AWM at SIAM 2016 Abstracts

Monday, July 11, 2016, 10:30 AM − 12:30 PM, Room: Room 253A, Boston Convention and Exhibition Center

AWM Workshop: Research Talks by Recent Ph.D.s & Invited Speakers – Dynamical Systems with Applications to Biology and Medicine – Part I of II

Diabetes Susceptibility and Sleep: Modeling Glucose Metabolism under Circadian Disruption

Erica J. Graham, Bryn Mawr College, U.S.,

Abstract. Long-term disruptions to the sleep-wake cycle can alter glucose metabolism and increase susceptibility to type 2 diabetes. Circadian misalignment occurs when the sleep-wake pattern is antiphase with the primary circadian clock. We develop a mathematical model of the glucose-insulin regulatory system with meal absorption to explain experimental data from a clinically forced, progressive circadian misalignment study. The resulting model incorporates circadian dependence of model parameters. Simulation results and long-term metabolic implications are discussed.

Modeling the Diffusion of Prion Aggregates in Budding Yeast

Karin Leiderman, University of California, Merced, USA,

Abstract. Prions are misfolded proteins that self-propagate by converging native proteins to the misfolded form, which are then prone to aggregation. These misfolded proteins are believed to act as the infectious agent in neurodegenerative diseases such as mad cow disease, scrapie, and Creutzfeldt-Jakob disease. The mechanism of prion transmission during cell division is not yet understood. Using data obtained from experiments we have developed a hindered diffusion model for prion aggregate transmission in budding yeast.

Flow Induced by Bacterial Carpets and Transport of Microscale Loads

Amy Buchmann, Tulane University, USA,

Abstract. Experimental work has suggested that the flagella of bacteria may be used as motors in microfluidic devices by creating a bacterial carpet. Mathematical modeling can be used to investigate this idea and to quantify flow induced by bacterial carpets. We simulate flow induced by bacterial carpets using the method of regularized Stokeslets, and also examine the transport of vesicles of finite size by arrays of rotating flagella.

Synchronization of Tubular Pressure Oscillations by Vascular and Hemodynamic Coupling in Interacting Nephrons

Hwayeon Ryu, St. Olaf College, USA,

Abstract. The kidney plays an essential role in regulating the blood pressure and a number of its functions operate at the functional unit of the kidney, the nephron. To understand the impacts of internephron coupling on the overall nephrons’ dynamics, we develop a mathematical model of a tubuloglomerular feedback (TGF) system, a negative feedback mechanism for nephron’s fluid capacity. Specifically, each model nephron represents a rigid thick ascending limb only and is assumed to interact with nearby nephrons through vascular and hemodynamic coupling along the pre-glomerular vasculature. We conduct a bifurcation analysis by deriving a characteristic equation obtained via a linearization of the model equations. (Joint work with Anita T. Layton)

Monday, July 11, 2016, 4:00 PM – 6:00 PM, Room 253A, Boston Convention and Exhibition Center

AWM Workshop: Research Talks by Recent Ph.D.s & Invited Speakers – Dynamical Systems with Applications to Biology and Medicine – Part II of II

Explicitly Separating Growth and Motility in a Glioblastoma Tumor Model

Tracy L. Stepien, Arizona State University, U.S.,

Abstract not available

Modeling Respiratory Dynamics in the Premature Infant

Laura Ellwein, Virginia Commonwealth University, USA,

Abstract. The survival rate for very premature infants is increasing, but these babies are at significant risk for developing chronic lung disease as a consequence of exposure to mechanical ventilation. Increased compliance (flexibility) of the chest wall due to early gestation bone undermineralization results in progressive lung collapse as the forces needed to open airspaces after each exhalation become insufficient. We present a mathematical model of respiratory dynamics in premature infants that accounts for changes in chest wall compliance, with the ultimate aim of developing a treatment that increases chest wall rigidity to allow for mechanical ventilation.

A Mathemaical Model of the Effects of Temperature on Human Sleep Patterns

Selenne Banuelos, California State University, Channel Islands, U.S.,

Abstract. Several studies have been done on human patients that suggest that different temperatures, such as room temperature, core body temperature, and distal skin temperature, have an important effect on sleep patterns, such as length and frequency of REM bouts. A mathematical model is created to investigate the effects of temperature on the REM/NonREM dynamics. Our model was based on previous well established and accepted models of sleep dynamics and thermoregulation models.

Using Delayed Feedback to Avoid Neural Synchrony

Shelby Wilson, Morehouse College, USA,

Abstract. The spontaneous synchronization of certain groups of neurons is responsible for epileptic seizures as well as some of the motor symptoms of Parkinson’s Disease. Breaking neural synchrony through deep brain electrical stimulation is a key method of treatment of these conditions. We will discuss the mathematics of how synchrony can be avoided in dynamic networks. In particular, we will highlight how time-delayed linear feedback can be used to avoid synchrony in an artificial neural network.

Tuesday, July 12, 2016, 4:00 PM – 6:00 PM, Room 253A, Boston Convention and Exhibition Center

AWM Workshop Career Panel: Addressing the Challenges Facing Female Scientists and Mathematicians

Abstract. This panel will bring together leading female mathematicians from academia, industry, national labs and funding agencies, who will talk about the challenges they encountered on their career paths and share lessons they learned along the way. There will be opportunities to ask questions and hear their advice on a variety of different topics in an informal discussion. We welcome graduate students, postdocs as well as more seasoned researchers to join us for this unique opportunity to discuss issues that affect female scientists and mathematicians.

