Data-Driven Motion Detection and Characterization in PET Brain Scans Using List Mode

Head motion during a Positron Emission Tomography (PET) brain scan can considerably degrade image quality. External motion-tracking devices have proven successful in minimizing this effect, but the associated time, maintenance, and workflow changes inhibit their widespread clinical use. List-mode PET acquisition allows for the retroactive analysis of coincidence events on any time scale throughout a scan, and therefore potentially offers a data-driven motion detection and characterization technique. An algorithm was developed to parse list-mode data, divide the full acquisition into short scan intervals, and calculate the line-of-response (LOR) midpoint average for each interval. These LOR midpoint averages, known as “radioactivity centroids,” were presumed to represent the center of the radioactivity distribution in the scanner, and it was thought that changes in this metric over time would correspond to intra-scan motion.

Several scans were taken of the 3D Hoffman brain phantom on a GE Discovery IQ PET/CT scanner to test the ability of the radioactivity to indicate intra-scan motion. Each scan incrementally surveyed motion in a different degree of freedom (2 translational and 2 rotational). The radioactivity centroids calculated from these scans correlated linearly to phantom positions/orientations. Centroid measurements over 1-second intervals performed on scans with ~1mCi of activity in the center of the field of view had standard deviations of 0.026 cm in the x- and y-dimensions and 0.020 cm in the z-dimension, which demonstrates high precision and repeatability in this metric. Radioactivity centroids are thus shown to successfully represent discrete motions on the submillimeter scale. It is also shown that while the radioactivity centroid can precisely indicate the amount of motion during an acquisition, it fails to distinguish what type of motion occurred.

Advances in Dynamic Modeling and Computation for Count Data

A class of multi-process models is developed for collections of time indexed count data. Autocorrelation in counts is achieved with dynamic models for the natural parameter of the binomial distribution. In addition to modeling binomial time series, the framework includes dynamic models for multinomial and Poisson time series. Markov chain Monte Carlo (MCMC) and Po ́lya-Gamma data augmentation (Polson et al., 2013) are critical for fitting multi-process models of counts. To facilitate computation when the counts are high, a Gaussian approximation to the P ́olya- Gamma random variable is developed.

Three applied analyses are presented to explore the utility and versatility of the framework. The first analysis develops a model for complex dynamic behavior of themes in collections of text documents. Documents are modeled as a “bag of words”, and the multinomial distribution is used to characterize uncertainty in the vocabulary terms appearing in each document. State-space models for the natural parameters of the multinomial distribution induce autocorrelation in themes and their proportional representation in the corpus over time.

The second analysis develops a dynamic mixed membership model for Poisson counts. The model is applied to a collection of time series which record neuron level firing patterns in rhesus monkeys. The monkey is exposed to two sounds simultaneously, and Gaussian processes are used to smoothly model the time-varying rate at which the neuron’s firing pattern fluctuates between features associated with each sound in isolation.

The third analysis presents a switching dynamic generalized linear model for the time-varying home run totals of professional baseball players. The model endows each player with an age specific latent natural ability class and a performance enhancing drug (PED) use indicator. As players age, they randomly transition through a sequence of ability classes in a manner consistent with traditional aging patterns. When the performance of the player significantly deviates from the expected aging pattern, he is identified as a player whose performance is consistent with PED use.

All three models provide a mechanism for sharing information across related series locally in time. The models are fit with variations on the P ́olya-Gamma Gibbs sampler, MCMC convergence diagnostics are developed, and reproducible inference is emphasized throughout the dissertation.