The elastic reconstruction of soft tissues

A finite element based nonlinear inverse scheme is presented to reconstruct the elastic properties of soft tissues subjected to an external compression. An objective function relating the least-square difference of model-predicted and measured displacement or strain fields from a sequence of images (B-mode or MRI) is minimized with respect to the unknown material parameters. To obtain physically meaningful solutions, the material properties (Young´s modulus, Poisson´s ratio etc.) are bounded with lower and upper limits. The solution of the ensuing linearly constrained nonlinear optimization problem, is performed by means of a modified Levenberg-Marquardt method and an active set strategy. To demonstrate the effectiveness of the method, simulated data was studied by adding up to 20% noise. The method has also been used to determine the Young´s modulus of a three-layer phantom. Preliminary numerical results with both simulated and experimental data suggest that the method is robust for reconstructing the elastic properties of soft tissues. If the boundary between normal tissues and suspicious tissues could be defined via image segmentation techniques, this method might accommodate more noise.