Two-dimensional waveform analysis in MR elastography of skeletal muscles.

A method for direct determination of anisotropic elastic coefficients using two-dimensional shear wave patterns is introduced. Thereby, the symmetry of the wave patterns is approximated by a squared elliptic equation yielding an explicit relation between waveform and elasticity. The method is used to analyse MR elastography wave images of the biceps acquired by a continuous harmonic excitation at the distal tendon of the muscle. Typically V-shaped wave patterns were observed in this type of tissue, which could be well reproduced by the proposed elliptic approximation of the waveform assuming incompressibility and a transverse isotropic model of elasticity. Without additional experiments, the analysis of straightness, slope and interferences of the wave fronts enabled us to deduce two Young's moduli and one shear modulus, which fully describe the anisotropy of the elasticity of muscles. The results suggest strong anisotropy of the living human biceps causing a shear wave speed parallel to the muscle fibres that is approximately four times faster than the perpendicular shear wave speed.