Validation of a Method for Non-rigid Registration of Prostate Images Using Finite Element Analysis

Purpose: Dose escalation to intraprostatic tumor domains detected by magnetic resonance spectroscopy imaging (MRSI) requires non-rigid registration of MRSI-positive volumes (visualized in a prostate gland deformed by the endorectal balloon coil) with ultrasound (US) and/or CT images used for treatment planning. Finite element analysis is a principled method for modeling physical deformation that can be applied for analyzing deformed anatomical structures in medical images. However current implementations of the finite element modeling (FEM) are too laborious and computationally inefficient for routine clinical use. The purpose of this investigation was to validate improved methodology based on deformable m-rep models, for automatically constructing FEM mesh models, defining boundary conditions for the starting and ending states of the deformation process, and efficiently solving the large system of FEM equations to yield a non-rigid transformation. In this paper this approach is referred to as m-rep-based finite element modeling (MFEM). Methods and Materials: A pelvis phantom was constructed from tissue-like materials to simulate the prostate and surrounding structures including bladder, expandable rectum, and bone. An inflatable balloon simulating the MR coil was placed in the rectal cavity and 75 dummy (non-radioactive) seeds were implanted in the prostate. CT images were acquired with the rectal balloon empty and inflated. The prostate was carefully contoured on all slices and the benchmark coordinates of the centers of all seeds were identified using an interactive point-and-click method. An m-rep model of the relaxed prostate was created by deforming a stock prostate model into the volume defined by the prostate contours. A multiscale FEM mesh model was then automatically generated from the m-rep model. The surfaces of the relaxed and deformed prostate were used to define boundary conditions, and the system of partial differential equations for a linear elastic system was solved using FEM in a computationally efficient multiscalar fashion facilitated by the properties of m-reps. The locations of seeds in the deformed prostate predicted by MFEM were compared to the benchmark coordinates. Results: The mean error of the MFEM-predicted seed coordinates compared to human labeling in the deformed prostate was slightly less than 1 pixel along the axes in the transverse plane and slightly less than one-half the slice thickness along the cephalocaudal axis. Conclusion: The MFEM-predicted seed locations agreed with human labeling within limitations imposed by the experimental conditions such as the discrete nature of the CT data and image artifacts. The automatic meshing algorithm and computational efficiency gained from m-rep methodology offer significant computational improvements that can move finite element modeling closer to clinically practical implementation.