Dissertations and Theses

Date of Award


Document Type



Chemical Engineering

First Advisor

David Rumschtzki

Second Advisor

Ilona Kretzschmar


cancer, growth, chemotherapy


Many mathematical models have focused on growth of a single tumor with their spreading rate with some have included its metastasis. Some of the earlier models focus on exponential growth and its shift with time on to a linear model. The Gompertzian model involves a quadratic terms and that limit growth. We looked into Iwata et al paper it discusses a different model and takes into account the growth and metastasis of a tumor population but does not look into tumor shrinking or chemotherapy. Our new model focuses on the extending Iwata et al model to take into account tumor regression, we design with a discrete tumor size model which focuses on a limited number of tumors and this will help us to extend the model to consider tumor size into continuum model. Cancer is the world’s deadly health killer and is the second leading cause of death in the United States [13]. Cancer has been found throughout history. Some evidence is also found in fossilized bone tumors and in human mummies and from ancient Egypt times. Cancer is largely a manifestation of abnormal cell growth with the potential of spreading to different parts of the body. They can form a new tumor, which is a group of the cells that undergoes unregulated growth often forming a mass or lump in certain parts of the body, it can distribute diffusely [13]. Untreated cancer usually causes serious illness and sometimes death. There are many signs of a cancer, like the formation of mass or lump growth, abnormal bleeding, weight loss, a change in bowl movement and so on. There are many different kinds of a cancer, like melanoma which kills about 8000 people in the US annually and 40000 people worldwide [14]. There are many causes associated with various cancers like tobacco use, obesity, poor diet, and consumption of alcohol and so on. Cancer productivity can also be hereditary where it can be passed from parents DNA [15]. It is very difficult to know exactly what could have caused any one person’s cancer. Cancer cells form tumors and invade other parts of the normal tissue. There are some cancers that rarely form tumors like leukemia where cancer cells involves the blood and blood forming organs and they circulate through other tissues as they grow. When cancer cells gets into the blood stream they can form new tumors after invading other normal tissue. This process of spreading is called metastasis [15].



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