Radiation therapy (RT) is commonly used to treat patients with lung cancer. One of the limitations of RT is that irradiation of the surrounding healthy lung tissues during RT may cause damage to the lungs. Radiation-induced pulmonary toxicity may be mitigated by minimizing doses to high-function lung tissues, which we refer to as functional avoidance RT. Lung function can be computed by image registration of treatment planning four-dimensional computed tomography (4DCT), which we refer to as CT ventilation imaging. However, the accuracy of functional avoidance RT is limited by lung function imaging accuracy and artifacts in 4DCT. The goal of this dissertation is to improve the accuracy of functional avoidance RT by overcoming those two limitations. A common method for estimating lung ventilation uses image registration to align the peak exhale and inhale 3DCT images. This approach called the 2-phase local expansion ratio is limited because it assumes no out-of-phase lung ventilation and may underestimate local lung ventilation. Out-of-phase ventilation occurs when regions of the lung reach their maximum (minimum) local volume in a phase other than the peak of inhalation (end of exhalation). This dissertation presents a new method called the N-phase local expansion ratio for detecting and characterizing locations of the lung that experience out-of-phase ventilation. The N-phase LER measure uses all 4DCT phases instead of two peak phases to estimate lung ventilation. Results show that out-of-phase breathing was common in the lungs and that the spatial distribution of out-of-phase ventilation varied from subject to subject. On average, 49% of the out-of-phase regions were mislabeled as low-function by the 2-phase LER. 4DCT and Xenon-enhanced CT (Xe-CT) of four sheep were used to evaluate the accuracy of 2-phase LER and N-phase LER. Results show that the N-phase LER measure was more correlated with the Xe-CT than the 2-phase LER measure. These results suggest that it may be better to use all 4DCT phases instead of the two peak phases to estimate lung function. The accuracy of functional avoidance RT may also be improved by reducing the impact of artifacts in 4DCT. In this dissertation, we propose a a geodesic density regression (GDR) algorithm to correct artifacts in one breathing phase by using artifact-free data in corresponding regions of the other breathing phases. Local tissue density change associated with CT intensity change during respiration is accommodated in the GDR algorithm. Binary artifact masks are used to exclude regions of artifacts from the regression, i.e., the GDR algorithm only uses artifact-free data. The GDR algorithm estimates an artifact-free CT template image and its time flow through a respiratory cycle. Evaluation of the GDR algorithm was performed using both 2D CT time-series images with simulated known motion artifacts and treatment planning 4DCT with real motion artifacts. The 2D results show that there is no significant difference (p-value = 0.95) between GDR regression of artifact data using artifact masks and regression of artifact-free data. In contrast, significant errors (p-value = 0.005) were present in the estimated Jacobian images when artifact masks were not used. We also demonstrated the effectiveness of the GDR algorithm for removing real duplication, misalignment, and interpolation artifacts in 4DCT. Overall this dissertation proposes methods that have the potential to improve functional avoidance RT by accommodating out-of-phase ventilation, and removing motion artifacts in 4DCT using geodesic image regression.

Digital medical atlases can contain anatomical information which is valuable for medical doctors in diagnosing and treating illnesses. The increased availability of such atlases has created an interest for computer algorithms which are capable of integrating such atlas information into patient specific dataprocessing. The field of medical image registration aim at calculating how to match one medical image to another. Here the atlas information could give important hints of which kinds of motion are plausible in different locations of the anatomy. Being able to incorporate such atlas specific information could potentially improve the matching of images and plausibility of image registration - ultimately providing a more correct information on which to base health care diagnosis and treatment decisions. In this licentiate thesis a generic signal processing framework is derived : Global Linear Optimization (GLO). The power of the GLO framework is first demonstrated quantitatively in a very high performing image denoiser. Important proofs of concepts are then made deriving and implementing three important capabilities regarding adaptive filtering of vector fields in medica limage registration: Global regularization with local anisotropic certainty metric. Allowing sliding motion along organ and tissue boundaries. Enforcing an incompressible motion in specific areas or volumes. In the three publications included in this thesis, the GLO framework is shown to be able to incorporate one each of these capabilities. In the third and final paper a demonstration is made how to integrate more and more of the capabilities above into the same GLO to perform adaptive processing on relevant clinical data. It is shown how each added capability improves the result of the image registration. In the end of the thesis there is a discussion which highlights the advantage of the contributions made as compared to previous methods in the scientific literature. / Dynamic Context Atlases for Image Denoising and Patient Safety

