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

The nonlinear inviscid 1D blood flow equations are studied analytically using the method of characteristics. The boundary value problem with a triangle-shaped boundary data at the aortic outlet is considered. The pressure-velocity profile, the shock conditions are derived as closed analytical expressions. Finally, the fully nonlinear wave separation expressions are obtained using the Riemann invariants. The results show good correspondence with the data from literature.