Seminars are listed in reverse chronological order. The
top of the list is subject to change, since more seminars
are still being planned. All seminars are held at 3:10p.m.
in 1431 Stevenson Center unless otherwise noted. For further
information on events in the department, you may also
consult the
colloquia schedule, the
weekly
calendar and past
calendars.
Friday, April 19th.
Caroline Torcaso, of the
Department of Mathematics
and Statistics,
University of North Carolina at
Wilmington.
Modeling molecular diffusion in soft tissues.
Articular cartilage is a soft tissue that acts as a load-bearing
surface in joints such as the knee, shoulder and hip. The structural
matrix of cartilage contains collagen fibers and charged macromolecules
(proteoglycans) in an extracellular matrix with embedded cells
(chondrocytes) responsible for its maintenance and repair. In fact, the
maintenance of healthy cartilage and its progressive degradation are
known to be highly dependent on the mechanical and electrochemical
properties of the extracellular matrix in the tissue. Since individual
cells respond to changes in their local environment, diffusion through
the tissue layer can influence cell response and, over time, the overall
health of the cartilage. Two important factors affecting diffusion in
cartilage are anisotropy and inhomogeneity of the structural matrix. At
the microscopic level, we develop and solve 2-D models of diffusion for
a fluorescence recovery after photobleaching (FRAP) experiment in order
to determine local effective diffusion coefficients for both isotropic
and anisotropic regions of articular cartilage. At the macroscopic level,
we consider both an analytical and numerical solution of a 1-D diffusive
transport model assuming the tissue is inhomogeneous due to variations
in porosity or the concentration of the proteoglycans within a tissue
layer.
Wednesday, April 17th.
Radu C. Cascaval, of the
Department of Mathematics,
University of Missouri-Columbia.
Mathematics of excitable media.
Some problems related to the mathematical modeling of
wave phenomena in excitable media will be described. For the two
variable models, such as the FitzHugh-Nagumo system, there is plenty
of numerical evidence for the existence of special types solutions,
such as spiral waves or target waves, although a rigorous proof is
still missing. Various approaches will be discussed, including a
free boundary formulation and singular perturbation theory.
Thursday, April 11th, 4:10p.m.
Yongzhi Steve Xu, of the
Department of Mathematics,
University of Tennessee, Chattanooga.
Two inverse problems of underwater sound.
Inverse problems of underwater sound have applications in many
areas, including ocean exploration and medical imaging. Two
applications will be discussed in this talk:
(1) Imaging floating objects from undersea.
(2) Evaluation of osteoporosis.
The oceans cover more than half of the earth's surface. With more
and more human activities on the sea surface and under the sea,
it has been an urgent issue to be able to effectively observe
floating objects from undersea. Sound wave is the only energy
form that can propagate effectively in water. Our research is
using mathematical and computational approaches to study properties
of acoustic waves scattering in an ocean, and developing new methods
for effective acoustic imaging. This talk presents new results of
imaging floating objects from underwater by an auto-filtering
generalized dual space indicator method.
The methodology we developed for sound waves in an ocean
may also be applied to evaluation of osteoporosis.
As bone is known to be poroelastic in structure, we consider
modeling it using Biot's formulation. In this talk We present
some new results in our ongoing research
on the reflection and transmission of ultrasonic wave in
cancellous bone. We investigate the relations among reflecting waves,
transmission waves and Biot coefficients. We also consider the
determination of the parameters of cancellous bone.
Wednesday, April 3rd.
Wieb van der Meer, of the
Department of Physics and Astronomy,
Vanderbilt University and Western Kentucky University.
Functional analysis approach to fluorescence decay.
When a sample of fluorescent molecules is excited by an infinitely
short pulse of light, the fluorescence is a single exponential.
This is true only in the ideal case. In practice the fluorescence
emitted by biomolecular systems is non-exponential. The standard
approach is to fit the data to a sum of exponentials. However, it
is well known that this is almost ambiguous in some cases. An
alternative is offered: a complete set of orthonormal functions is
presented that can be used to make a Fourier-like expansion of an
experimental decay. These are functions of the scaled time (time
times negative initial slope) and have the form of polynomial times
exponential. It will be shown that an expansion of a typical decay
as a sum of these functions rapidly converges. Moreover, it will
be demonstrated that this approach can detect a distinction between
two classic pairs of exponentials having a dissimilar appearance
but having an almost vanishing difference.
Wednesday, March 27th.
