A poroelastic model of transcapillary flow
by
Sean Speziale
University of Waterloo
Coauthors: S. Sivaloganathan G. Tenti

Transcapillary exchange is the movement of fluid and molecules across the porous capillary wall, and plays an

important role in maintaining homeostasis in tissues. To reach the cells of a given tissue, molecules must

traverse a porous matrix known as the interstitial space, whose main function is to mediate exchange of oxygen,

nutrients and waste products between the vascular and cellular compartments. The classical picture of

transcapillary exchange was suggested by Starling in 1896, namely that the forces determining fluid flow were the

hydrostatic and osmotic pressure differences between the capillary and surrounding interstitial space. However,

experimental observations indicated that this view must be revised, and subsequently Michel and Weinbaum put

forward the idea that the Starling principle should be applied not across the entire capillary wall but instead

across a structure lining the wall known as the endothelial glycocalyx. Existing ultrastructural models are quite

complicated, so our aim is to model transcapillary flow using a simpler approach, without losing the essential

characteristics. We adopt the Michel-Weinbaum hypothesis, but instead of looking at the microstructure we idealize

the capillary wall as a homogenized porous media, and introduce a slight modification to the theory of Biot. Due

to the presence of solutes, a modified version of Darcy's law is used, in which fluid flow is driven by both

hydrostatic and osmotic gradients. A unique feature of the present work is to be able to predict the stress and

strain distributions in the capillary wall, which had not been attempted previously. This work may have

implications in understanding edema formation, as well as in explaining the elevated interstitial fluid pressure

in tumours.

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Date received: May 9, 2008