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Abstract
A system of differential equations describing stationary vasomotion is formulated.
It incorporates the ionic transports, cell-membrane potential, muscle contraction
of the vessel smooth muscle cells, and the mechanics of a thick-walled cylinder. It
is shown that the interaction of Ca2+ and K+ fluxes mediated by voltage-gated and
voltage-calcium-gated channels, respectively, brings about periodicity of those transports.
This results on a time-periodic cytoplasmic calcium concentration, myosin light chains
phosphorylation, and crossbridges formation with the attending muscle stress. The
vessel's transmural pressure determines a hoop stress. The resultant hoop, elastic,
and muscle stresses determine the rate of change of the vessel's diameter: vasomotion.
The model results agree with the experimental observations. The sensitivity of the
vasomotion's dependence on parameter values and its significance to experimental protocols
are examined. Further, it is hypothesized that the dependence of calcium-channel openings
on voltage is shifted by changes on transmural pressure. Thus, Harder's experimental
results are reproduced, among them the decreasing of vessel diameter with increasing
pressure. Those behaviors are associated with a pattern of change of the singularities
of the system of equations describing the model. This suggests a functional relationship
on the interactions of Ca2+ and K+ fluxes responsible for the myogenic response; it
may not result from a single molecular mechanism. The model is constructed so that
additional experimental information can be readily incorporated.