Suitability of poroelastic and viscoelastic mechanical models for high and low frequency MR elastography

Abstract

Purpose: Descriptions of the structure of brain tissue as a porous cellular matrix support application of a poroelastic (PE) mechanical model which includes both solid and fluid phases. However, the majority of brain magnetic resonance elastography (MRE) studies use a single phase viscoelastic (VE) model to describe brain tissue behavior, in part due to availability of relatively simple direct inversion strategies for mechanical property estimation. A notable exception is low frequency intrinsic actuation MRE, where PE mechanical properties are imaged with a nonlinear inversion algorithm. Methods: This paper investigates the effect of model choice at each end of the spectrum of in vivo human brain actuation frequencies. Repeat MRE examinations of the brains of healthy volunteers were used to compare image quality and repeatability for each inversion model for both 50 Hz externally produced motion and ≈1 Hz intrinsic motions. Additionally, realistic simulated MRE data were generated with both VE and PE finite element solvers to investigate the effect of inappropriate model choice for ideal VE and PE materials. Results: In vivo, MRE data revealed that VE inversions appear more representative of anatomical structure and quantitatively repeatable for 50 Hz induced motions, whereas PE inversion produces better results at 1 Hz. Reasonable VE approximations of PE materials can be derived by equating the equivalent wave velocities for the two models, provided that the timescale of fluid equilibration is not similar to the period of actuation. An approximation of the equilibration time for human brain reveals that this condition is violated at 1 Hz but not at 50 Hz. Additionally, simulation experiments when using the "wrong" model for the inversion demonstrated reasonable shear modulus reconstructions at 50 Hz, whereas cross-model inversions at 1 Hz were poor quality. Attenuation parameters were sensitive to changes in the forward model at both frequencies, however, no spatial information was recovered because the mechanisms of VE and PE attenuation are different. Conclusions: VE inversions are simpler with fewer unknown properties and may be sufficient to capture the mechanical behavior of PE brain tissue at higher actuation frequencies. However, accurate modeling of the fluid phase is required to produce useful mechanical property images at the lower

Viscoelasticity of subcortical gray matter structures

“…Viscoelasticity, represented by the complex shear modulus, is the most widely used material model for inversion in brain MRE, though this model for attenuation may be inappropriate in SGM. Alternative material models, including Rayleigh damping [McGarry and Van Houten, 2008; Van Houten et al, 2011] and poroelasticity [McGarry et al, 2015; Pattison et al, 2014], may better explain attenuation in SGM structures and have shown promise in brain MRE [Johnson et al, 2013b; Weaver et al, 2012]. And, while GM is generally considered to be isotropic [Prange and Margulies, 2002; Velardi et al, 2006], the structure of SGM includes axonal pathways and may benefit from a direction-dependent material model as has been used in WM [Anderson et al, 2016; Romano et al, 2012].…”

Automated In Vivo Sub-Hertz Analysis of Viscoelasticity (SAVE) for Evaluation of Breast Lesions

“…However, a comprehensive model that can describe tissue biomechanics at a wide range of frequencies is still unknown. For example, using magnetic resonant elastography (MRE) the study in [13] shows that due to biphasic nature of tissue a single constitutive model cannot simultaneously explain tissue behavior at different frequency ranges. Hence, a unified approach to separate the dynamics of the two phases, i.e., a viscoelastic deformable solid response and a hydraulic fluid motion, in tissue-like materials is still an open problem [14], [15].…”

Gradient-Based Optimization for Poroelastic and Viscoelastic MR Elastography

“…Alternatively, NLI, which refers to a class of iterative schemes, recovers a set of unknown properties by minimizing an objective function defining the least-squares difference between the computed displacement field and measured data, and functions well across a wider range of frequencies than DI [28], however, at the expense of significantly increased computational cost. NLI has been demonstrated in MRE by Van Houten et.…”

“…Selecting an appropriate model is important to avoid model-data mismatch [31], and NLI has been extended and modified to incorporate other mechanical models, including viscoelastic [32], incompressible [33], Rayleigh damped [34], [35] and poroelastic [36], [28] governing equations. Computing one GN update involves calculation of a Jacobian matrix that requires one forward solution per unknown property value, and a costly inversion of a large, full Hessian matrix.…”