(Alphabetical order)

(P) = Plenary speaker, (I) = Industry

Ahmed, S. Ejaz
(Department of Mathematics & Statistics, University of Windsor)

-Title: **Improved Estimation Strategies for Tumor Growth Rate **

-Abstract:
From tumor to tumor, there is a great variation in the proportion
of cancer cells growing and making daughter cells that ultimately
metastasize. The differential growth within a single tumor, however,
has not been studied extensively and this may be helpful in predicting
the aggressiveness of a particular cancer type. The estimation problem
of tumor growth rates from several populations is studied. The baseline
growth rate estimator is based on a family of interacting particle
system models which generalize the linear birth process as models of
tumor growth. These interacting models incorporate the spatial structure
of the tumor in such a way that growth slows down in a crowded system.
Approximation-assisted estimation strategy is proposed when initial
values of rates are known from the previous study. Some alternative
estimation strategies are suggested and the relative dominance picture
to the benchmark estimator is investigated. The analytical and
numerical results demonstrate that our suggested estimator outperforms
the classical estimator.

Alber, Mark S. (P)
(Center for the Study of Biocomplexity, University of Notre Dame)

-Title: ** Multiscale Modeling in Biology**

-Abstract:

A multiscale model of blood clot formation will be
described which combines a detailed tissue factor pathway submodel
of blood coagulation, a blood flow submodel and a stochastic
discrete cell submodel [1,2]. It will be shown that low levels of
FVII in blood result in a significant delay in thrombin production
demonstrating that FVII plays an active role in promoting clot
development at an early stage. We will also describe a new
subcellular element method for simulating cellular blood components.
In addition, multiscale models of chemotactic cell motion [3] and
bacterial swarming will be discussed [4].

[1]. Xu, Z., J. Lioi, J. Mu, X. Liu, M.M. Kamocka, E.D. Rosen, D.Z.
Chen and M.S. Alber, A Multiscale Model of Venous Thrombus Formation
with Surface-Mediated Control of Blood Coagulation Cascade,
Biophysical Journal (to appear).

[2]. Xu, Z., Chen, N., , Kamocka, M.M., Rosen, E.D., and M.S. Alber
[2008], Multiscale Model of Thrombus Development, Journal of the
Royal Society Interface, 5 705-722.

[3]. Lushnikov, P.P., Chen, N., and M.S. Alber [2008], Macroscopic
dynamics of biological cells interacting via chemotaxis and direct
contact, Phys. Rev. E. 78, 061904

[4]. Wu, Y., Jiang, Y., Kaiser, D., and M. Alber [2009], Periodic
reversal of direction allows Myxobacteria to swarm, Proc. Natl.
Acad. Sci. USA, 106 4 1222-1227 (featured in the Nature News, January
20th, 2009, doi:10.1038/news.2009.43).

Arciero, Julia
(Mathematics, University of Pittsburgh)

-Title: **Simulating wound healing with a two dimensional continuum mechanical model**

-Abstract:

Collective cell migration is an important mode of cell movement during
wound healing. We have developed a two-dimensional continuum mechanical
model that is used to simulate cell sheet migration and that captures the
mechanical coupling between cells in the layer, the adhesion of cells to
the substrate, the forces generated by lamellipodia at the cell edge and
within the layer, and the proliferation and apoptosis of cells in the
layer. The governing equations are solved numerically using a level set
method. The model is calibrated by comparing the predicted density of the
layer with experimentally observed cell density. Model results show good
agreement with experimental observations of the dependence of the rate of
wound closure on time.

Bobeldyk, Denton (I)
(Davenport University and DJB Consulting L.L.C.)

-Title: ** Biometrics - Applications and Challenges**

-Abstract:

Biometrics is the science of teaching machines (computers)
to identify unique biological characteristics or traits
in humans; these identifications are then used to
authenticate people or pick out known terrorists in a crowd.
Uniquely identifying people based on biological traits
can be quite a challenge. Some modalities provide high
accuracy such as iris or fingerprint, while other modalities
provide the ability to identify from large distances such
as gait (the way you walk). A brief overview of the
algorithms currently being used for each of the modalities
will be discussed as well as areas that require further
mathematical research.

Chou, Ching-Shan
(Mathematics, Ohio State University)

-Title: ** Spatial Dynamics of Stem Cells and Multi-Stage
Cell Lineages in Tissue Stratification**

-Abstract:

In developing and self-renewing tissues, differentiated
cell types are typically specified through the actions of
multistage cell lineages. Such lineages commonly include a
stem cell and multiple progenitor (transit amplifying; TA)
cell stages, which ultimately give rise to terminally
differentiated (TD) cells. Typically, as the tissue reaches
a tightly controlled steady-state size, the cells at
different lineage stages also assume distinct spatial
locations within the tissue. Although significant genetic
information are revealed on locations of different type of
cells, the underlining mechanisms that cause the spatial
heterogeneity are not yet completely understood. In this
talk, I will present modeling and simulations to explore
several plausible strategies that can be utilized to create
stratification during development or regeneration of
olfactory epithelium (OE) in mouse.

Dr. Gideon Eden
(CEO, Biolumix Inc)

-Title: **Practical Aspects of Bacterial Growth Model**

-Abstract:
An automated optical instrument has been developed to
rapidly detect the presence of bacteria in a sample. The
instrument is based upon the analysis of bacterial growth
patterns manifested by their metabolic processes in a
mixture of growth media and optical indicators. A
mathematical model is presented to predict the nature of
the patterns detected by the instrument, and to derive
intrinsic properties of bacterial growth. Correlation to
the traditional "plate counts" performed in Petri dish is
demonstrated.

Friedman, Avner (P)
(Mathematical Biosciences Institute, Ohio State University)

-Title: ** What is mathematical biology and how useful is it?**

-Abstract:

I shall define what is meant by 'mathematical biology',
and then proceed to illustrate the degree of its usefulness
by examples taken from projects developed at the Mathematical
Biosciences Institute: chronic wound healing; modeling of the
immune rheostat of macrophages in the lung in response to
infection; neointimal hyperplasia occurring in dialysis,
tuberculosis as a disease with prognosis which depends on
the age of the patient, and viral treatment of glioblastoma.
All these examples are modeled by systems of differential
equations, and the challenges are:
1) Researching the biological literature in order to set
up a mathematical model;
2) Determining the rate parameters;
3) Simulating the model.
The final test is to show good fit with experimental results,
after which the model can be used to suggest new biologically
testable hypotheses.

Gurarie, David (Mathematics, Case Western Res University)

-Title: ** Immune regulation of malaria infection: model
calibration and Agent-Based Communities**

-Abstract:

The talk will outline basic biology of malaria infection
within host, and develop mathematical models that account for
parasite growth and its immune regulation. We shall discuss
how such models can be calibrated using malaria-therapy data,
and present some recent results.
Our calibrated in-host model can serve as a building block
for Agent-based Communities (ABC). We shall demonstrate a
few examples of such ABC, and look at the effect of
transmission intensity on the resulting patterns of parasitemia.
Our long-term goal is to apply 'agent-based' methodology to
study parasite transmission and control in realistic environment,
as an alternative to the standard population-based SIR
approach (Ross-Macdonald).

