Benedictine University - College of DuPage Biomathematics Seminar

Fall 2009 Speaker

Christina Weaver, Assistant Professor of Mathematics, Franklin and Marshall College

Computational Neuroscience: This is Your Brain on Math

Abstract:

The brain is too complex to be understood through experiments with animals or tissue alone. Mathematical models have been used to study the brain for more than fifty years, and are more important than ever today. We will discuss how mathematics plays an essential role in all levels of neuroscience research, from single cells, to neural networks, to higher level cognition and disease.

Dates and Locations:

October 19, 2009 7 p.m., Health and Sciences 1234, College of DuPage

October 20, 2009, 2:30pm, Second Floor, Krasa Center, Benedictine University

cells, to neural networks, to higher level cognition and disease.

What Derivatives Tell us About Model Neurons

Abstract:

We will show how to use mathematics to build model neurons that reproduce data recorded in the laboratory. Derivatives are important throughout the modeling process, whether quantifying rates of change or identifying a function's extrema. In particular, derivatives can measure how different characteristics of a single neuron affect the output it generates. Our models can predict how to counteract the changes that occur in a neuron's lifetime, with implications for aging, disease, and drug design.

 

Date and Location:

October 19, 2009, 9:30 a.m., Second Floor, Krasa Center, Benedictine University

Spring 2009 Speakers

Mike Martin, Professor of Mathematics, Johnson County Community College

 

MATHEMATICS OF BIOLOGICAL RHYTHMS, ECOLOGY, & SUSTAINABILITY

Abstract:

Biological systems are inherently complex and often involve a multitude of signals and responses, responses that turn into signals, and so forth. This talk will speak of some inherent biological rhythms (year, day, cycle), their timescales, and the mathematics involved. Rhythms in physiology, ecology, and for renewable resources will be featured. An overarching discussion of sustainability and the mathematics involved (rapid decay, rapid growth, renewable resources) will be highlighted.

Dates and Locations:

March 3, 2009 2 p.m., SRC 1544, College of DuPage

March 3, 2009, 7.p.m., SRC 1544, College of DuPage

 

PHARMACOLOGY, PHYSIOLOGY, & DISEASE

Abstract:

Aspects of drug administration, multiple dosing, and response will be examined in the context of diseased individuals and the physiology involved with a particular diseased state. For instance, among others, Lewis lung carcinomas will be examined using anti-vascular approaches, neurological diseases thought to involve myelination will be considered, and even treating a common headache.

Date and Location:

March 4 2009, 10 a.m., Birck Hall of Science 112, Benedictine University

Fall 2008 Speakers

Glenn Ledder, Associate Professor, Department of Mathematics, University of Nebraska at Lincoln

Structured population growth

Abstract:

The standard exponential function model for unrestricted population growth assumes that a population can be described using a single count of all individuals. But what if a population consists of individuals in several distinct stages of development, such as happens with many insect populations? Modeling questions such as this require intuition developed from scientific observation. In this talk, we explore the issue with the aid of the "BUGBOX-population" virtual biology laboratory. The BUGBOX is populated by a virtual insect species (called "boxbugs," of course) whose biology is just realistic enough for the purpose without any additional distracting features. Our observations of boxbug populations will give us the necessary insights to construct an appropriate mathematical model. Our study of this model will help us confirm that a population consisting of individuals in different stages (a "structured" population) can exhibit exponential growth, and we will use our model to determine the correct growth rate.

Dates and Locations:

November 11, 2008, 7 p.m., IC 3069, College of DuPage

November 12, 2008, 1.p.m., SRC 1544, College of DuPage

The Past, Present, and Future of Endangered Whale Populations

Abstract:

Whales are among the most controversial of endangered species, as environmental conservationists committed to helping whale populations recover clash with cultures for whom utilization of whale resources is important. In this talk, we use a mathematical model to shed light on how whale populations became endangered, why conservation doesn't seem to be making a large difference, and what must be done if whale populations are to recover. Our model is based on a differential equation, but we will gain a rich understanding of it using elementary algebra ideas and methods.

Date and Location:

November 12, 2008, 9:30 a.m., Second Floor, Krasa Center, Benedictine University

 

Holly Gaff, Assistant Professor, Community and Environmental Health, College of Health Sciences Virginia Modeling, Analysis and Simulation Center, Old Dominion University

Ticks can give you more than the creeps - mathematical modeling of tick-borne diseases

Abstract:

Recent increases in reported outbreaks of vector-borne diseases throughout the world have led to increased interest in understanding and controlling epidemics involving transmission vectors. Ticks have very unique life histories that create epidemics that differ from other vector-borne diseases. The differential equations underlying our tick-borne disease model are designed for the lone star tick (Amblyomma americanum) and the spread of human monocytic ehrlichiosis (Ehrlichia chaffeensis). Analytical results show that under certain criteria for the parameters, the epidemic would be locally stable. The system was then expanded to multiple patches to evaluate the effect of spatial heterogeneity on the spread of the disease. The use of control measures was added, and it was found that the relative success of disease eradication was dependent upon the patch structure and location of control application. Results from simulations using a twelve patch system are compared with field data from an outbreak of ehrlichiosis in eastern Tennessee, USA. Finally, optimal control techniques are used to evaluate the location and amount of control needed to eliminate the disease from different patch scenarios. There remain many open questions that can be addressed by using this model that we have just begun to explore.

