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

TL;DR

This paper analytically studies nonlinear pressure-velocity waveforms in large arteries, deriving explicit shock and wave separation expressions that align well with existing literature data.

Contribution

It provides the first closed-form analytical solutions for nonlinear pressure-velocity waveforms and shock conditions in large arteries using the method of characteristics.

Findings

Derived analytical expressions for pressure-velocity profiles

Obtained shock conditions as closed-form solutions

Achieved good agreement with literature data

Abstract

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.