Matching Items (29)
Description
A description of numerical and analytical work pertaining to models that describe the growth and progression of glioblastoma multiforme (GBM), an aggressive form of primary brain cancer. Two reaction-diffusion models are used: the Fisher-Kolmogorov-Petrovsky-Piskunov equation and a 2-population model that divides the tumor into actively proliferating and quiescent (or necrotic) cells. The numerical portion of this work (chapter 2) focuses on simulating GBM expansion in patients undergoing treatment for recurrence of tumor following initial surgery. The models are simulated on 3-dimensional brain geometries derived from magnetic resonance imaging (MRI) scans provided by the Barrow Neurological Institute. The study consists of 17 clinical time intervals across 10 patients that have been followed in detail, each of whom shows significant progression of tumor over a period of 1 to 3 months on sequential follow up scans. A Taguchi sampling design is implemented to estimate the variability of the predicted tumors to using 144 different choices of model parameters. In 9 cases, model parameters can be identified such that the simulated tumor contains at least 40 percent of the volume of the observed tumor. In the analytical portion of the paper (chapters 3 and 4), a positively invariant region for our 2-population model is identified. Then, a rigorous derivation of the critical patch size associated with the model is performed. The critical patch (KISS) size is the minimum habitat size needed for a population to survive in a region. Habitats larger than the critical patch size allow a population to persist, while smaller habitats lead to extinction. The critical patch size of the 2-population model is consistent with that of the Fisher-Kolmogorov-Petrovsky-Piskunov equation, one of the first reaction-diffusion models proposed for GBM. The critical patch size may indicate that GBM tumors have a minimum size depending on the location in the brain. A theoretical relationship between the size of a GBM tumor at steady-state and its maximum cell density is also derived, which has potential applications for patient-specific parameter estimation based on magnetic resonance imaging data.
ContributorsHarris, Duane C. (Author) / Kuang, Yang (Thesis advisor) / Kostelich, Eric J. (Thesis advisor) / Preul, Mark C. (Committee member) / Crook, Sharon (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2023
Description
\begin{abstract}The human immunodeficiency virus (HIV) pandemic, which causes the syndrome of opportunistic infections that characterize the late stage HIV disease, known as the acquired immunodeficiency syndrome (AIDS), remains a major public health challenge to many parts of the world. This dissertation contributes in providing deeper qualitative insights into the transmission dynamics and control of the HIV/AIDS disease in Men who have Sex with Men (MSM) community. A new mathematical model (which is relatively basic), which incorporates some of the pertinent aspects of HIV epidemiology and immunology and fitted using the yearly new case data of the MSM population from the State of Arizona, was designed and used to assess the population-level impact of awareness of HIV infection status and condom-based intervention, on the transmission dynamics and control of HIV/AIDS in an MSM community. Conditions for the existence and asymptotic stability of the various equilibria ofthe model were derived. The numerical simulations showed that the prospects for the effective control and/or elimination of HIV/AIDS in the MSM community in the United States are very promising using a condom-based intervention, provided the condom efficacy is high and the compliance is moderate enough. The model was extended in Chapter 3 to account for the effect of risk-structure, staged-progression property of HIV disease, and the use of pre-exposure prophylaxis (PrEP) on the spread and control of the disease. The model was shown to undergo a PrEP-induced \textit{backward bifurcation} when the associated control reproduction number is less than one. It was shown that when the compliance in PrEP usage is $50%(80%)$ then about $19.1%(34.2%)$ of the yearly new HIV/AIDS cases recorded at the peak will have been prevented, in comparison to the worst-case scenario where PrEP-based intervention is not implemented in the MSM community. It was also shown that the HIV pandemic elimination is possible from the MSM community even for the scenario when the effective contact rate is increased by 5-fold from its baseline value, if low-risk individuals take at least 15 years before they change their risky behavior and transition to the high-risk group (regardless of the value of the transition rate from high-risk to low-risk susceptible population).
