The effect of visco-elasticity and other physical properties on aortic and cerebral pulse waveforms: an analytical and numerical study

The nonlinear one-dimensional equations of blood ow in Voigttype visco-elastic vessels are numerically solved using both a TaylorGalerkin and a discontinuous Galerkin scheme to study the e ects on aortic and cerebral pulse waveforms of wall visco-elasticity, uid viscosity, wall compliances and resistances, ow inertia, cardiac ejection, and out ow pressure. A linear analysis of these equations shows that wave dispersion and dissipation is caused by wall viscosity at high frequencies and uid viscosity at low frequencies. During approximately the last three fourths of diastole the inertial e ects of the ow can be neglected, and pressures tend to a space-independent shape dictated by global quantities (cardiac ejection, total peripheral resistance and compliance, and out ow pressure) and the viscous modulus of each arterial segment. During this period, the area-pressure curve reduces to a line whose slope provides a better approximation to the local pulse wave speed than do current techniques based on simultaneous pressure and velocity measurements. The viscous modulus can be estimated from the area of the area-pressure loop. Our ndings are important for the identi cation and estimation of haemodynamic quantities related to the prevention, diagnosis and treatment of disease.