Unstable radii in muscular blood vessels

A model of a muscular blood vessel in equilibrium that predicts stable and unstable control of radius is presented. 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 maximal pressure (Pmax) and a relative minimal pressure (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 reveal evidence of this instability.