Search Content

A Mathematical Model of Cell Confluency In Vitro

Description

Cellular and molecular biologists often perform cellular assays to obtain a better understanding of how cells work. However, in order to obtain a measurable response by the end of an experiment, the cells must reach an ideal cell confluency. Prior to conducting the cellular assays, range-finding experiments need to be…

Cellular and molecular biologists often perform cellular assays to obtain a better understanding of how cells work. However, in order to obtain a measurable response by the end of an experiment, the cells must reach an ideal cell confluency. Prior to conducting the cellular assays, range-finding experiments need to be conducted to determine an initial plating density that will result in this ideal confluency, which can be costly. To help alleviate this common issue, a mathematical model was developed that describes the dynamics of the cell population used in these experiments. To develop the model, images of cells from different three-day experiments were analyzed in Photoshop®, giving a measure of cell count and confluency (the percentage of surface area covered by cells). The cell count data were then fitted into an exponential growth model and were correlated to the cell confluency to obtain a relationship between the two. The resulting mathematical model was then evaluated with data from an independent experiment. Overall, the exponential growth model provided a reasonable and robust prediction of the cell confluency, though improvements to the model can be made with a larger dataset. The approach used to develop this model can be adapted to generate similar models of different cell-lines, which will reduce the number of preliminary range-finding experiments. Reducing the number of these preliminary experiments can save valuable time and experimental resources needed to conduct studies using cellular assays.

ContributorsGuerrero, Victor Dominick (Co-author) / Guerrero, Victor (Co-author) / Watanabe, Karen (Thesis director) / Jurutka, Peter (Committee member) / School of Mathematical and Natural Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)

Created2020-05

Modeling the Dynamics of Heroin and Illicit Opioid Use Disorder, Treatment, and Recovery

Description

A leading crisis in the United States is the opioid use disorder (OUD) epidemic. Opioid overdose deaths have been increasing, with over 100,000 deaths due to overdose from April 2020 to April 2021. This dissertation presents two mathematical models to address illicit OUD (IOUD), treatment, and recovery within an epidemiological…

A leading crisis in the United States is the opioid use disorder (OUD) epidemic. Opioid overdose deaths have been increasing, with over 100,000 deaths due to overdose from April 2020 to April 2021. This dissertation presents two mathematical models to address illicit OUD (IOUD), treatment, and recovery within an epidemiological framework. In the first model, individuals remain in the recovery class unless they relapse. Due to the limited availability of specialty treatment facilities for individuals with OUD, a saturation treat- ment function was incorporated. The second model is an extension of the first, where a casual user class and its corresponding specialty treatment class were added. Using U.S. population data, the data was scaled to a population of 200,000 to find parameter estimates. While the first model used the heroin-only dataset, the second model used both the heroin and all-illicit opioids datasets. Backward bifurcation was found in the first IOUD model for realistic parameter values. Additionally, bistability was observed in the second IOUD model with the heroin-only dataset. This result implies that it would be beneficial to increase the availability of treatment. An alarming effect was discovered about the high overdose death rate: by 2038, the disease-free equilibrium would be the only stable equilibrium. This consequence is concerning because although the goal is for the epidemic to end, it would be preferable to end it through treatment rather than overdose. The IOUD model with a casual user class, its sensitivity results, and the comparison of parameters for both datasets, showed the importance of not overlooking the influence that casual users have in driving the all-illicit opioid epidemic. Casual users stay in the casual user class longer and are not going to treatment as quickly as the users of the heroin epidemic. Another result was that the users of the all-illicit opioids were going to the recovered class by means other than specialty treatment. However, the relapse rates for those individuals were much more significant than in the heroin-only epidemic. The results above from analyzing these models may inform health and policy officials, leading to more effective treatment options and prevention efforts.

ContributorsCole, Sandra (Author) / Wirkus, Stephen (Thesis advisor) / Gardner, Carl (Committee member) / Lanchier, Nicolas (Committee member) / Camacho, Erika (Committee member) / Fricks, John (Committee member) / Arizona State University (Publisher)

Created2022

Four-Dimensional Geometry Visualization in Augmented Reality

Description

This project aims to propose a novel approach for visualizing 4D geometry through the utilization of augmented reality (AR). While previous work has explored virtual reality (VR) as a means to bring 4D objects into a 3D environment, as well as 2D projections to display 4D geometry on screens, this…

This project aims to propose a novel approach for visualizing 4D geometry through the utilization of augmented reality (AR). While previous work has explored virtual reality (VR) as a means to bring 4D objects into a 3D environment, as well as 2D projections to display 4D geometry on screens, this project seeks to extend the possibilities by leveraging the immersive nature of AR technology. By overlaying virtual 4D objects onto the real world, users can experience a more tangible representation and gain a deeper understanding of the complex structures present in higher dimensions.

ContributorsHum, Aaron (Author) / Nishimura, Joel (Thesis director) / Wang, Haiyan (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Natural Sciences (Contributor)

Created2023-05

A Mathematical Analysis of a Model of Adderall Abuse

Description

Adderall remains to be one of the most commonly abused drug among college campuses. Although it is a prescription drug that is primarily used to treat attention deficit hyperactivity disorder (ADHD), it has become one of the many "study drugs" due to its usage among college students during stressful school…

Adderall remains to be one of the most commonly abused drug among college campuses. Although it is a prescription drug that is primarily used to treat attention deficit hyperactivity disorder (ADHD), it has become one of the many "study drugs" due to its usage among college students during stressful school times, such as exams, where increased concentration and energy levels are thought to improve work efficiency. However, Adderall is notable for having a high potential for abuse and a risk of psychological and physical side effects. In this paper, we conducted a mathematical analysis on an existing epidemiological model of Adderall abuse. We started by verifying the positivity of solutions using techniques from dynamical systems because this is a population model dealing with people. Then, we found and investigated different equilibrium solutions to analyze their stability using both analytical and graphical approaches. Finally, the results were tied back into the Adderall model and conclusions were drawn.

ContributorsKerseg, Cassidy (Author) / Wirkus, Stephen (Thesis director) / Brager, Danielle (Committee member) / School of Mathematical and Natural Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)

Created2021-05