Scott Adams, of the
Department of Pharmacology,
Vanderbilt University
Medical Center.
Permeation through membranes: Channels and transporters.
It is critical to cellular physiology that the lipid membrane, which
surrounds all cells, is selectively permeable to solute molecules.
Traditionally, we recognize two classes of proteins that accomplish this
task. Ion channels, which open and close under certain governing
conditions and which, when open, allow selected ions to pass through
membranes according to their driving electrochemical gradients. A
channel may be envisioned rather like a traditional door or swinging
gate. Transporters, on the other hand, are typically conceived as
cycling through a series of conformational changes, which result in the
transfer of solutes across the membrane without ever forming a true
opening. This may be envisioned as a revolving door. In spite of these
seemingly large dissimilarities, it is difficult to conceive of
experiments that distinguish between channels and transporters: for
example, the simple measure of solute flux does not distinguish a
channel from a transporter. In this presentation I will first review
our theoretical understanding of permeation in ion channels, and I will
contrast these mechanisms with classical transporter mechanisms. After
this introduction I will present a crude theory, which, by considering
single-file permeation through a narrow pore, demonstrates features of
both channels and transporters. Refinement of this theory may provide a
distinct molecular representation that joins these two apparently
disparate proteins-channels and transporters. Finally I will review some
of my own data, which supports this new model for the human serotonin
transporter.
Wednesday, March 20th.
Cammey E. Cole, of the
Department of Mathematics and Computer Science,
Meredith College.
Benzene and its effect on erythropoiesis: Models, optimal controls,
and analyses.
Benzene is a ubiquitous environmental pollutant, present in gasoline
vapors, automobile exhaust, cigarette smoke, and industrial
applications. Long-term, high-level exposure to benzene can lead to
leukemia in humans. A physiologically based pharmacokinetic model of
the uptake and disposition of benzene in mice was developed to predict
the tissue doses of benzene and its metabolites resulting from
inhalation and oral exposure. Since benzene is a known human
leukemogen, the toxicity of benzene in the bone marrow is of most
importance. And because blood cells are produced in the bone marrow,
we investigated the effects of benzene on hematopoiesis (blood cell
production and development). An age-structured model was used to
examine the process of erythropoiesis, the development of red blood
cells. Analysis was done to examine the existence and uniqueness of
solutions of both of these systems. Numerical results for both models
will also be presented.
Friday, March 15th.
Jan Modersitzki, of the
Institut für
Mathematik, Medizinische
Universität zu Lübeck.
Fast algorithms for image registration.
Image registration is one of the fundamental tasks in image processing.
Registration is needed whenever images are spatially distorted.
Typically, one has to deal with two images of an object, where the
images are taken at different times, from different perspectives, or
with different imaging devices. Another important source for
registration are images stemming from different but similar objects.
Given the two images, the goal of registration is to find a
transformation, such that the deformed image matches the other image
subject to a suitable distance measure.
In this talk, different medical applications are presented, each
demanding for its own particular registration technique.
A unified mathematical formulation for image registration
based on a variational approach is given. In this formulation the
desired transformation is characterized as a minimizer of a certain
functional, which does combine a similarity and a smoothness measure.
A variety of similarity and smoothness measures is discussed.
In particular, the diffusion- and the elastic-registration
are considered in detail. For the diffusion-registration an
O(n) algorithm based on an additive operator splitting
scheme is derived whereas for the elastic-registration an
O(n log n) algorithm based on fast Fourier transformation type
techniques is presented. Here, n denotes the number of voxels.
Finally, the performance of the schemes is demonstrated for typical
medical applications.
Thursday, March 14th, 4:10p.m.
Prahlad Ram, of the
Department of Pharmacology
and Biological Chemistry,
Mount Sinai School of Medicine.
Computational analysis of a biological signaling network.
Signaling networks receive and process information to control the
function of cellular machines. The MAP-kinase 1,2/protein kinase C
system is one such network that regulates many cellular machines,
including the cell cycle machinery and autocrine/paracrine factor
synthesizing machinery. We used a combination of computational analysis
and experiments in NIH-3T3 fibroblasts to understand some of the design
principles of this controller network. We find that the growth factor
stimulated MAP-kinase 1,2/protein kinase C network can operate as both a
monostable as well as a bistable system. At low concentrations of
MAP-kinase phosphatase the system exhibits bistable behavior, such that
brief stimulus results in sustained MAP-kinase activation. The
MAP-kinase induced increase in the levels of MAP-kinase phosphatase
moves the network to a monostable state, where it behaves as
proportional response system responding acutely to stimulus, but
incapable of sustained responses. Thus the MAP-kinase1, 2/protein kinase
C controller network is flexibly designed and MAP-kinase phosphatase is
the locus of flexibility.
