Inverse Problems in Mechanics

Mercoledi' 7 Luglio - prof. Assad Oberai


Mercoledi' 7 Luglio alle ore 11:30 nell'aula 2AB/45 di Torre Archimede il prof. Assad Oberai, del Rensselaer Polytechnic Institute di New York, terra' una conferenza dal titolo "Inverse Problems in Mechanics".

Recent advances in imaging technology allow remarkably accurate and detailed measurements of in-vivo tissue deformation under different types of loading. This type of interior displacement data contains a wealth of information about the macroscopic and microscopic mechanical properties of tissue. These properties are in turn closely connected to its health. For example, cancerous tumors are often stiffer than their surroundings, and fibrosis in a liver is associated with diffuse stiffening.
In this talk I will describe our efforts to determine the spatial distribution of the mechanical properties of tissue from measured displacement field. This process involves the solution of an inverse problem, where an appropriate mechanical model for tissue response is assumed and the spatial distribution of the material parameters is sought. I will focus on the case when the tissue is modeled as an elastic solid and describe new algorithms for solving the inverse problem. In particular I will present a fast, direct inversion algorithm that is applicable when total interior data is available, that is all components of the displacement field are measured. I will demonstrate that this method converges to the exact solution at optimal rates with mesh refinement, and is robust to noise. I will also describe an iterative algorithm based on the use of the adjoint elasticity equations and a continuation strategy in material parameters that is applicable when only partial interior data is measured. I will present clinical examples that demonstrate the utility of these algorithms.
I will conclude with a class of problems in wave propagation where only boundary data is measured. For these problems time-reversal iterations are often employed to determine the dominant eigenpairs of the scattering operator and hence locate strong inhomogeneities in the medium. By interpreting these iterations as the Power method, I will present a time-reversal methodology that is based on Lanczos iterations and has better focusing properties.

Rif. int. F. Marcuzzi