Palpation tomography - A new technique for modulus estimation in elastography

In Elastography, strain estimation has been shown to be far more reliable compared to the elastic properties obtained using reconstruction techniques. In this study, to make the method less sensitive to noise in the experimental data and inspired by the clinical practice of palpation (i.e., the use of sequential finger loading), we investigated the effect of using several different smaller quasi-static load cases (instead of a one-time load on the whole boundary), with the error indicator taken as the sum of the errors from each load case. This increased the ratio of measurements to the fitted parameters, which made the method less sensitive to random errors. To demonstrate this effect, we calculated displacements from a two-dimensional, quadrilateral, plane-strain, finite-element model of a 40-by-40 mm region containing a cylindrical inclusion (7 mm in diameter) three-times stiffer than the background. The ratio of nodal pressures was chosen to produce approximately 0.75% strain. Known amounts of random displacement errors were then added at a signal-to-noise ratio varying from 60 dB to 20 dB. Elastic modulus reconstructions using the noisy displacement results from a single, total-boundary, pressure load (as is typically applied in elastography) were compared to reconstructions using data from nine smaller-width loading cases, and the reconstructed modulus distributions were compared to the original model parameters. It was found that in the cases of 60 dB and 40 dB the multiple loading cases resulted in noise reduction in the modulus reconstruction by at least a two-fold compared to the single-loading case, at the expense of a 'shadowing' effect (i.e., erroneous modulus estimates) underneath the inclusion that could be eliminated by using larger loading areas for the individual loading cases. Finally, at 20 dB both the large single-load and combined, smaller five-load cases failed to accurately reconstruct the modulus of the inclusion; depicting thus a fundamental limit on the reconstruction method.