Stability Estimate for Identifying Viscoelasticity by an Interior Measurement

Gen Nakamura^*

A newly developed diagnosing modality called MRE (magnetic resonance elastography) can measure share wave images inside human tissues. By modeling the share waves as solutions of a PDE (partial differential equation), the so called elastogram of MRE tries to identify the storage modulus and loss modulus which are the coefficients of this PDE from a solution of this PDE. MRE has been efficiently used for diagnosing fibrosis. In this talk we consider the most simplest PDE model and present a local Holder stability estimate of the identification by assuming that the aforementioned moduli are continuously differentiable, piecewise analytic and satisfying some technical condition. If the loss modulus is known this technical condition is automatically satisfied. Concerning the uniqueness of identification, we can have the global uniqueness. This is a joint work with Naofumi Honda (Hokkaido University) and Joyce McLaughline (RPI).

Mathematics Subject Classification: 15A29

Keywords: stability, identification, viscoelasticity, interior measurement

Minisymposion: Inverse Problems in Elasticity