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The Biology Project > Biomath > Power Functions > Applications > Tumor Growth

Power Function Applications

Tumor Growth

Tumors arise when the control mechanism that limit cell division fail. This can happen as a result of DNA mutations in genes that control cell growth, as in skin cancers (see photo on the right) or from viral infections, such as hepatitis B induced liver cancer in humans or leukemia caused by feline leukemia virus in cats. For more information on the cellular mechanisms that control cell growth and division please see the Cell Biology module.

While your first thought when you hear the word tumor might be "cancer," tumors are in fact any collection of cells that grow and divide abnormally. Examples of such benign tumors include warts, fibroids, and adenomas found in polyps. The cells in a benign tumor appear very similar to those the cells in the tissue. In addition, benign tumors are encapsulated in connective tissue. Cells in benign tumors can accumulate additional mutations, further altering their growth patterns and causing the tumor to become malignant or cancerous. Malignant tumors can lose the capsule that holds the tumor in place, allowing the cancer to spread throughout the body.


Colon polyps contain benign tumors called adenomas that sometimes progress into the malignant tumors found in colon cancer. Photo Credit: Courtesy of the National Cancer Institute.


A simple model for tumor growth is given by the von Bertalanffy equation,

f (x) = axα -bxβ,

where a, α, b, and β are positive constants. In this equation, x represents tumor size, given in either mass or number of cells, as a function of time, and f (x) describes how tumor size changes over time. The term axα describes the growth of the tumor and bxβ describes the degradation of the tumor.

Use the von Bertalanffy equation to answer the following questions:

Find the tumor size where growth increases.

Find the size of the tumor where it begins to shrink.

Find the critical size where the tumor stops growing.


The Biology Project > Biomath > Power Functions > Applications > Tumor Growth

The Biology Project
Department of Biochemistry and Molecular Biophysics

The University of Arizona

March 2007
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