Skip to Main content Skip to Navigation
Journal articles

Mathematical modelling of Acoustic Radiation Force in transient shear wave elastography in the heart

Abstract : The aim of this work is to provide a mathematical model and analysis of the excitation and the resulting shear wave propagation in Acoustic Radiation Force (ARF)-based shear wave cardiac elastography. Our approach is based on asymptotic analysis; more precisely, it consists in considering a family of problems, parametrised by a small parameter inversely proportional to the excitation frequency of the probes, the viscosity and the velocity of pressure wave propagation. We derive a simplified model for the expression of the ARF by investigating the limit behaviour of the solution when the small parameter goes to zero. By formal asymptotic analysis - an asymptotic expansion of the solution is used - and energy analysis of the nonlinear elastodynamic problem, we show that the leading- order term of the expansion is solution of the underlying, incompressible, nonlinear cardiac mechanics. Subsequently, two corrector terms are derived. The first is a fast-oscillating pressure wave generated by the probes, solution of a Helmholtz equation at every time. The second corrector term consists in an elastic field with prescribed divergence, having a function of the first corrector as a source term. This field corresponds to the shear acoustic wave induced by the ARF. We also confirm that, in cardiac mechanics, the presence of viscosity in the model is essential to derive an expression of the shear wave propagation from the ARF, and that this phenomenon is related to the nonlinearity of the partial differential equation.
Complete list of metadatas

Cited literature [31 references]  Display  Hide  Download

https://hal.inria.fr/hal-01992069
Contributor : Sébastien Imperiale <>
Submitted on : Friday, March 27, 2020 - 4:28:23 PM
Last modification on : Monday, April 27, 2020 - 12:02:10 PM

File

ARF_Caforio_Imperiale (1).pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01992069, version 3

Citation

Federica Caforio, Sébastien Imperiale. Mathematical modelling of Acoustic Radiation Force in transient shear wave elastography in the heart. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, In press. ⟨hal-01992069v3⟩

Share

Metrics

Record views

71

Files downloads

302