Mathematical modeling and numerical simulation of tumor angiogenesis
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Mathematical modeling and numerical simulation of tumor angiogenesisAutor(es)
Director(es)
Gómez, HéctorColominas, Ignasi
Data
2015Resumo
[Abstract]Cancer is nowadays the second leading cause of death in the world. Cancer starts
with a single cell that has accumulated several mutations usually over a long
period of time. One of the main characteristics of this cell is its ability to replicate
unbounded producing, in most occasions, a mass of densely packed daughter cells
that form a solid tumor. Cancerous cells depend on nutrients and oxygen supplied
by pre-existent blood vessels to proliferate. This supply is not enough to maintain
the growth and most tumors remain small and benign due to this constraint.
Occasionally, however, some cells develop the ability to promote the growth of new
capillaries towards them. This process is called tumor-induced angiogenesis and
through it tumors acquire a constant supply of nutrients and oxygen and access to
the whole body through the circulatory system. Tumors that are able to trigger
angiogenesis become malignant as they can grow unbounded and metastasize.
Malignant tumors can grow large enough to damage the functionality of the host
organ and, eventually, lead to death.
A few decades ago, scientists have proposed that blocking angiogenesis could be an
effective treatment against cancer. This therapy, known as antiangiogenic therapy,
has shown promising results in pre-clinical trials, but has not translated into the
expected results in the clinic. A new emerging paradigm in Medicine, namely,
Predictive Medicine, is expected to change the Oncology field and may be the tool
to understand the problems with this therapy. Predictive Medicine is based on
mathematical modeling and computation and has been so far successfully applied
to several areas of Medicine. In the Oncology field it has only been started, but has
already produced sound advances. In particular, in tumor-induced angiogenesis
numerous researchers have proposed mathematical models to address the problem
of antiangiogenic therapies, although there is still a need for improvement to attain
this goal. Angiogenesis is a complex multiscale process that involves several key
mechanisms, many of them not yet accounted for in the models. In addition, most models are simulated in two-dimensional simple geometries, while angiogenesis is
a three-dimensional process and occurs in tissues with non-trivial geometries.
In this thesis we develop mathematical models of tumor-induced angiogenesis that
include key biological mechanisms and we simulate these models in relevant experimental
setups and in three-dimensional, subject-specific geometries. To achieve
our modeling and simulation goals, we develop adequate numerical algorithms.
Every model in this thesis is hybrid and involves coupling averaged continuous
theories and cellular-scale discrete agents. In addition, the models are grounded
on the phase-field method which requires solving higher-order partial differential
equations. To overcome these problems we developed a seamless coupling between
the continuous variables and the discrete elements to permit an efficient numerical
treatment of the coupled problem. For the resolution of the high-order partial
differential equations involved in the formulation we used isogeometric analysis,
which in addition provides accuracy, robustness, and the geometric flexibility that
we require to perform simulations in real geometries.
This manuscript presents three new mathematical models for tumor-induced angiogenesis.
In the first one we started with a previous model to which we added a
conceptual model for haptotaxis, one of the main mechanisms that governs capillary
growth. The extended model permitted us to assess the role of haptotaxis
in tumor angiogenesis. Furthermore, we developed for the first time a simulation
of one of the most widely used in vivo assays, the mouse corneal micropocket angiogenesis
assay, using a three-dimensional, subject-specific geometry. The results
are in agreement with the experiments and predict well-known vascular structures
in three dimensions. In addition, they suggest that, for mathematical models to
achieve the topological complexity observed in in vivo angiogenesis experiments,
two-dimensional simulations may not be enough.
The second model focuses on the long-term dynamics of tumor-induced angiogenesis,
that is, on the regression and regrowth events occurring after the first
growth of blood vessels. The model was simulated both in a two-dimensional
replication of the mouse corneal micropocket assay and in a reproduction of an
in vivo experimental setup. Our simulations predict plasticity and dynamic evolution
of angiogenesis at long time spans and are in quantitative agreement with
experiments.
Finally, we developed a fully continuum theory for fluid flow at the tissue scale,
which we coupled with our model for tumor angiogenesis. The model shows how
fluid flow alters tumor-induced vascular patterns through convection, which has
been overlooked in mathematical modeling. Our model predicts a substantial
impact of convection in angiogenesis and an increased malignancy of small solid
tumors.
Palabras chave
Células cancerosas-Crecimiento-Modelos matemáticos
Neovascularización
Tumores-Crecimiento-Simulación por ordenador
Neovascularización
Tumores-Crecimiento-Simulación por ordenador
Descrición
Programa Oficial de Doutoramento en Enxeñaría Civil . 5011V01
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