### Example 1

```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
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?
Model requirements
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
Initial cancer cell
Parameters and variables
 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
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
 http://www.cancerresearchuk.org/cancer-info/cancerstats/world/cancerworldwide-the-global-picture
 http://www.cancer.gov/cancertopics/types/commoncancers
 http://www.cancer.org/cancer/cancerbasics/thehistoryofcancer/thehistory-of-cancer-what-is-cancer