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Math Biosci. 2014 Aug;254:64-75. doi: 10.1016/j.mbs.2014.06.003. Epub 2014 Jun 17.

Mathematical model formulation and validation of water and solute transport in whole hamster pancreatic islets.

Author information

  • 1Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60178, USA. Electronic address: benson@math.niu.edu.
  • 2Eli Lilly & Co., Lilly Corporate Center, Indianapolis, IN 46285, USA. Electronic address: benson_charles_t@lilly.com.
  • 3Department of Veterinary Pathobiology, University of Missouri, Columbia, MO 65211, USA.


Optimization of cryopreservation protocols for cells and tissues requires accurate models of heat and mass transport. Model selection often depends on the configuration of the tissue. Here, a mathematical and conceptual model of water and solute transport for whole hamster pancreatic islets has been developed and experimentally validated incorporating fundamental biophysical data from previous studies on individual hamster islet cells while retaining whole-islet structural information. It describes coupled transport of water and solutes through the islet by three methods: intracellularly, intercellularly, and in combination. In particular we use domain decomposition techniques to couple a transmembrane flux model with an interstitial mass transfer model. The only significant undetermined variable is the cellular surface area which is in contact with the intercellularly transported solutes, Ais. The model was validated and Ais determined using a 3×3 factorial experimental design blocked for experimental day. Whole islet physical experiments were compared with model predictions at three temperatures, three perfusing solutions, and three islet size groups. A mean of 4.4 islets were compared at each of the 27 experimental conditions and found to correlate with a coefficient of determination of 0.87±0.06 (mean ± SD). Only the treatment variable of perfusing solution was found to be significant (p<0.05). We have devised a model that retains much of the intrinsic geometric configuration of the system, and thus fewer laboratory experiments are needed to determine model parameters and thus to develop new optimized cryopreservation protocols. Additionally, extensions to ovarian follicles and other concentric tissue structures may be made.

Copyright © 2014 Elsevier Inc. All rights reserved.


Cryobiology; Diffusion; Domain decomposition; Mass transport; Perfusion

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