Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, <em>i. e. </em> in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the dynamics of ensembles (statistical mechanics) and systems with uncertainty in the initial conditions. It is also the basis of ergodic theory--the study of probabilistic invariants of dynamical systems--which provides one framework for understanding chaotic systems whose time evolutions are erratic and for practical purposes unpredictable. Delay differential equations (DDEs) are a particular class of deterministic systems, distinguished by an explicit dependence of the dynamics on past states. DDEs arise in diverse applications including mathematics, biology and economics. A probabilistic approach to DDEs is lacking. The main problems we consider in developing such an approach are (1) to characterize the evolution of probability distributions for DDEs, <em>i. e. </em> develop an analog of the Perron-Frobenius operator; (2) to characterize invariant probability distributions for DDEs; and (3) to develop a framework for the application of ergodic theory to delay equations, with a view to a probabilistic understanding of DDEs whose time evolutions are chaotic. We develop a variety of approaches to each of these problems, employing both analytical and numerical methods. In transient chaos, a system evolves erratically during a transient period that is followed by asymptotically regular behavior. Transient chaos in delay equations has not been reported or investigated before. We find numerical evidence of transient chaos (fractal basins of attraction and long chaotic transients) in some DDEs, including the Mackey-Glass equation. Transient chaos in DDEs can be analyzed numerically using a modification of the "stagger-and-step" algorithm applied to a discretized version of the DDE.

DDT was extensively and globally used as a pesticide in agriculture and for malaria vector control from the 1940’s until the 1970’s. Due to its heavy use, DDT became ubiquitously distributed throughout the environment. DDT and several DDT metabolites are persistent organic pollutants. Two DDT metabolites, 3-MeSO2-DDE and o,p’-DDD have been proved to be tissue specific toxicants in the adrenal cortex. They are bioactivated to reactive intermediates which bind covalently to the adrenal cortex causing cell death. Due to its tissue specific toxicity o,p’-DDD has been used as a chemotherapy drug for adrenal cancer in humans. The efficacy and potency is however low and o,p’-DDD treatment is associated with serious side effects. 3-MeSO2-DDE has been suggested as a potential alternative therapeutic agent. A key aim of this thesis has been to improve the understanding of the kinetics of the two adrenocorticolytic compounds o,p’-DDD, its two enantiomers and 3-MeSO2-DDE. To meet this objective chemical synthesis and enantioselective analysis were required. Furthermore, in vitro toxicity of o,p’-DDD enantiomers and diastereomers were performed. An 11 step synthesis of 3-SH-DDE has been developed to promote both labelled and unlabelled synthesis of 3-alkylsulfonyl-DDE. Toxicokinetic studies showed that 3-MeSO2-DDE and o,p’-DDD were accumulated in tissues and retained in adipose tissue in minipigs. 3-MeSO2-DDE however had a twice as long biological t1/2 and a considerably lower Vd compared to o,p’-DDD. Suckling offspring were more exposed to 3-MeSO2-DDE than their mothers who were given 3-MeSO2-DDE orally. Interindividual differences in enantiomer kinetics in minipigs were observed suggesting polymorphism among the minipigs. Preparative isolation of the o,p’-DDD enantiomers is presented allowing determination of the absolute structures of the o,p’-DDD enantiomers by X-ray. The pure enantiomer of o,p’-DDD showed significant differences in toxicity in human adrenocortical cells.

Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, <em>i. e. </em> in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the dynamics of ensembles (statistical mechanics) and systems with uncertainty in the initial conditions. It is also the basis of ergodic theory--the study of probabilistic invariants of dynamical systems--which provides one framework for understanding chaotic systems whose time evolutions are erratic and for practical purposes unpredictable. Delay differential equations (DDEs) are a particular class of deterministic systems, distinguished by an explicit dependence of the dynamics on past states. DDEs arise in diverse applications including mathematics, biology and economics. A probabilistic approach to DDEs is lacking. The main problems we consider in developing such an approach are (1) to characterize the evolution of probability distributions for DDEs, <em>i. e. </em> develop an analog of the Perron-Frobenius operator; (2) to characterize invariant probability distributions for DDEs; and (3) to develop a framework for the application of ergodic theory to delay equations, with a view to a probabilistic understanding of DDEs whose time evolutions are chaotic. We develop a variety of approaches to each of these problems, employing both analytical and numerical methods. In transient chaos, a system evolves erratically during a transient period that is followed by asymptotically regular behavior. Transient chaos in delay equations has not been reported or investigated before. We find numerical evidence of transient chaos (fractal basins of attraction and long chaotic transients) in some DDEs, including the Mackey-Glass equation. Transient chaos in DDEs can be analyzed numerically using a modification of the "stagger-and-step" algorithm applied to a discretized version of the DDE.