ContributorsTollett, Queen Wiggs (Author) / Gumel, Abba (Thesis advisor) / Crook, Sharon (Committee member) / Fricks, John (Committee member) / Gardner, Carl (Committee member) / Nagy, John (Committee member) / Arizona State University (Publisher)
Created2023
Description
The concept of multi-scale, heterogeneous modeling is well-known to be central in the complexities of natural and built systems. Therefore, whole models that have parts with different spatiotemporal scales are preferred to those specified using a monolithic modeling approach and tightly integrated. To build simulation frameworks that are expressive and flexible, model composability is crucial where a whole model's structure and behavior traits must be concisely specified according to those of its parts and their interactions. To undertake the spatiotemporal model composability, a breast cancer cells chemotaxis exemplar is used. In breast cancer biology, the receptors CXCR4+ and CXCR7+ and the secreting CXCL12+ cells are implicated in spreading normal and malignant cells. As discrete entities, these can be modeled using Agent-Based Modeling (ABM). The receptors and ligand bindings with chemokine diffusion regulate the cells' movement gradient. These continuous processes can be modeled as Ordinary Differential Equations (ODE) and Partial Differential Equations (PDE). A customized, text-based BrSimulator exists to model and simulate this kind of breast cancer phenomenon. To build a multi-scale, spatiotemporal simulation framework supporting model composability, this research proposes using composable cellular automata (CCA) modeling. Toward this goal, the Cellular Automata DEVS (CA-DEVS) model is used, and the novel Composable Cellular Automata DEVS (CCA-DEVS) modeling is proposed. The DEVS-Suite simulator is extended to support CA and CCA Parallel DEVS models. This simulator introduces new capabilities for controlled and modular run-time animation and superdense time trajectory visualization. Furthermore, this research proposes using the Knowledge Interchange Broker (KIB) approach to model and simulate the interactions between separate geo-referenced CCA models developed using the DEVS and Modelica modeling languages. To demonstrate the proposed model composability approach and its use in the extended DEVS-Suite simulator, the breast cancer cells chemotaxis and others have been studied. The BrSimulator is used as a proxy for evaluating the proposed model composability approach using an integrated DEVS-Suite and OpenModelica simulator. Simulation experiments are developed that show the composition of spatiotemporal ABM, ODE, and PDE models reproduce the behaviors of the same model developed in the BrSimulator.
ContributorsZhang, Chao (Author) / Sarjoughian, Hessam S (Thesis advisor) / Crook, Sharon (Committee member) / Collofello, James (Committee member) / Pavlic, Theodore (Committee member) / Arizona State University (Publisher)
Created2021
Description
Ion channels in the membranes of cells in the body allow for the creation of action potentials from external stimuli, allowing us to sense our surroundings. One particular channel, TRPM8, is a trans-membrane ion channel believed to be the primary cold sensor in humans. Despite this important biological role and intense study of the channel, TRPM8 is not fully understood mechanistically and has not been accurately modeled. Existing models of TRPM8 fail to account for menthol activation of the channel. In this paper we re-implement an established whole cell model for TRPM8 with gating by both voltage and temperature. Using experimental data obtained from the Van Horn lab at Arizona State University, we refined the model to represent more accurately the dynamics of the human TRPM8 channel and incorporate the channel activation through menthol agonist binding. Our new model provides a large improvement over preexisting models, and serves as a basis for future incorporation of other channel activators of TRPM8 and for the modeling of other channels in the TRP family.
ContributorsAckerman, David (Author) / Crook, Sharon (Thesis director) / Van Horn, Wade (Committee member) / School of Earth and Space Exploration (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
The sport of Ultimate, formerly known as Ultimate Frisbee™, spread around the world in the mid-seventies and was considered an alternative sport that embraced a more casual atmosphere than other traditional, competitive sports. Ultimate is now receiving national and international attention as a competitive sport, with broadcasts of games on networks such as ESPN. As it transitions into a mainstream sport while attempting to maintain its alternative roots, it is possible that there are contrasting opinions between those who want to bring it further into the mainstream and those who want to maintain as much as possible of the original, alternative culture. In this work, we surveyed members of the Ultimate community for their perspectives on the unique culture of Ultimate.
Because the Ultimate community considers itself to be progressive, despite its largely Caucasian makeup, one topic of exploration was the political landscape of the Ultimate community. A second unique aspect of ultimate is the system for enforcing rules used by the players on the field, known as the spirit of the game. This system replaces referees and creates an ethical dynamic both during play and within the community that is not found in other sports. The last major topic of study here is the self-perception of the players as athletes. Because Ultimate continues to maintain a reputation as an alternative sport, athletes may perceive themselves differently than in more established sports.
When asked if Ultimate players perceived the Ultimate community as accepting of athletes who are people of color (POC) or members of the lesbian, gay, bisexual, or transgender community (LGBT), the community reported being accepting of all minorities. However, acceptance of POC athletes was rated significantly lower than the acceptance of LGBT athletes. When asked about comradery, the respondents rated comradery higher within the Ultimate community than in other sports. When asked how impartial players were in Ultimate compared to other sports, players with more experience tended to report perceiving themselves as more impartial. All demographics reported being more impartial in Ultimate than in other athletics. When asked about the seriousness of Ultimate, those who had not played another sport considered Ultimate to be more serious than those who had played another sport. In addition, players with more years of Ultimate experience also considered it to be more serious than those with fewer years of experience. Overall, additional studies on Ultimate culture are needed in order to obtain more viewpoints, as there is a lack of research in this field for comparison.