Dr. Heng, Henry (I)
(Center for Molecular Medicine and Genetics, and Karmanos Cancer Institute,
Wayne State University School of Medicine)

-Title: **Can mathematics solve the mystery of biology?**

-Abstract:
The interface between mathematics and biology presents both
a challenge and an opportunity for biologists and mathematicians.
Underscored by the explosion of biological data and the
increasing usage of computational modeling, 21st-Century biology
requires new mathematic tools to solve biological mysteries.
In this presentation, I will briefly review some of the key
features that are unique to biological systems, and some
corresponding limitations of current mathematic tools. By
asking a fundamental question, is mathematical theory required
for the maturation of biological science, this presentation
strives to call attention to this important issue and hopes
to develop collaboration with mathematicians.

Jain, Harsh
(Mathematical Biosciences Institute, Ohio State University)

-Title: **A Biochemical Perspective to an Agent-based
Model of VEGF-induced Capillary Formation**

-Abstract:

I present a hybrid model of VEGF-induced capillary network
formation, based on the theory of reinforced random walks.
A major component of such a model is endothelial cell (EC)
chemotaxis. I therefore begin with simulating the motion
of a single EC under the influence of a gradient of VEGF.
In this model, the cell responds by polarizing itself in
response to VEGF bound to cell-surface receptors. This is
in contrast to the classical modeling approach that
approximates motion as a function of free VEGF
concentrations. A novel chemotactic sensitivity function
is proposed for cellular motion, incorporating biological
details hitherto ignored by the phenomenological
sensitivity functions in current literature. Biologically
observed phenomena such as the ability of endothelial
cells to sense a chemical gradient as low as 1-2% across
their lengths, and their resulting polarization and
movement is captured by this model. Later, the model for
the motion of a single cell is modified to simulate
capillary network formation under the influence of VEGF.
Empirically observed proliferative regions behind
developing sprout tips match those in our simulations,
thereby validating this model. To our knowledge, this is
the first instance of the inclusion of this level of
molecular detail in a spatial model of VEGF-induced
angiogenesis. It provides a basic framework for the
addition of further cellular and sub-cellular events in
such models, in order to elucidate the mechanisms of
chemokine mediated vasculogenesis.

Kang, Yeona
(Materials Science & Engineering, SUNY at Stony Brook)

-Authors: Yeona Kang(*) and C. M. Fortmann

-Title: ** A structural basis for the Hodgkin and Huxley
relation**

-Abstract:

Neural channel transport was analyzed using a previously
reported relation for charged particle transport in two
energy-type gradients: the electric field and here a
water/strucural deformation energy. Neural channels are
lined with alpha-helix structures filled with water
vapor and sequestered hydrophobic amino acids arranged
to present minimum water vapor and water-hydrophobic
interface. Cation point charges generate enormous
electric fields on sub-nanometer distances. Electrostatic
energy reduction is characterized by dielectric water
being pulled toward the transporting ion deforming the
neural channel. An ion-water-structure coupling energy
is induced by changes in channel diameter width. The
resultant two energy gradient relation for cation
transport: reduces to the Hodgkin-Huxley relation
[A. L. Hodgkin and A. F. Huxley, J. Physiol. (London)
116, 449 (1952)], explains channel selectivity and
environmental sensitivity, predicts fast non-dispersive
transport under a narrow range of conditions, and produces
current-voltage characteristics consistent with observation.

Kao, Chiu-Yen
(Mathematics, Ohio State University)

Authors: Anastasios Matzavinos,Chiu-Yen Kao, J. Edward F.
Green, Alok Sutradhar, Michael Miller and Avner Friedman

-Title: ** Modeling oxygen transport in surgical tissue transfer**

-Abstract:
Reconstructive microsurgery is a clinical technique used to transfer large
amounts of a patient's tissue from one location used to another in order
to restore physical deformities caused by trauma, tumors, or congenital
abnormalities. The trend in this field is to transfer tissue using
increasingly smaller blood vessels, which decreases problems associated
with tissue harvest but increases the possibility that blood supply to the
transferred tissue may not be adequate for healing. It would thus be
helpful to surgeons to understand the relationship between the tissue
volume and blood vessel diameter to ensure success in these operations. As
a first step towards addressing this question, we present a simple
mathematical model that might be used to predict successful tissue
transfer based on blood vessel diameter, tissue volume, and oxygen
delivery.

Khain, Evgeniy
(Physics, Oakland University)

-Authors: E. Khain, C. M. Schneider-Mizell, M. O. Nowicki, E. A. Chiocca,
S. E. Lawler and L. M. Sander

-Title: ** Clustering of brain tumor cells: theory and experiment**

-Abstract:

We investigate clustering of malignant glioma cells [1]. In vitro
experiments in collagen gels identified a cell line that formed
clusters in a region of low cell density, whereas a very similar
cell line (which lacks an important mutation) did not cluster
significantly. We hypothesize that the mutation affects the
strength of cell-cell adhesion. We investigate this effect in
a new experiment, which follows the clustering dynamics of glioma
cells on a surface. We interpret our results in terms of a
stochastic model and identify two mechanisms of clustering. First,
there is a critical value of the strength of adhesion; above the
threshold, large clusters grow from a homogeneous suspension of
cells; below it, the system remains homogeneous, similarly to the
ordinary phase separation. Second, when cells form a cluster, we
have evidence that they increase their proliferation rate. We
have successfully reproduced the experimental findings and found
that both mechanisms are crucial for cluster formation and growth.

Ref. E. Khain, C. M. Schneider-Mizell, M. O. Nowicki, E. A. Chiocca,
S. E. Lawler and L. M. Sander, EPL (Europhysics Letters) 88, 28006
(2009).

Kim, Eunjung
(Mathematics, University of Notre Dame)

-Authors: Eunjung Kim, Zhiliang Xu, and Mark Alber

-Title: **Contributions of branching points to fibrin network
strength and stability**

-Abstract:
Blood clots are primarily composed of a network of branched fibrin
fibers. These fibrin networks stabilize the primary platelets and
enable blood clots to withstand the blood flow during wound healing
at sites of vascular injury. The structure of the network is believed
to be an essential component to its function. In the present study,
a three-dimensional mechanical model of a fibrin network was
developed to determine the detailed relationship between the network
structure and its mechanical properties. We compare the mechanical
responses of the network for two distinct structures; high branching
vs. low branching based on image analysis of in situ fibrin network
data.

Lee, Pilhwa
(Wolgemuth lab, Department of Cell Biology,
University of Connecticut Health Center, Courant Institute, New York University)

-Title: **Toward wound healing of MDCK tissue : model and experiments
**

-Abstract:

The migration of crawling cells is considered in their behavior of
wound closure. The talk is focused on the mechanical contribution of
crawling cells, i.e. dipole stress, and the stress dynamics derived
from Lacker-Peskin model. In our model, actomyosin driven purse-strings
or biochemical signaling of Rho family do not involve directly.
In simplified one-dimensional formulations, velocity profiles for
healing are explored in terms of turn-over rate and cell-to-cell
viscosity mediated by Cadherin proteins. For the circular wound assay,
we show a transition from closure to non-closure behavior with the
dead cell zone in the epithelial layers, which supports the
hypothesis that a crawling cell's dipole can close wounds without
purse strings or signaling. In a rigorous two-dimensional model, we
observe the healing speed is dependent on the assay width. There are
long-range correlations in the scale of 100 micron from streaming and
circulating cells. All of them are consistent with experimental data
from MDCK assay.
Interestingly, a bundle of tissue parameters applied in the
one-dimensional approximation is a good precursor for the parameter
exploration on two-dimensional simulation.