This thesis compares and contrasts currents- and varifolds-based diffeomorphic image registration approaches for registering tree-like structures in the lung and surface of the lung. In these approaches, curve-like structures in the lung—for example, the skeletons of vessels and airways segmentation—and surface of the lung are represented by currents or varifolds in the dual space of a Reproducing Kernel Hilbert Space (RKHS). Currents and varifolds representations are discretized and are parameterized via of a collection of momenta. A momenta corresponds to a line segment via the coordinates of the center of the line segment and the tangent direction of the line segment at the center. A momentum corresponds to a mesh via the coordinates of the center of the mesh and the normal direction of the mesh at the center. The magnitude of the tangent vector for the line segment and the normal vector for the mesh are the length of the line segment and the area of the mesh respectively. A varifolds-based registration approach is similar to currents except that two varifolds representations are aligned independent of the tangent (normal) vector orientation. An advantage of varifolds over currents is that the orientation of the tangent vectors can be difficult to determine especially when the vessel and airway trees are not connected. In this thesis, we examine the image registration sensitivity and accuracy of currents- and varifolds-based registration as a function of the number and location of momenta used to represent tree like-structures in the lung and the surface of the lung. The registrations presented in this thesis were generated using the Deformetrica software package, which is publicly available at www.deformetrica.org.

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.

Registration of medical imaging is essential for aligning in time and space different modalities and hence consolidating their strengths for enhanced diagnosis and for the effective planning of treatment or therapeutic interventions. The primary objective of this study is to develop an integrated registration method that is effective for registering both brain and whole-body images. We seek in the proposed method to combine in one setting the excellent registration results that FMRIB Software Library (FSL) produces with brain images and the excellent results of Statistical Parametric Mapping (SPM) when registering whole-body images. To assess attainment of these objectives, the following registration tasks were performed: (1) FDG_CT with FLT_CT images, (2) pre-operation MRI with intra-operation CT images, (3) brain only MRI with corresponding PET images, and (4) MRI T1 with T2, T1 with FLAIR, and T1 with GE images. Then, the results of the proposed method will be compared to those obtained using existing state-of-the-art registration methods such as SPM and FSL. Initially, three slices were chosen from the reference image, and the normalized mutual information (NMI) was calculated between each of them for every slice in the moving image. The three pairs with the highest NMI values were chosen. The wavelet decomposition method is applied to minimize the computational requirements. An initial search applying a genetic algorithm is conducted on the three pairs to obtain three sets of registration parameters. The Powell method is applied to reference and moving images to validate the three sets of registration parameters. A linear interpolation method is then used to obtain the registration parameters for all remaining slices. Finally, the aligned registered image with the reference image were displayed to show the different performances of the 3 methods, namely the proposed method, SPM and FSL by gauging the average NMI values obtained in the registration results. Visual observations are also provided in support of these NMI values. For comparative purposes, tests using different multi-modal imaging platforms are performed.

This dissertation presents a new inverse consistent image registration (ICIR) method called boundary-constrained inverse consistent image registration (BICIR). ICIR algorithms jointly estimate the forward and reverse transformations between two images while minimizing the inverse consistency error (ICE). The ICE at a point is defined as the distance between the starting and ending location of a point mapped through the forward transformation and then the reverse transformation. The novelty of the BICIR method is that a region of interest (ROI) in one image is registered with its corresponding ROI. This is accomplished by first registering the boundaries of the ROIs and then matching the interiors of the ROIs using intensity registration. The advantages of this approach include providing better registration at the boundary of the ROI, eliminating registration errors caused by registering regions outside the ROI, and theoretically minimizing computation time since only the ROIs are registered. The first step of the BICIR algorithm is to inverse consistently register the boundaries of the ROIs. The resulting forward and reverse boundary transformations are extended to the entire ROI domains using the Element Free Galerkin Method (EFGM). The transformations produced by the EFGM are then made inverse consistent by iteratively minimizing the ICE. These transformations are used as initial conditions for inverse-consistent intensity-based registration of the ROI interiors. Weighted extended B-splines (WEB-splines) are used to parameterize the transformations. WEB-splines are used instead of B-splines since WEB-splines can be defined over an arbitrarily shaped ROI. Results are presented showing that the BICIR method provides better registration of 2D and 3D anatomical images than the small-deformation, inverse-consistent, linear-elastic (SICLE) image registration algorithm which registers entire images. Specifically, the BICIR method produced registration results with lower similarity cost, reduced boundary matching error, increased ROI relative overlap, and lower inverse consistency error than the SICLE algorithm.

There is notable heterogeneity in clinical presentation of patients with chronic obstructive pulmonary disease (COPD). Classification of COPD is usually based on the severity of airflow limitation (pre- and post- bronchodilator FEV1), which may not sensitively differentiate subpopulations with distinct phenotypes. A recent advance of quantitative medical imaging and data analysis techniques allows for deriving quantitative computed tomography (QCT) imaging-based metrics. These imaging-based metrics can be used to link structural and functional alterations at multiscale levels of human lung. We acquired QCT images of 800 former and current smokers from Subpopulations and Intermediate Outcomes in COPD Study (SPIROMICS). A GPU-based symmetric non-rigid image registration method was applied at expiration and inspiration to derived QCT-based imaging metrics at multiscale levels. With these imaging-based variables, we employed a machine learning method (an unsupervised clustering technique (K-means)) to identify imaging-based clusters. Four clusters were identified for both current and former smokers. Four clusters were identified for both current and former smokers with meaningful associations with clinical and biomarker measures. Results demonstrated that QCT imaging-based variables in patients with COPD can derive statistically stable and clinically meaningful clusters. This sub-grouping can help better categorize the disease phenotypes, ultimately leading to a development of an efficient therapy.

