Browsing by Author "John Franke, Committee Member"

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Acute Inflammatory Response to Endotoxin Challenge: Model Development, Parameter Estimation, and Treatment Control.
(2010-08-03) Frank, Dennis; Hien Tran, Committee Chair; Stephen Campbell, Committee Member; Negash Medhin, Committee Member; John Franke, Committee Member
Differential Equation Models for the Hormonal Regulation of the Menstrual Cycle
(2002-04-24) Harris, Leona Ann; James F. Selgrade, Committee Chair; Sharon Lubkin, Committee Member; John Franke, Committee Member; Paul Schlosser, Committee Member
There are growing concerns about the effects of environmental substances on the sexual endocrine system. It is believed that estrogenic substances may disrupt the sexual endocrine system by initiating or promoting such adverse effects as cancer, developmental disorders, and the reduction of fertility [17,40]. While these effects appear to be more imminent during high levels of exposure to estrogenic substances, concerns are increasing because low levels of exposure to estrogenic substances occur more frequently for longer periods of time; in our diets (phytoestrogens), in the environment (pesticides), and in contraception (spermicides and birth control pills) and hormonal therapies [17,40]. These effects might have a profound effect on the menstrual cycle. Therefore, mathematical models that accurately predict the serum levels of hormones that control the menstrual cycle would be useful tools in evaluating the effects of environmental substances. The human menstrual cycle is controlled by the pituitary hormones, luteinizing hormone (LH) and follicle-stimulating hormone (FSH), and the ovarian hormones, estradiol, progesterone, and inhibin. The pituitary hormones stimulate the growth of ovarian follicles that secrete hormones and work to produce a fertilized ovum. The mathematical models to be presented in this work predict the blood levels of these five hormones as they interact to regulate and maintain the menstrual cycle. The unmerged model has a pituitary component and an ovarian component consisting of linear systems of ordinary differential equations with time dependent coefficients. The pituitary systems describe the synthesis, release, and clearance of LH and FSH during the menstrual cycle, based on their response to estradiol, progesterone, and inhibin. Functions representing the ovarian hormones are used as inputs into these systems. The ovarian system describes the roles of FSH and LH in the development of ovarian follicles and the production of estradiol, progesterone, and inhibin during the menstrual cycle. Functions representing the pituitary hormones are used as inputs into this system. The merged model is formed by merging the pituitary and ovarian systems together. The merged system is a highly nonlinear system of delay differential equations that describes the interactions between the five hormones throughout the menstrual cycle. This model predicts reasonably accurate blood levels of these hormones observed in normally cycling women as reported in the literature. The merged system is shown to have two stable periodic solutions for the same parameter set, a large amplitude solution that fits data found in the literature for normally cycling women and a small amplitude solution arising from Hopf bifurcation in the system parameters. The small amplitude cycle possesses many similarities to the menstrual cycle disorder referred to as polycystic ovarian syndrome (PCOS). Hormonal treatments for this abnormality are simulated and the large amplitude cycle fitting the data for normally cycling women is successfully recovered. In addition, simulations of exogenous estrogen exposure show that the large amplitude cycle can be perturbed into the small amplitude cycle. Therefore, in this modeling environment, an exogenous estrogen input disrupts the normal menstrual cycle.
Methods to Alleviate Processing Requirements of High-Fidelity Multibody Parachute Simulations Involving a Confluence Mass
(2009-11-16) Fuller, John D; Fred DeJarnette, Committee Co-Chair; Robert Tolson, Committee Chair; John Franke, Committee Member
Methods designed to reduce the numerical stiffness and processing requirements of high fidelity entry trajectory models involving parachutes are explored. Parachute deployment systems have often been simulated using rigid body dynamic models. The system is comprised of a parachute rigid body attached to the vehicle via a confluence mass with flexible lines. The simulations incorporating the confluence mass often take excessive amounts of processing time due to the relatively small mass of the confluence point and the resulting high frequency motion. The two methods investigated here seek to simplify the equations of motion to be integrated in the simulation, removing the numerical stiffness and increasing the required time step. Initially an analytic solution is derived from previous work on the subject and is used to linearize the confluence point equations of motion about an equilibrium point. The motion of the confluence point about the equilibrium point can then be reduced to that of a simple harmonic oscillator, resolved analytically and averaged over a larger time step than required for integration of the original set of equations of motion. This procedure allows the removal of the equations of motion of the confluence mass from the system, replacing them with analytic solutions for its position and velocity. The numerically stiff portion of the simulation is thus removed, significantly improving processing time. The second method developed is entitled the singular perturbation method, and involves suppressing the small inertia of the confluence mass responsible for high frequency motion. The singularly perturbed system allows simplification of the equations of motion by removing the confluence point velocity state equations. The velocity state vector may be estimated by taking the limit of the equations of motion of the confluence point as its mass approaches zero. The stiffness of the equations is again removed, thereby increasing the integration time step and decreasing overall processing time. The singular perturbation method is applied to parachute entry models of the Mars Exploration Rover mission as well as the Crew Exploration Vehicle abort mode. Results from both methods are compared to models in which a confluence point with mass is used with integration of the full set of equations of motion. Performance is evaluated in each case by way of comparing integration time step to measure the benefits of application of the methods. Necessary assumptions and the resulting implications for each approach are defined and evaluated to assess the convenience and application of the methods.
Vision based Control of Autonomous Vehicle Navigation.
(2010-08-18) Gupta, Rachana Ashok; Mo-Yuen Chow, Committee Chair; Wesley Snyder, Committee Chair; James Brickley, Committee Member; John Franke, Committee Member