Lim, Sookkyung
(Mathematics, University of Cincinnati)

-Title: **Electrostatic effects on the supercoiling DNA**

-Abstract:

We investigate the effects of electrostatic and steric
repulsion on the dynamics of pre-twisted circular DNA
in a viscous incompressible fluid. The DNA is modeled as
a charged elastic rod represented by a three-dimensional
closed axial curve and orthonormal triads embedded in each
cross-section. Equations of motion of the rod, which include
the fluid-structure interaction, are solved by the
generalized immersed boundary method combined with the
Cosserrat theory of an elastic rod. We include a modified
Debye-Huckel repulsive force in which the
electrostatic force depends on the salt concentration and
the distance between base pairs, and a close range steric
repulsion force to prevent self-penetration. We find that
after perturbation a pretwisted DNA circle collapses into
a compact supercoiled configuration. The collapse proceeds
along a complex trajectory that may pass near several
equilibrium configurations of saddle type, before it
settles in a locally stable equilibrium. The final
configuration is sensitive to the initial excess link,
ionic stregth of the solvent, and the initial perturbation.

Liu, Di (Richard)
(Depatment of Mathematics, Michigan State Univeristy)

-Title: ** Numerical methods for stochastic bio-chemical
reacting networks with multiple time scales**

-Abstract:

Multiscale and stochastic approaches play a crucial
role in faithfully capturing the dynamical features and
making insightful predictions of cellular reacting systems
involving gene expression. Despite their accuracy, the
standard stochastic simulation algorithms are necessarily
inefficient for most of the realistic problems with a
multiscale nature characterized by multiple time scales
induced by widely disparate reactions rates. In this talk,
I will discuss some recent progress on using asymptotic
techniques for probability theory to simplify the complex
networks and help to design efficient numerical schemes.

Matzavinos, Anastasios
(Mathematics, Iowa State University)

-Title: **Spectral clustering methods in data processing
and image analysis**

-Abstract:

The need to interpret and extract possible inferences from
high-dimensional datasets has led over the past decades to the
development of dimensionality reduction and data clustering techniques.
Scientific and technological applications of clustering methodologies
include among others computer imaging, data mining and bioinformatics.
Current research in data clustering focuses on identifying and
exploiting information on dataset geometry and on developing robust
algorithms for noisy datasets. Recent approaches based on spectral
graph theory have been devised to effciently handle dataset geometries
exhibiting a manifold structure, and fuzzy clustering methods
have been developed that assign cluster membership probabilities to
data that cannot be readily assigned to a specific cluster. In this
talk, we develop a novel fuzzy spectral clustering algorithm
that combines seamlessly the strengths of spectral approaches to
clustering with various desirable properties of fuzzy methods. The
developed methodology is applied to biomedical image segmentation
and registration problems.
(Work in collaboration with Sunder Sethuraman of Iowa State University
and Philip K. Maini, Radek Erban, and Ornella Cominetti of the
University of Oxford.)

Mikhaylov, Jessica
(Mathematical Sciences, United States Military Academy)

-Title: **Evaluating an improved two-compartment model
to determine tumor angiogenesis parameters using contrast-enhanced
dynamic imaging data**

-Abstract:
The most common methods for determining the efficacy of cancer
treatments against tumors involves a pair of pre/post-treatment
contrast-enhanced medical image sequences, such as MRI or CT.
Currently, this data is often analyzed using static images to do
a visual size comparison. Unfortunately, the time between image
sequences must be large, on the order of months, to see a
meaningful potential change in tumor size. With the goal of
reducing the time between tests to a time scale of weeks,
radiologists and mathematicians have explored methods of using
the dynamic data available from the tests to see if blood flow
parameters (perfusion, permeability, volume compartment sizes
for the plasma and the interstitial space) can be estimated
and if these measurements can in turn provide insight about
the efficacy of the treatment. In previous work, it was shown
that a fundamental assumption regarding capillary re-uptake
was flawed, and current work attempts to recover the parameters
without this assumption. Using model data sets and sampled
model data sets, two of the parameters can be recovered,
however, in the presence of noise, these methods show weakness.
This talk will give an overview of the background research
and will show the current results using model data sets
subjected to Gaussian noise (with and without smoothing) and
a fixed bias.

Rong, Libin
(Los Alamos National Laboratory, Dept of Mathematics, Oakland University)

-Title: ** Rapid emergence of hepatitis C virus protease
inhibitor resistance**

-Abstract:

Telaprevir, a novel hepatitis C virus (HCV) protease
inhibitor, has demonstrated substantial antiviral
activity in patients with chronic HCV infection. However,
drug-resistant variants emerge at frequencies of 5-20%
as early as day 2 after treatment initiation. Using
probabilistic and viral dynamic models, we show that
such rapid emergence of drug resistance is expected.
We calculate that all possible single and double mutants
preexist, and that one additional mutation is expected
to arise during therapy. Examining the case of telaprevir
therapy in detail, we show the model fits observed
dynamics of both drug-sensitive and resistant viruses,
and argue that combination therapy of direct antivirals
will require drug combinations that have a genetic
barrier of 4 or more mutations.

Sander, Leonard M.
(P) (Physics, University of Michigan-Ann Arbor)

Title: **Biomechanics of cell motility in Dictyostelium**

Abstract:

The mechanics of cell motility has a number of surprising
features that need to be included in models of the process.
Recent experiments on the motion of the ameba Dictyostelium
discoideum in chemotaxis show that contractile forces on the
substrate are two orders of magnitude larger than the force
necessary to propel the cell forward against fluid friction.
Most of the work done by the cell goes towards peeling it
from the substrate (breaking the adhesive bonds); viscoelastic
effects and friction are completely negligible. We give a
new mechanical model based on this idea, and show how it
agrees with experimental results on the cell speed of wild-type
and mutated dicty.

Sheng, Jim (I)
(U.S. Army Tank Automotive Research and Development)

- Title: **Occupant Injury Risk Assessment Under Vertical Loading**

- Abstract:
During the past five decades, tremendous efforts have been
made in understanding human injury during automotive crashes,
and in developing test devices for occupant protection studies.
In most cases of an automotive crash, occupants experience
lateral loadings. The occupant protection in vertical loading
conditions originated from the work in the early years of ejection
seat designs, where DRI is the main injury risk assessment index.
During the last few years, blast threats such as landmines and
improvised explosive devices (IED) posed a significant injury
and fatality risk to occupants in military ground vehicles. The
occupant injuries associated with severe vertical loading have
drawn more and more attention of researchers, and engineers.
While DRI is still a useful tool to assess occupant spinal
injury associated with vertical loading, Effective G and the
associated pulse duration is found to be a better index to be
correlated to occupant injuries. This presentation will discuss
DRI, Effective G and pulse duration and their correlation to
occupant injury during vertical loadings.

