Ocean Model (GCCOM) is a 3D curvilinear, structured-mesh, non-hydrostatic, large-eddy simulation model that is capable of running oceanic simulations. GCCOM is an inherently computationally expensive model: it uses an elliptic solver for the dynamic pressure; meter-scale simulations requiring memory footprints on the order of 10 12 cells and terabytes of output data. As a solution for parallel optimization, the Fortran-interfaced Portable–Extensible Toolkit for Scientific Computation (PETSc) library was chosen as a framework to help reduce the complexity of managing the 3D geometry, to improve parallel algorithm design, and to provide a parallelized linear system solver and preconditioner. GCCOM discretizations are based on an Arakawa-C staggered grid, and PETSc DMDA (Data Management for Distributed Arrays) objects were used to provide communication and domain ownership management of the resultant multi-dimensional arrays, while the fully curvilinear Laplacian system for pressure is solved by the PETSc linear solver routines. In this paper, the framework design and architecture are described in detail, and results are presented that demonstrate the multiscale capabilities of the model and the parallel framework to 240 cores over domains of order 10 7 total cells per variable, and the correctness and performance of the multiphysics aspects of the model for a baseline experiment stratified seamount.
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- Award ID(s):
- 0922702
- PAR ID:
- 10275321
- Date Published:
- Journal Name:
- Journal of Marine Science and Engineering
- Volume:
- 7
- Issue:
- 6
- ISSN:
- 2077-1312
- Page Range / eLocation ID:
- 185
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/jmse7060185
