The differentiation of human induced pluripotent stem cells (hiPSC) into retinal ganglion cells (RGC) is a lengthy process whose success depends on the conditions in the cellular microenvironment. Cells are traditionally cultured and differentiated in static culture in cell culture dishes, where the medium is replaced periodically. An alternative approach is offered by microfluidic systems with medium perfusion, in which fresh medium enters the microfluidic chamber continuously. The aim of this work was to evaluate and compare oxygen transport in the two systems by means of mathematical modelling, and to determine whether oxygen is a limiting factor in differentiation.
A mathematical model was developed for each of the two systems. For the static system, a one-dimensional model of time-dependent oxygen diffusion was formulated, and for the microfluidic system with a gas-permeable PDMS membrane, a two-dimensional convection–diffusion model. Both models were solved by the finite difference method and verified against a mass balance and against an independent analytical solution of the series resistance model. The biological parameters were estimated from the literature, and their influence was examined by a parametric sensitivity analysis.
The models show that oxygen transport is not a limiting factor in either of the systems considered. The oxygen concentration at the cell monolayer remains everywhere substantially higher than the Michaelis constant, so oxygen consumption proceeds in the zero-order kinetic regime and the cells are not exposed to hypoxia. The modelling results indicate that the failure of the differentiation experiment in the microfluidic device cannot be attributed to a lack of oxygen.
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