Dates and Locations:

October 28, 2008, 7 p.m., Second Floor, Krasa Center, Benedictine University

October 29, 2008, 1.p.m., SRC 1544, College of DuPage

Using Math to Tackle Things That Go Bump in the Night: Modeling Rift Valley Fever


Abstract:

Rift Valley fever is a mosquito-borne pathogen causing febrile illness in domestic animals and humans. Outbreaks of Rift Valley fever (RVF) are associated with widespread morbidity and mortality in livestock and morbidity in humans. Identified in Kenya in 1930, RVF is often considered a disease primarily of sub-Saharan Africa, but recent translocation to Saudi Arabia and Yemen has raised fears of accidental or intentional introduction into North America. Mathematical disease models are powerful tools that allow us to explore a large variety of scenarios and test hypotheses to hopefully identify ways to prevent disease and suffering. We developed a mathematical model to examine the dynamics of RVF within Africa. The results of this model show promising potential for predicting RVF outbreaks as will be demonstrated using the 2006-2007 outbreak in Kenya.

Additionally, we use the model to identify areas of potential risk within Africa with future applications to North America. We also examine the impact of various control measures on containing new or existing epidemics. Through the process of developing and applying our model, we have and continue to identify key data gaps and gain insights into the dynamics and potential control of RVF.

Date and Location:

October 29, 2008, 9:30 a.m., Second Floor, Krasa Center, Benedictine University

Spring 2008 Speakers

Evans Afenya, Professor of Mathematics, Elmhurst College

Perspectives on Modeling Biomedical Phenomena

Abstract:

Biology and medicine are becoming increasingly quantitative in scope and content and are presenting questions and challenges that demand novel mathematical approaches that aid in overcoming the challenges. Within this framework, we introduce and discuss various perspectives that are driving the needed coalescence between biomedicine and mathematics. In this pursuit, biomedically-driven mathematical models will be formulated and used to describe and capture essential characteristics of biomedical phenomena. Predictions engendered by the models and the insights they produce will be highlighted and discussed.


Dates and Locations:

April 22, 2008, 7 p.m., Krasa Presentation Room, Krasa Center, Benedictine University

April 24, 2008, 2.p.m., SRC 1544, College of DuPage

Can We Capture Physical Reality With Mathematical Models?

Abstract:

Definition of mathematical modeling in the process of scientific enquiry and engagement is examined. Examples of how things can go wrong and serious flaws could arise when modeling principles are ignored or rendered unimportant are shown. Using appropriate techniques, mathematical models of biomedical phenomena are introduced and surveyed. The models are then validated through investigation of their predictive capabilities in capturing physical reality and certain projections are made.

Date and Location:

April 25, 9 a.m., Birck Hall of Science 112, Benedictine University

Louis J. Gross, Professor of Ecology and Evolutionary Biology and Mathematics; Director, The Institute for Environmental Modeling, The University of Tennessee, Knoxville

Mathematics and Ecology: Bears, Panthers, and Equations

Abstract:

In this presentation, the speaker explores how some mathematical applications are used to analyze ecological problems, such as in the Everglades and in the Great Smoky Mountains. Ecology is the science that deals with interactions between living organisms and their environment.

Historically, it has focused on such questions as: Why do we observe certain organisms in certain places and not others? What limits the abundance of organisms and controls their dynamics? What causes the observed groupings of organisms of different species, called the community, to vary across the planet? What are the major pathways for movement of matter and energy within and between natural systems? As the language of science, mathematics allows us to carefully phrase questions concerning each of the above areas of ecology. The speaker discusses how, through mathematical systems, scientists can discover the basic principles of these systems and determine their implications.

February 19, 2008, 7 p.m., SRC 1544, College of DuPage

February 20, 2008, 2.p.m., IC 3001, College of DuPage

Managing Natural Resources:
Mathematics meets Politics, Greed and the Army Corps of Engineers

Abstract:

The availability of satellite-based remote sensing, computers capable of handling large databases, rapid communication networks, and small radio sensors able to transmit details on individual animals has fostered the development of computational ecology. By combining mathematical and computer models of natural systems with geographically-explicit details of the biotic and abiotic components of the environment, we can compare alternative virtual futures to better plan sustainable ecosystems. Opportunities exist for mathematicians to develop and apply models for harvest regulation, control of invasive species, fire management, and disease and pest control. This optimistic view of the potential for computational methodologies to aid in managing natural systems is tempered by the reality that factors other than scientific best practices are involved. I will discuss a range of applications from relatively simple models for invasive plant control to models applied to long-term planning of an immense restoration effort in the Everglades of South Florida.

