Modeling Tumor Growth Sam Kupfer and Joseph Ahmad

Background/Outline  Cancer is a group of diseases in which abnormal cells divide uncontrollably, forming tumors that interrupt the normal functioning of nearby cells and organs  Cancer has existed throughout recorded history. It was first described by ancient Egyptians around 3000 BC, who wrote of the disease: “There is no treatment”  14.1 million adults were diagnosed with cancer in 2012  8.2 million people died from cancer in 2012  The most common types of cancer include breast, prostate, lung, colon, and skin cancer

 When a tumor grows via cell division, it pushes on the adjacent normal cells, eventually moving them out of the way  The tumor may also release chemicals that signal nearby blood vessels to sprout new branches towards the tumor, which supply it with the oxygen and nutrients it needs to grow. This process is called angiogenesis

Problem Formulation  Problem: Cancer is among the leading causes of death worldwide. It is not yet fully understood how cancerous tumors spread. A better understanding of this process could help with the development of a cure or new treatment.  Questions:  How do the sizes, shapes, and density of cells impact tumor growth?  How does tumor growth differ in different types of cancer?  How fast is the growth of the tumor in comparison to other bodily processes?  How does a tumor’s proximity to blood vessels affect its growth?

To answer these questions we propose to develop a model with the following characteristics:  The model will start with a single cancerous cell on a 2-dimensional plane, surrounded by a network of normal cells  The growth of the tumor through the division and re-division of cancerous cells will be analyzed  The single cancerous cell will initially be positioned a given distance away from a blood vessel  The model will be run with a variety of sets of initial conditions. We will examine the effects of changing these conditions Model requirements

Initial cancer cell

 Cancer cell size and shape  Normal cell size and shape  Distance from initial cancer cell to blood vessel  Time between cancer cell divisions  Frequency of cell death in oxygen-deprived normal cells  Normal cells’ resistance to being pushed/moved by cancerous cells  Speed of angiogenesis and growth increase effect of blood vessel on tumor  These conditions will be varied to emulate the properties of different types of cells, and optimized to fit data from real tumor growth studies Parameters and variables

What is missing  What type of model is proposed?  Distinction between variables and parameters  Diagram showing flow of model  How will the model be solved and analyzed

Works Cited  worldwide-the-global-picture worldwide-the-global-picture   history-of-cancer-what-is-cancer history-of-cancer-what-is-cancer  cancer/grow/how-a-cancer-grows cancer/grow/how-a-cancer-grows  :-Clara-Jacobi- :-Clara-Jacobi-  against-Kidney-Cancer.aspx against-Kidney-Cancer.aspx