This thesis is for a sensitivity analysis of magnetic resonance elastography, a hybrid imaging technique used in early-stage cancer screening. To quantitatively analyze the sensitivity, we introduce a notion of detectability, which is dened as a relative amplitude drop in a small sti tumor region. This analysis is accomplished in both the full elastic and viscoelastic models and compared with that of the simpler scalar model which is frequently used in the actual application. Some of the highlights are 1) a useful formula for detectability in terms of physical parameters, which will help the design of experiments; 2) the discrepancy between the full elastic model and the scalar model that provides a criterion when the simple scalar model is acceptable; 3) a theoretical limit of the smallest tumor that magnetic resonance elastography can reconstruct; 4) the existence of optimal frequency when the Voigt (viscoelastic) model is adopted; and 5) the limit behavior of the solution when the inclusion stiness or attenuation becomes innitely high. We expect that this detectability approach is extendable to many hybrid imaging techniques to quantify their sensitivities and cross-compare them to determine which modality is the most powerful in detecting early-stage cancer
