Matching Items (158)
Description
Cancer is a major health problem in the world today and is expected to become an even larger one in the future. Although cancer therapy has improved for many cancers in the last several decades, there is much room for further improvement. Mathematical modeling has the advantage of being able to test many theoretical therapies without having to perform clinical trials and experiments. Mathematical oncology will continue to be an important tool in the future regarding cancer therapies and management.
This dissertation is structured as a growing tumor. Chapters 2 and 3 consider spheroid models. These models are adept at describing 'early-time' tumors, before the tumor needs to co-opt blood vessels to continue sustained growth. I consider two partial differential equation (PDE) models for spheroid growth of glioblastoma. I compare these models to in vitro experimental data for glioblastoma tumor cell lines and other proposed models. Further, I investigate the conditions under which traveling wave solutions exist and confirm numerically.
As a tumor grows, it can no longer be approximated by a spheroid, and it becomes necessary to use in vivo data and more sophisticated modeling to model the growth and diffusion. In Chapter 4, I explore experimental data and computational models for describing growth and diffusion of glioblastoma in murine brains. I discuss not only how the data was obtained, but how the 3D brain geometry is created from Magnetic Resonance (MR) images. A 3D finite-difference code is used to model tumor growth using a basic reaction-diffusion equation. I formulate and test hypotheses as to why there are large differences between the final tumor sizes between the mice.
Once a tumor has reached a detectable size, it is diagnosed, and treatment begins. Chapter 5 considers modeling the treatment of prostate cancer. I consider a joint model with hormonal therapy as well as immunotherapy. I consider a timing study to determine whether changing the vaccine timing has any effect on the outcome of the patient. In addition, I perform basic analysis on the six-dimensional ordinary differential equation (ODE). I also consider the limiting case, and perform a full global analysis.
This dissertation is structured as a growing tumor. Chapters 2 and 3 consider spheroid models. These models are adept at describing 'early-time' tumors, before the tumor needs to co-opt blood vessels to continue sustained growth. I consider two partial differential equation (PDE) models for spheroid growth of glioblastoma. I compare these models to in vitro experimental data for glioblastoma tumor cell lines and other proposed models. Further, I investigate the conditions under which traveling wave solutions exist and confirm numerically.
As a tumor grows, it can no longer be approximated by a spheroid, and it becomes necessary to use in vivo data and more sophisticated modeling to model the growth and diffusion. In Chapter 4, I explore experimental data and computational models for describing growth and diffusion of glioblastoma in murine brains. I discuss not only how the data was obtained, but how the 3D brain geometry is created from Magnetic Resonance (MR) images. A 3D finite-difference code is used to model tumor growth using a basic reaction-diffusion equation. I formulate and test hypotheses as to why there are large differences between the final tumor sizes between the mice.
Once a tumor has reached a detectable size, it is diagnosed, and treatment begins. Chapter 5 considers modeling the treatment of prostate cancer. I consider a joint model with hormonal therapy as well as immunotherapy. I consider a timing study to determine whether changing the vaccine timing has any effect on the outcome of the patient. In addition, I perform basic analysis on the six-dimensional ordinary differential equation (ODE). I also consider the limiting case, and perform a full global analysis.
