A viscoelastic model of mechanically induced and spontaneous contractions of vascular smooth muscle.

A new viscoelastic model was developed for the mathematical characterisation of mechanically induced and intrinsic contractional responses of the vascular smooth muscle. To this end, the elastic and viscous analogue elements were supplemented with a new active element generating stress proportional to its momentary elongation. The four-element model consisting of an active element, a parallel viscous element and both series and parallel elastic elements predicted biphasic or damped oscillatory stress relaxation and creep responses which were similar to that found experimentally earlier. Above a certain exciting frequency the model exhibited dissipative and below energy producing behaviour, as indicated by the sign change of the hysteresis loop area. In the case of sinusoidal modulation of the stress generation parameter the model showed parametric resonance, which was regarded as a simulation of intrinsic oscillation of the smooth muscle.