Pulse-wave propagation in an artery with leakage into small side branches.

Linear pulse propagation theory is applied to a network of elastic tubes. The network is specialized to one having a main branch with many low-admittance side branches. Continuum approximations and an asymptotic analysis of side-branch network input admittance reduce the original network to a tapered leaky tube. The outflow law is equivalent to distributed Windkessels. The conductance and time constant of the Windkessels are related to the geometry of the side-branch networks. Viscous effects are included in the theory. Asymptotic methods are used to determine the dispersion relation and waveform amplitude in the frequency domain. Periodic pressure and flow waveforms are computed using Fourier synthesis.