The goal of many human disease-oriented studies is to detect molecular mechanisms different between healthy controls and patients. Yet, commonly used gene expression measurements from any tissues suffer from variability of cell composition. This variability hinders the detection of differentially expressed genes and is often ignored. However, this variability may actually be advantageous, as heterogeneous gene expression measurements coupled with cell counts may provide deeper insights into the gene expression differences on the cell type-specific level. Published computational methods use linear regression to estimate cell type-specific differential expression. Yet, they do not consider many artifacts hidden in high-dimensional gene expression data that may negatively affect the performance of linear regression. In this dissertation we specifically address the parameter space involved in the most rigorous use of linear regression to estimate cell type-specific differential expression and report under which conditions significant detection is probable. We define parameters affecting the sensitivity of cell type-specific differential expression estimation as follows: sample size, cell type-specific proportion variability, mean squared error (spread of observations around linear regression line), conditioning of the cell proportions predictor matrix, and the size of actual cell type-specific differential expression. Each parameter, with the exception of cell type-specific differential expression (effect size), affects the variability of cell type-specific differential expression estimates. We have developed a power-analysis approach to cell type by cell type and genomic site by site differential expression detection which relies upon Welch’s two-sample t-test and factors in differences in cell type-specific expression estimate variability and reduces false discovery. To this end we have published an R package, LRCDE, available in GitHub (http://www.github.com/ERGlass/lrcde.dev) which outputs observed statistics of cell type-specific differential expression, including two-sample t- statistic, t-statistic p-value, and power calculated from two-sample t-statistic on a genomic site- by-site basis.

Inflammation in the lungs can occur for many reasons, from bacterial infections to stretch by mechanical ventilation. In this work we compare and contrast various mathematical models for lung injuries in the categories of acute infection, latent versus active infection, and particulate inhalation. We focus on systems of ordinary differential equations (ODEs), agent-based models (ABMs), and Boolean networks. Each type of model provides different insight into the immune response to damage in the lungs. This knowledge includes a better understanding of the complex dynamics of immune cells, proteins, and cytokines, recommendations for treatment with antibiotics, and a foundation for more well-informed experiments and clinical trials. In each chapter, we provide an in-depth analysis of one model and summaries of several others. In this way we gain a better understanding of the important aspects of modeling the immune response to lung injury and identify possible points for future research.

The complexity of the interface between the muscular system and the nervous system is still elusive. We investigated how the neuromuscular system functions and how it is influenced by various perturbations. Postural stability was selected as the model system, because this system provides complex output, which could indicate underlying mechanisms and feedback loops of the neuromuscular system. We hypothesized that aging, physical pain, and mental and physical perturbations affect balancing strategy, and based on these observations, we constructed a model that simulates many aspects of the neuromuscular system. Our results show that aging changes the control strategy of balancing from more chaotic to more repetitive. The chaotic elements ensure quick reactions and strong capacity to compensate for the perturbations; this adeptly reactive state changes into a less reactive, slower, probably less mechanically costly balancing strategy. Mental tasks during balancing also decreased the chaotic elements in balancing strategy, especially if the subject experienced chronic pain. Additional motoric tasks, such as tying knots while balancing, were correlated with age but unaffected by chronic pain. Our model competently predicted the experimental findings, and we proceeded to use the model with an external data set from Physionet to predict the balancing strategy of Parkinson’s patients. Our neurological model, comprised of RLC circuits, provides a mechanistic explanation for the neuromuscular system adaptations.

Carbon monoxide (CO) is an odorless, colorless, tasteless gas that binds to hemoglobin with high affinity. This property underlies the use of low doses of CO to determine hemoglobin mass (MHb) in the fields of clinical and sports medicine. However, hemoglobin bound to CO is unable to transport oxygen and exposure to high CO concentrations is a significant environmental and occupational health concern. These contrasting aspects of CO—clinically useful in low doses but potentially lethal in higher doses—mandates a need for a quantitative understanding of the temporal profiles of the uptake and distribution of CO in the human body. In this dissertation I have (i) used a mathematical model to analyze CO-rebreathing techniques used to estimate total hemoglobin mass and proposed a CO-rebreathing procedure to estimate hemoglobin mass with low errors, (ii) enhanced and validated a multicompartment model to estimate O2, CO and CO2 tensions, bicarbonate levels, pH levels, blood carboxyhemoglobin (HbCO) levels, and carboxymyoglobin (MbCO) levels in all the vascular (arterial, mixed venous and vascular subcompartments of the tissues) and tissue (brain, heart and skeletal muscle) compartments of the model in normoxia, hypoxia, CO hypoxia, hyperoxia, isocapnic hyperoxia and hyperbaric oxygen, and (iii) used this developed mathematical model to propose a treatment to improve O2 delivery and CO removal by comparing O2 and CO levels during different treatment protocols administered for otherwise-healthy CO-poisoned subjects.