February 20, 9 a.m., Birck Hall of Science 112, Benedictine University.

Fall 2007 Speakers

Mark A. Anastasio, Associate Professor of Biomedical Engineering and Associate Professor of Electrical and Computer Engineering, and Associate Director, Medical Imaging Research Center (MIRC) Illinois Institute of Technology

X-ray Computed Tomography (CT)
and the Radon Transform

Abstract:

Tomographic imaging modalities seek to reconstruct a volumetric (three-dimensional) function of some physical or physiological property of an object from knowledge of a collection of two-dimensional projections of the object. Mathematically, this represents an inverse problem, in which one wishes to reconstruct a function from knowledge of a collection of indirect measurements of that function. The archetypical tomographic inverse problem is X-ray computed tomography (CT). In this case, the imaging model is described by the so-called Radon transform, and the measured projections of the object correspond to a collection of line-integrals through the object property. In this lecture, we review the Radon transform, and demonstrate that it can be inverted readily by use of integral calculus. Some practical problems associated with tomographic image reconstruction are also investigated.

November 5, 2007, 9:30 a.m., Krasa Presentation Room, Krasa Center, Benedictine University

Modern Medical Imaging Modalities
and their Mathematical Underpinnings

Abstract:

There are few aspects of modern life that have not benefited from biomedical imaging science in some way. Microscopy and other biomedical imaging systems are invaluable tools of discovery in a broad range of fundamental scientific disciplines. It is almost painful to imagine how medicine would be practiced if it were not for the availability of
modern medical imaging systems that can non-invasively reveal information regarding the structure and function of internal organs. Two Nobel Prizes in Medicine for medical imaging contributions have been awarded over the past 25 years. In this talk, we review some important modern imaging modalities. With only a few exceptions, these imaging modalities are tomographic in nature, and computational algorithms based on the relevant mathematics and physics are employed to form a three-dimensional image. Examples of tomographic imaging modalities include magnetic resonance imaging (MRI) and X-ray computed tomography (CT). The mathematics and physics of these imaging modalities along with open problems and current research trends in medical imaging are described. We also describe some emerging X-ray imaging modalities that are based on the mathematics of wave physics, which may soon revolutionize diagnostic radiology.

November 5, 2007, 2:30 p.m., SRC 1544, College of DuPage (in conjuction with the Science & Its Application Mini Lecture Series)

November 5, 2007 7 p.m., SRC 1544, College of DuPage (in conjuction with the Science & Its Application Mini Lecture Series)

Anton E. Weisstein, Assistant Professor of Biology, Division of Science, Truman State University

Unveiling the Past:

New Analyses for Inferring Evolutionary and Demographic Histories from Current Patterns of Genetic Variation

Abstract:

Many different statistical tests are available for inferring specific events in a population's history from the current patterns of variation in that population's genetic sequence. One of these, Tajima's D test, compares two measures of genetic diversity to assess the relative frequency of common vs. rare polymorphisms. A significant preponderance of rare polymorphisms suggests a recent drop in genetic diversity (perhaps due to a selective sweep or population bottleneck), while a preponderance of common polymorphisms suggests the reverse. In this talk, I will discuss my lab group's ongoing efforts to modify Tajima's test by analyzing synonymous and nonsynonymous polymorphisms separately, thereby distinguishing between the effects of selection and those of genetic drift. This procedure has the potential to substantially improve our ability to resolve a population's history.

October 18, 2007, 7 p.m., Scholl 101, Benedictine University

October 19, 2007 1 p.m., 1000 IC, College of DuPage (in conjuction with the Science & Its Application Mini Lecture Series)

Biomedical Modeling:
Applications of Differential Equations in Pharmacology and Public Health

Abstract:

Mathematical models are among the most useful tools of modern biology. Modeling a biological system not only helps encapsulate a researcher's assumptions about how that system works, but can also enable simulated experiments that would be too costly, too time-intensive, or too dangerous to actually perform. In this talk, we will build and analyze two multi-compartment models that simulate the movement of particles (molecules or organisms) between compartments. Using our first model, we will project the likely course of an infectious disease epidemic and predict the efficacy of different intervention strategies. Our second model will allow us to analyze drug absorption and metabolism.

October 19, 2007, 9:30 a.m., Krasa Presentation Room, Krasa Center, Benedictine University.

 

Past Speakers

2006-2007

Eric Marland, Appalachian State University

Olcay Akman, Illinois State University

Raina Robeva, Sweet Briar College

The Benedictine University - College of DuPage Biomathematics Seminar is designed to introduce undergraduate students to current trends in biomathematics. Students and faculty from BU and COD are encouraged to attend. This seminar is currently funded by NSF CCLI Grant #DUE-0633232, "Biocalculus: Text Development, Dialog, and Assessment." The project summary for the grant proposal is located here.

For additional information, please contact the organizer of the seminar, Tim Comar, at tcomar@ben.edu or (630) 829-6555.

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