Combination antiviral drug therapy improves the survival rates of patients chronically infected with hepatitis B virus by controlling viral replication and enhancing immune responses. Some of these drugs have side effects that make them unsuitable for long-term administration. To address the trade-off between the positive and negative effects of the combination therapy, we investigated an optimal control problem for a delay differential equation model of immune responses to hepatitis virus B infection. Our optimal control problem investigates the interplay between virological and immunomodulatory effects of therapy, the control of viremia and the administration of the minimal dosage over a short period of time. Our numerical results show that the high drug levels that induce immune modulation rather than suppression of virological factors are essential for the clearance of hepatitis B virus.

Obesity is a disease that increases risk of developing metabolic diseases including insulin resistance (IR), metabolic syndrome (MS), and type 2 diabetes (T2D). Adipose tissue expansion during obesity leads to immune cell infiltration, causing local inflammation and disruption of lipid homeostasis. There is an association between exposure to environmental chemicals, like p,p’-DDE, a metabolite of p,p’-DDT, and diagnosis of obesity, dyslipidemia, IR, and prevalence of MS and T2D. DDE accumulates in fatty tissues and has been shown to have immunomodulatory properties, affecting macrophage and T cell populations. Potential mechanisms were studied by which DDE could modulate adipocyte and immune cell function and facilitate an increased risk of obesity and immune dysregulation, potentially through cyclooxygenase-2 (COX-2). 3T3-L1 preadipocytes and J774A.1 macrophages were studied for the effects of DDE on adipogenesis and macrophage reactivity, respectively. 3T3-L1 cells were induced to differentiate to adipocytes using a sub-optimal differentiation cocktail with increasing concentrations of DDE (0.5uM-100uM). It was determined that DDE enhanced adipogenesis in a concentration dependent manner and the expression of adipogenic and lipogenic genes, indicating that DDE enhances adipogenesis. In J774A.1 cells, the ability of DDE or 10uM NS-398, a specific COX-2 inhibitor, to inhibit the production of the prostaglandins PGE2, PGD2, PGF2a, was assessed in vitro and in a cellree system. DDE or NS-398 followed by immune challenge reduced cellular PG secretion and reduced PG production in a cell free system, indicating that DDE may interfere with lipid mediator signaling. Additionally, DDE or NS-398 exposure altered gene expression in J774A.1 cells following M1 or M2 polarization stimulus. Lastly, male C57Bl mice were exposed to 2mg/kg DDE for 5 days and the macrophage population of the adipose stromal vascular fraction was analyzed by flow cytometry. Adipose from DDE treated animals contained approximately 40% F4/80+CD11b+ macrophages. These results indicate that DDE may alter the homeostasis of adipose tissue by both enhancing adipogenesis and altering the reactivity of the resident macrophage population in a manner that may contribute to adipose dysfunction. These data suggest a possible mechanism by which DDE exposure may contribute to adiposity and adipose tissue dysfunction commonly seen in metabolic disease.

Type 2 diabetes mellitus (T2DM) is classified as a metabolic disorder characterized by hyperglycemia that results from defects in insulin action and/or secretion, and currently affects 8.3% of the US population according to the CDC’s 2011 National Diabetes Fact Sheet. Several contributing factors have been identified to development of this disease. Published evidence indicates type 2 diabetes mellitus (T2DM) patients display lower overall paraoxonase activity and that this may be partially due to genetic variations in the paraoxonase-1 (PON-1) gene. Some bioaccumulative organochlorine (OC) pesticides have been shown to contribute to increased T2DM prevalence. In addition, these OC compound levels have been associated with alterations in adipocyte cytokine levels as well as increased inflammatory markers. Three hundred blood samples with clinical and demographic information were obtained from two US Air Force hospitals. A total of 151 non-diabetics and 149 T2DM subjects were evaluated for PON-1 activity, PON-1 Q192R and L55M genetic polymorphisms, OC compound concentrations, inflammatory marker levels and adipokine concentrations. PON-1 activity, using diazoxon as the substrate, was decreased in the T2DM subjects. Some of the PON-1 genetic polymorphisms tested were also associated with decreased PON-1 activity. OC compound levels were increased in the T2DM subjects. The non-diabetic subjects possessing elevated DDE and trans-nonachlor were associated with increased inflammation, a common hallmark of early T2DM development. Additionally, elevated OC levels were seen in association with altered adipokine concentrations. Overall, a decrease in the antioxidant properties of PON-1 as well as factors contributing to chronic low level inflammation such as elevated OC plasma concentration appear to be significant contributors to T2DM prevalence in the population studied.

