A nonlinear method for the analysis of forward and reflected waves in elastic conduits

A new method for the analysis of forward and reflected waves in elastic conduits, with possible extension to arterial flows, has been developed. The mathematical model is based on the one-dimensional flow equations which allow the treatment of non-periodic or transient pressure and flow pulses. The method is fully nonlinear and includes the effects of convective acceleration and pressure-dependent vessel compliance, without any linearizing assumption. The application of the method requires the knowledge of the elastic properties, the instantaneous pressure and flow, as well as the instantaneous spatial derivatives of pressure and flow. Analysis of simulated data shows good results and suggests that the proposed method, unlike previous quasi-nonlinear and frequency domain methods, can be applied to strongly nonlinear and/or nonperiodic flows.