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.

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.