Abstract
Mathematical modelling can be used to investigate a wide variety of physiological phenomena. In this talk we will look at work we’ve done recently on two different systems.
Cirrhosis is a life-threatening condition that represents a leading cause of death in the western world. In this condition, the structure of the liver tissue is altered by the development of fibrosis, which means it becomes stiffer and its permeability to blood and interstitial flow within the tissue that are vital to its function are reduced. We develop a new mathematical model to investigate the changes in liver volume, blood flow and lymphatic uptake, which measures interstitial flow, that occur as the tissue becomes progressively stiffer. Our results suggest that the typical changes that develop during cirrhosis have a significant effect on the permeability properties, highlighting the seriousness of this condition.
The aqueous is produced by the ciliary body behind the iris of the eye, and flows through first the posterior chamber, second anteriorly through the pupil and third through the anterior chamber before leaving the eye at an approximately constant rate. We investigate the effect of iridotomy, which is when a small hole is surgically made in the iris tissue in order to allow flow to pass more easily from the posterior to the anterior chamber to reduce the risk of possible high pressures, such as might occur in closed angle glaucoma. The fluid flow is investigated in the posterior chamber: we make use of the narrowness of this chamber, use a formula for the flow through the iridotomy itself, prescribe the pressure at the pupil, and prescribe the production rate of the aqueous by the ciliary body.
Biography
Jennifer Tweedy obtained a degree and PhD in Applied Mathematics from the University of Cambridge. Her PhD studies were in understanding pattern formation in the context of dynamical systems, before undertaking postdoctoral work in blood flow and urology, before joining the Department of Bioengineering at Imperial in 2006. Her current research involves mathematical modelling of problems arising in medicine, medical practice and biology, especially problems involving fluid dynamics. For more details on her research, please see her research pages.