Wednesday, February 27th.
Terry Lybrand, of the
Department of Chemistry and the
Center for Structural Biology,
Vanderbilt University.
Molecular modeling of protein-ligand interactions: Detailed
simulations of a biotin-streptavidin complex.
Wednesday, February 6th.
Rakesh, of the
University of Delaware,
and Vanderbilt University.
Inverse problems for hyperbolic PDE.
We examine some inverse problems for Hyperbolic PDE motivated
by problems from seismology. Here the goal is to determine the
coefficients of a PDE from the value of the solution of the PDE on the
boundary of the domain - the coefficients representing the properties of
the interior of the earth and the solution of the PDE representing the
acoustical measurements. We describe uniqueness and reconstruction
results when the domain is one dimensional and some partial results
in the multidimensional case.
Friday, February 1st.
Radu C. Cascaval, of the
Department of Mathematics,
University of Missouri-Columbia.
Pulse wave propagation in blood vessels.
The pulse wave in the circulatory system is initiated in the heart and
propagates along the vascular tree. The elasticity of the vascular walls
and the change in the cross-section area are major factors in the
deformation of the wave. I will describe a simplified one-dimensional
model for the pulse wave propagation through the blood vessels, which
takes into account the elasticity of the wall as well as the tapering
effect. The spatial dynamics in this model is governed by a variable
coefficient dispersive equation with initial conditions given at the
inflow. An existence theory for the associated evolution equation, based
on a semilinear Hille-Yosida theory, will be detailed.
Wednesday, January 30th.
K. Renee Fister, of the
Department of Mathematics and Statistics,
Murray State University.
Optimal control of a competitive age-structured system.
The existence and uniqueness of an optimal control that maximizes
a given objective functional over an admissible set of controls for a
competitive population system will be proven. Ekeland's principle is a
vital mechanism for these results. In the process of determining the
well-posedness of the optimal control, the optimality system, which is
the state system coupled with the adjoint system, is developed.
Monday, January 21st.
Shigui Ruan, of the
Department of Mathematics and Statistics,
Dalhousie University
and the
Department of Mathematics,
Vanderbilt University.
Multiple Parameter Bifurcations in Ecological and Epidemiological
Models.
In this talk we will see that many biological systems such as
predator-prey models with constant harvesting, epidemiological models
with nonlinear incidence rate, predator-prey models with nonmonotonic
functional response, etc. exhibit codimension two bifurcations which
include Hopf, saddle-node, and homoclinic bifurcations. Examples of
codimension three bifurcations will also be given.
Wednesday, January 16th.
John Hotchkiss, of the
University
of Minnesota Medical School.
Mathematical aspects of mechanical ventilation: What
lies beneath.
Mechanical ventilation is best known as a lifesaving supportive
therapy applied to critically ill patients who are unable to
breathe for themselves. Unfortunately, mechanical ventilation
also has several serious associated problems: it can damage the
lungs, the level of support may be inadequate for the patients'
needs, and it may provoke discomfort or irregular breathing
patterns. Each of these problems-ventilator induced lung
injury, titration of support, and patient-ventilator synchrony,
is amenable to rigorous mathematical analysis. In this talk,
we will discuss our recent work in which such mathematical
analyses have been employed to address clinical problems arising
from mechanical ventilation, focusing on those findings with
the most direct clinical implications and greatest potential
for improving patient care.
Wednesday, January 9th.
Walter Chazin, of the
Department of Biochemistry,
Department of Physics,
Center for Structural Biology
and the Biomolecular NMR Center,
Vanderbilt University.
Determination of atomic resolution structures of proteins from
nuclear magnetic resonance data and computational analysis.
The development of multi-dimensional nuclear magnetic resonance (NMR)
spectroscopy more than 20 years ago opened up the possibility of
applying this powerful spectroscopic tool to the analysis of
biomacromolecules including proteins, DNA and RNA. It is now
possible to determine the three dimensional structure at atomic
resolution of proteins with a molecular weight up to 30,000 Da.
This presentation will cover some of the basic principles of the
application of NMR to biological molecules, highlight the
challenges, and summarize how structural information is used in
biomedical
research.
Previous semesters:
