Studying Complex Systems: 2005 Research Awards
University of Michigan-Ann Arbor, Ann Arbor, Michigan
Principal Investigator: Trachette L. Jackson, $436,735 over five years.
Combining continuous and discrete approaches to study sustained angiogenesis associated with vascular tumor growth
The recent explosion in the understanding of the strongly linked, multiple scale
processes that drive the advancement of cancer is allowing useful mathematical models
of the tumorigenesis to be developed. Such models have the potential to facilitate a
deeper understanding of the mechanisms associated with tumor initiation and progression
and can also be used to develop and test novel therapeutic approaches designed to attack
this complex system at various levels. In fact, many of the challenges cancer researchers
are facing lie at the intersection of the mathematical and biomedical sciences. The
potential for progress is immense; as an example, the popular scientific journal NATURE
recently published an article entitled Mathematical Oncology: Caner Summed Up where
the authors stated, "understanding the complex, non-linear systems in cancer biology will
require ongoing interdisciplinary, interactive research in which mathematical models,
informed by extant data and continuously revised by new information, guide
experimental design and interpretation."
This article and many others like it, highlight the fact that mathematicians, scientists
and engineers must work together with the rest of society to understand and deal with
problems arising the biological sciences and in medicine. Often, these issues cannot be
fully understood by the experimental approach alone. Mathematical and computational
models are increasingly called upon to help piece together the many seemingly unrelated
parts of complex systems and cancer is no exception.
Cancer is a distinct type of genetic disease in which not one, but several, mutations
are required to drive a wave of cellular multiplication. The continued proliferation of one
or more transformed cells eventually forms an avascular tumor. Having no blood vessels
of its own, the growing mass obtains vital nutrients such as oxygen and glucose via
diffusion from the vasculature in the surrounding normal tissue. As the colony expands,
the diffusion of nutrients and the removal of cellular waste products becomes insufficient.
Cells on the outer rim of the tumor thrive in the presence of abundant resources while
cells in the center are starved. There is often an interior layer of quiescent cells that
receive sufficient nutrient for survival but not proliferation. Researches believe that it is
this balance between growth on the periphery and death in the center leads to the
observed nutrient-limited growth of avascular tumors to a size of a few millimeters in
diameter. An avascular tumor therefore can become dormant when growth stops for an
indefinite period. However, a tumor can overcome this deficiency by acquiring a blood
supply and it does so by inducing neighboring blood vessels to grow towards the tumor
through a process known as angiogenesis.
Angiogenesis is a complex cascade of events that involves many sequential steps. The
first event associated with tumor-induced angiogenesis (i.e. the angiogenic switch)
involves the secretion, by tumor cells, of a wide variety of chemicals known as
angiogenic factors. Experimental evidence suggests that this up-regulated expression of
angiogenic factors could be in response to deficiencies in oxygen (hypoxia) or glucose
(hypoglycemia). These tumor-derived angiogenic factors (TAFs) diffuse throughout the
surrounding tissue laying down a chemical gradient between the tumor and the exiting
host vasculature. Under the influence of the TAFs, the endothelial cells that line the
existing vessels switch from a previously resting, nonregenerating state to a rapidly
dividing group of regenerating cells capable of forming new capillary sprouts that can
grow at the rate of 1 mm per day. Endothelial cells begin to migrate and accumulate in
the region where the concentration of TAFs has first reached a threshold level. The
migrating endothelial cells elongate and align with one another to form a solid sprout
from the vessel wall. The endothelial cells then produce enzymes that in turn degrade the
basal lamina of the parent vessel, allowing the endothelial cell sprouts to move through
the disrupted membrane towards the tumor.
The outgrowing sprouts start to re-associate with each other and lead to the formation
of tube-like structures. Initially the sprouts are parallel with each other but tend towards
each other as they elongate. Neighboring sprouts will eventually fuse together at their tips
to form loops (anastomosis), which signal the beginning of circulation of blood. The
looped vessels may bud or loops may fuse with other loops until a complex network of
vessels develop. Finally this vessel network penetrates the tumor, providing it with the
circulatory system and the supply of nutrients that it requires for tumor growth and
progression.
Tumor-induced angiogenesis results in the explosive growth of a vascular tumor that
is now connected to the body's blood supply and once initiated the process continues
indefinitely. True to its metaphor, the War on Cancer is incorporating a standard military
technique: cutting off the enemy's supply lines. A growing army of researchers is
experimenting with potential drugs aimed not at tumors themselves but at the network of
new blood vessels that develop to feed a tumor. Recall that without its own network of
blood vessels, a tumor can't grow beyond a harmless few millimeters in diameter.
Interrupting tumor-induced angiogenesis is promising avenue for cancer treatment that
can lead to tumor regression and possibly cures.
The concept of treating solid tumors by inhibiting tumor angiogenesis was first
articulated almost 30 years ago. For the next 10 years it attracted little scientific interest.
However, the last decade has witnessed a remarkable transformation in both attitude and
interest in tumor angiogenesis and anti-angiogenic drug development. In fact,
concentrated efforts in this area of research are leading to the discovery of a growing
number of pro- and anti-angiogenic molecules which can be targeted against this process,
some of which are already in clinical trials. The complex interactions among these
molecules and endothelial cells and the extracellular matrix, and how they affect vascular
structure and function in different environments are now beginning to be elucidated. This
integrated understanding is leading to the development of a number of exciting and bold
approaches to treat cancer and other angiogenesis-dependent diseases. Our proposal is
aimed at advancing this understanding through a multiscale, mathematical model of
sustained angiogenesis and vascular tumor growth.
Mathematical modeling and experimental observations provide substantial evidence that
tumor-induced angiogenesis is a multipscale process that is governed by both mechanical
and chemical process and that interactions between tumor cells and endothelial cells with
the host environment cannot be ignored. Previous modeling investigations of tumor
induced angiogenesis have aimed to capture the qualitative feature of the processes
involved but fall short in three major areas: (1) all but a few studies ignore the role of the
forces generated by endothelial cells on extracellular matrix, (2) none of the previous
models consider the role of inhibitors of angiogenesis, and (3) all existing models treat
the extracellular matrix as a passive medium for endothelial cell migration, whereas
experimental evidence has shown that ECM regulates angiogenesis by providing not only
scaffold support, but by serving as a reservoir and modulator for angiogenic growth
factors. Now that experimental models are able to account for such processes, which
appear to be critical to angiogenesis on the cellular and molecular levels, mathematical
models that include these dynamics and address the question of mechanism can be
constructed. In addition, anti-angiogenic therapeutic strategies are clinically recognized
has having enormous potential in the treatment of cancer. Mathematical modeling of
sustained angiogenesis and vascular tumor growth has an increasingly important role in
the development and testing of these strategies.
This research will combine mathematical modeling, numerical simulation and in vivo
tumor vascularization experiment to gain deeper understanding of angiogenesis, tumor
growth and vascular structure. Specifically, by developing such a multiscale tumor
vascularization model, we will investigate:
1. the molecular signaling pathways that promote endothelial cell growth and survival;
2. the interplay between intracellular regulation, intercellular interactions and cell- environment interactions and their effect of vascular structure and tumor composition; and
3. the therapeutic strategies that target angiogenesis in tumors.
