A CASE STUDY IN PHARMACOLOGIC IMAGING USING PRINCIPAL CURVES IN SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY

In this manuscript we are concerned with functional imaging of the colon to assess the kinetics of a microbicide lubricant. The overarching goal is to understand the distribution of the lubricant in the colon. Such information is crucial for understanding the potential impact of the microbicide on HIV viral transmission. The experiment was conducted by imaging a radiolabeled lubricant distributed in the subject’s colon. The tracer imaging was conducted via single photon emission computed tomography (SPECT), a non-invasive, in-vivo functional imaging technique. We develop a novel principal curve algorithm to construct a three dimensional curve through the colon images. The developed algorithm is tested and debugged on several difficult two dimensional images of familiar curves where the original principal curve algorithm does not apply. The final curve fit to the colon data is compared with experimental sigmoidoscope collection.

A Mechanistic Latent Variable Model for Estimating Drug Concentrations in the Male Genital Tract

The purpose of this study is to develop statistical methodology to facilitate indirect estimation of the concentration of antiretroviral drugs and viral loads in the prostate gland and the seminal vesicle. The differences in antiretroviral drug concentrations in these organs may lead to suboptimal concentrations in one gland compared to the other. Suboptimal levels of the antiretroviral drugs will not be able to fully suppress the virus in that gland, lead to a source of sexually transmissible virus and increase the chance of selecting for drug resistant virus. This information may be useful selecting antiretroviral drug regimen that will achieve optimal concentrations in most of male genital tract glands. Using fractionally collected semen ejaculates, Lundquist (1949) measured levels of surrogate markers in each fraction that are uniquely produced by specific male accessory glands. To determine the original glandular concentrations of the surrogate markers, Lundquist solved a simultaneous series of linear equations. This method has several limitations. In particular, it does not yield a unique solution, it does not address measurement error, and it disregards inter-subject variability in the parameters. To cope with these limitations, we developed a mechanistic latent variable model based on the physiology of the male genital tract and surrogate markers. We employ a Bayesian approach and perform a sensitivity analysis with regard to the distributional assumptions on the random effects and priors. The model and Bayesian approach is validated on experimental data where the concentration of a drug should be (biologically) differentially distributed between the two glands. In this example, the Bayesian model-based conclusions are found to be robust to model specification and this hierarchical approach leads to more scientifically valid conclusions than the original methodology. In particular, unlike existing methods, the proposed model based approach was not affected by a common form of outliers.

NONLINEAR TUBE-FITTING FOR THE ANALYSIS OF ANATOMICAL AND FUNCTIONAL STRUCTURES

We are concerned with the estimation of the exterior surface of tube-shaped anatomical structures. This interest is motivated by two distinct scientific goals, one dealing with the distribution of HIV microbicide in the colon and the other with measuring degradation in white-matter tracts in the brain. Our problem is posed as the estimation of the support of a distribution in three dimensions from a sample from that distribution, possibly measured with error. We propose a novel tube-fitting algorithm to construct such estimators. Further, we conduct a simulation study to aid in the choice of a key parameter of the algorithm, and we test our algorithm with validation study tailored to the motivating data sets. Finally, we apply the tube-fitting algorithm to a colon image produced by single photon emission computed tomography (SPECT)and to a white-matter tract image produced using diffusion tensor `imaging (DTI).