Browsing by Author "Dr. Mette Olufsen, Committee Member"

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Determination of Impedance Boundary Conditions for the Pulmonary Vasculature
(2007-04-27) Clipp, Rachel Betany; Dr. Brooke N. Steele, Committee Chair; Dr. Carol Lucas, Committee Member; Dr. Mette Olufsen, Committee Member
Computational modeling can be used to achieve a better understanding of fluid analysis within the pulmonary circulation. Boundary conditions are used in fluid analysis to determine the pressure and flow profiles of the blood as it moves through the lung. Accurate boundary conditions are critical in providing accurate models of blood pressure and blood flow. An important consideration when determining boundary conditions for the pulmonary vasculature is the effect of respiration on the impedance of the pulmonary vasculature. An additional consideration for the pulmonary vasculature is the physiologic differences between the pulmonary circulation and that of the systemic circulation. This research determines impedance boundary conditions for the pulmonary vasculature that reflect the specific geometry of the lung and correspond to maximal inspiration and maximal expiration. The analysis was performed using an existing one-dimensional finite element analysis system. The boundary conditions were defined by a bifurcating structure tree with a number of variables that were used to change the resistance of the pulmonary vessels. The variables within the structure tree were altered to reflect the differences between the pulmonary circulation and the systemic circulation. These variables include the length to radius ratio of the vessels in the structure tree and the asymmetry as the branches. A respiration factor was used to scale the vessels of the structure tree to reflect the effects of respiration on the geometry of the lung. The compliance of the vessels was also changed to reflect the more distensible vessels found in the pulmonary system. The geometry of the lung was defined with the structured tree parameters at maximal inspiration and the respiration factor was used to scale the defined geometry and reflect maximal expiration. The parameters were determined by utilizing an optimization technique. The Levinberg-Marquardt least-squares non-linear optimization algorithm was used to find a set of non-unique optimal parameters. The computed data was validated using measured pressure and flow data collected in a previous study.
Partial Differential Equations of Thin Liquid Films: Analysis and Numerical Simulation
(2005-07-26) Levy, Rachel; Dr. Tom Witelski, Committee Member; Dr. Mette Olufsen, Committee Member; Dr. Michael Shearer, Committee Chair; Dr. Alina Chertock, Committee Member
We consider four problems related to Marangoni-driven thin liquid films. The first compares two models for the motion of a contact line: the precursor model and the Navier slip model. We restrict attention to traveling wave solutions of the thin film PDE for a film driven up an inclined planar solid surface by a thermally induced surface tension gradient. The range of effective contact slopes and parameter values are explained with the aid of Poincaré sections of the phase diagram of the third order ODE. In the second problem, we use theory from hyperbolic conservation laws to map classical shocks, nonclassical shock waves (known as undercompressive shocks) and rarefactions that arise as solutions to the Cauchy problem. To create such a 'Riemann map', we employ a kinetic relation that describes admissible nonclassical shock waves, and a nucleation condition that determines when a nonclassical solution is selected. The hyperbolic theory captures features observed in thin film flow, such as multiple long-time solutions for the same initial upstream and downstream states. The third problem incorporates localized heating by an infrared (IR) laser to the model of a Marangoni-driven thin film from the previous problems. We analyze two types of steady state solutions, using a dynamical systems approach to explain homoclinic solutions and PDE simulations to explain heteroclinic solutions. We discuss several methods for controlling the downstream height and the strength of forcing required to create homoclinic solutions from uniform or monotonic initial data. The fourth problem explores a model for a different physical scenario, in which a thin film is driven down a solid substrate by gravity and surfactant. The model couples the thin film PDE for the height of the film with an equation for the transport of surfactant. Solutions of the parabolic-hyperbolic system include a complicated [em double wave solution], with discontinuities in the height and surfactant concentration gradient. Agreement of analytical solutions with data from numerical simulations indicates that we have successfully modeled long-time wave structures.
Physiologically Based Model Development and Parameter Estimation: Benzene Dosimetry in Humans and Respiratory Irritation Response in Rodents
(2005-07-11) Yokley, Karen Alyse; Dr. Hien Tran, Committee Chair; Dr. Mette Olufsen, Committee Member; Dr. Paul Schlosser, Committee Member; Dr. James Selgrade, Committee Member
One can form mathematical equations based on a combination of chemistry, physics, and biological information to represent a physiological system. Once a model is formulated based on the physiological system, we must make sure that the inputs or parameters to the model also faithfully represent the system. In this study, we adapt and combine existing mathematical models to describe different physiological systems. Benzene is myelotoxic and causes leukemia in humans when they are exposed to high doses by inhalation (<1 ppm) for extended periods; however, leukemia risks in humans at lower exposures are uncertain. Benzene occurs widely in the work environment and in outdoor air, although mostly at concentrations below 1 ppm. Hence, we recognize the importance of assessing the risk to humans when they are exposed to benzene at low concentrations. In Chapter 2, we describe a physiologically based pharmacokinetic (PBPK) model for the uptake and elimination of benzene in humans to relate the concentration of inhaled benzene to the tissue doses of benzene and its key metabolites, benzene oxide, phenol, and hydroquinone. To account for variability among humans, the mathematical model must be integrated into a statistical framework that acknowledges sources of variation in the data due to inherent intra- and inter-individual variation, measurement error, and other data collection issues. The main contribution of Chapter 2 is the estimation of population distributions of key PBPK model parameters. In particular, a Markov Chain Monte Carlo (MCMC) technique is employed to fit the mathematical model to two data sets, thereby updating the estimated parameter distributions. We first considered only variability in metabolic parameters, as observed in previous in vitro studies, but found that it was not sufficient to explain observed variability in benzene pharmacokinetics. Variability in physiological parameters, such as organ weights, must also be included to faithfully predict the observed human population variability. Inhaled gases can also cause respiratory depression by irritating (stimulating) nerves in the nasal cavity. In order to better understand how the nervous system responds to such chemicals, we have created a model to describe how the presence of irritants affects respiration in the rat. By combining and adapting two previous models, one that evaluates the relationship between inhaled acrylic acid vapor concentration and the tissue concentration in various regions of the nasal cavity and another model which describes the baroreflex-feedback mechanism regulating human blood pressure, we created a system of equations that models the sensory irritant response in rats. The adapted model in Chapter 3 focuses on the dosimetry of these reactive gases in the respiratory tract, with particular focus on the physiology of the upper respiratory tract, and on the neurological control of respiration rate due to signaling from the irritant-responsive nerves in the nasal cavity. Further, the model is evaluated and improved through optimization of particular parameters to describe formaldehyde-induced respiratory response data and through sensitivity analysis. The model in Chapter 3 describes this formaldehyde data well and is expected to translate well to other irritants.