Separate determination of the pulsatile elastic and viscous forces developed in the arterial wall in vivo

Abstract

The viscoelastic behaviour of arteries in vivo is analyzed by separate representation of the purely elastic and the purely viscous properties, using natural pressure and diameter pulses of various dog arteries recorded under steady-state conditions. The circumferential wall stress (sigma) and the radius (r) of the mean wall layer are calculated as functions of time and the hysteresis of the sigma-r diagram is represented. The stress is regarded as the sum of an elastic stress (sigma el) which is a function of r, and a viscous stress (sigma vis) which is a function of dr/dt. Thus sigma el = sigma - sigma vis. Since the sigma el-r diagram must be free from hysteresis, the disappearance of the loop is the criterion that indicates that sigma el has been found. sigma vis is formulated as a second degree polynomial of dr/dt whose coefficients are determined using that criterion. The sigma el-r curve is always nonlinear and the elastic modulus increases with increasing radius. The sigma vis-dr/dt curve, too, is nonlinear. Its slope decreases with increasing dr/dt. The same applies to the wall viscosity (pseudoplastic behaviour). The nonlinear properties can be represented adequately by processing the experimental data in the time domain. Problems inherent in investigations based on the frequency domain, as reported in the literature, are pointed out.