Dispersion in Perifusion Systems and Data Enhancement
by
David J.N. Wall
Biomathematics Research Centre, University of Canterbury
Coauthors: Paul Shorten, (Biomathematics Research Centre, University of Canterbury)

The temporal architecture of the endocrine glandular signaling process is believed to convey biochemical information to the target tissue, and also represent a signature of the responsive endocrine cells. The perifusion apparatus has been used to investigate the hormonally stimulated rate of release of other hormones. This apparatus can be modelled as providing mass transport down a tube when the flowing medium has a two-dimensional velocity profile. This velocity profile provides shear dispersion in the mass flow. We discuss inverse problems associated with this apparatus. In particular the inverse problem of estimation of a temporally varying concentration at one end of the tube, from measurement of a concentration at the opposite end is discussed. Various inverse problems are examined by considering a number of features of the flow. Firstly when the flow involved is a non-Newtonian fluid --- which occurs in practice for some perifusion measurements. Secondly we incorporate molecular diffusion effects. The nature of the ill-conditioning of these inverse problems is examined, and regularisation procedures are introduced to provide well-posed formulations of the inverse problems.

Date received: September 7, 1999