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A "Vuggy" Medium Approach to Fluid and Drug Transport in Tumours
by
Rebecca Shipley
Mathematical Institute, University of Oxford
Coauthors: Prof. S. J. Chapman
The neoplastic vasculature of solid tumours comprises a network of capillaries with highly permeable walls. Understanding the flow of blood through this vasculature and the surrounding porous interstitium of the tumour is important for two main reasons. Firstly, it is a key ingredient when predicting the oxygen distribution within the tumour, which is crucial for predicting the micro-environment and growth rate of cancer cells. Secondly, it is vital for predicting the treatment of cancer by therapeutic drugs administered intraveneously. For example, the success of treatment by chemotherapy drugs has been limited by low transport rates across the vasculature into the main tumour body. Increased convection induced by elevating the systemic blood pressure or applying intratumoural infusion has been shown to improve drug delivery by 40% and several orders of magnitude respectively.
Here we develop a multiscale model of the tumour vasculature, using a similar approach to that used in the petrochemical industry to model groundwater aquifiers and petroleum reservoirs. We assume that the tumour has a locally periodic structure, comprised of a network of capillaries embedded in the surrounding interstitium (a porous medium). The capillaries are small compared to the size of the tumour itself, but much larger than the pore size of the tissue, and so these disparate length-scales can be exploited to describe fluid and drug transport in a tumour. On the local scale, we describe the flow of blood through the capillaries and across the vascular boundary into the interstitium. A multiple-scales technique is then used to move from the local to the global descriptions and so determine the equations describing the effective fluid transport on the tumour-scale. This approach is extended to describe drug transport, and finally numerical simulations are presented.
Date received: May 12, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawd-77.