MR Elastography of muscle tissue

Introduction

MR elastography (MRE) is capable of monitoring bulk shear vibrations in soft biological tissues (1-3). Muscle MR elastography (4-10) is currently developing towards a straightforward technique for detecting several diseases which affect muscle elasticity such as hypogonadism (11) or obstructive pulmonary disease (12). In MRE, the sensitivity of shear wavelengths to elasticity changes is usually exploited for mapping elastic heterogeneities by elastograms. For muscle tissue additionally the anisotropy of the elasticity has to be taken into account. This specific property causes a direction dependency of shear wavelengths giving rise to misinterpreting isotropic elastograms (13). On the other hand anisotropic wave propagation bears valuable information about the mechanical structure of the material. Therefore, different approaches have been made to measure the shear wave speed in skeletal muscles as a function of directionality (5,9,14-17).

Theoretical and technical aspects of muscle MRE

Elastic waves in anisotropic solids are governed by three distinct wave modes corresponding to the eigenvalues of the wave speed tensor (18). Two of them, the slow and the fast transverse wave mode determine the appearance of wave patterns in shear-wave based elastography. In literature a simple relationship between anisotropic wave propagation and elasticity is given by the slow-transverse wave mode (cST). There, the waves are emanating from a point-source in ellipsoidal patterns with wave numbers (k) corresponding to the anisotropy of the shear elasticity:

Here, in addition to the shear moduli m_xy and m_xz, the ratio of the Young’s moduli E_z / E_x determines the form and the polarization of the shear waves. Please note, both eqs.1 and 2 apply for transverse isotropy but only eq.2 is bound to the condition of incompressibility.

To analyze experiments, it is necessary to know whether the observed waves in MRE are due to the ST-mode, the FT-mode or a superposition of both wave modes. Fortunately, MRE allows the encoding and, in some cases, also the excitation of single components of the wave field with an arbitrary image slice position. In general, the experimental setup is chosen in such a way as to avoid a superposition of ST- and FT-wave modes. The image plane must thus be aligned with the principal axes of the wave field which in turn should be polarized along one principal stress. For capturing the preferred ST-waves the excitation direction and the motion sensitization direction have to be through-plane. Then, the shear wave length l_z (along the muscle fibers) directly indicates mu_xz while mu_xy is deducible from waves running along a perpendicular profile. This approach is valid as long as the wave propagation is non-dispersive and boundary effects are negligible. The profile-based analysis of shear stiffness in human muscle was demonstrated in (4,5,16,17).

Other authors have shown that boundary effects cause wave speed components and waveforms which are not in explained by a model of infinite anisotropic medium (9,15). Therefore, current developments in muscle MRE should address such limits caused by an extended wave source and the boundary constraints of the examined object.

References

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