### Dynamical characteristics of microvascular networks with a myogenic response gradient

#### Abstract

*Purpose:*Myogenic response is the ability of smooth muscle cells lining the vascu-lar wall to react to changing intravascular pressure: increasing pressure normallyinduces contraction whereas decreasing pressure leads to dilatation. Experimentalstudies show that the intensity of the myogenic response is dierent in arteriolarvessels of dierent radii: smaller arterioles react relatively more intensely, but overa more narrow range of pressures, than larger arterioles. In a network of vessels,this gives rise to a myogenic response gradient. The physiological significance of this gradient is, nonetheless, debated. Our purpose is to investigate the dynamical characteristics of microvascular networks with a myogenic response gradient by means of mathematical modeling.

*Methods:*We present a mathematical vascular network model which includes a de-tailed description of vessel wall mechanics and the myogenic response gradient. Wefocus on the influence of this gradient on short-term network dynamics. We performa series of numerical simulations in both symmetrical and asymmetrical vasculartrees in which the individual vessel is given a realistic morphology, i.e., relative wallthickness is smaller in larger vessels.

*Results:*Our main findings show that the presence of a myogenic response gradient:1. adjusts flow and pressure in the capillary bed to an adequate level and dampensoscillations transmitted from upstream feeding vessels;2. provides the network as a whole with a basal level of tone necessary for theoperation of vasomotor mechanisms other than the myogenic response; and3. provides the system with the overall ability to autoregulate network flowsmoothly.

*Conclusion:*The mathematical model shows that networks with a myogenic response gradient present advantages regarding the physiological function of regulating flow in a bifurcating network compared to networks without myogenic response and passive networks

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