Spagnuolo, Anna
(Mathematics, Oakland University)

-Title: ** A Mathematical Model for Vibrio Cholera
Colonization in the Human Intestine**

-Abstract:
* Vibrio cholera* is a strict human pathogen that causes
pandemic cholera. It is an old-world pathogen that has
re-emerged as a new threat since the early 1990s.
* V. cholera* colonizes the upper, small intestine where
it produces a toxin that leads to the watery diarrhea,
characterizing the disease. Colonization dynamics of
the bacteria are largely unknown. Although a large
initial infectious dose is required for infection, data
suggests that only a smaller sub-population colonizes
a portion of the small bowel leading to the disease.
There are many barriers to colonization in the
intestines. In this talk, I will elaborate on the
dynamics of * V. cholera* infection by describing a
mathematical model that governs the colonization process
for the bacterial dynamics.

Srinivasan, Parthasarathy
(Mathematics, Cleveland State University)

-Title: ** Estimating Biophysical Properties of Nitric Oxide**

-Abstract:

Nitric oxide (NO) derived from the endothelium is a
potent vasodilator, and plays a crucial role in
maintaining vascular tone. Being a small diatomic
molecule, it has so far been assumed that the diffusion
rate of NO is the same as in solution. However, this
hypothesis has not been tested experimentally. Recent
methods have enabled us to measure the flux of NO
across the aortic wall directly. We present a simple
mathematical model from which we can obtain the
diffusion and partition coefficients of NO across the
aortic wall using these measurements. Our results show
that the diffusion coefficient of NO in tissues is
four times slower than in solution under normal
physiological conditions, which indicates that the
diffusion of NO (and hence its bioavailability) in the
vascular wall is crucially dependent on the environment
where the molecule diffuses. We also examine the role
that oxygen plays in the bioavailability of NO in the
vasculature. Our results suggest that the
oxygen-dependent NO consumption could play an important
role in dilating blood vessels during hypoxia by
increasing the effective NO diffusion distance.

Stolarska, Magdalena
(Mathematics, University of St. Thomas)

- Authors: Magdalena A. Stolarska

- Title: ** A model of cellular movement and its effect on
substrate traction patterns**

- Abstract:

Mechanical interactions between a cell and the substrate
are vital for cell migration and are involved in various
cellular processes, such as wound healing, embryonic
development, and metastasis of cancerous tumors. As a
result, understanding the nature of force generation by
single cells and the mechanical interaction of a cell
with the substrate is extremely important, and
mathematical models are being used in furthering this
understanding. In this talk, we present a continuum
model of the mechanics of single cell motility in which
the stresses that result from the active deformation of
the cell are transmitted to a deformable substrate via
adhesion sites that are modeled as either fixed
connections or frictional interaction between the cell
and the substrate. A finite element implementation of
this model is used to numerically examine the nature of
the stresses generated by the cell and the resulting
traction patterns that occur at the substrate. We use
the model to better understand what are the local active
deformation profiles and the adhesion types necessary
to replicate experimentally observed motion and traction
patterns of different cell types.

Thomas, Peter J. (Department of Mathematics, Department of Biology, Case Western Reserve University)

-Authors: Suparat Chuechote (1), Harihara Baskaran (2,3), Peter Thomas (1,4,5)

(Case Western Reserve University, Departments of (1)
Mathematics, (2)Chemical Engineering, (4) Biomedical
Engineering, (4) Biology, (5)Cognitive Science)

-Title: ** Effects of Fluctuations in a 2D Model of Gradient Sensing**

-Abstract:

Chemotaxis is the directed migration of cells guided by chemical
gradients. This process plays a role in embryogenesis, immune response,
wound healing and tumor metastasis. During chemotaxis, a cell detects
extracellular chemoattractants and translates these signals into a
complex cellular response resulting in morphological reorganization and
motility. The accuracy with which a cell can determine an external
chemical gradient is limited by fluctuations arising from the discrete
nature of second messenger release and diffusion processes within the
small volume of a living cell. These sources of intrinsic noise have
the potential to attenuate or disperse gradient information transduced
by
the membrane bound receptors. At the same time, models of the
intracellular signaling network have been devised that use a combination
of local excitation and global inhibition to sharpen the intracellular
gradient signal. In this study, we implement a stochastic version one
such model, the "balanced inactivation" model (Levine et. al. 2006), in
a two dimensional geometry. We develop a fixed timestep approach in
which the probabilities of individual molecules making spatial or
chemical transitions is treated as a system of multinomial random
variables. With this numerical framework we investigate the
relationship
between the amplification of the gradient signal, the propagation of
noise in the signaling pathway, and fundamental limits on the accuracy
of the gradient sensing mechanism.

Tian, Jianjun Paul
(Mathematics, College of William and Mary)

-Title: **A challenging problem in the competition between
two stem cells**

-Abstract:

In this talk, I will briefly introduce a difficult problem arising
from two germline stem cell competition process. In the female germline
stem cell niche, there are 2 or 3 stem cells. Recent biological
experiments showed that there is a competition for the niche space
occupancy among stem cells. Stem cells compete by means of physical
interaction. This is a new mechanism of cell interactions, and it is
different from the well-understood cell interaction via sending and
receiving chemical signals. The stem cell physical interaction
involves a series of biochemical and biophysical processes. It is
difficult to understand without considering these processes in
molecular level. We propose a model that is a reaction-diffusion
system over cell surfaces with two free boundaries. I will report
the model and some research on simplified version of the model.

Umulis, David
(Agricultural and Biological Engineering, Purdue University)

-Title: ** Systems biology of tissue patterning:
insights from Drosophila embryos, Zebrafish embryos,
and the Drosophila germarium**

-Abstract:

The spatiotemporal regulation of cell differentiation
relies on numerous extracellular cues, intracellular
responses, and feedback interactions between the
intra- and extracellular environment. However, the
classic view of morphogen-mediated patterning considers
decoupled gradient formation and cell-interpretation
events. To investigate the dynamic signaling landscape
of cells embedded in a tissue we focused on models of
stem cell regulation and early embryo development. For
each unique patterning context, we developed 3D finite
element models based on available image data and employed
a common approach to address the following question:
How does feedback between intra- and extracellular
environments impact morphogen activity and patterning?
To address this question in the context of stem-cell
regulation by Bone Morphogenetic Proteins (BMPs), we
developed a 3D model of the Drosophila germarium. We found
that positive feedback that enhances ligand endocytosis
leads to cell competition for limited amounts of BMP
ligands and support for only 2-3 stem cells per niche,
consistent with experimental observations. We extended
the study to embryonic patterning by BMPs and found
that positive feedback that leads to increased endocytosis
capacity leads to a similar cell-competition event and
autoregulation of the number of high BMP-signaling cells.
In the context of developing Zebrafish embryos, positive
feedback on an extracellular regulator called Sizzled
autoregulates the morphogen distribution shape, ensuring
robust patterning of multiple target genes. In summary,
the autoregulation of morphogens by feedback provides
a mechanism to ensure robust delineation of cell
populations through competition and modification of
gradient shape.

