Real Time Tracking of Liver Motion and Deformation in Navigated Liver Surgery by Means of an Electromagnetic System and FEM Simulation

Abstract

In this thesis, I present a framework for real time tracking of liver motion and deformation based on FEM by means of an electromagnetic system. The first part of this thesis describes achieving rigid registration between the liver phantom and its MR image by least square estimation of transformational parameters between two point patterns based on ficudial marker mapping. Due to the optimized estimation method the good results are obtained even when the data is corrupted. This transformation matrix obtained enables us to bring all the components in the image space and thus the surgical tool can be localized. This rigid registration can efficiently handle translational and rotational motion. Second part of the thesis describes the physical simulation and visualization of a liver phantom based on implicit finite element method where the physical simulation is driven by displacement field defined by vector drawn on its 2D image. A non-nested hierarchical tetrahedral volumetric mesh of the liver phantom from is generated and the finite element model of this volumetric mesh is formulated by corotated Cauchy strain. Dirichlet boundary conditions are assigned for surface vertices fixation where deformations are not intended. The marker position is rendered on the volumetric mesh and then the displacement field defined by the vector from marker base alters the finite element model which is solved by a multigrid solver and the mesh geometry is updated. Both the rigid registration and deformation simulation are then combined into a single system and the deformations are induced by real time external forces defined by displacement field obtained from an electromagnetic tracking sensor attached on the surface on the phantom. This interplay allows for real time visualization of tracking translational and rotation along with deformations performed on the liver phantom.