We introduce a novel Bayesian nonparametric model that uses the concept of disease trajectories for disease subtype identification. Although our model is general, we demonstrate that by treating fractions of tissue patterns derived from medical images as compositional data, our model can be applied to study distinct progression trends between population subgroups. Specifically, we apply our algorithm to quantitative emphysema measurements obtained from chest CT scans in the COPDGene Study and show several distinct progression patterns. As emphysema is one of the major components of chronic obstructive pulmonary disease (COPD), the third leading cause of death in the United States [1], an improved definition of emphysema and COPD subtypes is of great interest. We investigate several models with our algorithm, and show that one with age , pack years (a measure of cigarette exposure), and smoking status as predictors gives the best compromise between estimated predictive performance and model complexity. This model identified nine subtypes which showed significant associations to seven single nucleotide polymorphisms (SNPs) known to associate with COPD. Additionally, this model gives better predictive accuracy than multiple, multivariate ordinary least squares regression as demonstrated in a five-fold cross validation analysis. We view our subtyping algorithm as a contribution that can be applied to bridge the gap between CT-level assessment of tissue composition to population-level analysis of compositional trends that vary between disease subtypes.

The main contribution of this work is a framework to register anatomical structures characterized as a point set where each point has an associated symmetric matrix. These matrices can represent problem-dependent characteristics of the registered structure. For example, in airways, matrices can represent the orientation and thickness of the structure. Our framework relies on a dense tensor field representation which we implement sparsely as a kernel mixture of tensor fields. We equip the space of tensor fields with a norm that serves as a similarity measure. To calculate the optimal transformation between two structures we minimize this measure using an analytical gradient for the similarity measure and the deformation field, which we restrict to be a diffeomorphism. We illustrate the value of our tensor field model by comparing our results with scalar and vector field based models. Finally, we evaluate our registration algorithm on synthetic data sets and validate our approach on manually annotated airway trees.

Chronic obstructive pulmonary disease (COPD) is a lung disease characterized by airflow limitation usually associated with an inflammatory response to noxious particles, such as cigarette smoke. COPD is currently the third leading cause of death in the United States and is the only leading cause of death that is increasing in prevalence. It also represents an enormous financial burden to society, costing tens of billions of dollars annually in the U.S. It is widely accepted by the medical community that COPD is a heterogeneous disease, with substantial evidence indicating that genetic variation contributes to varying levels of disease susceptibility. This heterogeneity makes it difficult to predict health decline and develop targeted treatments for better patient care. Although researchers have made several attempts to discover disease subtypes, results have been inconclusive, in part because standard clustering methods have not properly dealt with disease manifestations that may worsen with increased exposure. In this paper we introduce a transformative way of looking at the COPD subtyping task. Specifically, we model the relationship between risk factors (such as age and smoke exposure) and manifestations of disease severity using Gaussian Processes, which allow us to represent so-called "disease trajectories". We also posit that individuals can be associated with multiple disease types (latent clusters), which we assume are influenced by genetics. Furthermore, we predict that only subsets of the numerous disease-related quantitative features are useful for describing each latent subtype. We model these associations using two separate beta process priors, and we describe a variational inference approach to discover the most probable latent cluster assignments. Results are validated with associations to genetic markers.

Motivated by the need to identify new and clinically relevant categories of lung disease, we propose a novel clustering with constraints method using a Dirichlet process mixture of Gaussian processes in a variational Bayesian nonparametric framework. We claim that individuals should be grouped according to biological and/or genetic similarity regardless of their level of disease severity; therefore, we introduce a new way of looking at subtyping/clustering by recasting it in terms of discovering associations of individuals to disease trajectories (i.e., grouping individuals based on their similarity in response to environmental and/or disease causing variables). The nonparametric nature of our algorithm allows for learning the unknown number of meaningful trajectories. Additionally, we acknowledge the usefulness of expert guidance by providing for their input using must-link and cannot- link constraints. These constraints are encoded with Markov random fields. We also provide an efficient variational approach for performing inference on our model.