Elasticity tomography: reconstruction using stable implicit-integration method

To non-invasively quantify soft tissue elasticity for differentiating malignancy, the authors previously proposed a 2D mechanical inverse problem that is a simultaneous partial differential equations expressing the target distribution of globally relative shear moduli with respect to reference shear moduli. The authors also showed that the relative values can be determined from strain distributions obtained by US or NMR imaging-based analysis. However, by examining the authors´ original approach, it is clarified that the problem is inevitably ill-conditioned in real-world conditions, i.e., it cannot be guaranteed that there exists a stable unique global distribution due to the noise-contamination in measurement data and improper configurations of mechanical sources and reference regions. Based on this clarification, a numerical-based implicit-integration approach-which incorporates a computationally-efficient regularization method such that smoothed strains are effectively used-is developed. The demonstrated ability to stably reconstruct an acceptable unique global distribution, i.e., under intensionally created ill-conditions, is concluded to confirm the novelty and high world value of the presented approach