Wei, Guowei
(Mathematics, Michigan State University)

-Title: **Differential geometry based multiscale models for
biomolecular systems**

-Abstract:

This talk focuses on a new multiscale paradigm developed at MSU
--- the differential geometry based multiscale models of
biomolecules. Under the physiological condition, most biological
processes, such as signal transduction, ion channel transport and
protein folding, occur in water, which consists of 65-90 percent
human cell weight. Therefore, solvent and synergy of solvent-solute
are important to the understanding of biomolecular structure,
function, dynamics and transport. I will discuss the use of differential
geometry theory of surfaces for coupling microscopic and macroscopic
scales at an equal footing. The biomolcule of interest is described
by discrete atomic and quantum mechanical variables. While the aquatic
invironment is described by continuum hydrodynamical variables. We
derive the coupled geometric flow equation, Navier-Stokes equation,
and generalized Poisson-Boltzmann equation (PBE) to describe the dynamics
of the biomolecular systems. Applications will be discussed to protein
folding, ion channels, micro/nanofluidics, and nano-bio sensors.

Acknowledgment:
This work was supported by NSF and NIH grants.

Xue, chuan
(Mathematical Biosciences Institute, Ohio State University)

-Title: ** Modeling Ischemic Cutaneous Wounds**

-Abstract:

Chronic wounds represent a major public health problem affecting 6.5
million people in the United States. Ischemia, primarily caused by
peripheral artery diseases, represents a major complicating factor in
cutaneous wound healing. In this talk, we present a mathematical model
of ischemic dermal wounds. The model consists of a coupled system of
partial differential equations in the partially healed region, with
the wound boundary as a free boundary. The extracellular matrix (ECM)
is assumed to be viscoelastic, and the free boundary moves with the
velocity of the ECM at the boundary. The model equations involve the
concentration of oxygen, PDGF and VEGF, the densities of macrophages,
fibroblasts, capillary tips and sprouts, and the density and velocity
of the ECM. Simulations of the model demonstrate how ischemic
conditions may limit macrophage recruitment to the wound-site and
impair wound closure. The results are in general agreement with
experimental findings.

Yamada, Richard
(Mathematics, University of Michigan-Ann Arbor)

-Title: ** Molecular Noise Enhances Oscillations in the Supra-Chiasmatic
Nuclei Network**

-Abstract:
In this talk, we will discuss a detailed mathematical model
for circadian timekeeping within the SCN. Our proposed model consists
of a large population of SCN neurons, with each neuron containing a
network of biochemical reactions involving the core circadian
components. Using mathematical modeling, our results show that both
intracellular molecular noise and intercellular coupling (nonlinear
in nature) are required to sustain stochastic oscillations in the SCN
oscillator network. Our work focuses on the problem of overcoming
noise in oscillator systems, and our results highlight the importance
of transcriptional noise in enhancing oscillations rather than
dampening them. Surprisingly, our predictions from our model have
been confirmed experimentally; we conclude with a short discussion of
these results.

Zhang, Yongtao
(Mathematics, University of Notre Dame)

-Title: ** Implicit integration factor methods for PDEs on
structured and unstructured meshes and their applications in
morphogenesis**

-Abstract:

Integration factor methods are a class of "exactly linear part"
methods. In [1], a class of efficient implicit integrating factor
(IIF) methods are developed for solving systems with both stiff
linear and nonlinear terms, arising from numerical spatial
discretization of time-dependent partial differential equations
(PDEs) with linear high order terms and stiff lower order
nonlinear terms. A novel property of the scheme is that the exact
evaluation of the linear part is decoupled from the implicit
treatment of the nonlinear part. As a result, the size of the
nonlinear system arising from the implicit treatment is
independent of the number of spatial grid points. The tremendous
challenge in applying IIF temporal discretization for
time-dependent PDEs on high spatial dimensions is how to evaluate
the matrix exponential operator efficiently. I shall first
present the compact IIF methods to deal with this issue for
spatial discretization on structured meshes. For spatial
discretization on unstructured meshes to solve PDEs on complex
geometrical domains, how to apply the compact IIF approach is
unclear. To solve this problem, we apply the Krylov subspace
approximations to the matrix exponential operator and obtain
an efficient and accurate Krylov subspace based IIF method. This
novel time discretization technique is applied to Discontinuous
Galerkin (DG) methods on unstructured meshes for solving
reaction-diffusion equations. Numerical examples are shown
to demonstrate the accuracy, efficiency and robustness of the
method in resolving the stiffness of the DG spatial operator
for PDEs which have high order spatial derivatives. Application
of the methods to numerically solving mathematical models
arising in morphogenesis during Drosophila and zebrafish
embryos development, and vertebrate limb development will be
shown.

[1] Nie, Q., Zhang, Y.-T., and Zhao, R., Efficient semi-implicit
schemes for stiff systems. Journal of Computational Physics, 2006.
214: p. 521-537.

Zheng, Xiaoming
(Mathematics, Central Michigan University)

-Authors: Trachette Jackson (Mathematics, University of Michigan),
Gou Young Koh (National Research Laboratory of Vascular Biology, Korea
Advanced Institute of Science and Technology)

-Title: ** A continuous model of angiogenesis: initiation, extension and
maturation**

-Abstract:

Angiogenesis, formation of new blood vessels, is essential to many
physiological and pathological processes, such as wound healing and
tumor growth. Angiogenesis is one of the fastest growing biomedical
research disciplines in the past 20 years. However, there are very few
mathematical models of angiogenesis compared with the explosion in
experimental data. In this talk, we will present a brand new
mathematical model of angiogenesis, which covers three critical events:
endothelial cell activation (or the new blood vessel initiation),
sprout extension, and maturation of new blood vessels. We
investigate the regulating mechanisms of three families of growth
factors: Vascular Endothelial Growth Factor (VEGF), Angiopoietins
(including Ang1 and Ang2), and Platelet-Derived Growth Factor (PDGF-B).
The biochemical and biophysical properties of two types of cells,
endothelial cells that line the inner wall of blood vessels and
perictyes that coat the outer surface of blood vessels,
will be examined. These growth factors and cells form a complex
multiscale system composed of molecular reactions, cellular responses
and tissue growth. The numerical simulations of the mathematical model
will be presented along with the main results of the study, which
include: demonstrating how the balance of the angiopoietin system serves
as angiogenic switch; highlighting that a proper mechanical model is
necessary to address the blood vessel extension; showing that pericytes
and angiopoietins are central to the maturation process.

Baek, Seunghyeon
(Mathematics, Korea University, South Korea)

-Authors: Inkyung Ahn, Wonlyul Ko and Seunghyeon Baek, Korea University,
South Korea

-Title: **Stationary pattern and stability in a tumor-immune interaction model with immunotherapy**

-Abstract:

A diffusive tumor-immune system with immunotherapy is investigated
under homogeneous Neumann boundary conditions. The large time behavior
of nonnegative equilibria and the persistence of the solution in the
time-dependent system are studied. Especially, a sufficient condition
for the tumor-free states is provided. Furthermore, for this coupled
reaction-diffusion system, we obtain the results for the existence
of nonconstant positive steady state solutions in case that the
parameter for immunotherapy effect is small.

