DEPARTMENT OF MATHEMATICAL &
STATISTICAL SCIENCES

UNIVERSITY OF ALBERTA

**MATHEMATICAL
BIOLOGY SEMINAR**

**MONDAY February 2, 2004**

**3:00-4:00 p.m.**

**CAB 657**

**Dr. Janet A.W. Elliott**

## Professor of Chemical Engineering

**Canada Research Chair in
Interfacial Thermodynamics, University of Alberta**

**Currently Visiting
Professor, Chemical Engineering and Mechanical Engineering, M.I.T.**

** **

*Mathematical and
thermodynamics modeling in cryobiology*

Abstract:

The challenge in using fundamentals from the
physical sciences to model biological systems is to have enough complexity in
the mathematical model to capture the behaviour of interest while at the same
time having a simple enough biological model that the problem is tractable.
Particular applications of thermodynamics in cryobiology will be used to
illustrate this point. Cryobiology is the study of the effects of extremely low
temperature on biological systems with a major application being preserving
cells and tissues for transplantation or research.

An
example of a ubiquitous rudimentary thermodynamic model is the Boyle van’t Hoff
equation used to relate equilibrium cell volume to the osmolality of the
surrounding solution. This relationship is used extensively in cryobiological
calculations. The Boyle van’t Hoff equation is only valid if the cell contents
form a thermodynamically ideal dilute solution (i.e. osmolality linear in
concentration). This is a rather extreme requirement and one consequence of the
inappropriate use of the Boyle van’t Hoff equation is the unreasonably large
value obtained for the osmotically inactive fraction of many types of cells,
such as human red blood cells. When a replacement for the Boyle van’t Hoff
equation is combined with a hemoglobin-plus-salt osmotic virial equation (i.e.
osmolality given by a polynomial expansion in concentration rather than being
linear), the inferred osmotically inactive fraction for human red blood cells
is reduced by 25%.

We
are putting various mathematical models such as the above into a computer
simulation tool being developed to predict transport and freezing during the
cooling of cells and their environment. The simulations are becoming so
accurate that we are beginning to use them in a predictive way to find and
optimize novel cryoprotection protocols. In addition, current mathematical
research involves examining the stability of coupled flux equations using the
osmotic virial equation that may be relevant to cryobiology.

(with L. E. McGann, J. D. Benson, R. Bannerman, L. Ross-Rodriguez, H. Y.
Elmoazzen)