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A body force concentrated at a point and moving at a high speed can induceshear-wave Mach cones in dusty-plasma crystals or soft materials, as observedexperimentally and named the elastic Cherenkov effect (ECE). The ECE in softmaterials forms the basis of the supersonic shear imaging (SSI) technique, anultrasound-based dynamic elastography method applied in clinics in recentyears. Previous studies on the ECE in soft materials have focused on isotropicmaterial models. In this paper, we investigate the existence and key featuresof the ECE in anisotropic soft media, by using both theoretical analysis andfinite element (FE) simulations, and we apply the results to the non=invasiveand non-destructive characterization of biological soft tissues. We alsotheoretically study the characteristics of the shear waves induced in adeformed hyperelastic anisotropic soft material by a source moving with highspeed, considering that contact between the ultrasound probe and the softtissue may lead to finite deformation. On the basis of our theoretical analysisand numerical simulations, we propose an inverse approach to infer both theanisotropic and hyperelastic parameters of incompressible transverselyisotropic (TI) soft materials. Finally, we investigate the properties of thesolutions to the inverse problem by deriving the condition numbers inanalytical form and performing numerical experiments. In Part II of the paper,both ex vivo and in vivo experiments are conducted to demonstrate theapplicability of the inverse method in practical use.

Elastic Cherenkov effects in transversely isotropic soft materials-I: Theoretical analysis, simulations and inverse method