This thesis mainly focuses on proposing a 4D (three spatial dimensions plus time) tissue-volume preserving non-rigid image registration algorithm for pulmonary 4D computed tomography (4DCT) data sets to provide relevant information for radiation therapy and to estimate pulmonary ventilation. The sum of squared tissue volume difference (SSTVD) similarity cost takes into account the CT intensity changes of spatially corresponding voxels, which is caused by variations of the fraction of tissue within voxels throughout the respiratory cycle. The proposed 4D SSTVD registration scheme considers the entire dynamic 4D data set simultaneously, using both spatial and temporal information. We employed a uniform 4D cubic B-spline parametrization of the transform and a temporally extended linear elasticity regularization of deformation field to ensure temporal smoothness and thus biological plausibility of estimated deformation. A multi-resolution multi-grid registration framework was used with a limited-memory Broyden Fletcher Goldfarb Shanno (LBFGS) optimizer for rapid convergence rate, robustness against local minima and limited memory consumption. The algorithm was prototyped in Matlab and then fully implemented in C++ in Elastix package based on the Insight Segmentation and Registration Toolkit (ITK). We conducted experiments on 2D+t synthetic images to demonstrate the effectiveness of the proposed method. The 4D SSTVD algorithm was also tested on clinical pulmonary 4DCT data sets in comparison with existing 3D pairwise SSTVD algorithm and 4D sum of squared difference (SSD) algorithm. The mean landmark error and mean landmark irregularity were calculated based on manually annotated landmarks on publicly available 4DCT data sets to evaluate the accuracy and temporal smoothness of the registration results. A 4D landmarking software tool was also designed and implemented in Java as an ImageJ plug-in to help facilitate the landmark labeling process in 4DCT data sets.

Graphics Processing Units (GPUs) have grown in popularity beyond the original video game enthusiast audience. They have been embraced by the high-performance computing community due to their high computational throughput, low cost, low energy demands, wide availability, and ability to dramatically improve application performance. In addition, as hybrid computing continues into mainstream applications, the use of GPUs will continue to grow. However, due to architectural difference between the CPU and GPU, adapting CPU-based scientific computing applications to fully exploit the potential speedup that GPUs offer is a non-trivial task. Algorithms must be designed with the architecture benefits and limitations in mind in order to unlock the full performance gains afforded by the use GPU. In this work, we develop fast GPU methods to improve the performance of two important components in computational lung modeling - image registration and particle tracking. We first propose a novel method for multi-level mass-preserving deformable image registration. The strength of this method is that it allows for flexibility of choice for the similarity criteria to be used by the registration method, making possible the implementation of simple and complex similarity measures on the GPU with excellent performance results. The method is tested using three similarity criteria for registering two CT lung datasets - the commonly used sum of squared intensity differences (SSD), the sum of squared tissue value differences (SSTVD), and a symmetric version of SSTVD currently being developed by our research group. The GPU method is validated against a previously validated single-threaded CPU counterpart using six healthy human subjects, and demonstrated strong agreement of results. Separately, three GPU methods were developed for tracking particle trajectories and deposition efficiencies in the human airway tree, including a multiple-GPU method. Though parallelization was straightforward, the complex geometry of the lungs and use of an unstructured mesh provided challenges that were addressed by the GPU methods. The results of the GPU methods were tested for various numbers of particles and compared to a previously validated single-threaded CPU version and demonstrated dramatic speedup over the single-threaded CPU version and 12-threaded CPU versions.