Unstable radii in muscular blood vessels.
Quick, Christopher M., Heather L. Baldick, Nina Safabakhsh, Timothy J.
Lenihan, John K. J. Li, Hans W. Weizs[umlaut]acker, and Abraham
Noordergraaf.
Cardiovascular Research Lab, Department of Biomedical Engineering,
Rutgers University, Piscataway, NJ 08855-0909, Tel. (908) 445-4803,
Fax. (908) 445-3753, Cardiovascular Studies Unit, Department of
Bioengineering, University of Pennsylvania, Philadelphia, PA 19104,
Physiologisches Institut der Karl-Franzens-Universit[umlaut]at Graz,
Harrachgasse 21, Graz, Austria
APStracts 3:0153H, 1996.
A model of a muscular blood vessel in equilibrium is presented that
predicts stable and unstable control of radius. The equilibrium wall
tension is modeled as the sum of a passive exponential function of
radius and an active parabolic function of radius. The magnitude of
the active tension is varied to simulate the variable level of smooth
muscle activation. This tension-radius relationship is then converted
to an equilibrium pressure-radius relationship via Laplace's Law.
This model predicts the traditional ability to control the radius
below a critical level of activation. However, when the active
tension is raised above this critical level, the pressure-radius
relationship (with pressure plotted on the ordinate and radius on the
abscissa) becomes N-shaped with a relative maximum pressure Pmax and
a relative minimum Pmin. For this N-shaped curve there are three
equilibrium radii for any pressure between Pmin and Pmax. Analysis
shows that the middle radius is unstable, and thus cannot be
maintained at equilibrium. Previously unexplained experimental data
reveals evidence of this instability.
Received 17 January 1995; accepted in final form 4 March 1996.
APS Manuscript Number H43-5.
Article publication pending Am. J. Physiol. (Heart Circ. Physiology).
ISSN 1080-4757 Copyright 1996 The American Physiological Society.
Published in APStracts on 23 April 96