Recovering Displacements and Deformations from 3D Medical Images Using Biomechanical Models

Abstract

This chapter describes the use of biomechanical models for the estimation of non-rigid displacement fields from sequences of three-dimensional medical images. Later, the chapter describes two case studies—namely, (1) the estimation of brain shift for neurosurgery and (2) the estimation of left ventricular deformation, the proper modeling of the underlying tissue is important in order to ensure reliable and robust estimation of the underlying displacement and consequently the deformation. Modeling is needed as the image-derived displacement estimates generated from a number of methods have the following characteristics: (1) they are sparse, (2) they are noise-corrupted, and (3) they may contain only partial information. The both case studies illustrate the use of this underlying mathematical framework. The chapter also describes methodology to compensate for brain shift in image guided neurosurgery and algorithms to estimate the deformation of the left ventricle of the heart. The specifics of the mechanical model are presented, followed by validation results on real and simulated data.