Unstable radii in muscular blood vessels
Quick, C. M., J. K-J. Li, H. L. Baldick, H. W. Weizsäcker,
and A. Noordergraaf
3rd Annual Southern Biomedical Engineering Conference, Washington, DC, 1994
Abstract
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 radius below a critical level of activation. However,
when the active tension is raised above this critical level, the graph of
the pressure-radius relationship (with pressure on the abscissa and radius
on the ordinate) becomes N-shaped with a relative maximum pressure P
max 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 no radii between the outer two can
be maintained at equilibrium. Previously unexplained literature data
reveals evidence of this instability.