Pressure peaking in pulsatile flow through arterial tree structures

An analytical iterative scheme is presented for computing the local characteristics of pressure and flow waves as they progress along a tree structure and become modified by wave reflections. Results are obtained to illustrate the phenoenon of pressure peaking under two different sets of circumstances. In the first case, the propagation of a single harmonic wave along a simple tree is considered, where wave reflections modify the amplitude of the pressure wave as it travels. In the second case, the propagation of a composite wave along a tree with multiple branches is considered, where wave reflections modify the shape of the wave as it travels and cause it to peak. The results demonstrate unambiguously that the root cause of this phenomenon is wave reflections caused by stepwise decreases in admittance, as has been previously suggested, rather than due to nonlinear interactions, as has also been previously suggested. It is shown clearly that even when wave reflections combine linearly, they lead to considerable peaking in the pressure waveform.