Refinement of the Acoustoelastic Theory in TI Quasi-Incompressible Media for Robust Muscle Nonlinear Elasticity Quantification

Acoustoelasticity (AE) aims at measuring the elastic nonlinearity of a medium based on the evolution of its shear wave speed as the medium is uniaxially stressed. In the field of biomedical imaging, AE was first applied on isotropic tissues such as breast and was recently adapted for transversely isotropic (TI) tissues such as muscles. However, the consideration of the TI geometry complexifies the AE equations, by adding supplementary NL terms (and NL elastic moduli) as well as by requiring the consideration of one more direction: the principal axis of the TI medium. Up to now, the development of AE in TI quasi-incompressible medium covers the nine simplest configurations where the principal axis of the TI medium, stress, polarization and propagation directions of the shear waves are either parallel or perpendicular one to the other. These requirements are difficult to meet experimentally and can lead to experimental biases. Therefore, the goal of the present work is to consider the angle dependency of the polarization and propagation directions with respect to the principal axis. Shear horizontal (SH) mode waves were considered and AE equations relating the speed of such waves to the applied stress as well as to the propagation angle with respect to the principal direction of the TI medium were retrieved. These relations were then experimentally validated on a TI Polyvinyl alcohol phantom. In the AE framework, this work highlights the necessity of considering the propagation angle, since the evolution of the SH mode wave speed with stress depends on that angle, and contributes to refining the AE theory in TI quasi-incompressible media.