Magnetic resonance elastography in nonlinear viscoelastic materials under load

Abstract

Characterisation of soft tissue mechanical properties is a topic of increasing interest in translational and clinical research. Magnetic resonance elastography (MRE) has been used in this context to assess the mechanical properties of tissues in vivo noninvasively. Typically, these analyses rely on linear viscoelastic wave equations to assess material properties from measured wave dynamics. However, deformations that occur in some tissues (e.g. liver during respiration, heart during the cardiac cycle, or external compression during a breast exam) can yield loading bias, complicating the interpretation of tissue stiffness from MRE measurements. In this paper, it is shown how combined knowledge of a material's rheology and loading state can be used to eliminate loading bias and enable interpretation of intrinsic (unloaded) stiffness properties. Equations are derived utilising perturbation theory and Cauchy's equations of motion to demonstrate the impact of loading state on periodic steady-state wave behaviour in nonlinear viscoelastic materials. These equations demonstrate how loading bias yields apparent material stiffening, softening and anisotropy. MRE sensitivity to deformation is demonstrated in an experimental phantom, showing a loading bias of up to twofold. From an unbiased stiffness of [Formula: see text] Pa in unloaded state, the biased stiffness increases to 9767.5 [Formula: see text]1949.9 Pa under a load of [Formula: see text] 34% uniaxial compression. Integrating knowledge of phantom loading and rheology into a novel MRE reconstruction, it is shown that it is possible to characterise intrinsic material characteristics, eliminating the loading bias from MRE data. The framework introduced and demonstrated in phantoms illustrates a pathway that can be translated and applied to MRE in complex deforming tissues. This would contribute to a better assessment of material properties in soft tissues employing elastography.

Towards noninvasive estimation of tumour pressure by utilising MR elastography and nonlinear biomechanical models: a simulation and phantom study

“…Unlike the linear wave theory utilised above, tissue is generally considered to have a nonlinear response to large deformation 10,[28][29][30][31][32] . Subject to such deformation, stiffness can rarely be thought of as a single parameter.…”

“…While in many cases stiffness can be reduced to fewer parameters, large deformation of isotropic tissue will result in at least some apparent anisotropy in stiffness as, for example, compression (and therefore softening) in one direction will lead to tension (and therefore hardening) in another direction. As described in Capilnasiu et al 10 , the shear waves will generally observe the stiffness component corresponding to the propagation direction (as MRE uses steady state vibrational waves this is better understood as the k vector direction). So in a simple case of orthogonal deformation and wave propagation the interaction may be well understood.…”

“…The method from Capilnasiu et al 10 , used to extend the stiffness reconstruction method from Fovargue et al 27 , is able to reconstruct the unbiased intrinsic stiffness of a deformed material given the macroscale deformation and nonlinear material law as input. This method is constructed in a mathematically rigorous manner using a perturbation analysis relating the two scales defined by v and u, the small scale wave displacements and the large scale deformation, respectively.…”

“…A stiffness reconstruction method is then responsible for solving an inverse problem using these wave images to create an image of the tissue stiffness (most often the shear modulus) 9 . Recent work has introduced an MRE reconstruction method that accounts for stiffness bias due to large deformation 10 . This latter approach is extended here to account for and utilise the effect of the tissue deformation due to tumour pressure.…”

An orthotropic electro-viscoelastic model for the heart with stress-assisted diffusion

“…The simulation of mechanically-induced ectopic activity, as well as prediction of the risk of sudden cardiac death are also part of our long-term goals. For sake of model validation we are also interested in marrying our results to experimental observations obtained through elastography (using for instance the novel approach advanced in [7]). 1 (1 − H(v − θ 2 ))(r 2,inf − r 2 )/τ − 2 − H(v − θ 2 )r 2 /τ + 2 ((1 + tanh(k 3 (v − v 3 )))/2 − r 3 )/τ 3   .…”