Direct vibro-elastography FEM inversion in Cartesian and cylindrical coordinate systems without the local homogeneity assumption

Abstract

To produce images of tissue elasticity, the vibro-elastography technique involves applying a steady-state multi-frequency vibration to tissue, estimating displacements from ultrasound echo data, and using the estimated displacements in an inverse elasticity problem with the shear modulus spatial distribution as the unknown. In order to fully solve the inverse problem, all three displacement components are required. However, using ultrasound, the axial component of the displacement is measured much more accurately than the other directions. Therefore, simplifying assumptions must be used in this case. Usually, the equations of motion are transformed into a Helmholtz equation by assuming tissue incompressibility and local homogeneity. The local homogeneity assumption causes significant imaging artifacts in areas of varying elasticity. In this paper, we remove the local homogeneity assumption. In particular we introduce a new finite element based direct inversion technique in which only the coupling terms in the equation of motion are ignored, so it can be used with only one component of the displacement. Both Cartesian and cylindrical coordinate systems are considered. The use of multi-frequency excitation also allows us to obtain multiple measurements and reduce artifacts in areas where the displacement of one frequency is close to zero. The proposed method was tested in simulations and experiments against a conventional approach in which the local homogeneity is used. The results show significant improvements in elasticity imaging with the new method compared to previous methods that assumes local homogeneity. For example in simulations, the contrast to noise ratio (CNR) for the region with spherical inclusion increases from an average value of 1.5-17 after using the proposed method instead of the local inversion with homogeneity assumption, and similarly in the prostate phantom experiment, the CNR improved from an average value of 1.6 to about 20.

Reverberant shear wave phase gradients for elastography

“…For example, the multi-frequency dual elastovisco inversion technique derives the shear modulus and a viscous component, by a least squares error solution based on the Helmholtz equation (Hirsch et al 2014, Hetzer et al 2019. Furthermore, in ultrasound inversion techniques, vibro-elastography is a multi-frequency shear wave strategy whereby an external source is applied to the tissue and a model is fit to the resulting steady state tissue motion (Turgay et al 2006, Eskandari et al 2008, Abeysekera et al 2015, Honarvar et al 2015. In addition, other harmonic shear wave approaches have unique features.…”

Phase‐regularized and displacement‐regularized compressed sensing for fast magnetic resonance elastography

“…The complex shear modulus was calculated using a scalar shear finite‐element model 26 to evaluate the effect of undersampling on viscosity. The reconstruction method is described in Appendix C1.…”

“…For the 2D displacement model, a plane strain assumption was used. The model was discretized using a finite-element model method 26 and reorganized as a linear model with respect to μ. The complex viscoelastic map was reconstructed using the following regularized optimization problem, similar to our previous work ERSA 36 :…”

Elastography imaging: the 30 year perspective

“…Alternatively in ultrasound inversion techniques, vibro-elastography is a multi-frequency HE approach in which an external shear wave source is used to excite the tissue and a model is fit to the resulting steady state tissue motion (Turgay et al 2006, Eskandari et al 2008, Abeysekera et al 2015, Honarvar et al 2015.…”