Application of Topological Sensitivity toward Tissue Elasticity Imaging Using Magnetic Resonance Data

Abstract

AbstractThis work investigates the application of topological sensitivity (TS) toward reconstructing and identifying tissue anomalies from magnetic resonance elastography (MRE) measurements. The basic idea of MRE imaging is to apply time–harmonic vibration to a tissue inside the magnetic resonance (MR) scanner and to capture the induced three-dimensional motion response (i.e., wave patterns) via suitable sequencing of the phase-coordinated, freeze-frame MR scans. To account for the facts that (1) the displacement of a material point captured by the MRE signifies the volume average over a reference voxel size, and (2) any given measurement voxel may contain, at least partially, the lesion of interest, the concept of TS is extended to allow for (1) averaged volumetric measurements and (2) overlapping interrogation and measurement domains. To circumvent the difficulties involved in the numerical modeling of an entire organ, the latter is subdivided into an array of cubic subdomains, each consisting of N3 vox...