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All Subjects: Mathematical Modeling
Creators: Caplan, Michael
Member of: Barrett, The Honors College Thesis/Creative Project Collection
Resource Type: Text

Diurnal Cycle Modeling of Nutrient Transport through the Intervertebral Disc to Prevent Future Degeneration after Transplantation

Description

The intervertebral disc goes through degenerative changes with age, which leads to disc thinning, bulging, or herniation. Spinal fusion treatments are ineffective as they cause quicker degeneration of adjacent discs and fail in nearly 20% of cases, so researchers have turned to tissue-engineering biocompatible intervertebral discs for transplantation. However novel and effective as this may seem, these transplanted discs still show evidence of degeneration after just 5 years. I hypothesize that these discs are degenerating due to a blockage of the cartilaginous endplates post-transplantation that is hindering nutrient transport through the intervertebral disc. In order to test this hypothesis, I developed a mathematical model of nutrient transport through the intervertebral disc in one diurnal daily loading cycle. This model was used to simulate open endplates and blocked endplates and then compare differences in nutrient concentration and nutrient transport to the center of the disc. Results from the math model simulations were then compared to in vitro experimental data collected in lab to verify the findings on a physiological level. Results showed significant differences, both in vitro and in the model, between nutrient transport in open endplates vs blocked endplates, lending support to the original hypothesis. This study only presents preliminary results, but could hold the key to preventing future disc degeneration post-transplantation.

ContributorsMunter, Bryce Taylor (Author) / Santello, Marco (Thesis director) / Caplan, Michael (Committee member) / Giers, Morgan (Committee member) / Barrett, The Honors College (Contributor) / Harrington Bioengineering Program (Contributor)

Created2015-05

Branching Worlds: Quantum Mechanics and Hugh Everett's Many-Worlds Interpretation

Description

This thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make up the framework of quantum physics. Through these concepts, we reveal why interpretations are necessary to map the quantum world onto our classical world. We then introduce the Copenhagen interpretation, and how many-worlds differs from it. From there, we dive into the concepts of entanglement and decoherence, explaining how worlds branch in an Everettian universe, and how an Everettian universe can appear as our classical observed world. From there, we attempt to answer common questions about many-worlds and discuss whether there are philosophical ramifications to believing such a theory. Finally, we look at whether the many-worlds interpretation can be proven, and why one might choose to believe it.

ContributorsSecrest, Micah (Author) / Foy, Joseph (Thesis director) / Hines, Taylor (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)

Created2021-05

Mathematical Assessment of the Impact of Insecticide-Based Intervention on Malaria Transmission Dynamics

Description

Malaria is a deadly, infectious, parasitic disease which is caused by Plasmodium parasites and transmitted between humans via the bite of adult female Anopheles mosquitoes. The primary insecticide-based interventions used to control malaria are indoor residual spraying (IRS) and long-lasting insecticide nets (LLINs). Larvicides are another insecticide-based intervention which is less commonly used. In this study, a mathematical model for malaria transmission dynamics in an endemic region which incorporates the use of IRS, LLINS, and larvicides is presented. The model is rigorously analyzed to gain insight into the asymptotic stability of the disease-free equilibrium. Simulations of the model show that individual insecticide-based interventions will not realistically control malaria in regions with high endemicity, but an integrated vector management strategy involving the use of multiple interventions could lead to the effective control of the disease. This study suggests that the use of larvicides alongside IRS and LLINs in endemic regions may be more effective than using only IRS and LLINs.

ContributorsJameson, Leah (Author) / Gumel, Abba (Thesis director) / Huijben, Silvie (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Civic & Economic Thought and Leadership (Contributor)

Created2022-05