Regulatory interaction between myogenic and shear-sensitive arterial segments : Conditions for stable steady states

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 model parameters need to satisfy for a stable steady state to exist are expressed by the numerical solution of simultaneous nonlinear equations. Also, if a vessel is put into an initial state that is not an equilibrium state, then the system must occupy a range of initial conditions to arrive at a stable equilibrium. These are described graphically for three cases. In general, the initial shear stress should be higher than the equilibrium value of shear stress, and/or the initial transmural pressure should be low, compared with the imposed feed pressure. Increasing 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 experimental observations that, during angiogenesis, vessels with low flow are often eliminated.