ContributorsRutter, Erica Marie (Author) / Kuang, Yang (Thesis advisor) / Kostelich, Eric J (Thesis advisor) / Frakes, David (Committee member) / Gardner, Carl (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Arizona State University (Publisher)
Created2016
Description
Positive alcohol outcome expectancies (AOEs) are consistent longitudinal predictors of later alcohol use; however, exclusion of solitary drinking contexts in the measurement of AOEs may have resulted in an underestimation of the importance of low arousal positive (LAP) effects. The current study aimed to clarify the literature on the association between AOEs and drinking outcomes by examining the role of drinking context in AOE measurement. Further, exclusion of contextual influences has also limited understanding of the unique effects of AOEs relative to subjective responses (SR) to alcohol. The present study addressed this important question by exploring relations between AOEs and SR when drinking context was held constant across parallel measures of these constructs. Understanding which of these factors drives relations between alcohol effects and drinking behavior has important implications for intervention. After conducting confirmatory factor analysis (CFA) and tests of measurement invariance for the AOE and SR measures, 4 aims collectively examined the role of context in reporting of AOEs (Aims 1 and 2), the extent to which context specific AOEs uniquely relate to drinking outcomes (Aim 3), and the importance of context effects on correspondence between AOEs and SR (Aim 4). Results of Aims 1 and 2 demonstrated that participants are imagining contexts when reporting on measures of AOEs that do not specify the context, and found significant mean differences in high and low arousal positive AOEs across contexts. Contrary to the hypotheses of Aim 3, context-specific AOEs were not significantly associated with drinking behavior. Results of Aim 4 indicated that while LAP AOEs for both unspecified and solitary contexts were associated with LAP SR in a solitary setting, unspecified context AOEs had a stronger relation than the solitary context AOEs. No significant relations between high arousal positive (HAP) AOEs and HAP SR emerged. The findings suggest that further investigation of the relation between context-specific AOEs and drinking outcomes/SR is warranted. Future studies of these hypotheses in samples with a wider range of drinking behavior, or at different stages of alcohol involvement, will elucidate whether mean level differences in context specific AOEs are important in understanding alcohol related outcomes.
ContributorsScott, Caitlin (Author) / Corbin, William (Thesis advisor) / MacKinnon, David (Committee member) / Barrera, Manuel (Committee member) / Chassin, Laurie (Committee member) / Arizona State University (Publisher)
Created2016
Description
Recent advances in hierarchical or multilevel statistical models and causal inference using the potential outcomes framework hold tremendous promise for mock and real jury research. These advances enable researchers to explore how individual jurors can exert a bottom-up effect on the jury’s verdict and how case-level features can exert a top-down effect on a juror’s perception of the parties at trial. This dissertation explains and then applies these technical advances to a pre-existing mock jury dataset to provide worked examples in an effort to spur the adoption of these techniques. In particular, the paper introduces two new cross-level mediated effects and then describes how to conduct ecological validity tests with these mediated effects. The first cross-level mediated effect, the a1b1 mediated effect, is the juror level mediated effect for a jury level manipulation. The second cross-level mediated effect, the a2bc mediated effect, is the unique contextual effect that being in a jury has on the individual the juror. When a mock jury study includes a deliberation versus non-deliberation manipulation, the a1b1 can be compared for the two conditions, enabling a general test of ecological validity. If deliberating in a group generally influences the individual, then the two indirect effects should be significantly different. The a2bc can also be interpreted as a specific test of how much changes in jury level means of this specific mediator effect juror level decision-making.
ContributorsLovis-McMahon, David (Author) / Schweitzer, Nicholas (Thesis advisor) / Saks, Michael (Thesis advisor) / Salerno, Jessica (Committee member) / MacKinnon, David (Committee member) / Arizona State University (Publisher)
Created2015
Description
Variability in subjective response to alcohol has been shown to predict drinking behavior as well as the development of alcohol use disorders. The current study examined the extent to which individual differences in alcohol pharmacokinetics impact subjective response and drinking behavior during a single session alcohol administration paradigm. Participants (N = 98) completed measures of subjective response at two time points following alcohol consumption. Pharmacokinetic properties (rate of absorption and metabolism) were inferred using multiple BAC readings to calculate the area under the curve during the ascending limb for absorption and descending limb for metabolism. Following the completion of the subjective response measures, an ad-libitum taste rating task was implemented in which participants were permitted to consume additional alcoholic beverages. The amount consumed during the taste rating task served as the primary outcome variable. Results of the study indicated that participants who metabolized alcohol more quickly maintained a greater level of subjective stimulation as blood alcohol levels declined and reported greater reductions in subjective sedation. Although metabolism did not have a direct influence on within session alcohol consumption, a faster metabolism did relate to increased ad-libitum consumption indirectly through greater acute tolerance to sedative effects and greater maintenance of stimulant effects. Rate of absorption did not significantly predict subjective response or within session drinking. The results of the study add clarity to theories of subjective response to alcohol, and suggest that those at highest risk for alcohol problems experience a more rapid reduction in sedation following alcohol consumption while simultaneously experiencing heightened levels of stimulation. Variability in pharmacokinetics, namely how quickly one metabolizes alcohol, may be an identifiable biomarker of subjective response and may be used to infer risk for alcohol problems.
