Robust numerical solution for the two parameter solute solvent transport model |
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| Institution: | 1. Sorbonne Universités, UPMC Univ. Paris 06, UMS 2348, Centre de Ressources Biologiques Marines, Observatoire Océanologique de Banyuls sur mer, F-75005 Paris, France;2. IRD, UMR DIADE, 911 Avenue Agropolis, BP 64501, 34394 Montpellier Cedex 5, France;3. Aquarium de Canet-en-Roussillon, 2 boulevard de la Jetée, 66140 Canet-en-Roussillon, France;4. Océanopolis, Port de plaisance du Moulin Blanc, BP 91039, 29210 Brest Cedex 1, France;1. Sorbonne Universités, UPMC Univ Paris 06, UMS 2348, Centre de Ressources Biologiques Marines, Observatoire Océanologique, F-66650 Banyuls/Mer, France;2. IRD, UMR DIADE, 911 Avenue Agropolis, BP 64501, 34394 Montpellier Cedex 5, France;3. Aquarium de Canet-en-Roussillon, 2 boulevard de la Jetée, 66140 Canet-en-Roussillon, France;4. Océanopolis, Port de plaisance du Moulin Blanc, BP91039, 29210 Brest Cedex 1, France;1. Department of Biological Sciences, Northern Illinois University, DeKalb, IL 60115, USA;2. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA;3. University of Missouri Comparative Medicine Center, 4011 Discovery Drive, Columbia, MO 65201, USA;1. Department of Biological Sciences, Northern Illinois University, DeKalb, IL 60115, USA;2. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA;3. University of Missouri Comparative Medicine Center, 4011 Discovery Drive, Columbia, MO 65201, USA;1. Centre for Biomedical Engineering, Department of Electronic Science and Technology, University of Science and Technology of China, Hefei 230027, Anhui, China;2. Anhui Provincial Engineering Technology Research Center for Biopreservation and Artificial Organs, Hefei 230027, Anhui, China;3. School of Mechanical and Automotive Engineering, Hefei University of Technology, Hefei 230009, China |
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| 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. |
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| Keywords: | Mass transport Exact solution Numerical integration Stiff Optimization Tissue Jacobs |
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