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5)
Multiscale modeling of solid tumor growth and angiogenesis
Principal organiser: Professor John Lowengrub
Departments
of Mathematics and Biomedical Engineering UC Irvine, Irvine
CA 92697
Summary
Significance. Cancer is a fundamental scientific and societal
problem, and in the past few decades, vast resources have been
expended in an effort to understand the root causes of cancer,
to elucidate the intricacies of cancer invasion, and to develop
effective prevention and treatment strategies. Nevertheless,
there are numerous examples of puzzling and seemingly inconsistent
observations. Therefore, there is critical need for biologically
realistic mathematical modeling.
A
key aspect of the complexity of cancer progression is the coupling
of processes occurring across a wide range of length and time
scales; this coupling must be addressed if key tumor dynamics
are to be captured. While the biomathematics literature is replete
with models that provide useful insight into cancer-related
processes at particular time and length scales, considerably
less effort has been devoted to coupling biological phenomena
across various scales. One important example, which we will
focus on in this minisymposium, is the nonlinear coupling between
cancer invasion, the angiogenic response of the host and the
implications of this coupling on potential treatment strategies.
Scope
In
this minisymposium, we will focus on solid tumor growth. Tumors
evolve through increasingly aggressive stages of development.
After carcinogenesis, the next stage of development is the avascular
growth phase whereby the cancer cells proliferate and form an
in situ tumor. Since the tumor lacks a vasculature, nutrients
and vital growth factors are received only by diffusion from
the surrounding tissue. This may lead to hypoxia and acidosis.
The following stage of tumor growth, angiogenesis, is characterized
by the development of a tumor-induced neovasculature that grows
from the main circulatory system toward the tumor in response
to pro-angiogenic growth factors released by hypoxic tumor cells
(or stressed host cells). After the recruitment and/or cooption
of blood vessels, the vascularized tumor may invade the surrounding
host tissue and metastasize to distant parts of the body. Sustained
angiogenesis is a hallmark of cancer.
Here,
the speakers will present multiscale mathematical models that
are capable of describing all stages of tumor growth and in
particular, the nonlinear coupling between the tumor progression
and the angiogenic response of the host. State-of-the-art hybrid
continuum-discrete models will be presented that will underscore
the importance of the nonlinear coupling of biophysical processes
across a range of scales and in particular coupling between
the growing tumor and the development and remodeling of a tumorinduced
neovascular network with blood flowing through it. The implications
of treatment strategies on tumor progression will be discussed.
While there are currently few such models of this highly complex
and nonlinearly coupled system in the literature, this is an
area of intense research activity because of its importance.
This
minisymposium brings together ideas that have been explored
very recently in the mathematical biology community and thus
fits perfectly within the SMB conference. To our knowledge,
this may be the first minisymposium that would specifically
address the nonlinear modeling of the critical transition from
avascular to vascular growth of solid tumors.
Audience
This minisymposium, and in particular the multiscale modeling
aspect of the approach, should appeal to a wide range of mathematical
modellers. The relevance of the problems to in vivo cancer progression
and treatment should also attract experimentalists, clinicians
and industry professionals.
Speakers
1. Computational modeling identifies morphologic predictors
of tumor invasion
Vittorio Cristini, School of Health Information Sciences
University of Texas MD Anderson Cancer Center
University Texas Health Science Center at Houston
Mathematical
modeling based on first principles quantifies tumor growth's
dependence on interactions between a set of variables-including
genomic instability producing variations in sub-tumor clonal
expansion and generating nutrient diffusion gradients-and
demonstrates that these determinants of heterogeneity, and
not angiogenesis per se, conspire to produce the typical morphologic
patterns of infiltrative tumor boundaries in histopathology.
We demonstrate that heterogeneity in sub-tumor clonal expansion
and nutrient consumption drives migration and proliferation
of the emerging more aggressive clones up a nutrient concentration
gradient within and beyond the central tumor mass. This heterogeneity
and loss of cell adhesion trigger a gross morphologic instability
that leads to replacement of less aggressive clones and separation
of tumor cell strands or clusters infiltrating into adjacent
tissue. This model allows all variables that characterize
the biophysics of tumor growth to be considered and could
be applied to determine the probabilistic behavior of tumors
given their pathologic appearance.
