Theoretical Analysis of Complex Oscillations in Multibranched Microvascular Networks

Abstract

A mathematical model was used to study the origin of complex self-sustained diameter oscillations in multibranched microvascular networks. The model includes three branching levels (order 3, 2, and 1 arterioles) of a microvascular network derived fromin vivoobservation in the hamster dorsal cutaneous muscle. The main biomechanical aspects covered by the model are (1) the dependence of the elastic and active wall stress on the inner radius and (2) the static and dynamic myogenic response. Simulations on isolated arterioles indicate that self-sustained periodic diameter oscillations may occur at constant transmural pressure. Conversely, simulations on the entire network reveal different oscillatory patterns, including periodic, quasiperiodic, and chaotic fluctuations. Chaos in the model is revealed by the presence of a broad noise-like component in the frequency spectrum and by the sensitivity dependence of model results on small perturbations. Our results suggest that, owing to the intrinsic nonlinearity of the system, a contracting mechanism, such as the myogenic response, may induce different oscillatory patterns. The change from periodic to chaotic oscillations may be a consequence of a modest variation in a parameter (systemic pressure or arterial resistance) not necessarily related to pathophysiological conditions. Accordingly, ourin vivoobservations in the skeletal muscle showed that in some instances arteriolar vasomotion is converted from regular to highly irregular patterns in basal conditions. Vasomotion is found to affect mean blood flow compared with the nonoscillatory steady state. Chaotic oscillations tend to maintain a constant ratio of blood flows entering into bifurcation vessels, whereas periodic vasomotion determines a different flow distribution at branches.