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A 1-D model to explore the effects of tissue loading and tissue concentration gradients in the revised Starling principle

¹Departments of Biomedical and Mechanical Engineering, The City College of The City University of New York, New York, New York; and ²Department of Physiology and Membrane Biology, University of California, Davis, California

Submitted 2 November 2005 ; accepted in final form 24 July 2006

The recent experiments in Hu et al. (Am J Physiol Heart Circ Physiol 279: H1724–H1736, 2000) and Adamson et al. (J Physiol 557: 889–907, 2004) in frog and rat mesentery microvessels have provided strong evidence supporting the Michel-Weinbaum hypothesis for a revised asymmetric Starling principle in which the Starling force balance is applied locally across the endothelial glycocalyx layer rather than between lumen and tissue. These experiments were interpreted by a three-dimensional (3-D) mathematical model (Hu et al.; Microvasc Res 58: 281–304, 1999) to describe the coupled water and albumin fluxes in the glycocalyx layer, the cleft with its tight junction strand, and the surrounding tissue. This numerical 3-D model converges if the tissue is at uniform concentration or has significant tissue gradients due to tissue loading. However, for most physiological conditions, tissue gradients are two to three orders of magnitude smaller than the albumin gradients in the cleft, and the numerical model does not converge. A simpler multilayer one-dimensional (1-D) analytical model has been developed to describe these conditions. This model is used to extend Michel and Phillips’s original 1-D analysis of the matrix layer (J Physiol 388: 421–435, 1987) to include a cleft with a tight junction strand, to explain the observation of Levick (Exp Physiol 76: 825–857, 1991) that most tissues have an equilibrium tissue concentration that is close to 0.4 lumen concentration, and to explore the role of vesicular transport in achieving this equilibrium. The model predicts the surprising finding that one can have steady-state reabsorption at low pressures, in contrast to the experiments in Michel and Phillips, if a backward-standing gradient is established in the cleft that prevents the concentration from rising behind the glycocalyx.

endothelial glycocalyx; tight junction; capillary permeability; vesicular transport

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