A novel algorithm for the inverse problem in elasticity imaging by means of variational r-adaption



Elasticity imaging or elastography is a powerful technique in medicinal imaging for visualizing the stiffness distribution in soft tissue in vivo. It is motivated by the observation that the stiffness in soft tissue is affected by pathologies in many cases. More precisely, diseased tissue tends to be stiffer than the healthy surrounding tissue. The two steps involved in elasticity imaging are: first deforming the tissue and measuring the displacement field in the region of interest using ultrasound or MRI signals; second calculating the underlying stiffness distribution using an inverse analysis. While in common approaches this inverse analysis is based on minimizing the distance between the measured and the computed deformation field depending only on the unknown stiffness distribution, an additional variation of the underlying finite element discretization is the focus of the present work. In doing so, the triangulation is optimized improving the accuracy of the results and increasing the efficiency of the computational framework. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)