Doctor of Philosophy

dissertationWe develop mathematical models relating measured biological markers to how animals process nutrients and toxins. Our models track molecules as they are ingested, transformed through metabolic processes, and excreted, and relate measurements of biological markers to these processes. We focus on specific problems of practical interest. We begin by developing a model of acetaminophen metabolism and use our model to estimate outcome of acetaminophen overdose patients. Acetaminophen overdose increasingly occurs as a result of chronic use. We analyze the dynamics of chronic use and find threshold dynamics that result from the structure of acetaminophen metabolism. We next study animal nitrogen metabolism. Nitrogen stable isotope ratios in consumer tissue are used by ecologists to estimate diet and trophic dynamics, but feedbacks between diet and physiology complicate the relationship between diet and the nitrogen isotope ratio of consumer tissue. We develop a model of animal nitrogen metabolism to study the influence of diet on stable nitrogen isotope ratios of consumer tissue. Finally, hair is often measured to understand how animals process nutrients and toxins because organic and inorganic substances are incorporated into hair, remaining inert for long periods of time. We develop a model based on the known physiology of hair growth to describe the signal averaging caused by bundling multiple hairs for segmental analysis

Deconvolution of isotope signals from bundles of multiple hairs

pre-printSegmental analysis of hair has been used in diverse fields ranging from forensics to ecology to measure the concentration of substances such as drugs and isotopes. Multiple hairs are typically combined into a bundle for segmental analysis to obtain a high-resolution series of measurements. Individual hair strands cycle through multiple phases of growth and grow at different rates when in the growth phase. Variation in growth of hair strands in a bundle can cause misalignment of substance concentration between hairs, attenuating the primary body signal. We developed a mathematical model based on the known physiology of hair growth to describe the signal averaging caused by bundling multiple hairs for segmental analysis. The model was used to form an inverse method to estimate the primary body signal from measurements of a hair bundle. The inverse method was applied to a previously described stable oxygen isotope chronology from the hair of a murder victim and provides a refined interpretation of the data. Aspects of the reconstruction were confirmed when the victim was later identified

Mathematical modeling of liver injury and dysfunction after acetaminophen overdose: early discrimination between survival and death

pre-printAcetaminophen is the leading cause of acute liver injury in the developed world. Timely administration of N-Acetylcysteine (N-Ac) prevents the progression of serious liver injury and disease, while failure to administer N-Ac within a critical time frame allows disease progression and in the most severe cases may result in liver failure or death. In this situation, liver transplantation may be the only life-saving measure. Thus, the outcome of an acetaminophen overdose depends upon the size of the overdose and the time to first administration of N-Ac. We developed a system of differential equations to describe acute liver injury due to acetaminophen overdose. The Model for Acetaminophen-induced Liver Damage (MALD) uses a patient's AST, ALT, and INR measurements on admission to estimate overdose amount, time elapsed since overdose, and outcome. The mathematical model was then tested on 53 patients from the University of Utah. With the addition of serum creatinine, eventual death was predicted with 100% sensitivity, 91% specificity, 67% PPV, and 100% NPV in this retrospective study. Using only initial AST, ALT, and INR measurements, the model accurately predicted subsequent laboratory values for the majority of individual patients. This is the first dynamical rather than statistical approach to determine poor prognosis in patients with life-threatening liver disease due to acetaminophen overdose. Conclusion: MALD provides a method to estimate overdose amount, time elapsed since overdose, and outcome from patient laboratory values commonly available on admission in cases of acute liver failure due to acetaminophen overdose and should be validated in multicentric prospective evaluation

Recombinant transmissible vaccines will be intrinsically contained despite the ability to superinfect

Introduction: Transmissible vaccines offer a novel approach to suppressing viruses in wildlife populations, with possible applications against viruses that infect humans as zoonoses – Lassa, Ebola, rabies. To ensure safety, current designs propose a recombinant vector platform in which the vector is isolated from the target wildlife population. Because using an endemic vector creates the potential for preexisting immunity to block vaccine transmission, these designs focus on vector viruses capable of superinfection, spreading throughout the host population following vaccination of few individuals. Areas covered: We present original theoretical arguments that, regardless of its R0 value, a recombinant vaccine using a superinfecting vector is not expected to expand its active infection coverage when released into a wildlife population that already carries the vector. However, if superinfection occurs at a high rate such that individuals are repeatedly infected throughout their lives, the immunity footprint in the population can be high despite a low incidence of active vaccine infections. Yet we provide reasons that the above expectation is optimistic. Expert Opinion: High vaccine coverage will typically require repeated releases or release into a population lacking the vector, but careful attention to vector choice and vaccine engineering should also help improve transmissible vaccine utility