Because the Ultimate community considers itself to be progressive, despite its largely Caucasian makeup, one topic of exploration was the political landscape of the Ultimate community. A second unique aspect of ultimate is the system for enforcing rules used by the players on the field, known as the spirit of the game. This system replaces referees and creates an ethical dynamic both during play and within the community that is not found in other sports. The last major topic of study here is the self-perception of the players as athletes. Because Ultimate continues to maintain a reputation as an alternative sport, athletes may perceive themselves differently than in more established sports.
When asked if Ultimate players perceived the Ultimate community as accepting of athletes who are people of color (POC) or members of the lesbian, gay, bisexual, or transgender community (LGBT), the community reported being accepting of all minorities. However, acceptance of POC athletes was rated significantly lower than the acceptance of LGBT athletes. When asked about comradery, the respondents rated comradery higher within the Ultimate community than in other sports. When asked how impartial players were in Ultimate compared to other sports, players with more experience tended to report perceiving themselves as more impartial. All demographics reported being more impartial in Ultimate than in other athletics. When asked about the seriousness of Ultimate, those who had not played another sport considered Ultimate to be more serious than those who had played another sport. In addition, players with more years of Ultimate experience also considered it to be more serious than those with fewer years of experience. Overall, additional studies on Ultimate culture are needed in order to obtain more viewpoints, as there is a lack of research in this field for comparison.
ContributorsRandall, Sean Edward (Co-author) / Furey, Michael (Co-author) / Mebane, Tyler (Co-author) / Crook, Sharon (Thesis director) / Arrowsmith, Ramon (Committee member) / Simeone, Michael (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
Electrical stimulation can be used to activate peripheral nerve fibers to restore sensation to individuals with amputation and the technique is also being investigated as a means of treating a wide range of diseases. Longitudinal intrafascicular electrodes (LIFEs) are one of several types of electrodes that have been used to activate peripheral nerves. LIFEs can be used to activate small groups of fibers within a peripheral nerve fascicle, but the degree of their selectivity is uncertain. To investigate the effects of intrafascicular stimulation on nerve fiber activation, a mathematical, conductance-based model of an axon drawn from the literature was implemented and used to simulate the firing response of sensory nerve fibers in the presence of an applied monopolar electric field. Several axons were simulated to represent axons of different size, conductivity, spatial composition and location with respect to the electrode. Electric field profiles produced by pulses of different pulse widths and pulse amplitudes were created. Each fiber was placed within each resulting electric field and the firing threshold was determined. The effects of changes in pulse width, pulse amplitude, and distance on firing patterns were shown; all of these results were consistent with published experimental findings. The models showed lower firing threshold for smaller fibers than larger fibers and for fibers that were farther from the stimulating electrode than those that were closer. Firing threshold was also lower for stimuli of greater pulse width. Analysis of axon recruitment upon increases in pulse amplitude showed that the effects of fiber distance may be more pronounced than the effects of fiber size. This model can serve as a basis for further development to more accurately represent the effects of LIFEs and eventually may assist in the design of stimulation paradigms and waveforms to improve selectivity of axon activation when using LIFEs.
ContributorsSira, Alarmel (Author) / Abbas, James (Thesis director) / Crook, Sharon (Committee member) / Harrington Bioengineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
Dengue is a mosquito-borne arboviral disease that causes significant public health burden in many trophical and sub-tropical parts of the world (where dengue is endemic). This dissertation is based on using mathematical modeling approaches, coupled with rigorous analysis and computation, to study the transmission dynamics and control of dengue disease. In Chapter 2, a new deterministic model was designed and used to assess the impact of local fluctuation of temperature and mosquito vertical (transvasorial) transmission on the population abundance of dengue mosquitoes and disease in a population. The model, which takes the form of a deterministic system of nonlinear differential equations, was parametrized using data from the Chiang Mai province of Thailand. The disease-free equilibrium of the model was shown to be globally-asymptotically stable when a certain epidemiological quantity is less than unity. Vertical transmission was shown to only have marginal impact on the disease dynamics, and its effect is temperature-dependent. Dengue burden in the province is maximized when the mean monthly temperature lie in the range [26-28] C. A new deterministic model was designed in Chapter 3 to assess the impact of the release of Wolbachia-infected mosquitoes on curtailing the mosquito population and dengue disease in a population. The model, which stratifies the mosquito population in terms of sex and Wolbachia-infection status, was rigorously analysed to characterize the bifurcation property of the model as well as the asymptotic stability of the various disease-free equilibria. Simulations, using Wolbachia-based mosquito control from Queensland, Australia, showed that the frequent release of mosquitoes infected with the bacterium can lead to the effective control of the local wild mosquito population, and that such effective control increases with increasing number of Wolbachia-infected mosquitoes released (up to 90% reduction in the wild mosquito population, from their baseline values, can be achieved). It was also shown that the well-known feature of cytoplasmic incompatibility has very little effect on the effectiveness of the Wolbachia-based mosquito control.
