Publication: Cellular dynamics models of angiogenesis
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2021-01
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2021-01-15
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Abstract
Cancer kills 26.4% of Spanish people. It is the second cause of death, just behind
diseases of the circulatory system, 28.3% [1]. The growth of new blood vessels from
the existing vasculature in response to chemical signals from a tumor is called tumorinduced
angiogenesis and it is closely related to cancer and metastasis. The growth rate
of a tumor is considerably increased in its vascular stage compared to its avascular and
solid stage, therefore treating cancer turns excessively difficult and the survival rates
rapidly decrease [2].
Among diseases that cause disability but not substantial mortality, age-related macular
degeneration may cause severe loss of vision or blindness in many people, particularly
the elderly. It is projected that 196 million people will be affected by age-related macular
degeneration in 2020, increasing to 288 million by 2040 [3], which is likely an underestimation
[4]. With age, Bruch’s membrane gets thicker and some damaged cells in
the retina become inflamed. The secretion of chemical signals from those cells due to
their inflammation induces angiogenesis, but the new blood vessels are disorganized and
leaky causing the loss of vision.
John Hunter was the pioneer in describing the vessel formation process in 1787 [5], but
the first person who coined the word “angiogenesis” was Arthur T. Hertig in 1935 [6]. He
was studying the formation of new blood vessel in the primary placenta of the macaque
monkey when this word was used for the first time. Years later, in 1971, Judah Folkman
hypothesized that tumors emit Tumor Angiogenic Factors (TAF) to attract blood vessels
to them [7]. This investigation triggered the research field of angiogenesis in cancer and
in 1989 one of the most important angiogenic factors was discovered: the Vascular
Endothelial Growth Factor (VEGF). Since then, drugs with antiangiogenic effects have
been investigated for cancer, age-related macular degeneration and other diseases, as it
is involved in more than seventy different diseases.
However, angiogenesis also occurs in normal and vital processes such as wound healing or
the growth of a fetus. The difference between physiological and pathological angiogenic
processes is a matter of balance. In a healthy process, angiogenesis develops to its proper
extent and then stops, while in pathological processes angiogenesis does not stop or it
does not develop sufficiently. Angiogenesis keeps the number of blood vessels needed in
balance: few blood vessels cause tissue death, while uncontrolled vascular proliferation
can lead to cancer, macular degeneration and other diseases.
Angiogenesis is a complex, multistep and well regulated process where biochemistry and
physics are intertwined. The process entails signaling in vessel cells being driven by both
chemical and mechanical mechanisms that result in vascular cell movement, deformation
and proliferation. In a later stage of angiogenesis, vessel cells rearrange to form lumen
and allow the perfusion of the blood inside the sprout. Depending on what induces the
angiogenesis, different environments and cells should be considered, for instance in the
retina. A detailed review of the processes involved in angiogenesis from the biological
point of view is given in section 1.1.
Beyond experimental investigations, mathematical models of angiogenesis try to help in
understanding the process and how the relevant mechanisms of angiogenesis interact.
The approach of some models focus on a single scale or a single process of those involved
to deepen the knowledge about it. Others span multiple scales or the whole process to
give an idea about how to prevent or favor angiogenesis. In section 1.2, we briefly review
the mathematical models of angiogenesis that have been used to date as well as those
when angiogenesis occurs in the retina and models of lumen formation, the late stage of
angiogenesis.
A crucial question about modeling is how to integrate the multiple scales and mechanisms
present in angiogenesis in a mathematical model. A model is expected to be
useful to explore methods for promoting and inhibiting angiogenesis. However, answering
this question with this expectation is not a simple task. Assembling all the processes
involved with their different time and length scales requires to develop a cellular dynamics
model combined with models for the continuum fields. We achieved this objective
by developing a hybrid cellular Potts model of early stage angiogenesis, given in chapter
2. In contrast to recent models, this mathematical and computational model is able to
explore the role of biochemical signaling and tissue mechanics. A exhaustive description
of the results of the numerical simulations complete the chapter 2.
The advantages of discovering the reasons why angiogenesis starts in the retina or inhibitory
mechanisms are innumerable. Unraveling the causes of neovascularization in
the retina and giving possible solutions for age-related macular degeneration are our
motivation to adapt the angiogenesis model of chapter 2 to the retina. In chapter 3, we
present the model and the numerical results.
If mathematical models of angiogenesis that incorporate multiple scales and cellular
signaling processes are not that common, those that also include lumen formation are
almost nonexistent. In chapter 4, we describe two models of lumen formation and their
results. The lumen formation in the first model takes place in a already developed sprout.
Although some restrictions in the model make its applications and possibilities limited,
its study is convenient to establish the basis of the second proposed model. In this second
model, the lumenization occurs while the sprout is developing and the pressure of the
blood is involved, following recent experiments of lumen formation during angiogenesis.
This model is work in progress, but we believe that showing the preliminary results in
chapter 4 may be interesting.
A critical step in the development of a mathematical and computational model is to
analyze the viability of its simulations. The simulations of the model in chapter 2 have
been carried out thanks to the parallel computing on Graphics Processing Units (GPUs),
as well as simulations of chapters 3 and 4. The large amount of square elements of the
grid, nodes, cells and sprouts make this type of computation suitable for these models.
The way they have been implemented is explained in chapter 5.
Finally, conclusions of this thesis and future work are drawn in the last chapter 6. This
chapter highlights and summarizes the research that has been carried out and proposes
future extensions and applications of this work.
Description
Mención Internacional en el título de doctor
Keywords
Angiogenesis, Age-related macular degeneration, Cellular potts model, Mathematical model, Computational model