Measuring transmembrane water exchange can provide potential biomarkers for tumors and brain disorders. Diffusion Magnetic Resonance Imaging (dMRI) is a well-established tool that can non-invasively measure water exchange across cell membranes. Diffusion Exchange Spectroscopy (DEXSY) is one of the dMRI-based frameworks used to estimate exchange. DEXSY provides a detailed picture of multi-site exchange processes but requires a large quantity of data. Several models based on the DEXSY framework have been proposed to reduce the acquisition time. Filter Exchange Imaging (FEXI) and curvature models are two of them that only require certain samples of the DEXSY dataset. Diffusion-Exchange Weighted (DEW) Imaging model is another data reduction method accounting for restricted diffusion within cells and can use a specific subset of the DEXSY dataset to measure exchange. Furthermore, a more general expression of the DEXSY signal, referred to as the general model, can theoretically analyze the full space or reduced DEXSY datasets and estimate exchange. However, the results of the subsampling schemes and the data reduction models have not been compared to the full space estimation.  Therefore, this thesis aims to experimentally explore the feasibility of estimating exchange using these four models (the general, FEXI, curvature and DEW models) with the data acquired using a low-field benchtop MR scanner, and compare the estimates from the general model with different subsampling schemes and the data reduction models to the full space estimation. For this purpose, a double diffusion encoding (DDE) sequence was modified from an existing sequence on the benchtop MR scanner and a DEXSY experiment was conducted on this MR scanner and a yeast phantom to acquire a full space dataset. The exchange parameters estimated from the full space dataset using the general model were used as "ground truths" to evaluate the estimates from the reduced datasets analyzed using the general, FEXI and curvature models. Moreover, two alternative subsampling schemes named the shifted DEW and new trajectory schemes were proposed and employed to measure exchange. The results indicate that all the methods except the curvature sampling scheme employed with both the general and curvature models provided comparable estimates to the "ground truths". The shifted DEW and new trajectory sampling schemes performed better over others in terms of consistency with the "ground truths" and low variations between voxels, suggesting the theoretical and experimental optimization of these two subsampling schemes can be further studied and developed.

<p>The shallow soils of a former orchard area in Point Pelee National Park, near Leamington, Ontario, Canada have elevated concentrations of chlorinated pesticides above the regulatory limits. Previous studies in this area have shown that the DDT, DOE and ODD are highly persistent with an estimated half-life of DDT in the range of 15-30 years. In 2002 a pilot-scale field remediation experiment involving the application of cyclodextrin was conducted. This experiment resulted in substantial decrease of DDT, DDE and DDD concentrations in the upper soil layer within the remediation grid. Soil samples were collected within the treatment plots a year after the cyclodextrin application was completed to assess any further changes in concentrations of DDT, DDE and DDD. Groundwater samples were collected in the vicinity of the soil remediation grid which provided DDT, DDE and DDD concentrations in groundwater to assess the vertical mobilization of the compounds. Mass balance of the "soil - groundwater" system was calculated in order to estimate the degradation rate of DDT within the remediation zone. The 2-D unsaturated/saturated flow and solute transport numerical model "HYDRUS 2-D" was used to gain a better estimation of DDT, DDE and DDD mass and distribution in groundwater. The effectiveness of cyclodextrin application for remediation of DDT contaminated soils was assessed. After remediation treatments had stopped, there was no indication of further degradation of DDT and its metabolites in the upper layer of soil. The groundwater concentration of DDT, DDE and DDD near the remediation grid was 10-100 times higher than background value. This increase in groundwater concentration is a direct indication of DDT, DDE and DDD mobilization by cyclodextrin. The estimates of total mass of DDT in groundwater are less than 1% of mass leached from the soil. It was concluded that the application of cyclodextrin promoted enhanced co-metabolic biodegradation of DDT and it metabolites DDE and DDD. The estimated half-life for the displaced DDT was less than 2 months. This work demonstrates that cyclodextrin can be a highly effective agent for remediation of DDT contaminated soils.<p> / Thesis / Master of Science (MSc)

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L'hexaclorobenzè (HCB) és un compost organoclorat àmpliament distribuït per tot el planeta, altament lipofílic que s'acumula als sistemes biològics. Els nounats s'exposen a aquests compostos organoclorats (OCs) a través de la placenta i de la lactància materna. Tot i que l'HCB és un dels OCs més comuns, la seva transferència a través de la placenta de la mare al fetus durant la gestació i a través de l'alletament matern està poc documentada. El coneixement sobre els seus possibles efectes sobre la salut infantil és també bastant limitat. A Flix, un poble de la Ribera d'Ebre, es van detectar nivells molt elevats d'HCB a l'atmosfera degut a la seva proximitat a una empresa electroquímica. Els objectius del present treball són els d'avaluar l'exposició a OCs a través de la placenta i de la lactància materna i els seus efectes sobre la salut infantil durant el primer any de vida en el conjunt de nounats d'aquesta població. / Hexachlorobenzene (HCB) is an organochlorine compound widely spread in the environment, highly lipophyilic which accumulates in all biological systems. Newborns are exposed to organochlorine compounds (OCs) through placenta and via breastfeeding. Although HCB is one of the most common OCs, its transference from the mother to the child through placenta and via breastfeeding is poorly documented. The knowledgement of the possible adverse effects on infant's health is also limited. In Flix, a small village in the Ribera d'Ebre area, high levels of HCB were detected in the atmosphere of the village due to the vicinity of an electrochemical factory. The objectives of the present study are to evaluate OCS exposition through placenta and breastfeeding and its effects on infant's health during the first year of life.