AJP - Regulatory, Integrative and Comparative Physiology, Vol 261, Issue 1 247-R256, Copyright © 1991 by American Physiological Society
Mathematical analysis of perifusion data: models predicting elution concentration
W. R. Smith, G. C. Wake, J. E. McIntosh, R. P. McIntosh, M. Pettigrew and R. Kao
Department of Mathematics, University of Guelph, Ontario, Canada.
System models are constructed and analyzed for combined convective flow and
for dispersion in distorting concentrations of a chemical signal as it
passes through a packed column. We derive general analytical solutions for
these models. The results have applications to analyses such as in
biological experiments involving hormonal stimulation of perifused cells,
elution chromatography, adsorption columns, and studies of groundwater
flow. The models reveal that the column distorts an incoming signal (such
as a change in solute concentration in the flowing liquid) at the inlet.
This distortion is greatest at low values of the Peclet number of the flow
and is small at larger values. We explore the effects of the approximations
inherent in the mathematical models of the system. Specification of the
boundary conditions of the problem are shown to be particularly important.
With the use of incorrect models, it is possible to obtain accurate
interpolations to data obtained from perfusion experiments. However, the
parameters derived (in particular the dispersion constant and the peak
concentration of a solute concentration pulse) may be considerably in
error. This may lead to errors when these parameter estimates are used to
predict results in other experimental situations.