Aberrant Water Homeostasis Detected by Stable Isotope Analysis

While isotopes are frequently used as tracers in investigations of disease physiology (i.e., 14C labeled glucose), few studies have examined the impact that disease, and disease-related alterations in metabolism, may have on stable isotope ratios at natural abundance levels. The isotopic composition of body water is heavily influenced by water metabolism and dietary patterns and may provide a platform for disease detection. By utilizing a model of streptozotocin (STZ)-induced diabetes as an index case of aberrant water homeostasis, we demonstrate that untreated diabetes mellitus results in distinct combinations, or signatures, of the hydrogen (δ2H) and oxygen (δ18O) isotope ratios in body water. Additionally, we show that the δ2H and δ18O values of body water are correlated with increased water flux, suggesting altered blood osmolality, due to hyperglycemia, as the mechanism behind this correlation. Further, we present a mathematical model describing the impact of water flux on the isotopic composition of body water and compare model predicted values with actual values. These data highlight the importance of factors such as water flux and energy expenditure on predictive models of body water and additionally provide a framework for using naturally occurring stable isotope ratios to monitor diseases that impact water homeostasis

Identifying the genetic basis of viral spillover using Lassa virus as a test case

The rate at which zoonotic viruses spill over into the human population varies significantly over space and time. Remarkably, we do not yet know how much of this variation is attributable to genetic variation within viral populations. This gap in understanding arises because we lack methods of genetic analysis that can be easily applied to zoonotic viruses, where the number of available viral sequences is often limited, and opportunistic sampling introduces significant population stratification. Here, we explore the feasibility of using patterns of shared ancestry to correct for population stratification, enabling genome-wide association methods to identify genetic substitutions associated with spillover into the human population. Using a combination of phylogenetically structured simulations and Lassa virus sequences collected from humans and rodents in Sierra Leone, we demonstrate that existing methods do not fully correct for stratification, leading to elevated error rates. We also demonstrate, however, that the Type I error rate can be substantially reduced by confining the analysis to a less-stratified region of the phylogeny, even in an already-small dataset. Using this method, we detect two candidate single-nucleotide polymorphisms associated with spillover in the Lassa virus polymerase gene and provide generalized recommendations for the collection and analysis of zoonotic viruses

Adherence to HAART: A Systematic Review of Developed and Developing Nation Patient-Reported Barriers and Facilitators

BACKGROUND: Adherence to highly active antiretroviral therapy (HAART) medication is the greatest patient-enabled predictor of treatment success and mortality for those who have access to drugs. We systematically reviewed the literature to determine patient-reported barriers and facilitators to adhering to antiretroviral therapy. METHODS AND FINDINGS: We examined both developed and developing nations. We searched the following databases: AMED (inception to June 2005), Campbell Collaboration (inception to June 2005), CinAhl (inception to June 2005), Cochrane Library (inception to June 2005), Embase (inception to June 2005), ERIC (inception to June 2005), MedLine (inception to June 2005), and NHS EED (inception to June 2005). We retrieved studies conducted in both developed and developing nation settings that examined barriers and facilitators addressing adherence. Both qualitative and quantitative studies were included. We independently, in duplicate, extracted data reported in qualitative studies addressing adherence. We then examined all quantitative studies addressing barriers and facilitators noted from the qualitative studies. In order to place the findings of the qualitative studies in a generalizable context, we meta-analyzed the surveys to determine a best estimate of the overall prevalence of issues. We included 37 qualitative studies and 47 studies using a quantitative methodology (surveys). Seventy-two studies (35 qualitative) were conducted in developed nations, while the remaining 12 (two qualitative) were conducted in developing nations. Important barriers reported in both economic settings included fear of disclosure, concomitant substance abuse, forgetfulness, suspicions of treatment, regimens that are too complicated, number of pills required, decreased quality of life, work and family responsibilities, falling asleep, and access to medication. Important facilitators reported by patients in developed nation settings included having a sense of self-worth, seeing positive effects of antiretrovirals, accepting their seropositivity, understanding the need for strict adherence, making use of reminder tools, and having a simple regimen. Among 37 separate meta-analyses examining the generalizability of these findings, we found large heterogeneity. CONCLUSIONS: We found that important barriers to adherence are consistent across multiple settings and countries. Research is urgently needed to determine patient-important factors for adherence in developing world settings. Clinicians should use this information to engage in open discussion with patients to promote adherence and identify barriers and facilitators within their own populations

Developing transmissible vaccines for animal infectious diseases

No abstract available

Evolution and the duration of a doomed population

Many populations are doomed to extinction, but little is known about how evolution contributes to their longevity. We address this by modeling an asexual population consisting of genotypes whose abundances change independently according to a system of continuous branching diffusions. Each genotype is characterized by its initial abundance, growth rate, and reproductive variance. The latter two components determine the genotype's “risk function” which describes its per capita probability of extinction at any time. We derive the probability distribution of extinction times for a polymorphic population, which can be expressed in terms of genotypic risk functions. We use this to explore how spontaneous mutation, abrupt environmental change, or population supplementation and removal affect the time to extinction. Results suggest that evolution based on new mutations does little to alter the time to extinction. Abrupt environmental changes that affect all genotypes can have more substantial impact, but, curiously, a beneficial change does more to extend the lifetime of thriving than threatened populations of the same initial abundance. Our results can be used to design policies that meet specific conservation goals or management strategies that speed the elimination of agricultural pests or human pathogens