Quantitative elastography, solving the inverse elasticity problem using the Gauss-Newton method.

Abstract

This work presents the application of a constrained Gauss Newton method for the solution of an inverse elasticity problem in ultrasound elastography. This algorithm was written taking care of real constraints, like the limited and noisy data used to estimate the volume's properties and the speed necessary to have a real time application in a real medical environment. The algorithm is tested on data acquired on polyvinyl alcohol (PVA) phantoms. The role of the amount of elements used to discretized the volume, the role of the regularization and the role of noise are investigated. The possible application of the algorithm is in the use of quantitative elastography as tactile sensor for tactile feedback in minimally invasive surgery.

Algorithms for ultrasound elastography: a survey

“…This is in perfect agreement with the observations made by Barbone and Bamber (2002) and Barbone and Gokale (2004). Sette et al (2008) and Camino et al (2007) presented a new strategy to improve the speed of iterative algorithms for YM reconstruction. The optimisation problem of (15) is posed as follows: find a set of YM (15) are that the minimisation variables are both YM E and the forward problem solution x.…”

“…Regularisation has a direct effect on CTE and depends on the FEM spatial resolution (size and number of nodes used in the FEM). As demonstrated later, also by Sette et al (2008), the reconstructed elasticity will be smooth when g k in (26) is large at the cost of a loss in CTE and spatial resolution. In Kallel and Bertrand (1996), the authors conclude that a better knowledge of the stress distribution at the compressor interface could improve YM reconstruction.…”