Acoustoelasticity in transverse isotropic soft tissues: quantification of muscles' nonlinear elasticity

Quantification of the elastic nonlinearity of biological tissues is a recent refinement of measures available in ultrasound elastography. The measurement of the third order nonlinear elastic modulus of biological tissues using ultrasound elastography relies on acoustoelasticity (AE), consisting in measuring the shear wave velocity in tissues under uniaxial stress. Up to now, the AE theory has been developed under the hypothesis of tissue isotropy. However, this assumption does not hold for all tissues, such as muscles. Indeed, the direction of alignment of muscular fibers defines a rotation symmetry axis, justifying the modelling of muscles in terms of transverse isotropic (TI) media. Such tissues require a more complex elastic description, considering their anisotropy. In this work, the AE theory is transposed to quasi-incompressible TI media and tested experimentally. After developing the elastic energy of TI quasi-incompressible media up to the third order, the relations between the shear wave speed and the applied stress are derived. In addition to the 3 linear elastic moduli describing a quasi-incompressible TI medium, 4 nonlinear elastic moduli appear. This theoretical development is tested experimentally on TI PVA phantoms and on ex vivo beef muscle tissues using an experimental setup designed to apply controlled uniaxial stresses to the sample, and one of the third order nonlinear coefficients, coefficient A, is estimated. This work contributes to opening the path towards the nonlinear characterization of muscles, which has potential applications in muscle biomechanics and in muscular pathology diagnosis.