Relative Young’s modulus identification using elastography - Fehrenbach, Jérôme; Masmoudi, Mohamed; Souchon, Rémi; Trompette, Philippe (European Journal of Computational Mechanics, 2006)
Some biological tissues like the prostate can be considered as a linear isotropic medium, at least for small strains. An interesting problem - from the medical point of view - is to detect heterogeneities where the Young’s modulus takes a different value from the background. A homogeneous medium is considered here, except in some regions where Young’s modulus takes a different value. A method is proposed to reconstruct an approximation of relative Young’s modulus, that is the ratio of Young’s moduli. The main tool is a general method for inverse problems: it is an implementation of Gauss-Newton’s method that uses few memory and few computations, based on the use of direct and adjoint derivative. This method is illustrated with experimental results on a gelatin phantom: the regularization property of Gauss-Newton’s algorithm allows to locate the larger heterogeneities.