Non-linear analysis and modelling of the cellular mechanisms that regulate arterial vasomotion

Abstract

Non-linearity intrinsic to the ion transport systems that regulate intracellular [Ca2+] and smooth muscle tone allows the emergence of fluctuations in vascular diameter and resistance in isolated arteries (vasomotion) that can be classified as chaotic. Correlation analysis suggests an underlying low dimensional system and a four-dimensional model of vasomotion has been formulated to simulate the effects of pharmacological manipulation of smooth muscle tone or nitric oxide (NO) synthesis by the vascular endothelium. The oscillatory patterns observed experimentally and in modelling studies may be considered ‘universal’ in the sense that they also occur in many physico-chemical systems and include: (a) period-doubling, a feature of the Feigenbaum route to chaos; (b) mode-locking and quasiperiodicity, which reflect the interaction of two nonlinear oscillatory subsystems; and (c) intermittency, in which segments of nearly periodic oscillations of variable duration are interrupted by short chaotic bursts. Low dimensionality allows the construction of iterative maps that confirm the existence of types I and III Pomeau-Manneville intermittency in vascular dynamics, with attractor reconstructions indicating that the reinjection mechanism underlying the type III scenario involves a Shil'nikov-type homoclinic trajectory. Dimensional analysis of experimental data and corresponding surrogate time series generated by randomization of Fourier phase also provide evidence for underlying nonlinear structure in fluctuations in red cell velocity and arteriolar calibre in vivo.