1.
Mark Alber (University of Notre Dame)
Multiscale Model of Thrombus Development
To prevent the loss of blood following a break in blood vessels,
components in blood and the vessel wall interact rapidly to
form a
thrombus (clot) to limit hemorrhage. In this talk we will
describe a multiscale model of thrombus formation consisting
of components for modeling viscous, incompressible blood plasma;
coagulation pathway; quiescent and activated platelets; blood
cells; activating chemicals; fibrinogen; the vessel walls
and their interactions. At macro scale blood flow field is
described by the incompressible Navier-Stokes equations and
is numerically solved using the projection method. At micro
scale, cell movement, cell-cell adhesion, cell-flow and cell-vessel
wall interactions are described through an extended stochastic
discrete Cellular Potts Model (CPM). Model is tested for robustness
with respect to fluctuations of basic parameters. Simulation
results demonstrate the development of an inhomogeneous internal
structure of the thrombus which is conformed by the preliminary
experimental data. We also make predictions about different
stages in thrombus development which can be tested experimentally
and suggest specific experiments. Lastly, we demonstrate that
dependence of the thrombus size on the blood flow rate in
simulations is close to the one observed experimentally.
2. Amy Bauer (Los Alamos National Lab)
From Molecule to Morphology:A Multi-Scale Cell-Based
Model of Angiogenesis
Tumor-induced
angiogenesis, which is the formation of new blood vessels
from existing vasculature in response to chemical signals
from a tumor, is a crucial step in cancer invasion and metastasis.
Although the sequential steps involved in tumor-induced angiogenesis
are well known, the interplay between the biochemical and
biomechanical mechanisms (e.g., cell-cell and cell-matrix
interactions, and intracellular signaling pathways) that affect
angiogenesis is largely unresolved. In this talk, I will introduce
a novel multi-scale cell-based model of tumor-induced angiogenesis
and present results from numerical simulations that elucidate
some mechanisms controlling vascular formation in the context
of pro- and anti-angiogenesis treatment strategies. In particular,
I will discuss how extracellular matrix topology influences
cell migration and vascular structure, and the relationship
between external stimuli, cell phenotype, and vascular morphology.
This model is the first to simulate emergent vessel branching,
anastomosis, and the brush border effect. These macroscale
structures arise as a result of microscale behavior without
any rules prescribing the formation of such complex structures.
Key features of this biophysical model include: (1) linking
processes occurring on multiple time scales, (2) controlling
processes at the level of the individual cell, (3) using physical
and energy reduction constraints to capture emergent behaviors
without prescribing phenomenological rules, and (4) quantifying
morphological details that are not currently possible to capture
with continuous models alone. These results translate and
synthesize a large body of compartmentalized research on angiogenesis
and are meant to inform and advance efforts to develop new
approaches for treating cancer and other angiogenesis-dependent
diseases.
3. Bridget S. Wilson and Tomáš Mazel (University
of New Mexico)
Influence
of 3D cellular geometry on IP3-mediated calcium responses:
a multi-scale mathematical modeling problem
Release of inflammatory mediators by mast cells in type 1
immediate hypersensitivity allergic reactions relies on the
antigen-dependent increase in cytosolic calcium. Here we used
a series of electron microscopy images to build a 3D reconstruction
of a rat tumor mast cell, which then served as a basis for
modeling IP3-mediated calcium responses. We consider the influence
of IP3 receptor clustering on IP3-mediated release, as well
as the local proximity of the endoplasmic reticulum (ER) to
both the plasma membrane and to mitochondria. We find that
both flux and local cytoplasmic/ER luminal calcium concentrations
are markedly affected by nearby organelles. In addition to
compartmental and PDE-based approaches, we describe the first
application of stochastic reaction-diffusion modeling within
a complete 3D cell geometry. These combined approaches help
to bridge the gap between measured single molecule kinetic
constants and overall cellular calcium dynamics.
4.
Qing Nie (UC Irvine)
Specificity and Robustness of Cell Signalling
Intra-cellular and cell-to-cell signalling are the fundamental
biological processes. In this talk, through examples I shall
study specificity of signalling pathways in yeast and robustness
of morphogen systems in Drosophila embryo. In particular,
I shall discuss mathematical and computational challenges
associated with such study, and present a new class of numerical
algorithms for reaction-diffusion equations.
