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.
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.)
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.)
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.)
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.
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.
- Resection:
Resection is the surgical removal of a tumor, along with some surrounding tissue. A positive aspect of resection is that it is very localized: a skilled surgeon can remove a tumor while minimizing damage to the surrounding tissue and the rest of the body. However, the boundary of a tumor can be difficult to locate precisely, raising the possibility of missing some tumor cells that can grow to form new tumors.
- Radiation:
In radiation therapy, high energy radiation (e.g., X-rays) is focused on the tumor. The ionizing radiation injects extra energy into the tissue and releases electrons from atoms in the region. This, in turn, creates reactive chemical species that tend to damage large molecules like DNA. Many cancers have a diminished ability to repair damaged DNA, which means that radiation affects tumor cells more than normal cells. Radiation therapy is fairly targeted, in that the beams can be precisely focused on a tumor and its surrounding tissue. However, it causes side effects, and more importantly, many tumors cannot be targeted without passing the radiation through healthy tissue.
- Chemotherapy:
In chemotherapy, a cytotoxic chemical is administered to the patient, typically intravenously. The chemotherapeutic agent generally acts by interfering with cell division, and so it usually has less of an impact on cells that are in the resting G0 phase. (Learn more about the cell cycle and chemotherapy.) Because cancerous cells are the most likely to be dividing, they are the most affected by chemotherapy. Chemotherapy is not a targeted therapy: it affects all proliferating cells in the body, and as such, it has many negative side effects. However, the systemic nature of chemotherapy is particularly useful when the cancer has spread beyond its primary site.
- Targeted:
Targeted therapies attack cellular or higher-level biological processes that are specific to cancer. For example, antiangiogenic drugs (e.g., Avastin) have been developed to prevent angiogenesis. Other targeted therapies attempt to disrupt pathways only expressed by a patient's tumor, or target cells that express specific mutant or overexpressed proteins characteristic of some cancers. Gleevec is one such example.
In experimental treatments, researchers have used proteins unique to the cell walls of tumors as a target for "smart bombs:" a molecule that can only bind to a cancer-specific protein attached to a chemotherapeutic agent or a small radioactive particle. Other experimental approaches include crafting nanoparticles (a combination of chemotherapeutic drugs and a binding material) that are too large to exit normal capillaries but can exit the blood vessels formed by tumor angiogenesis.
- Immunotherapy:
In this newer approach to therapy, the immune system is primed to recognize tumor cells, which it then attacks with a natural immune response. Initial results have been mixed, and the approach may be most effective when combined with other therapy techniques.
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.