Robust numerical solution for the two parameter solute solvent transport model

Abstract

Prediction of solute and solvent transport in cells is central to developing and testing cryopreservation protocols. As we show here, however, the models used can be difficult to accurately numerically integrate in some key cases, and thus are a challenge to implement when determining the time dependent cell state during cryoprotectant equilibration and cooling. Exact solution techniques exist for overcoming this problem, but their implementation is also challenging: inversion of a nonlinear function is required that negates much of the utility of the approach. This communication describes a simple approach for more robust numerical integration that can be implemented using any numerical differential equation solver, and can facilitate arbitrarily accurate solutions to transport models without the complication of inversion formulae or complicated numerical integration schemes. Further, a simple relevant example of red blood cell equilibration with 40% glycerol is presented with comments on extending the approach to other settings.

Keywords: Exact solution; Jacobs; Mass transport; Numerical integration; Optimization; Stiff; Tissue.