Mixed-effects shape models for estimating longitudinal changes in anatomy

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Doctor of Philosophy in Computing

dissertationStatistical shape analysis has emerged as an important tool for the quantitative analysis of anatomy in many medical imaging applications. The correspondence based approach to evaluate shape variability is a popular method, based on comparing configurations of carefully placed landmarks on each shape. In recent years, methods for automatic placement of landmarks have enhanced the ability of this approach to capture statistical properties of shape populations. However, biomedical shapes continue to present considerable difficulties in automatic correspondence optimization due to inherent geometric complexity and the need to correlate shape change with underlying biological parameters. This dissertation addresses these technical difficulties and presents improved shape correspondence models. In particular, this dissertation builds on the particle-based modeling (PBM) framework described by Joshua Cates' 2010 Ph.D. dissertation. In the PBM framework, correspondences are modeled as a set of dynamic points or a particle system, positioned automatically on shape surfaces by optimizing entropy contained in the model, with the idea of balancing model simplicity against accuracy of the particle system representation of shapes. This dissertation is a collection of four papers that extend the PBM framework to include shape regression and longitudinal analysis and also adds new methods to improve modeling of complex shapes. It also includes a summary of two applications from the field of orthopaedics. Technical details of the PBM framework are provided in Chapter 2, after which the first topic related to the study of shape change over time is addressed (Chapters 3 and 4). In analyses of normative growth or disease progression, shape regression models allow characterization of the underlying biological process while also facilitating comparison of a sample against a normative model. The first paper introduces a shape regression model into the PBM framework to characterize shape variability due to an underlying biological parameter. It further confirms the statistical significance of this relationship via systematic permutation testing. Simple regression models are, however, not sufficient to leverage information provided by longitudinal studies. Longitudinal studies collect data at multiple time points for each participant and have the potential to provide a rich picture of the anatomical changes occurring during development, disease progression, or recovery. The second paper presents a linear-mixed-effects (LME) shape model in order to fully leverage the high-dimensional, complex features provided by longitudinal data. The parameters of the LME shape model are estimated in a hierarchical manner within the PBM framework. The topic of geometric complexity present in certain biological shapes is addressed next (Chapters 5 and 6). Certain biological shapes are inherently complex and highly variable, inhibiting correspondence based methods from producing a faithful representation of the average shape. In the PBM framework, use of Euclidean distances leads to incorrect particle system interactions while a position-only representation leads to incorrect correspondences around sharp features across shapes. The third paper extends the PBM framework to use efficiently computed geodesic distances and also adds an entropy term based on the surface normal. The fourth paper further replaces the position-only representation with a more robust distance-from-landmark feature in the PBM framework to obtain isometry invariant correspondences. Finally, the above methods are applied to two applications from the field of orthopaedics. The first application uses correspondences across an ensemble of human femurs to characterize morphological shape differences due to femoroacetabular impingement. The second application involves an investigation of the short bone phenotype apparent in mouse models of multiple osteochondromas. Metaphyseal volume deviations are correlated with deviations in length to quantify the effect of cancer toward the apparent shortening of long bones (femur, tibia-fibula) in mouse models

Entropy-based particle correspondence for shape populations

Statistical shape analysis of anatomical structures plays an important role in many medical image analysis applications such as understanding the structural changes in anatomy in various stages of growth or disease. Establishing accurate correspondence across object populations is essential for such statistical shape analysis studies

Image registration driven by combined probabilistic and geometric descriptors

pre-printDeformable image registration in the presence of considerable contrast dierences and large-scale size and shape changes represents a signicant challenge for image registration. A representative driving application is the study of early brain development in neuroimaging, which requires co-registration of images of the same subject across time or building 4-D population atlases. Growth during the first few years of development involves significant changes in size and shape of anatomical structures but also rapid changes in tissue properties due to myeli-nation and structuring that are reflected in the multi-modal Magnetic Resonance (MR) contrast measurements. We propose a new registration method that generates a mapping between brain anatomies represented as a multi-compartment model of tissue class posterior images and geometries. We transform intensity patterns into combined probabilistic and geometric descriptors that drive the matching in a diffeomorphic framework, where distances between geometries are represented using currents which does not require geometric correspondence. We show preliminary results on the registrations of neonatal brain MRIs to two-year old infant MRIs using class posteriors and surface boundaries of structures undergoing major changes. Quantitative validation demonstrates that our proposed method generates registrations that better preserve the consistency of anatomical structures over time

Efficient probabilistic and geometric anatomical mapping using particle mesh approximation on GPUs

pre-printDeformable image registration in the presence of considerable contrast differences and large size and shape changes presents significant research challenges. First, it requires a robust registration framework that does not depend on intensity measurements and can handle large nonlinear shape variations. Second, it involves the expensive computation of nonlinear deformations with high degrees of freedom. Often it takes a significant amount of computation time and thus becomes infeasible for practical purposes. In this paper, we present a solution based on two key ideas: a new registration method that generates a mapping between anatomies represented as a multicompartment model of class posterior images and geometries and an implementation of the algorithm using particle mesh approximation on Graphical Processing Units (GPUs) to fulfill the computational requirements. We show results on the registrations of neonatal to 2-year old infant MRIs. Quantitative validation demonstrates that our proposed method generates registrations that better maintain the consistency of anatomical structures over time and provides transformations that better preserve structures undergoing large deformations than transformations obtained by standard intensity-only registration. We also achieve the speedup of three orders of magnitudes compared to a CPU reference implementation, making it possible to use the technique in time-critical applications

Model selection for spatiotemporal modeling of early childhood sub-cortical development

Spatiotemporal shape models capture the dynamics of shape change over time and are an essential tool for monitoring and measuring anatomical growth or degeneration. In this paper we evaluate non-parametric shape regression on the challenging problem of modeling early childhood sub-cortical development starting from birth. Due to the flexibility of the model, it can be challenging to choose parameters which lead to a good model fit yet does not overfit. We systematically test a variety of parameter settings to evaluate model fit as well as the sensitivity of the method to specific parameters, and we explore the impact of missing data on model estimation