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.

The application of the Lattice Boltzmann method to the one-dimensional modeling of blood flow in elastic vessels

“…The evolution of the nonlinear wave which has triangle shaped form in the initial moment of time is considered in a semi-infinite vessel x > 0 with constant elastic properties. For a forward traveling wave one has the relation between the wave velocity u and the luminal area A [29]…”

“…The case n = 1/2 is considered in (12) which corresponds to the Laplace law. The analytical solutions to this problem are obtained in [29]. For the sake of brevity this solution is not given here.…”