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. An****astasio,
**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.