Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Foundations of modeling in cryobiology I: Concentration, Gibbs energy, and chemical potential relationships



Daniel M. Anderson, James Benson, Anthony J. Kearsley


Mathematical modeling plays an enormously important role in understanding the behavior of cells, tissues, and organs undergoing cryopreservation. Uses of these models range from explanation of phenomena, exploration of potential theories of damage or success, development of equipment, and re nement of optimal cryopreservation/cryoablation strategies. Over the last half century there has been a considerable amount of work in bio-heat and mass-transport, and these models and theories have been readily and repeatedly applied to cryobiology with much success. However, there are signi cant gaps between experimental and theoretical results that suggest missing links in models. One source for these potential gaps is that cryobiology is at the intersection of several very challenging aspects of transport theory: it couples multi-component, moving boundary, multiphase solutions that interact through a semipermeable elastic membrane with multicomponent solutions in a second time-varying domain, during a two-hundred Kelvin temperature change with multi-molar concentration gradients and multi-atmosphere pressure changes. In order to better identify potential sources of error, and to point to future directions in modeling and experimental research, we present a three part series to build from rst principles a theory of coupled heat and mass transport in cryobiological systems accounting for all of these e ects. The hope of this series is that by presenting and justifying all steps, conclusions may be made about the importance of key assumptions, perhaps pointing to areas of future research or model development, but importantly, lending weight to standard simpli cation arguments that are often made in heat and mass transport. In this rst part, we review concentration variable relationships, their impact on choices for Gibbs energy models, and their impact on chemical potentials.


cryobiology, Gibbs free energy, di usion, chemical potential gradient


Anderson, D. , Benson, J. and Kearsley, A. (2014), Foundations of modeling in cryobiology I: Concentration, Gibbs energy, and chemical potential relationships, Cryobiology, [online],, (Accessed June 15, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created September 20, 2014, Updated October 12, 2021