Modeling the Delivery of Dissolved Gases for Diabetes Research

Abstract

Understanding cellular metabolism and its interaction with oxygen is vital in diabetes research. This requires a quantitative understanding of the oxygen concentration at the tissue. To address this issue, a 2-D flow model is developed to quantify the oxygen reaction rate of the tissue. In addition, an experimental setup was developed to provide a precise, rapid control over the delivered gas concentration. Mass flow controllers were implemented to accurately regulate the gas flow rate, integrating Arduino and Python programming to remove the need for manual adjustments. This approach also shortened the steady state time of the oxygen concentration within the media, thereby significantly cutting down the time required to conduct experiments. The purpose of the computational model is to help understand the rate controlling processes governing the uptake by oxygen by the cells. This is broadly governed by two processes that are in series: 1. The transport of O2 from the free stream to the reaction sites. 2. The rate of O2 consumption at the reaction sites. This model used the finite difference method to discretize the governing equations, which included oxygen diffusion, advection, and most importantly, the oxygen reaction around the tissue. Appropriate boundary conditions were applied at the inflow, outflow, walls, and for the tissue surface. To model the enzyme kinetics of the oxygen reaction, the Michaelis Menten equation was utilized along the surface of the cell. The concentration field was calculated by solving a large system of equations, for which the Newton Raphson method was employed. The concentration field provided a visual representation of the flow field, and was used to calculate the oxygen consumption rate (OCR) of the tissue, which was then compared with experimental data. The results were in broad agreement with the oxygen consumption rates seen in the experiments.