There is no doubt that one of the biggest challenges in medical science is to find a cure for cancer. Some of the main problems facing the scientists in understanding cancer are the disease’s uncontrolled growth and ability to expand without limit. Recently, mathematics has proven to play an important part in understanding many aspects of cancer, especially in the area of tumor growth. Through mathematical modeling and computer simulation, many scientists are not only able to improve cancer therapy and treatments, but they can also predict the rate of growth for many cancer tumors. In the summer of 2008, I worked on understanding the underlying biological aspects in cancer and cancer cells. I explored elementary models that predict the tumor size and the number of cells. This summer, I studied more sophisticated mathematical models that would be more realistic. Building on the achievements of last year’s NSERC USRA research term, I mainly focused on a two-parameter equation for tumour growth. More specifically, I have considered an equation that encompasses three of the most common equations used for cancer and tumour growth. The specific cases of this generalized nesting equation have significant applications in terms of predicting and studying the kinematics of tumour growth.

I hope to be able to present a general equation for tumour growth that could be used to study different models found in literature for cancerous cells and their growth patterns.

The results of my research project can be used to investigate the validity of some of the existing mathematical equations for tumour growth and their applicability to clinical data.

The significance of cancer research cannot be overstated, and the growing role that mathematics plays in this area cannot be overlooked. After taking math courses (especially courses based on numerical analysis and differential equations), and after starting a project on biomedical mathematics in the research I conducted last summer, I wanted to enhance my understanding of the subject through deeper exploration and more advanced analyses.

The broad applications it can have to the study of cancer and tumour growth. I gained a sound understanding of some of the most common and widely-used mathematical models for cancer research.

Aside from learning a lot about the mathematics of cancer, I managed and took part in two math camps held at UPEI.

I expanded and improved my understanding of the real-life applications that math has in cancer research.