Ordinary Differential Equations and Applied Dynamics Commons^™

Application Of Symplectic Integration On A Dynamical System, William Frazier

Electronic Theses and Dissertations

Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic …

A Physiologically-Based Pharmacokinetic Model For The Antibiotic Levofloxacin, Paezha M. Mccartt

Undergraduate Honors Theses

Levofloxacin is in a class of antibiotics known as fluoroquinolones, which treat infections by killing the bacteria that cause them. A physiologically-based pharmacokinetic (PBPK) model was developed to investigate the uptake, distribution, and elimination of Levofloxacin after a single dose. PBPK modeling uses parameters such as body weight, blood flow rates, partition coefficients, organ volumes, and several other parameters in order to model the distribution of a particular drug throughout the body. Levofloxacin is only moderately bound in human blood plasma, and, thus, for the purposes of this paper, linear bonding is incorporated into the model because the free or …

A Physiologically-Based Pharmacokinetic Model For Vancomycin, Rebekah White

Undergraduate Honors Theses

Vancomycin is an antibiotic used for the treatment of systemic infections. It is given

intravenously usually every twelve or twenty-four hours. This particular drug has a

medium level of boundedness, with approximately fty percent of the drug being free

and thus physiologically eective. A physiologically-based pharmacokinetic (PBPK)

model was used to better understand the absorption, distribution, and elimination of

the drug. Using optimal parameters, the model could be used in the future to test

how various factors, such as BMI or excretion levels, might aect the concentration

of the antibiotic.

Comparison Of Two Parameter Estimation Techniques For Stochastic Models, Thomas C. Robacker

Electronic Theses and Dissertations

Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a …