BACKGROUND: Several studies have demonstrated the association between the time to hypertension event and multiple baseline measurements for adults, yet other survival cardiovascular disease (CVD) outcomes such as high cholesterol and heart attack have been somewhat less considered. The Fels Longitudinal Study (FLS) provides us an opportunity to connect adult blood pressure (BP) at certain ages to the time to first CVD outcomes. The availability of long-term serial BP measurements from FLS also potentially allows us to evaluate if the trend of the measured BP biomarkers over time predicts survival outcomes in adulthood through statistical modeling. METHODS: When the reference standard is right-censored time-to-event (survival) outcome, the C index or concordance C, is commonly used as a summary measure of discrimination between a survival outcome that is possibly right censored and a predictive-score variable, say, a measured biomarker or a composite-score output from a statistical model that combines multiple biomarkers. When we have subjects longitudinally followed up, it is of primary interest to assess if some baseline measurements predict the time-to-event outcome. Specifically, in this study, systolic blood pressure, diastolic blood pressure, as well as their variation over time, are considered predictive biomarkers, and we assess their predictive ability for certain time-to-event outcomes in terms of the C index. RESULTS: There are a few summary C index differences that are statistically significant in predicting and discriminating certain CVD metric at certain age stage, though some of these differences are altered in the presence of medicine treatment and lifestyle characteristics. The variation of systolic BP measures over time has a significantly different predicting ability comparing with systolic BP measures at certain given time point, for predicting certain survival outcome such as high cholesterol level. CONCLUSIONS: Adult systolic and diastolic BP measurements may have significantly different ability in predicting time to first CVD events. The fluctuation of BP measurements over time may have better association than BP measurement at a single baseline time point, with the time to first CVD events.

For this project, we use a modified version of a previously developed mathematical model, which describes the relationships among matrix metalloproteinases (MMPs), their tissue inhibitors (TIMPs), and extracellular matrix (ECM). Our ultimate goal is to quantify and understand differences in parameter estimates between patients in order to predict future responses and individualize treatment for each patient. By analyzing parameter confidence intervals and confidence and prediction intervals for the state variables, we develop a parameter space reduction algorithm that results in better future response predictions for each individual patient. Moreover, use of another subset selection method, namely Structured Covariance Analysis, that considers identifiability of parameters, has been included in this work. Furthermore, to estimate parameters more efficiently and accurately, the standard error (SE- )optimal design method is employed, which calculates optimal observation times for clinical data to be collected. Finally, by combining different parameter subset selection methods and an optimal design problem, different cases for both finding optimal time points and intervals have been investigated.

Blood coagulation is a series of biochemical reactions that take place to form a blood clot. Abnormalities in coagulation, such as under-clotting or over- clotting, can lead to significant blood loss, cardiac arrest, damage to vital organs, or even death. Thus, understanding quantitatively how blood coagulation works is important in informing clinical decisions about treating deficiencies and disorders. Quantifying blood coagulation is possible through mathematical modeling. This review presents different mathematical models that have been developed in the past 30 years to describe the biochemistry, biophysics, and clinical applications of blood coagulation research. This review includes the strengths and limitations of models, as well as suggestions for future work.

<p>Regardless of their origin or pathology, many, if not all, diseases have long been regarded as complex. Yet, despite the progression in the understanding of complexity and the development of systems biology, the majority of biomedical research has been derived from qualitative principles. In comparison to the ethical, temporal and logistical limitations of human experimentation, <em>in vivo</em> animal models have served to provide a more advantageous means to elucidate the underlying disease mechanisms. However, given the additional limitations presented by such models, <em>in silico </em>models have emerged as an effective complement, and, in some cases, a replacement for <em>in vivo</em> experimentation. The <em>in silico </em>models presented in this thesis were developed using mathematical and computational methods to investigate the evolution of two complex, diverse diseases from a systems biology perspective: allergic asthma and cancer.</p> <p>We generated two novel <em>in silico</em> models of allergic asthma aimed at clarifying some dynamic aspects of allergic responses. Experimentally, we utilized an <em>in vivo</em> murine model of chronic exposure to the most pervasive aeroallergen worldwide, house dust mite (HDM), for up to 20 weeks, equivalent to at least 20 human years. Using a range of HDM concentrations, experimental data were collected to study local and systemic effects. The first model applied empirical mathematical techniques to establish equations for airway inflammation and HDM-specific immunoglobulins using an iterative approach of experimentation and validation. Using the equations generated, we showed that the model was able to accurately predict and simulate data. The model also demonstrated the non-linear relationship between HDM exposure and both airway inflammation and allergic sensitization and identified system thresholds.</p> <p>The second model used mechanistic mathematical techniques to investigate the trafficking of eosinophils as they migrated from bone marrow to the blood and, ultimately, to the lungs. Making use of a limited data set, the model determined the effect of individual processes on the system. We identified eosinophil production, survival and death as having the greatest impacts, while migration played a relatively minor role. Furthermore, the model was used to simulate knockout models and the use of antibodies <em>in silico</em>.</p> <p>In the context of cancer growth and metastasis, we developed a theoretical model demonstrating the spatio-temporal development of a tumour in two-dimensions. The model was encoded to create a computer graphic simulation program, which simulated the effects of various parameters on the size and shape of a tumour. Through simulations, we demonstrated the importance of the diffusion process in cancer growth and metastasis.</p> <p>Ultimately, we believe the greatest benefit of each <em>in silico</em> model is the ability to provide an understanding of each respective disease recognized as dynamic and formally complex, but predominantly studied in reductionist, static or un-integrated approaches.</p> / Doctor of Philosophy (Medical Science)