Journal of Theoretical Medicine
Volume 3 (2001), Issue 3, Pages 191-211

A Model of Dispersion in Perifusion Systems

Biomathematics Research Centre, Department of Mathematics & Statistics, University of Canterbury, Private Bag 4800, Christchurch, 1, New Zealand

Received 4 September 2000

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The perifusion apparatus is an experimental tool used to model information transfer in endocrine systems. The major drawback of the perifusion system derives from the dispersion, diffusion and mixing of the hormone within the apparatus which distort the original released hormone concentration profile. In this paper we develop a mathematical model of the perifusion system that accounts for a number of observable features in the measured secretory profile. We also consider associated inverse problems, the solution of which enhance perifusion data measurements and unmask the underlying secretory events. In contrast with the raw data, the deconvolved data supports the concentration dependent, rapid activation of CRH-induced ACTH secretion. The perifusion chamber can be modeled by an advection-diffusion equation, and we develop general theory analysing the validity of this approximation. We also provide a characterisation of the degree of ill-posedness of the inverse advection-diffusion equation in terms of the perifusion parameters.