Doctor of Philosophy
Dr. Angela Reynolds
Mathematical models apply to a multitude physiological processes and are used to make predictions and analyze outcomes of these processes. Specifically, in the medical field, a mathematical model uses a set of initial conditions that represents a physiological state as input and a set of parameter values are used to describe the interaction between variables being modeled. These models are used to analyze possible outcomes, and assist physicians in choosing the most appropriate treatment options for a particular situation. We aim to use mathematical modeling to analyze the dynamics of processes involved in the inflammatory process.
First, we create a model of hematopoiesis, the processes of creating new blood cells. We analyze stem cell collection regimens and statistically sample parameter space in order to create a model accounts for the dynamics of multiple patients. Next, we modify an existing model of the wound healing response by introducing a variable for two inflammatory cell types. We analyze the timing of the inflammatory response and introduce the presence of systemic estrogen in the model, as there is evidence that the presence of estrogen leads to a more efficient wound healing response. Last, we mathematically model the gas exchange process in the lungs and body in order to lay the foundation for a model of the inflammatory response in the lung under conditions of mechanical ventilation. We introduce normal and ventilation breathing waveforms and a third state of hemoglobin in a closed loop partial differential equations model. We account for gas exchange in the lung and body compartments in addition to introducing a third discretized well-mixing compartment between the two.
We use ordinary and partial differential equations to model these systems over one or more independent variables, as well as classical analysis techniques and computational methods to analyze systems. Statistical sampling is also used to investigate parameter values in order for the mathematical models developed to account for patient-to-patient variability. This alters the traditional mathematical model, which yields a single set of parameter values that represent one instance of the physiology, into a mathematical model that accounts for many different instances of physiology.}
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Available for download on Wednesday, May 12, 2021