ContributorsBoyd, Stephen (Author) / Corbin, William R. (Thesis advisor) / Chassin, Laurie (Committee member) / MacKinnon, David (Committee member) / Olive, Michael Foster (Committee member) / Arizona State University (Publisher)
Created2014
Description
The present study utilized longitudinal data from a high-risk community sample (n=254, 52.8% female, 47.2% children of alcoholics, 74% non-Hispanic Caucasian) to test questions concerning the effects of genetic risk, parental knowledge, and peer substance use on emerging adult substance use disorders (SUDs). Specifically, this study examined whether parental knowledge and peer substance use mediated the effects of parent alcohol use disorder (AUD) and genetic risk for behavioral undercontrol on SUD. The current study also examined whether genetic risk moderated effects of parental knowledge and peer substance use on risk for SUD. Finally, this study examined these questions over and above a genetic "control" which explained a large proportion of variance in the outcome, thereby providing a stricter test of environmental influences.
Analyses were performed in a path analysis framework. To test these research questions, the current study employed two polygenic risk scores. The first, a theory-based score, was formed using single-nucleotide polymorphisms (SNPs) from receptor systems implicated in the amplification of positive effects in the presence of new/exciting stimuli and/or pleasure derived from using substances. The second, an empirically-based score, was formed using a data-driven approach that explained a large amount of variance in SUDs. Together, these scores allowed the present study to test explanations for the relations among parent AUD, parental knowledge, peer substance use, and SUDs.
Results of the current study found that having parents with less knowledge or an AUD conferred greater risk for SUDs, but only for those at higher genetic risk for behavioral undercontrol. The current study replicated research findings suggesting that peer substance use mediated the effect of parental AUD on SUD. However, it adds to this literature by suggesting that some mechanism other than increased behavioral undercontrol explains relations among parental AUD, peer substance use, and emerging adult SUD. Taken together, these findings indicate that children of parents with AUDs comprise a particularly risky group, although likelihood of SUD within this group is not uniform. These findings also suggest that some of the most important environmental risk factors for SUDs exert effects that vary across level of genetic propensity.
Analyses were performed in a path analysis framework. To test these research questions, the current study employed two polygenic risk scores. The first, a theory-based score, was formed using single-nucleotide polymorphisms (SNPs) from receptor systems implicated in the amplification of positive effects in the presence of new/exciting stimuli and/or pleasure derived from using substances. The second, an empirically-based score, was formed using a data-driven approach that explained a large amount of variance in SUDs. Together, these scores allowed the present study to test explanations for the relations among parent AUD, parental knowledge, peer substance use, and SUDs.
Results of the current study found that having parents with less knowledge or an AUD conferred greater risk for SUDs, but only for those at higher genetic risk for behavioral undercontrol. The current study replicated research findings suggesting that peer substance use mediated the effect of parental AUD on SUD. However, it adds to this literature by suggesting that some mechanism other than increased behavioral undercontrol explains relations among parental AUD, peer substance use, and emerging adult SUD. Taken together, these findings indicate that children of parents with AUDs comprise a particularly risky group, although likelihood of SUD within this group is not uniform. These findings also suggest that some of the most important environmental risk factors for SUDs exert effects that vary across level of genetic propensity.
ContributorsBountress, Kaitlin (Author) / Chassin, Laurie (Thesis advisor) / Crnic, Keith (Committee member) / Lemery-Chalfant, Kathryn (Committee member) / MacKinnon, David (Committee member) / Arizona State University (Publisher)
Created2015
Description
In recent decades, marine ecologists have conducted extensive field work and experiments to understand the interactions between bacteria and bacteriophage (phage) in marine environments. This dissertation provides a detailed rigorous framework for gaining deeper insight into these interactions. Specific features of the dissertation include the design of a new deterministic Lotka-Volterra model with n + 1 bacteria, n
+ 1 phage, with explicit nutrient, where the jth phage strain infects the first j bacterial strains, a perfectly nested infection network (NIN). This system is subject to trade-off conditions on the life-history traits of both bacteria and phage given in an earlier study Jover et al. (2013). Sufficient conditions are provided to show that a bacteria-phage community of arbitrary size with NIN can arise through the succession of permanent subcommunities, by the successive addition of one new population. Using uniform persistence theory, this entire community is shown to be permanent (uniformly persistent), meaning that all populations ultimately survive.
