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Pharmacokinetics describes the movement and processing of a drug in a body, while Pharmacodynamics describes the drug's effect on a given subject. Pharmacokinetic/Pharmacodynamic(Pk/Pd) models have become a fundamental tool when predicting bacterial behavior and drug development. In November of 2009, Katsube et al. published their paper detailing their Pk/Pd model for the drug Doripenem and the bacteria P. aeruginosa. In their paper, they determined that there is a dependent relationship between the drug's effectiveness and the dosing strategy of the drug. Therefore, this thesis has applied optimal control in order to optimize the drug's effectiveness, while not burdening the subject with the side effects of the drug. Optimal Control is a mathematical tool used to balance two competing factors. As a result, it has become a useful tool used to make decisions involving complex behavior. By using Optimal Control, the model will maximize the drug's effect on the bacterial population of P. aeruginosa, while minimizing the drug concentration of Doripenem. In doing so, our research will enable doctors and clinicians to maximize a drug's effectiveness on the body, while minimizing side effects.
ContributorsSawkins, Bryan Thomas (Author) / Camacho, Erika (Thesis director) / Wirkus, Stephen (Committee member) / School of Mathematical and Natural Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Using object-oriented programming in MATLAB, a collection of functions, named Fourfun, has been created to allow quick and accurate approximations of periodic functions with Fourier expansions. To increase efficiency and reduce the number of computations of the Fourier transform, Fourfun automatically determines the number of nodes necessary for representations that are accurate to close to machine precision. Common MATLAB functions have been overloaded to keep the syntax of the Fourfun class as consistent as possible with the general MATLAB syntax. We show that the system can be used to efficiently solve several differential equations. Comparisons with Chebfun, a similar system based on Chebyshev polynomial approximations, are provided.
ContributorsMcleod, Kristyn Noelle (Author) / Platte, Rodrigo (Thesis director) / Gelb, Anne (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor)
Created2014-05
Description
The objective goal of this research is to maximize the speed of the end effector of a three link R-R-R mechanical system with constrained torque input control. The project utilizes MATLAB optimization tools to determine the optimal throwing motion of a simulated mechanical system, while mirroring the physical parameters and constraints of a human arm wherever possible. The analysis of this final result determines if the kinetic chain effect is present in the theoretically optimized solution. This is done by comparing it with an intuitively optimized system based on throwing motion derived from the forehand throw in Ultimate frisbee.
ContributorsHartmann, Julien (Author) / Grewal, Anoop (Thesis director) / Redkar, Sangram (Committee member) / Barrett, The Honors College (Contributor) / School of International Letters and Cultures (Contributor) / Mechanical and Aerospace Engineering Program (Contributor)
Created2022-05