The aim of this study is to investigate the functional and structural differences between normal subjects and asthmatics via image registration and computational fluid dynamics (CFD), together with pulmonary function test's (PFT) and one-image-based variables. We analyzed three populations of CT images: 50 normal, 42 non-severe asthmatic and 52 severe asthmatic subjects at total lung capacity (TLC) and functional residual capacity (FRC). A mass preserving image registration technique was employed to match CT images at TLC and FRC for assessments of regional volume change and anisotropic deformation. Instead of existing threshold-based air-trapping measure, a fraction-based air-trapping measure was proposed to account for inter-site and inter-subject variations of CT density. We also analyzed structural alterations of asthmatic airways, including bifurcation angle, hydraulic diameter, luminal area and wall area. CFD and particle tracking simulations are employed with physiologically-consistent boundary condition. As compared with normal subjects, severe asthmatics exhibit reduced air volume change (consistent with air-trapping) and more isotropic deformation in the basal lung regions, but increased air volume change associated with increased anisotropic deformation in the apical lung regions. In the multi-center study, the traditional air-trapping measure showed the significant site-variability due to the differences of scanners and coaching methods. The proposed fraction-based air-trapping measure is able to overcome the inter-site and inter-subject variations, allowing analysis of large data sets collected from multiple centers. We further demonstrate alterations of bifurcation angle, constriction, wall thickness and non-circularity at local branch level in severe asthmatics. The bifurcation angle, non-circularity and especially reduced hydraulic diameter significantly affect the increase of particle deposition in severe asthmatics. In summary, the two-image registration-based deformation provides a tool for distinguishing differences in lung mechanics among populations. The new fraction-based air-trapping measure significantly improves the association of air-trapping with the presence and severity of asthma and the correlation with forced expiratory volume in 1 second over forced vital capacity (FEV1/FVC) than existing approaches. The altered functions and structures such as air-volume change, branching angles, non-circular shapes, wall thickness and hydraulic diameters that found in asthmatics are strongly associated with the flow structures and particle depositions.

Image registration is the process of aligning two images such that their mutual features overlap. This is of great importance in several medical applications. In 2008 a novel method for simultaneous T1, T2 and proton density quantification was suggested. The method is in the field of quantitative Magnetic Resonance Imaging or qMRI. In qMRI parameters are quantified by a pixel-to-pixel fit of the image intensity as a function of different MR scanner settings. The quantification depends on several volumes of different intensities to be aligned. If a patient moves during the data aquisition the datasets will not be aligned and the results are degraded due to this. Since the quantification takes several minutes there is a considerable risk of patient movements. In this master thesis three image registration methods are presented and a comparison in robustness and speed was made. The phase based algorithm was suited for this problem and limited to finding rigid motion. The other two registration algorithms, originating from the Statistical Parametrical Mapping, SPM, package, were used as references. The result shows that the pixel-to-pixel fit is greatly improved in the datasets with found motion. In the comparison between the different methods the phase based algorithm turned out to be both the fastest and the most robust method.

Image registration is widely used in different areas nowadays. Usually, the efficiency, accuracy, and robustness in the registration process are concerned in applications. This thesis studies these issues by presenting an efficient intensity-based mono-modality rigid 2D-3D image registration method and constructing a novel mathematical model for intensity-based multi-modality rigid image registration. For mono-modality image registration, an algorithm is developed using RapidMind Multi-core Development Platform (RapidMind) to exploit the highly parallel multi-core architecture of graphics processing units (GPUs). A parallel ray casting algorithm is used to generate the digitally reconstructed radiographs (DRRs) to efficiently reduce the complexity of DRR construction. The optimization problem in the registration process is solved by the Gauss-Newton method. To fully exploit the multi-core parallelism, almost the entire registration process is implemented in parallel by RapidMind on GPUs. The implementation of the major computation steps is discussed. Numerical results are presented to demonstrate the efficiency of the new method. For multi-modality image registration, a new model for computing mutual information functions is devised in order to remove the artifacts in the functions and in turn smooth the functions so that optimization methods can converge to the optimal solutions accurately and efficiently. With the motivation originating from the objective to harmonize the discrepancy between the image presentation and the mutual information definition in previous models, the new model computes the mutual information function using both the continuous image function representation and the mutual information definition for continuous random variables. Its implementation and complexity are discussed and compared with other models. The mutual information computed using the new model appears quite smooth compared with the functions computed by others. Numerical experiments demonstrate the accuracy and efficiency of optimization methods in the case that the new model is used. Furthermore, the robustness of the new model is also verified.