Tuesday, July 12, 2016, 8:00 PM – 10:00 PM, Galleria Level, The Westin Boston Waterfront

AWM Workshop Poster Presentations

Modeling of Mrna Localization in Xenopus Egg Cells

Maria-Veronica Ciocanel, Brown University, U.S.,

Abstract. mRNA localization is essential for Xenopus egg and embryo development. This accumulation of RNA at the cell periphery is not well understood, but is thought to depend on diffusion, bidirectional movement and anchoring mechanisms. Our goal is to test these proposed mechanisms using partial differential equations models and analysis, informed by parameter estimation. Our results confirm that diffusion coefficients and transport speeds are different in various regions of the cell cytoplasm.

Fitness Effects of Defense Strategies on Plants under Herbivory

Karen M. Cumings, Rensselaer Polytechnic Institute, USA,

Abstract. Abstract: When attacked by insect herbivores, plants emit volatile chemicals. These chemicals are known to induce local defenses, prime neighboring plants for defense, and attract predators and parasitoids to combat the herbivores, but these chemical defenses are coupled with fitness costs. We examine the interactions between the model plant goldenrod and one of its insect herbivores, Trirhabda virgata, in order to explore how a plant’s defense strategy can increase or decrease its fitness.

Quantifying Dynamic Growing Roots in 3D by Persistent Homology

Mao Li, Florida State University, USA,

Abstract. Quantifying changes in root architecture, as a function of growth and environmental interactions constitutes a major challenge and emerging frontier in plant biology. Persistent homology is a powerful topological data analysis technique that holds great promise for modeling and quantifying variation in complex shapes. Starting with existing 4D root data, we develop technique based on persistent homology to analyze variation of root form and shape during growth and to investigate size-shape developmental constraints.

A Numerical Investigation of a Simplied Human Birth Model

Roseanna Pealatere, Tulane University, USA,

Abstract. We explore the effects of fetal velocity and fluid viscosity on the forces associated with human birth. The numerical model represents the fetus moving through the birth canal using a rigid cylinder that moves at a constant velocity through a passive elastic tube (modeled by a network of springs) immersed in viscous fluid. The Stokes equations, solved with the method of regularized Stokeslets, describe the relationship between velocity and forces in the system.

Identification of the Vasodilatory Stimulus from Cerebral Blood Flow Data

Jamie Prezioso, Case Western Reserve University, U.S.,

Abstract. A localized increase in neural activity is accompanied by a significant increase in cerebral blood flow (CBF) and cerebral blood volume (CBV) in the surrounding brain tissue, a process known as functional hyperemia. Existing mathematical models that explain functional hyperemia following a vasodilatory stimulus assume that the stimulus is known. Rather than modeling the hemodynamic response as a system of differential algebraic equations, we reformulate the model as an inverse problem, using CBF data to find the underlying stimulus. This results in accurate estimates of the vasodilatory stimulus, its vascular location, and the underlying blood flows and blood volumes of the system.

Little’s Law Applied to a Stochastic Model of Poliomyelitis

Celeste Vallejo, University of Florida, USA,

Abstract. Poliomyelitis is an infectious disease that is currently endemic in regions such as Afghanistan and Pakistan. The oral poliovirus vaccine (OPV) is an attenuated form of the virus that is used to prevent polio in these endemic regions. OPV is contagious, so it can provide herd immunity. A disadvantage is that OPV can cause paralysis and is no longer used in many countries. The main concern in regards to the eradication of polio is the silent circulation. After an individual has had an initial contact with the virus, whether through infection or vaccination, the individual will be asymptomatic after any subsequent infection with the virus. We want to answer the following question. In a community of individuals whose immunity to poliovirus has waned, how long can the silent circulation persist? We developed a stochastic model to analyze the silent circulation.

Diffusion Maps for Image Segmentation

Marilyn Yazmin Vazquez, George Mason University, USA,

Abstract. Efficient representation of high dimensional data is an active area of research. We present our solution by introducing diffusion maps as a way to achieve a faithful Fourier-like representation of the data. This method will only need the assumption that data lives on or close to a manifold, and will be able to detect intrinsic features. While this approach can be used for different purposes on data, we will apply it for image segmentation purposes.

Modeling Cooperation and Competition

Karen E Wood, University of California, Irvine, USA,

Abstract. Sympatric speciation is a complex phenomenon which is not yet well understood. In my research I am examining sympatric speciation arising from cooperation. I am investigating how a single population of generalists or non-cooperators might then evolve into two populations of cooperating specialists to an extent that the different cooperators are considered different species. In working to model this occurrence I used systems of ordinary differential equations, adaptive dynamics, and numerical simulations.

A Multi-Scale Model of Escherichia Coli Chemotaxis from Intracellular Signaling Pathway to Motility and Nutrient Uptake in Nutrient Gradient and Isotropic Fluid Environments

Feifei Xu, Florida State University, USA,

Abstract. We present a multi-scale mathematical model of Escherichia coli chemotaxis in a fluid environment that links the biochemical dynamics of intracellular signaling and flagellar dynamics to the behavior of cells and the surrounding nutrients and fluid flow. The resulting feedback between hydrodynamics and chemotaxis not only shows expected run and tumble behaviors of bacterial cells but also depicts the importance of fluid dynamical effects on the transport and consumption of chemoeffectors.

Online Adaptive Model Reduction for Flows in Heterogeneous Porous Media

Yanfang Yang, Texas A&M University, USA,

Abstract. We propose an online adaptive model reduction method for flows in heterogeneous porous media. Our approach constructs a reduced system by proper orthogonal decomposition (POD) Galerkin and the discrete empirical interpolation method (DEIM). Moreover, we adapt the reduced system online by changing the reduced solution space and the DEIM approximation of the nonlinear functions. The online adaptation incorporates new data becoming available online to yield a reduced system that accurately approximates dynamics not anticipated in the offline stage.