University of Alberta

Modeling Heat and Mass Transport In
Biological Tissues During Freezing


Christopher Val Studholme

A thesis submitted to the Faculty of Graduate Studies and Research in partial
fulfillment of the requirements for the degree of Master of Science


Applied Mathematics

Department of Mathematical Sciences

Edmonton, Alberta
Spring 1997


Cryobiology, the study of life at low temperatures, requires modeling to extend understanding and predict responses of living systems. A compartment model was developed to represent complex biological tissues as a hierarchy of compartments. To implement this model, a description of phase behaviour in real solutions was developed using thermodynamic principles. Osmotic pressures in solutions, derived from phase behaviour, were used to predict water and solute movements across semi-permeable membranes. The heat conduction equation was solved with a piece-wise quadratic model of temperature and concentrations profiles. This diffusion model includes effects of moving phase boundaries within tissues, and allows for planar and dendritic ice formation. Constitutional supercooling was calculated for prediction of dendritic breakdown. This model was applied to real tissue systems to predict responses on tissue and cellular scales. The model's generality and use of biophysical mechanisms and parameters allows applications to a wide variety of real tissue systems.

My supervisory committee consisted of:

I have choosen to release my thesis under the terms of the GNU Free Documentation License (GFDL). You may download a complete copy of the thesis from this site in either PDF (2.0MB) or postscript (1.0MB) format. Feel free to make a copy of the thesis for anyone who may be interested.

Papers related to this thesis.

By request, I am also making the source code for the software used to do the simulations described in my thesis available. Beware that this code may be rather difficult to compile and use, and that it does not come with documentation (as none exists). The code is available only in gziped tar format.

Last modified: 30-March-2006
by Chris Studholme
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