It is shown that a modified version of the original NIN Lotka-Volterra model with implicit nutrient considered by Jover et al. (2013) is permanent. A new one-to-one infection network (OIN) is also considered where each bacterium is infected by only one phage, and that phage infects only that bacterium. This model does not use the trade-offs on phage infection range, and bacterium resistance to phage. The OIN model is shown to be permanent, and using Lyapunov function theory, coupled with LaSalle’s Invariance Principle, the unique coexistence equilibrium associated with the NIN is globally asymptotically stable provided that the inter- and intra-specific bacterial competition coefficients are equal across all bacteria.
Finally, the OIN model is extended to a “Kill the Winner” (KtW) Lotka-Volterra model
of marine communities consisting of bacteria, phage, and zooplankton. The zooplankton
acts as a super bacteriophage, which infects all bacteria. This model is shown to be permanent.
+ 1 phage, with explicit nutrient, where the jth phage strain infects the first j bacterial strains, a perfectly nested infection network (NIN). This system is subject to trade-off conditions on the life-history traits of both bacteria and phage given in an earlier study Jover et al. (2013). Sufficient conditions are provided to show that a bacteria-phage community of arbitrary size with NIN can arise through the succession of permanent subcommunities, by the successive addition of one new population. Using uniform persistence theory, this entire community is shown to be permanent (uniformly persistent), meaning that all populations ultimately survive.
It is shown that a modified version of the original NIN Lotka-Volterra model with implicit nutrient considered by Jover et al. (2013) is permanent. A new one-to-one infection network (OIN) is also considered where each bacterium is infected by only one phage, and that phage infects only that bacterium. This model does not use the trade-offs on phage infection range, and bacterium resistance to phage. The OIN model is shown to be permanent, and using Lyapunov function theory, coupled with LaSalle’s Invariance Principle, the unique coexistence equilibrium associated with the NIN is globally asymptotically stable provided that the inter- and intra-specific bacterial competition coefficients are equal across all bacteria.
Finally, the OIN model is extended to a “Kill the Winner” (KtW) Lotka-Volterra model
of marine communities consisting of bacteria, phage, and zooplankton. The zooplankton
acts as a super bacteriophage, which infects all bacteria. This model is shown to be permanent.
ContributorsKorytowski, Daniel (Author) / Smith, Hal (Thesis advisor) / Gumel, Abba (Committee member) / Kuang, Yang (Committee member) / Gardner, Carl (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2016
Description
Anxiety and depression are among the most prevalent disorders in youth, with prevalence rates ranging from 15% to 25% for anxiety and 5% to 14% for depression. Anxiety and depressive disorders cause significant impairment, fail to spontaneously remit, and have been prospectively linked to problematic substance use and legal problems in adulthood. These disorders often share a high-degree of comorbidity in both clinical and community samples, with anxiety disorders typically preceding the onset of depression. Given the nature and consequences of anxiety and depressive disorders, a plethora of treatment and preventative interventions have been developed and tested with data showing significant pre to post to follow-up reductions in anxiety and depressive symptoms. However, little is known about the mediators by which these interventions achieve their effects. To address this gap in the literature, the present thesis study combined meta-analytic methods and path analysis to evaluate the effects of youth anxiety and depression interventions on outcomes and four theory-driven mediators using data from 55 randomized controlled trials (N = 11,413). The mediators included: (1) information-processing biases, (2) coping strategies, (3) social competence, and (4) physiological hyperarousal. Meta-analytic results showed that treatment and preventative interventions reliably produced moderate effect sizes on outcomes and three of the four mediators (information-processing biases, coping strategies, social competence). Most importantly, findings from the path analysis showed that changes in information-processing biases and coping strategies consistently mediated changes in outcomes for anxiety and depression at both levels of intervention, whereas gains in social competence and reductions in physiological hyperarousal did not emerge as significant mediators. Knowledge of the mediators underlying intervention effects is important because they can refine testable models of treatment and prevention efforts and identify which anxiety and depression components need to be packaged or strengthened to maximize intervention effects. Allocating additional resources to significant mediators has the potential to reduce costs associated with adopting and implementing evidence-based interventions and improve dissemination and sustainability in real-world settings, thus setting the stage to be more readily integrated into clinical and non-clinical settings on a large scale.
