I've moved!

I've started a new position at the University of Texas Health Science Center-Houston as an assistant professor in the School of Health Information Sciences. Please visit my new webpage:

http://biomathematics.shis.uth.tmc.edu

Thank you! -- Paul (September 7, 2007)

A Cancer Primer

Introduction

Cancer is marked by several stages of development, each of which is progressively more aggressive than the last. On this page, we'll explore the essential features of an evolving tumor. Please check back frequently, as this page will be revised and updated frequently!

Note on Jan. 15, 2007:
I plan on updating this section with better information soon. It meshes well with my dissertation writing. Thanks -- Paul

Carcinogenesis

As we age, our cells divide in a prescribed manner to maintain healthy, constant cell populations in our tissues and organs. However, with every cell division, there is a small chance that there will be an error when copying the DNA. If left uncorrected, that error will result in a mutated daughter cell. Ordinarily, this rate is very low, and healthy cells have a tremendous capacity to repair DNA damage. However, this damage can occasionally lead to a gradual accumulation of genetic damage in cells, and the process can be accelerated by environmental (e.g., radiation, repeated injury, carcinogens) and biological (e.g., viruses) factors.

Carcinogenesis
Figure 1: Early carcinogenesis: cells accumulate genetic damage and become pre-cancerous (blue region).

If cells acquire mutations that down-regulate apoptotic pathways, they fail to respond to signals to enter apoptosis (programmed cell death). If cells acquire mutations that cause the over-expression of growth pathways, uncontrolled cell proliferation can result. Both irregularities give the cells and their offspring a survival advantage over the surrounding cells, as their net reproductive rate is higher. This is the first stage in forming a tumor. (See Figure 1.) Furthermore, as the cells age past their normal "warranty period," they can become genetically unstable, lose their ability to repair DNA damage, and accumulate further genetic mutations.

Early Tumor Growth

Early tumor growth is nutrient diffusion-dominated. As the tumor expands, it exerts pressure that strains and deforms the surrounding tissue. Among other effects, this means that the tumor displaces healthy tissue as it grows, including blood vessels. Because the tumor has no vascular system of its own, it must receive its nutrients (e.g., glucose and oxygen) solely by diffusion from the surrounding tissue. (See Figure 2.)

Early Tumor Growth
Figure 2: Early growth: The tumor (magenta) grows to a size determined by the limit of nutrient supply. A necrotic core (black region) forms in the center of the tumor, where the nutrient level is so low that cells starve. Notice that the growing tumor introduces stresses that deform the surrounding tissue.

As nutrients diffuse into the tumor from the external tissue, they are absorbed and consumed by the tumor cells. Thus, the nutrient level decreases with distance from the edge of the tumor, with the lowest nutrient level in the center of the tumor. When the tumor grows large enough, the nutrient level in the center drops so low that the cells become necrotic (i.e., they begin to die due to lack of nutrients).

At this point, the tumor has two major parts: a viable, proliferating rim (where the nutrient level is high), and a dead, necrotic core (where the nutrient level is low). In the necrotic core, dead tumor cells are broken down by enzymes and carried away by macrophages, which tends to decrease the tumor volume. At the same time, proliferating cells in the viable rim tend to increase the tumor volume, leading to an eventual balance between necrosis and proliferation. This balance places a natural limit on the size of a non-vascularized tumor. Generally, this size is on the order of a few millimeters or less.

Angiogenesis

The lack of nutrients in a non-vascularized tumor limits its size. However, as dead tumor cells are broken down in the necrotic core, they release angiogenic growth factors (e.g., VEGF-β) and other molecules. These angiogenic growth factors diffuse outward from the tumor until they reach nearby blood vessels, where they stimulate the growth and movement of endothelial cells (the cells that comprise the walls of blood vessels). The endothelial cells move chemotactically and haptotactically toward the tumor and align themselves to form new blood vessels. This provides the tumor with a fresh, direct supply of nutrients. (See Figure 3.)

Angiogenesis
Figure 3: Angiogenesis: Necrotic cells and degraded extracellular matrix release angiogenenic growth factors, which promote the growth of new blood vessels toward the tumor (orange).

At this point, lack of nutrient supply is no longer a limiting factor on the size of the tumor, and it can spread throughout the surrounding tissue.

Metastasis

For a tumor to spread beyond the tissue that contains it, it must break through tougher tissue membranes. In some cases, a tumor can acquire a genetic mutation that enables it to secrete molecules (e.g., protease) that can degrade the surrounding tissue structure, such as by attacking the extracellular matrix or stromal (structural) cells. Once a tissue membrane has been sufficiently weakened, the tumor can break through and enter the neighboring tissue. (See Figure 4.)

Early Cancer Metastasis
Figure 4: Early Metastasis: To spread to other tissues, the tumor must break through tissue membranes. It does this by releasing degrading molecules like protease.

A metastasizing tumor can use this mechanism in other ways to spread beyond its original site. If the tumor degrades a blood vessel wall, metastatic cells can enter the bloodstream and migrate to distant tissues. (See Figure 5.) If metastatic tumor cells enter a lymphatic duct or node, they can travel through the lymphatic system to metastasize to distant locations. This is frequently observed in breast cancer.

Later Cancer Metastasis
Figure 5: Later Metastasis: Once a tumor has degraded a tissue membrane, it can grow into the neighboring tissue. In a similar manner, tumor cells can enter and travel through the vascular and lymphatic systems and metastasize (spread) to other, distant sites.

We note that metastasis is an extremely complex process and is still poorly understood. In December 2005, it was reported that some tumors signal distant bone marrow cells to degrade their surrounding tissues, enter the bloodstream, migrate to a new tissue, and then secrete additional compounds at their new location. This creates a new "niche," where loose tumor cells can readily start growing. This mechanism is still not understood, and is indicative of the complex interaction between cancer and the host body.

Main Treatment Methods

Several different treatment techniques are in use or under development today, which can generally be grouped in five categories: resection, radiation, chemotherapy, targeted, and immunotherapy.

In practice, these approaches often are combined. A patient's tumor may be resected, followed by chemotherapy, for instance.

Further Reading

If you're interested in learning more about the biology of cancer, I'd recommend browsing through my research links and publications. Furthermore, there are several excellent books that range in their level of scientific detail:

R. Weinberg, One Renegade Cell, Basic Books, 1999, ISBN 0465072763
This books is a good, brief overview of cancer in layman's terms. The most interesting aspect for the researcher is its historical perspective. I'd also recommend giving this short book to relatives and/or family members who might be interested in your work.
D. Wodarz and N. Komarova, Computational Biology of Cancer: Lecture Notes and Mathematical Modeling, World Scientific Publishing Company, 2005, ISBN 9812560270
This book was written by my colleagues to cover cancer from a mathematical point of view while paying particular attention to genetics and population dynamics. I'll write more on this reference as I get a chance to read it.
M. Knowles and P. Selby, Introduction to the Cellular and Molecular Biology of Cancer, 4th Edition, Oxford University Press, 2005, ISBN 019852563X
This is a great overview of cancer from a biological point of view. While the details are a little heavy, it's helpful for the mathematical biologist to see more of the actual mechanics of cancer and gain more of the oncological vocabulary.