Many important fields of basic research in medicine and biology routinely employ tools for the statistical analysis of collections of similar shapes. Biologists, for example, have long relied on homologous, anatomical landmarks as shape models to characterize the growth and development of species. Increasingly, however, researchers are exploring the use of more detailed models that are derived computationally from three-dimensional images and surface descriptions. While computationally-derived models of shape are promising new tools for biomedical research, they also present some significant engineering challenges, which existing modeling methods have only begun to address.In this dissertation, I propose a new computational framework for statistical shape modeling that significantly advances the state-of-the-art by overcoming many of the limitations of existing methods. The framework uses a particle-system representation of shape, with a fast correspondence-point optimization based on information content. The optimization balances the simplicity of the model (compactness) with the accuracy of the shape representations by using two commensurate entropy metrics and no free parameters. The idea is to maximize both the geometric accuracy and the statistical simplicity of the shape model, in accordance with the principle of parsimony in model selection. The nonparametric representation allows the method to be applied to a larger class of problems than existing methods, including nonspherical surfaces, open surfaces, and sets of multiple surfaces.The relative simplicity of the surface representation and the low number of free parameters results in a framework that is easy to use and can operate directly on image segmentations. In collaboration with scientists from several important areas of biomedicine, I have demonstrated that the proposed method is indeed an e↵ective tool for scientific research.The specific research contributions of this dissertation are as follows. First, I describe a mathematical framework and a robust numerical algorithm for computing optimized correspondence-point shape models using an entropy-based optimization and particle-system technology. Second, I develop a series of extensions of the framework to more general classes of shape analysis problems, including the analysis of multiple-object complexes, the generalization to correspondence based on generic functions of position, an extension to handle surfaces with open boundaries, and shape modeling with simple regression. Third, I describe the application of statistical hypothesis testing, regression analysis, and multiple-analysis of covariance to the proposed shape models. I also introduce new techniques for visualization and interpretation of these statistics. Finally, in cooperation with biomedical researchers, I present validation of the above research contributions by their successful application to real-world research problems.

Abstract.While level sets have demonstrated a great potential for 3D medical image segmentation, their usefulness has been limited by two problems. First, 3D level sets are relatively slow to compute. Second, their formulation usually entails several free parameters which can be very difficult to correctly tune for specific applications. This paper presents a tool for 3D segmentation that relies on level-set surface models computed at interactive rates on commodity graphics cards (GPUs). The interactive rates for solving the level-set PDE give the user immediate feedback on the parameter settings, and thus users can tune three separate parameters and control the shape of the model in real time. We have found that this interactivity enables users to produce good, reliable segmentation, as supported by qualitative and quantitative results.

Objectives The aim of this study was to assess acute ablation injuries seen on late gadolinium enhancement (LGE) magnetic resonance imaging (MRI) immediately post-ablation (IPA) and the association with permanent scar 3 months post-ablation (3moPA). Background Success rates for atrial fibrillation catheter ablation vary significantly, in part because of limited information about the location, extent, and permanence of ablation injury at the time of procedure. Although the amount of scar on LGE MRI months after ablation correlates with procedure outcomes, early imaging predictors of scar remain elusive. Methods Thirty-seven patients presenting for atrial fibrillation ablation underwent high-resolution MRI with a 3-dimensional LGE sequence before ablation, IPA, and 3moPA using a 3-T scanner. The acute left atrial wall injuries on IPA scans were categorized as hyperenhancing (HE) or nonenhancing (NE) and compared with scar 3moPA. Results Heterogeneous injuries with HE and NE regions were identified in all patients. Dark NE regions in the left atrial wall on LGE MRI demonstrate findings similar to the “no-reflow” phenomenon. Although the left atrial wall showed similar amounts of HE, NE, and normal tissue IPA (37.7 ± 13%, 34.3 ± 14%, and 28.0 ± 11%, respectively; p = NS), registration of IPA injuries with 3moPA scarring demonstrated that 59.0 ± 19% of scar resulted from NE tissue, 30.6 ± 15% from HE tissue, and 10.4 ± 5% from tissue identified as normal. Paired t-test comparisons were all statistically significant among NE, HE, and normal tissue types (p < 0.001). Arrhythmia recurrence at 1-year follow-up correlated with the degree of wall enhancement 3moPA (p = 0.02). Conclusions Radiofrequency ablation results in heterogeneous injury on LGE MRI with both HE and NE wall lesions. The NE lesions demonstrate no-reflow characteristics and reveal a better predictor of final scar at 3 months. Scar correlates with procedure outcomes, further highlighting the importance of early scar prediction.

A key step to improve the coincidence time resolution of positron emission tomography detectors that exploit small populations of promptly emitted photons is improving the single photon time resolution (SPTR) of silicon photomultipliers (SiPMs). The influence of electronic noise has previously been identified as the dominant factor affecting SPTR for large area, analog SiPMs. In this work, we measure the achievable SPTR with front end electronic readout that minimizes the influence of electronic noise. With this readout circuit, the SPTR measured for one FBK NUV single avalanche photodiode (SPAD) was also achieved with a [Formula: see text] mm FBK NUV SiPM. SPTR for large area devices was also significantly improved. The measured SPTRs for [Formula: see text] mm Hamamatsu and SensL SiPMs were [Formula: see text]150 ps FWHM, and SPTR [Formula: see text]100 ps FWHM was measured for [Formula: see text] mm and [Formula: see text] mm FBK NUV and NUV-HD SiPMs. We also explore additional factors affecting the achievable SPTR for large area, analog SiPMs when the contribution of electronic noise is minimized and pinpoint potential areas of improvement to further reduce the SPTR of large area sensors towards that achievable for a single SPAD.

Coincidence time resolution (CTR), an important parameter for time-of-flight (TOF) PET performance, is determined mainly by properties of the scintillation crystal and photodetector used. Stable production techniques for LGSO:Ce (Lu1.8Gd0.2SiO5:Ce) with decay times varying from ∼ 30-40 ns have been established over the past decade, and the decay time can be accurately controlled with varying cerium concentration (0.025-0.075 mol%). This material is promising for TOF-PET, as it has similar light output and equivalent stopping power for 511 keV annihilation photons compared to industry standard LSO:Ce and LYSO:Ce, and the decay time is improved by more than 30% with proper Ce concentration. This work investigates the achievable CTR with LGSO:Ce (0.025 mol%) when coupled to new silicon photomultipliers. Crystal element dimension is another important parameter for achieving fast timing. 20 mm length crystal elements achieve higher 511 keV photon detection efficiency, but also introduce higher scintillation photon transit time variance. 3 mm length crystals are not practical for PET, but have reduced scintillation transit time spread. The CTR between pairs of 2.9 × 2.9 × 3 mm(3) and 2.9 × 2.9 × 20 mm(3) LGSO:Ce crystals was measured to be 80 ± 4 and 122 ± 4 ps FWHM, respectively. Measurements of light yield and intrinsic decay time are also presented for a thorough investigation into the timing performance with LGSO:Ce (0.025 mol%).