ContributorsStoll, Ryan (Author) / Pina, Armando A (Thesis advisor) / MacKinnon, David (Committee member) / Knight, George (Committee member) / Arizona State University (Publisher)
Created2015
Description
There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. This fast growing theory provides new constraints and mechanisms that can be formulated into mathematical models. Stoichiometric models incorporate the effects of both food quantity and food quality into a single framework that produce rich dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insufficient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This phenomenon, known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, needs to be incorporated into mathematical models. Here we present Lotka-Volterra type models to investigate the growth response of Daphnia to algae of varying P:C ratios. Using a nonsmooth system of two ordinary differential equations (ODEs), we formulate the first model to incorporate the phenomenon of the stoichiometric knife edge. We then extend this stoichiometric model by mechanistically deriving and tracking free P in the environment. This resulting full knife edge model is a nonsmooth system of three ODEs. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, leads to quantitatively different predictions than previous models that neglect to track free nutrients. The full model shows that the grazer population is sensitive to excess nutrient concentrations as a dynamical free nutrient pool induces extreme grazer population density changes. These modeling efforts provide insight on the effects of excess nutrient content on grazer dynamics and deepen our understanding of the effects of stoichiometry on the mechanisms governing population dynamics and the interactions between trophic levels.
ContributorsPeace, Angela (Author) / Kuang, Yang (Thesis advisor) / Elser, James J (Committee member) / Baer, Steven (Committee member) / Tang, Wenbo (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
In 1968, phycologist M.R. Droop published his famous discovery on the functional relationship between growth rate and internal nutrient status of algae in chemostat culture. The simple notion that growth is directly dependent on intracellular nutrient concentration is useful for understanding the dynamics in many ecological systems. The cell quota in particular lends itself to ecological stoichiometry, which is a powerful framework for mathematical ecology. Three models are developed based on the cell quota principal in order to demonstrate its applications beyond chemostat culture.
First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
ContributorsPacker, Aaron (Author) / Kuang, Yang (Thesis advisor) / Nagy, John (Committee member) / Smith, Hal (Committee member) / Kostelich, Eric (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
Methods to test hypotheses of mediated effects in the pretest-posttest control group design are understudied in the behavioral sciences (MacKinnon, 2008). Because many studies aim to answer questions about mediating processes in the pretest-posttest control group design, there is a need to determine which model is most appropriate to test hypotheses about mediating processes and what happens to estimates of the mediated effect when model assumptions are violated in this design. The goal of this project was to outline estimator characteristics of four longitudinal mediation models and the cross-sectional mediation model. Models were compared on type 1 error rates, statistical power, accuracy of confidence interval coverage, and bias of parameter estimates. Four traditional longitudinal models and the cross-sectional model were assessed. The four longitudinal models were analysis of covariance (ANCOVA) using pretest scores as a covariate, path analysis, difference scores, and residualized change scores. A Monte Carlo simulation study was conducted to evaluate the different models across a wide range of sample sizes and effect sizes. All models performed well in terms of type 1 error rates and the ANCOVA and path analysis models performed best in terms of bias and empirical power. The difference score, residualized change score, and cross-sectional models all performed well given certain conditions held about the pretest measures. These conditions and future directions are discussed.
ContributorsValente, Matthew John (Author) / MacKinnon, David (Thesis advisor) / West, Stephen (Committee member) / Aiken, Leona (Committee member) / Enders, Craig (Committee member) / Arizona State University (Publisher)
Created2015