Requirements for accurate estimation of anisotropic material parameters by magnetic resonance elastography: A computational study

Abstract

Purpose Establish the essential requirements for characterization of a transversely isotropic material by magnetic resonance elastography (MRE). Theory and Methods Three methods for characterizing nearly incompressible, transversely isotropic (ITI) materials were used to analyze data from: closed-form expressions for traveling waves; finite element (FE) simulations of waves in homogeneous ITI material; and FE simulations of waves in heterogeneous material. Key properties are the complex shear modulus μ2, shear anisotropy ϕ = μ1/μ2 − 1, and tensile anisotropy ζ = E1/E2 − 1. Results Each method provided good estimates of ITI parameters when both slow and fast shear waves with multiple propagation directions were present. No method gave accurate estimates when the displacement field contained only slow shear waves, only fast shear waves, or waves with only a single propagation direction. Methods based on directional filtering are robust to noise and include explicit checks of propagation and polarization. Curl-based methods led to more accurate estimates in low noise conditions. Parameter estimation in heterogeneous materials is challenging for all methods. Conclusion Multiple shear waves, both slow and fast, with different propagation directions, must be present in the displacement field for accurate parameter estimates in ITI materials. Experimental design and data analysis can ensure these requirements are met.

Real‐time MR elastography for viscoelasticity quantification in skeletal muscle during dynamic exercises

“…19 ). 20 The transversely isotropic viscoelastic coefficients related to the plane of symmetry and x 3 -axis have not been addressed in our present study. Instead, we intentionally chose our image plane and directions of motion encoding such that predominantly slow-transverse (ST) wave modes were captured, whereas contributions of fast-transverse wave modes (FT) were minimized or fully canceled.…”

“…In our previous work, we exploited the directional filter capabilities of the curl operator to retrieve 3 independent elasticity parameters and 3 independent viscosity parameters according to the constitutive laws of incompressible transversely isotropic materials . These are 2 storage moduli (, ) and 2 loss moduli (, ) for the shear components, as well as Young’s modulus for storage and loss (, ) . The transversely isotropic viscoelastic coefficients related to the plane of symmetry and x 3 ‐axis have not been addressed in our present study.…”

“…By contrast, MR elastography (MRE) can quantify viscoelastic tissue parameters in several organs across extended FOVs . MRE can also encode any strain components, which is especially favorable for studying anisotropic elastic coefficients in muscle tissue . However, MRE is limited by long acquisition times of the order of several minutes, during which organs move or muscle load changes .…”

“…14 MRE can also encode any strain components, which is especially favorable for studying anisotropic elastic coefficients in muscle tissue. [15][16][17][18][19][20] However, MRE is limited by long acquisition times of the order of several minutes, during which organs move or muscle load changes. 21 Therefore, so far MRE has only been used to study muscle mechanical parameters either in a relaxed state, 19,[22][23][24] under sustained loading with the assumption that submaximal contraction was maintained at a constant level, 2,15,[25][26][27] or-as in the case of myocardial tissue-by assuming periodic changes in elastic parameters to which MRE data acquisition can be repetitively synchronized.…”

Relative identifiability of anisotropic properties from magnetic resonance elastography

“…However, the mean global estimate of ζ was always underestimated and varied by 40 % . Estimating E 3 necessitates the existence of fast shear waves,() which induce fiber stretching, in the MRE displacement field. In the LV simulations in this study, a lack of adequate fast shear waves may account for the fact that E 3 was consistently less identifiable than E 1 and G 13 .…”