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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. |