ContributorsTaghikhani, Rahim (Author) / Gumel, Abba (Thesis advisor) / Crook, Sharon (Committee member) / Espanol, Malena (Committee member) / Kuang, Yang (Committee member) / Scotch, Matthew (Committee member) / Arizona State University (Publisher)
Created2020
Description
The representation of a patient’s characteristics as the parameters of a model is a key component in many studies of personalized medicine, where the underlying mathematical models are used to describe, explain, and forecast the course of treatment. In this context, clinical observations form the bridge between the mathematical frameworks and applications. However, the formulation and theoretical studies of the models and the clinical studies are often not completely compatible, which is one of the main obstacles in the application of mathematical models in practice. The goal of my study is to extend a mathematical framework to model prostate cancer based mainly on the concept of cell-quota within an evolutionary framework and to study the relevant aspects for the model to gain useful insights in practice. Specifically, the first aim is to construct a mathematical model that can explain and predict the observed clinical data under various treatment combinations. The second aim is to find a fundamental model structure that can capture the dynamics of cancer progression within a realistic set of data. Finally, relevant clinical aspects such as how the patient's parameters change over the course of treatment and how to incorporate treatment optimization within a framework of uncertainty quantification, will be examined to construct a useful framework in practice.
ContributorsPhan, Tin (Author) / Kuang, Yang (Thesis advisor) / Kostelich, Eric J (Committee member) / Crook, Sharon (Committee member) / Maley, Carlo (Committee member) / Bryce, Alan (Committee member) / Arizona State University (Publisher)
Created2021
Description
Non-invasive visualization of the trigeminal nerve through advanced MR sequences and methods like tractography is important for studying anatomical and microstructural changes due to pathology like trigeminal neuralgia (TN), facial dystonia, multiple sclerosis, and for surgical pre-planning. The use of specific anatomical markers from CT, MPRAGE and cranial nerve imaging (CRANI) sequences, enabled successful tractography of patient-specific trajectory of the frontal, nasociliary, infraorbital, and mandibular nerve branches extending beyond the cisternal brain stem region and leading to the face. Performance of MPRAGE sequence together with the advanced T2-weighted CRANI sequence with and without a gadolinium contrast agent, was studied to characterize identification efficiency in smaller nerve structures in the extremities. A large FOV nerve visualization exam inclusive of the anatomy of all trigeminal nerve distal branches can be obtained within an acquisition time of 20 minutes using pre-contrast CRANI and MPRAGE. Post-processing with MPR and MIP images improved nerve visualization.Transcranial electrical stimulation techniques (TES) have been used for the treatment of multiple neurodegenerative diseases. These techniques involve placing electrodes on the scalp with multiple peripheral branches of the trigeminal nerve crossing directly under that may be stimulated. This was studied through hybrid computational realistic axon models. These models also facilitated studying the effects of electrode drift during experiments on the recruitment of peripheral nerves. An optimal point of lowest threshold was found while displacing the nerve horizontally i.e., the activation thresholds of both myelinated and unmyelinated axons increased when the electrodes were displaced medially and decreased to a certain extend when the electrodes were displaced laterally, after which further lateral displacement led to increase of thresholds. Inclusion of unmyelinated axons in the modeling provided the capability of finding maximum stimulation amplitude below which side effects like pain sensation may be avoided. In the case of F3 – F4 electrode montage the maximum amplitude was 2.39 mA and in case of RS – LS montage the maximum amplitude was 2.44 mA. Such modeling studies may be useful for personalization of TES devices for finding optimal positioning of electrodes with respect to target and stimulation amplitude range that minimizes side effects.
ContributorsSahu, Sulagna (Author) / Sadleir, Rosalind (Thesis advisor) / Tillery, Stephen H (Committee member) / Crook, Sharon (Committee member) / Beeman, Scott (Committee member) / Abbas, James (Committee member) / Arizona State University (Publisher)
Created2023