Viscoelastic characterization of soft tissue from dynamic finite element models

Abstract

An iterative solution to the inverse problem of elasticity and viscosity is proposed in this paper. A new dynamic finite element model that is consistent with known rheological models has been derived to account for the viscoelastic changes in soft tissue. The model assumes known lumped masses at the nodes, and comprises two vectors of elasticity and viscosity parameters that depend on the material elasticity and viscosity distribution, respectively. Using this deformation model and the observed dynamic data for harmonic excitation, the inverse problem is solved to reconstruct the viscosity and elasticity in the medium by using a Gauss-Newton-based approach. As in other inverse problems, previous knowledge of the parameters on the boundaries of the medium is necessary to assure uniqueness and convergence and to obtain an accurate map of the viscoelastic properties. The sensitivity of the solutions to noise, model and boundary conditions has been studied through numerical simulations. Experimental results are also presented. The viscosity and elasticity of a gelatin-based phantom with inclusion of known properties have been reconstructed and have been shown to be close to the values obtained using standard rheometry.

Stiffness reconstruction methods for MR elastography

“…Eskandari et al solved the time‐harmonic equations in a similar fashion using Levenburg–Marquardt. This implementation was later used in a study on bandpass sampling and was extended to employ mesh adaptation .…”

“…In Fovargue et al, computation times of approximately 50–90 seconds were reported for data sets with approximately 24 000–33 000 voxels for a mixed heterogeneous implementation with Tikhonov regularization (MATLAB with an Intel Xeon 4‐core, 8‐thread, 3.6 GHz processor). In Eskandari et al, compute times for the 2D heterogeneous direct method were compared with those of an iterative method and local method for varying image sizes (Figure ).…”

“…Plot comparing the computational cost of various methods considering 2D data (measured on a quad‐core CPU with two 2.82‐GHz processors): a single iteration of an iterative method, a heterogeneous direct method, a local direct method, and the quadratic programming technique outlined in Eskandari et al (©IOP Publishing. Reproduced with permission.…”

Modeling the high-frequency complex modulus of silicone rubber using standing lamb waves and an inverse finite element method

“…G. Jonsson small and the strain rates were rapid (faster than 0.5/s) [7], [16], [17]. modeling the frequency dependence of the elastic modulus in soft tissue is a key to gaining information about the existence of lesions.…”

2-D high-frame-rate dynamic elastography using delay compensated and angularly compounded motion vectors: Preliminary results

“…However, estimation of both axial and lateral components of the motion is required for several elastography techniques [32], and has been shown to improve the reconstruction of elasticity images [3].…”