2. Three dimensional multiscale modeling of solid tumor
growth
John Lowengrub: Organizer University of California, Irvine
We
present and investigate models for solid tumor growth that incorporate
features of the tumor microenvironment including tumor-induced
angiogenesis. Using analysis and nonlinear numerical simulations,
we explore the effects of the interaction between the genetic
characteristics of the tumor and the tumor microenvironment
on the resulting tumor progression and morphology. We account
for variable cell-cell/cell-matrix adhesion in response to microenvironmental
conditions (e.g. hypoxia) and to the presence of multiple tumor
cell species. We focus on glioblastoma and quantify the interdependence
of the tumor mass on the microenvironment and on the cellular
phenotypes. The model provides resolution at various tissue
physical scales, including the microvasculature, and quantifies
functional links of molecular factors to phenotype that for
the most part can only be tentatively established through laboratory
or clinical observation. This allows observable properties of
a tumor (e.g. morphology) to be used to both understand the
underlying cellular physiology and to predict subsequent growth
or treatment outcome, thereby providing a bridge between observable,
morphologic properties of the tumor and its prognosis.
3. Multiphase
modelling of tissue growth in dynamic culture conditions
Sarah Waters, Department of Mathematics, Oxford
Co-authors: O’Dea, R., Byrne, H.M., El-Haj, A
The
growth of biological tissue is a complex process, resulting
from the interaction of numerous processes on disparate spatio-temporal
scales. Much research has been concentrated on the study of
cartilage and bone tissue re-generation, motivated by the
notorious incapacity of the former to self-repair and the
response of the latter to its mechanical environment. Advances
in the understanding of tissue growth processes promise to
improve the viability and suitability of the resulting tissue
constructs; the clinical applications are evident. Mechanical
force is an important factor affecting the behaviour of a
variety of different cell types; however, it remains unclear
how this stimulus is inte-grated into the cellular response.
Employing a macroscale multiphase model, the influence of
(i) cell-cell and cell-scaffold interactions, and (ii) the
mechanical environment, on tissue growth is investigated.
The approach taken enables a macroscale model to be obtained
that does not contain the precise details of the material
at the microscale, but whose terms are shown to arise from
appropriate microscopic considerations. The model equations
are solved using asymptotic and numerical methods and the
implications of these results are discussed.
4.
An Alternate Approach to Predictive Oncology: Computer Modeling
of Drug Pharmacokinetics and Effect in Vascularized Tumors
Sandeep
Sanga (U.Texas Health Science Center, Houston TX): replacement
for Paul Macklin
Co-authors: John P. Sinek, Sandeep Sanga, Xiaoming Zheng, Hermann
B. Frieboes, Mauro Ferrari, Vittorio Cristini
The
field of predictive oncology conventionally applies methodologies
such as microarrays and immunohistochemical staining for comprehensively
profiling gene expression and protein activities of genes in
cancer tissue, and identifying biomarkers and signatures that
are either prognostic and/or predictive of chemotherapy response.
However, the complex nature of cancer has made it difficult
to identify unique molecular and pathophysiological signatures
for each disease variant, consequently hindering the ability
to predict the performance of therapies in individual patients.
Here, we take an alternate approach; we investigate the pharmacokinetics
and pharmacodynamics of doxorubicin and cisplatin in vascularized
tumors and show that microenvironmental considerations such
as lesion-scale drug and nutrient distributions may significantly
hamper therapeutic efficacy and should be considered as carefully
as genetic and proteomic determinants. Our model takes into
account tumor vascularity and morphology as well as cellular
and lesion-scale pharmacokinetics determinants such as p-glycoprotein
efflux and cell density. Drug transport is encapsulated using
a multi-compartment model calibrated from published experimental
data; this model tracks drug as it extravasates from the blood
stream into the tumor interstitial space, diffuses through the
lesion, enters cells and eventually reaches its intended target:
DNA. Cell inhibition is modeled as a function of this DNA-bound
drug. Unlike a truly in vivo situation, our in silico model
provides the means to quantify expected in vivo IC50 under varying
drug, oxygen, nutrient , and drug transporter conditions. The
nonlinear interaction among various determinants representing
cell and lesion phenotype as well as therapeutic strategies
is a unifying theme of our results. Our results suggest that
macroscopic environmental conditions, notably drug and nutrient
distributions, give rise to considerable variation in tumor
response to chemotherapy, hence clinical resistance. Moreover,
the synergy or antagonism of combined therapeutic strategies
depends heavily upon this environment.
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