|Abstract:|| The nonlinear one-dimensional equations of blood flow in Voigttype visco-elastic vessels are numerically solved using both a Taylor-Galerkin and a discontinuous Galerkin scheme to study the effects on aortic and cerebral pulse waveforms of wall visco-elasticity, fluid viscosity, wall compliances and resistances, flow inertia, cardiac ejection, and outflow pressure. A linear analysis of these equations shows that wave dispersion and dissipation is caused by wall viscosity at high frequencies and fluid viscosity at low frequencies. During approximately the last three fourths of diastole the inertial effects of the flow can be neglected, and pressures tend to a space-independent shape dictated by global quantities (cardiac ejection, total peripheral resistance and compliance, and outflow 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 findings are important for the identification and estimation of haemodynamic quantities related to the prevention, diagnosis and treatment of disease.
Keywords: Pulse wave propagation; pulse wave speed; circulatory system; circle of Willis; one-dimensional modelling; Voigt-type viscoelasticity; Taylor-Galerkin methods; discontinuous Galerkin methods.|