Tp. Harrigan, REGULATORY INTERACTION BETWEEN MYOGENIC AND SHEAR-SENSITIVE ARTERIAL SEGMENTS - CONDITIONS FOR STABLE STEADY-STATES, Annals of biomedical engineering, 25(4), 1997, pp. 635-643
Myogenic and shear stress-sensitive mechanisms control the caliber of
a small blood vessel in this modeling study. This blood vessel in our
model was composed of a pressure-sensitive (myogenic) component and a
series-connected shear-sensitive component. The response of this model
to imposed pressure and the conditions that result in a stable steady
-state vessel diameter were investigated. The requirement that the mod
el parameters need to satisfy for a stable steady state to exist are e
xpressed by the numerical solution of simultaneous nonlinear equations
. Also, if a vessel is put into an initial state that is not an equili
brium state, then the system must occupy a range of initial conditions
to arrive at a stable equilibrium. These are described graphically fo
r three cases. In general, the initial shear stress should be higher t
han the equilibrium value of shear stress, and/or the initial transmur
al pressure should be low, compared with the imposed feed pressure. In
creasing the imposed pressure on the vessel can lead to elimination of
the equilibrium state and vasospasm, according to this model. When a
stable steady state is not reached, the model predicts elimination of
the vessel or vasospasm. The model is in qualitative agreement with ex
perimental observations that, during angiogenesis, vessels with low fl
ow are often eliminated.