Krogh-cylinder and infinite-domain models for washout of an inert diffusible solute from tissue.
OBJECTIVE
Models based on the Krogh-cylinder concept are developed to analyze the washout from tissue by blood flow of an inert diffusible solute that permeates blood vessel walls. During the late phase of washout, the outflowing solute concentration decays exponentially with time. This washout decay rate is predicted for a range of conditions.


METHODS
A single capillary is assumed to lie on the axis of a cylindrical tissue region. In the classic "Krogh-cylinder" approach, a no-flux boundary condition is applied on the outside of the cylinder. An alternative "infinite-domain" approach is proposed that allows for solute exchange across the boundary, but with zero net exchange. Both models are analyzed, using finite-element and analytical methods.


RESULTS
The washout decay rate depends on blood flow rate, tissue diffusivity and vessel permeability of solute, and assumed boundary conditions. At low blood flow rates, the washout rate can exceed the value for a single well-mixed compartment. The infinite-domain approach predicts slower washout decay rates than the Krogh-cylinder approach.


CONCLUSIONS
The infinite-domain approach overcomes a significant limitation of the Krogh-cylinder approach, while retaining its simplicity. It provides a basis for developing methods to deduce transport properties of inert solutes from observations of washout decay rates.
Department of Physiology, University of Arizona, Tucson, Arizona, USA.
Timothy W
TW
Secomb
D000818:Animals; D001693:Biological Transport, Active / Q000502:physiology; D001783:Blood Flow Velocity / Q000502:physiology; D006801:Humans; D008955:Models, Cardiovascular
diffusion; mathematical models; microvessels; solute transport