Byun, Jonghyuk
(Mathematics, University of Cincinnati)

-Authors: Donald A. French, Jonghyuk Byun, M.Kupferle, Nick G. Cogan, Sookkyung Lim

-Title: **Fluid motion in an urban pipe with various surfaces**

-Abstract:
We investigate the motion of the fluid dynamics in an urban pipe
system in which the geometry of the pipe surfaces varies. The fluid
motion is compared in two different types of surfaces, cylindrical
surface and curved surfaces. We expect the shear force near the
surface to be influenced by the fluid motion and hence the wall shear
stress may affect on the thickness of the bioflim along the pipe
surface.

Chen, Duan
(Department of Mathematics, Michigan State University)

-Title: **Multiscale Modeling and Simulation for Proton
Translocation in the Ion Channel**

-Abstract:

Aiming at the special properties of the proton and
unique transport mechanism, a general multiscale partial
differential equations model, containing classical and quantum
mechanical theories, is proposed to simulate the translocation
of protons in the ion channel with reasonable biological
assumptions and approximations. Several associated numerical
schemes are employed to solve the model numerically with high
accuracy and efficiency. At last, the validity of this model
is tested through a specific proton channel, the well-known
Gramicidin A, by the channel electrostatic profile and
conductance. With parameters taken in the physiological ranges,
the simulation results agree with the experimental data well.
The limitation of this model will be addressed in future work.

Du, Huijing
(Mark Alber group, Mathematics, University of Notre Dame)

-Authors: Hujing Du, Mark Alber, Zhiliang Xu

-Title: **Multiscale Models of Bacterial Swarming**

-Abstract:

We present an off lattice stochastic model which incorporates
the different motility engines and the reversing capability
to examine the swarming of M. Xanthus. The model also accounts
for the interactions of individual cells with the slime on the
surface left by other cells. Simulations involving the variation
of cell density, aspect ratio, and reversing period were made
and we present some of the results including the optimization
of M. Xanthus reversing period at eight minutes which was
observed experimentally.

Holmes, William (Mathematics, Indiana University)

-Title: ** A 3D computational model of the Mammalian
Cochlea with Asymptotics **

-Abstract:

We seek to build a computational model for the simplified
Mammalian Cochlea with the standard coupled fluid-plate
equations as our base. Physiological data shows a clear
wave nature in the response of the basilar membrane to
stimulus. We seek to explain the presence of this wave
nature and use it as inspiration for a 3D numerical solver.
The results of simulations along with asymptotic arguments
suggest a relationship between the form and function of
the cochlea which we compare to physiological data.

Hengenius, James
(Gribskov and Rundell Labs, Agricultural and Biological Engineering, Purdue University)

-Authors: James Hengenius (*), Ann E. Rundell, Michael
Gribskov, and David M. Umulis

-Title: ** Effects of a realistic 3D domain on models
of Drosophila melanogaster gap gene regulation**

-Abstract:

The fruit fly * Drosophila* melanogaster is a model
organism for studying spatio-temporal dynamics of animal
development. In the gap gene regulatory network, an
initial non-uniform distribution of the transcription
factor Bicoid controls downstream expression of additional
interacting transcription factors. This leads to the
formation of non-uniform protein distributions along the
anterior-posterior axis of the embryo. Previous studies
have considered gap gene regulation as a reaction-diffusion
system in one dimension, fitting models to protein
expression data from a limited lateral region of the embryo.
While these models agree with data in the sampled lateral
region, the embryo has a complex three-dimensional geometry.
Because poor agreement over the full embryo geometry would
indicate incomplete understanding of gap gene regulation,
we evaluated existing model structures over this domain.
Additionally, we optimized model parameters on the 3D domain.
We first implemented a full 3D model using the finite
element method with a mesh derived embryonic nuclei positions.
Model output was fit to expression data from the Quantitative
Spatiotemporal Gene Atlas (Fowlkes et al., 2008) by minimizing
a sum-of-squared-error function. Model outputs from the best
parameter sets were compared to results using previously
published 1D model parameters. While previously published
parameter values recapitulated data in the lateral region,
the model deviated from data over most of the 3D domain. Our
parameter optimization recovered parameter sets that fit the
full 3D model better than previously published parameters.
Our findings indicate that the current models of gap gene
regulation are incomplete and must be revised to account for
geometric effects and possible genetic interactions occurring
outside the lateral region.

Im, Jeong Sook
(Mathematics, Ohio State University)

-Title: ** Boundary integral method for shallow water and
evaluation of the KdV equation in random wave field**

-Abstract:

Consider the two-dimensional incompressible, inviscid and
irrotational fluid flow of finite depth bounded above by a
free interface. Ignoring viscous and surface tension effects,
the fluid motion is governed by the Euler equations and
suitable interface boundary conditions.
A boundary integral technique(BIT) which has an an
advantage of reducing the dimension by one is used to
solve the Euler equations. For convenience, the bottom
boundary and interface are assumed to be 2pi-periodic.
The complex potential is composed of two integrals, one
along the free surface and the other along the rigid bottom.
When evaluated at the surface, the integral along the
surface becomes weakly singular and must be taken in the
principal-value sense. The other integral along the
boundary is not singular but has a rapidly varying
integrand, especially when the depth is very shallow.
This rapid variation requires high resolution in the
numerical integration. By removing the nearby pole, this
difficulty is removed.
In situations with long wavelengths and small amplitudes,
one of the approximations for the Euler equations is
the KdV equation. I compare the numerical solution of
Euler equation and the solution of KdV equation and
calculate the error in the asymptotic approximation.
For larger amplitudes, there is significant disagreement.
Indeed, the waves tend to break and the boundary integral
technique still works well. The comparison is also done
in random wave field. The strong nonlinearity has made
a huge difference in the power spectrum between Euler
equation and KdV equation.

Jordan, Benjamin
(Department of Organismic & Evolutionary Biology, Harvard University)

-Title: ** Coupling tissue growth and reaction kinetics to
model chick limb development**

-Abstract:

The limb of the chicken (G. gallus ) is a model organism
in developmental biology used to study the patterning of
tissues, cell specication, and cell fates. The developing
limb bud tissue responds to protein-gradients in a
concentration-specic manner. Amongst the myriad cellular
responses to these signals, division, dierentiation, death,
and changes to the extracellular matrix are crucial to
our understanding. These responses feed back into both
the chemical interactions and the material properties of
the growing limb bud. To understand the interplay between
growth and patterning, we have developed a model that
couples the production, diusion, reaction and advection
of the relevant chemical species to the growing tissue
domain. By assuming that growth is a plastic-process which
occurs beyond some given yielding threshold, we model the
tissue as a viscous free-boundary uid with a volumetric
source, which is in turn dependent on the concentration
of specic growth factors included in the kinetics network.
In this poster, I describe the mathematical model, discuss
the parametrization, and explain the algorithm for the
numerical solution. Specically, details on the remeshing,
convection, and split-time stepping are discussed.
Preliminary results suggest that both the shape and
protein distribution can be described accurately by such
a model, and the next steps of this work are discussed.

