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Dynamics of A Three-Variable Nonlinear Model of Vasomotion: Comparison of Theory and Experiment

D. Parthimos ^*, R. E. Haddock , C. E. Hill  and T. M. Griffith ^*

^* Wales Heart Research Institute, Department of Diagnostic Radiology, Cardiff University, Cardiff, United Kingdom; and Division of Neuroscience, John Curtin School of Medical Research, Australian National University, Canberra, Australia

Correspondence: Address reprint requests to Professor T. M. Griffith, Wales Heart Research Institute, Dept. of Diagnostic Radiology, Cardiff University, Heath Park, Cardiff, CF14 4XN, UK. Tel.: 44-2920–743070; Fax: 44-2920–744726; E-mail: Griffith{at}Cardiff.ac.uk.

The effects of pharmacological interventions that modulate Ca²⁺ homeodynamics and membrane potential in rat isolated cerebral vessels during vasomotion (i.e., rhythmic fluctuations in arterial diameter) were simulated by a third-order system of nonlinear differential equations. Independent control variables employed in the model were [Ca²⁺] in the cytosol, [Ca²⁺] in intracellular stores, and smooth muscle membrane potential. Interactions between ryanodine- and inositol 1,4,5-trisphosphate-sensitive intracellular Ca²⁺ stores and transmembrane ion fluxes via K⁺ channels, Cl^– channels, and voltage-operated Ca²⁺ channels were studied by comparing simulations of oscillatory behavior with experimental measurements of membrane potential, intracellular free [Ca²⁺] and vessel diameter during a range of pharmacological interventions. The main conclusion of the study is that a general model of vasomotion that predicts experimental data can be constructed by a low-order system that incorporates nonlinear interactions between dynamical control variables.