Nonlinear pressure–velocity waveforms in large arteries, shock waves and wave separation

Abstract

Nonlinear inviscid 1D blood flow equations were studied analytically using the method of characteristics. The initial–boundary value problem for a class of the initial–boundary conditions (including a triangle-shaped profile) at the aortic outlet was considered. The nonlinear pressure–velocity profile and shock conditions were derived as closed analytical expressions with second order accuracy on the relative luminal area change. Finally, the fully nonlinear wave separation expressions were obtained using the Riemann invariants. The results show good correspondence with the data from the literature.