Karim, Mohammad Shahriar
(Electrical and Computer Engineering, Purdue University)

-Authors: Mohammad Shahriar Karim(*), Gregery T. Buzzard,
and David M. Umulis

-Title: ** Secreted, receptor-associated BMP regulators
reduce stochastic noise intrinsic to many extracellular
morphogen distributions**

-Abstract:

Morphogens specify cell-fate in a concentration dependent
manner. Intriguingly, recent measurements of ligand-receptor
binding suggest that many morphogens saturate receptors
at concentrations less than 1nM or less than 20
molecules/cell. Low molecule number, combined with slow
binding kinetics leads to a noisy interpretation of
extracellular concentration that fluctuates on the
time-scale of hours, however many morphogen patterning
networks are remarkably robust. To investigate mechanisms
of biological robustness and signal interpretation we
developed a stochastic model of the local ligand-receptor
dynamics and extended this work to consider spatial
patterning and measure the errors in positional information
expected for each local regulatory mechanism. We find
that if a secreted non-receptor such as Crossveinless-2
(Cv-2) partially regulates ligand-receptor interactions,
the amplitude of ligand-receptor fluctuations can be
reduced by about 2-folds depending on specific parameter
values and non-receptor concentration. Receptor-ligand
regulation by secreted factors can also modify the
binding dynamics to increase the frequency of fluctuations,
which can be buffered out immediately downstream by the
intracellular network if the time-scale for intracellular
dynamics are slow relative to ligand-receptor fluctuations.
This phenomenon of non-receptor imitates performance of
a simple low pass filter for the system. Together, these
data indicate that one of the benefits of receptor-ligand
regulation by secreted non-receptors may be greater
reliability of morphogen patterning mechanisms and we
are developing experiments to test these conclusions.

Kim, Jae Kyoung
(Mathematics, University of Michigan-Ann Arbor)

-Title: Modeling the Interaction between Circadian and
Metabolic Regulation.

-Abstract:

Recent experimental evidence has discovered strong links between
circadian timekeeping and metabolic regulation. Because of the
complexity of the biochemical networks that underlie these systems,
mathematical modeling has the potential to help clarify experimental
results and predict new phenomena. Here we review mathematical models
that can be used to understand the links between circadian and
metabolic regulation. We present a preliminary model for the role of
SIRT1 in circadian rhythms. This model predicts experimental findings
that can be used to understand the link between circadian regulation
and metabolism. Further modeling can account for other links beyond
these systems; one current interest is how circadian rhythm affect
cancer through metabolism.

Lee, Sang-hun
(Agricultural and Biological Engineering, Purdue University)

-Authors: Sang-hun Lee (*), and David M. Umulis

-Title: **Dynamic simulation of Bone Morphogenetic
Protein patterning in a 3D finite-element model of the
Danio rerio embryo**

-Abstract:

Zebrafish development relies on the spatiotemporal
distribution of molecules called morphogens that pattern
anterior/posterior (AP) and dorsal/ventral (DV) axes in
a concentration-dependent manner. Numerous secreted
regulators control the spatiotemporal distributions of
BMP signaling along the DV axis, however, the mechanisms
of dynamic regulation of BMP signaling remain unclear.
To determine the relative contributions of the Alk8
receptors, Chordin, Tolloid-like molecules, and Sizzled,
we developed and tested a full 3D mathematical model of
a developing zebrafish embryo. We developed an image
registration algorithm to assign point-cloud experimental
data to a reference set and determine both the stage of
development and the orientation of the embryo. Following
development of the image registration methodology, we
converted the point-cloud reference into 3D finite
element meshes for each 1.5 minute time-point during
growth from early blastula through gastrula stages
(200-500 minutes post fertilization (MPF)). We then
developed a seamless modeling strategy to test
alternative hypotheses regarding the mechanism of
BMP-mediated patterning on the dynamically evolving mesh
and found that Sizzled-mediated regulation of Tld
leads to robust mechanism to regulate gradient shape
of BMP activity. We also investigated mechanisms of
dynamic morphogen scale-invariance in zebrafish embryos
and present a summary of these findings.

Lioi, Josh
(Mark Alber group, Mathematics, University of Notre Dame)

-Authors: Joshua Lioi(1), Zhiliang Xu(1), Malgorzata M.
Kamocka(3), Danny Z. Chen(2), Elliot D. Rosen(3), Mark Alber(1)
((1) Department of Mathematics, University of Notre Dame,
(2) Computer Science University of Notre Dame,
(3) Medical and Molecular Genetics, Indiana University School of Medicine
)

- Title: **Study of the role of Factor VII in Venous Thrombus
Formation Using a Combination of a Multiscale Model and Experiment**

- Abstract:

We extend a two-dimensional multiscale model of thrombus
formation by including surface-mediated control of the coagulation
pathway. The model was used to simulate thrombus formation in normal
or limited levels Factor VII (FVII). Simulation predictions were
compared with experimental results involving thrombogenesis following
laser-induced injury of venules in wild type and FVII deficient mice.
It is shown that low levels of FVII in blood results in a significant
delay in thrombin production demonstrating that FVII plays an active
role in promoting thrombus development at an early stage.

Liu, Sijia
(Mathematics, Iowa State University)

- Title : **Novel clustering methods for the analysis of biological
data**

- Abstract:

The need to interpret and extract possible inferences from
high-dimensional datasets has led over the past decades to the development
of dimensionality reduction and data clustering techniques. In this poster,
we present a novel family of clustering algorithms that combine seamlessly
the strengths of existing spectral approaches to clustering with various
desirable properties of fuzzy methods. We discuss examples of gene
expression datasets for which the developed methodology outperforms other
frequently used algorithms.

Liu, Yuan
(Mathematics, University of Notre Dame)

- Title : **A preliminary study of two models on angiogenesis**

- Abstract:

We are studying two PDE models regarding to angiogenesis. One model
is proposed by G. Serini et.al in [1], in which the cell population is
described by a continuous distribution of density and velocity. The
other one is a PDE system derived from a two-dimensional stochastic
cellular Potts model (CPM) describing cell moving in a medium and
reacting to each other through direct contact, cell-cell adhesion, and
long-range chemotaxis [2]. In the first system, we successfully solved
the hyperbolic system in third order finite difference weno scheme
and third order finite volume weno scheme on triangular mesh., in
both way, we could observe the formation of blood vessel networks
similar to those observed in the experiments. We also quantitatively
studied the relationship between the endothelial cell number, the range
of activity of chemo-attractant and the vascular network formation
and size. However, the numerical simulation will blow up as is expected.
In the model derived from CPM, the networks are also observed. And the
numerical solutions of the model with/without the excluded volume
indicate that the excluded volume interactions are important in the
chosen range of values of parameters. Contrary to classical Keller-Segel
model, solutions of this one do not collapse in finite time.

[1] G. Serini, D. Ambrosi, E. Giraudo, A. Gamba, L. Preziosi and F.
Bussolino, Modeling the early stages of vascular network assembly,
The EMBO Journal, Vol.22, No.8, (2003), pp1771-1779.

