Affiliations: [a] Department of Diagnostic Radiology, University of Wales College of Medicine, Heath Park, Cardiff, CF4 4XN, UK | [b] Department of Cardiology, University of Wales College of Medicine, Heath Park, Cardiff, CF4 4XN, UK
Abstract: Nonlinear mathematical techniques now make it possible to quantify the complexity of an irregular time series through calculation of a parameter known as fractal dimension. In the present study, we use such an analysis to provide evidence that histamine-induced pressure oscillations in an isolated rabbit ear resistance artery are generated by deterministic rather than stochastic mechanisms, and that a minimum of 3 independent control variables is necessary to account for the complexity of the dynamics of these oscillations. The fractal dimension of the responses was independent both of the concentration of histamine used to induce rhythmic behavior, and the level of activity of the endogeneous nitrovasodilator, EDRF. While both superficially influenced the form of the oscillations, it follows that neither are key control variables involved in their genesis. Nonlinear analysis of data obtained in the presence of NG-nitro-L-arginine methyl ester (L-NAME), which blocks EDRF synthesis, provided insights into the intrinsic smooth muscle control mechanisms responsible for generating rhythmic activity. The oscillations exhibited distinct “fast” and “slow” components (periods of 5–20 secs and 1–5 min. respectively). The former involved ion movements at the cell membrane and was inhibited by low [Ca2+]o, verapamil (which blocks voltage-dependent Ca2+ influx) and tetraethylammonium (which blocks Ca2+-activated outward K+ channels), whereas the latter involved Ca2+-induced Ca2+ release from intracellular stores and was inhibited by ryanodine. All such interventions decreased the overall fractal dimension of the responses to a value <2, thus removing one degree of complexity (and hence control variable) from the dynamics. We conclude that the nonlinear interaction between a fast membrane oscillator and a slow intracellular oscillator generates chaos in vascular smooth muscle and that exogeneous constrictor agonists and EDRF may be regarded as permissive and modulatory influences, respectively.