[2] P. Lushnikov, N. Chen and M. Alber, Macroscopic dynamics of
biological cells interacting via chemotaxis and direct contact,
Phys. Rev. E. 78, 061904.

Luterek, Adam (
Brad Roth Group
, Physics, Oakland University)

- Authors : Adam Luterrek and Bradley J. Roth

- Title : ** Studying the Movement of Nerve Axons
Under the Influence of Strong Magnetic Fields**

- Abstract:

We extend a model introduced by Roth and Basser (Magn. Reson.
Med., 61:59-64, 2009) to study the movement of a nerve during magnetic
resonance imaging. When exposed to a magnetic field, neural action
currents are subjected to a Lorentz force that moves the nerve.
Roth and Basser considered action currents that were uniform along
the length of the nerve. In our study, we examine the full
three-dimensional distribution of current. We calculate the nerve
displacement for the case of the nerve perpendicular to the magnetic
field. Additionally, if the magnetic field is parallel to the nerve,
it may be possible for the axon to twist due to the Lorentz force.

Osorio, Mauricio Andres (Mathematics, University of Cincinnati)

Pargett, Michael
(Weldon School of Biomedical Engineering, Purdue University)

-Title: **Brat-mediated bi-stability and cell-competition
autoregulate stem cell number in the Drosophila germarium**

-Authors: Michael Pargett, Robin Harris, Hillary Ashe, and David Umulis

-Abstract:

Complex organisms must maintain stable populations of stem
cells to remain healthy and support somatic tissues. In the
germline stem cells (GSC) of the Drosophila ovary, Bone
Morphogenetic Protein (BMP) signaling regulates the decision
between stem cell self renewal or differentiation. Our
collaborators have elucidated key players in the intracellular
network that regulates cell-receptivity to extracellular BMPs,
however the interaction between the intra- and extracellular
regulation of BMP distributions and interpretations remains
unknown. To determine the relative contribution of intra- and
extracellular control of BMP regulation we developed a local
model for a single cell receiving an extracellular cue and
a 3D extracellular model of the germarium. The proposed
intracellular feedback mechanism exhibits bistabilty in
response to levels of BMP signaling, making cells refractory
to additional signal. By combining intracellular and
extracellular regulation in the 3D multi-cell model, we find
that cell-mediated competition for limiting amounts of
ligand leads to autoregulation of stem cell number in the
niche. Competition, combined with the bistable intracellular
system supports the maintenance of the constrained stem cell
population, causing differentiation of extraneous GSCs and
repopulating if GSCs are lost.

Srivastava, Prashant
(IIT Kanpur, INDIA)

-Title: ** Dynamical Model of HIV and CD4+ T cell with
drug therapy**

-Abstract:

Here we shall propose and analyse a dynamical model of
HIV and CD 4+ T cells under the influence of drugs
Reverse transcriptase inhibitor and protease inhibitor.
The infection develops as HIV infects CD4+ T cells.
Infected cells are divided into two sub classes:
infected cells before completion of reverse transcription
and infected cells after reverse transcription. It is
assumed that a fraction of infected cells revert back
to uninfected class. We performed stability and also
solved model numerically to analyse the analytical results.

Stevens, Joshua B.
(School of Medicine, Wayne State University)

-Authors: Joshua B. Stevens, Guo Liu, Steven Bremer, Christine J Ye, Henry H. Heng

-Title: **Dynamics of Somatic Cell Evolution During Cancer Progression**

-Abstract:

For decades cancer progression has been believed to be a
linear process that was driven by stepwise accumulation of
a small number of common gene mutations. Identification of
these gene mutations and subsequent drug targeting of their
functions promised to cure cancer. However, recent large
scale cancer genome sequencing projects have failed to detect
these expected common gene mutations. Similarly we have show
that on the chromosomal level, there is no recurrent pattern
of change which has lead to the development of the genome
theory of cancer which states that cancer progression is a
stochastic process driven by system replacement manifested
by chromosomal change. During cancer progression population
diversity increases during periods of stress such as prior to
immortalization and during chemotherapy. This diversity
increases the probability that a cell (or number of cells)
will survive the stress, promoting further progression.
Despite the recent success of the genome theory, many questions
still exist. These questions include: What level (gene,
epigenetic, or genome) has the most utility in predicting
cancer progression, and how can measurements at all levels be
integrated? Are there more or less favorable types of diversity?
How do responses of populations of cells react to differing
circumstances if one population is largely genomically
homogenous and one is heterogeneous, but both populations
share a similar level of some molecular marker? Answering
these important questions will require a bio-mathematic
approach to integrate these new cancer progression findings
into clinically applicable models and treatment designs.

Wang, Xiaoxia
(Mathematics, Case Western Reserve University)

-Title: ** A NEW APPROACH TO MODELING SCHISTOSOMIASIS
TRANSMISSION BASED ON STRATIFIED WORM BURDEN**

-Abstract:

Multiple factors affect schistosomiasis transmission
in distributed meta-population systems including age,
behavior, and environment. Traditional modeling approach
to macroparasite transmission often exploits ``mean
worm burden formulation'' (MWB) for human hosts. Such
approach oversimplifies the system, and can give wrong
predictions for control interventions. Typical worm
distribution in humans is overdispersed, and classic
models either ignore it or make ad-hoc assumptions
about its pattern (e.g. `negative binomial'). We
propose a new modeling approach to macro-parasite
transmission by stratifying human populations according
to burden, and replacing MWB dynamics with that of
`population strata'. The Stratified Worm Burden (SWB)
approach offers many advantages; it accounts naturally
for overdispersion, and accommodates other important
factors and measures of human infection and demographics.
We developed the calibration procedure for such extended
(multi-component) systems, and run it for a specific
data set collected in the Msabweni region of Eastern
Kenya. The calibrated model was validated against
additional data, and applied to study control interventions
(drug treatment). In particular, we simulated several
control strategies proposed by WHO and examined their
long term outcomes. We believe our model can provide
useful information and tools for future WHO policies
on eradication of schistosomiasis.

Xu, Dan (
Brad Roth Group
, Physics, Oakland University)

- Authors : Dan Xu and Bradley J Roth

- Title: ** The Magnetic Field Produced by the Heart
and Its influence on MRI**

- Abstract:

Recently, much work has been done to detect neuronal
activation by using the magnetic field produced by biocurrents.
In general, these magnetic fields are too tiny to measure
by magnetic resonance imaging. However, the heart is the
source of the largest biocurrents in the body, so it may
be easier to detect cardiac action currents using MRI
compared to neural action currents. There are two sources
that produce a magnetic field in cardiac tissue. One is the
intracellular current in the tissue with the "return" current
through an adjacent volume conductor; the other is the
anisotropy of the tissue. In this study, we examine a
simplified "spherical heart" model with a simple transmembrane
potential distribution and calculate the resulting action
currents and magnetic field, and estimate their impact on
an MRI signal. This research was supported by the National
Institutes of Health Grant R01EB008421.

Coming...

Kim, Yangjin (Department of Mathematics & Statistics, University of Michigan-Dearborn)

Remski, Joan (Department of Mathematics & Statistics, University of Michigan-Dearborn)