Modeling Cancer Cell Growth Of Cancer - 1791 Words

Modeling Cancer Cell Growth When researching mathematics in nature, one thing that my teacher had repeated was to find something that interested me. Wanting to become a biomedical engineer and having suffered many losses in my family due to cancer, exploring cancer was the obvious choice. Cancer is the leading cause of all human deaths in the world, and the financial costs of cancer have been estimated at $1.16 trillion US dollars per year as of 2010. The development of mathematical models of tumor cells is important to the growth kinetics, which may lead to the development of successful treatment strategies. Because of the great variance in malignant neoplasms (the cause of cancer), research has not been great enough to save the†¦show more content†¦For this exploration, I decided to try to model the growth rate of tumor cells through calculus in order to discover the advantages and disadvantages of certain models, including the exponential model, the Gompertz model, and the Universal Law. Premise of the Exploration For this exploration, I will be using the data on the growth of tumor size found by a 1970 mouse mammary study (citation needed). This data was collected over the course of 40 days for two different types of cancer. This data has been used to create the Gompertzian model and the Fundamental Law, which I will use later in this exploration. Lung Cancer in Mice Breast Cancer in Mice Day Volume (mm ³) Day Volume (mm ³) 4 23 18 314 5 68 19 423 6 61 20 401 7 107 21 675 8 147 22 487 9 132 23 813 10 192 24 560 11 226 25 785 13 315 26 803 14 387 27 817 15 490 28 849 16 714 29 936 17 945 30 1065 18 1013 31 1162 19 1141 34 1134 20 1201 35 1467 21 1156 36 1279 23 1378 37 1298 Graph A has the averages of all of the data points along with error propagation, while Graph B has the individual data for each group studied. Exponential Growth Model When I first started researching this, one conclusion that I made was that big cells grow faster, and small cells grow smaller akin to a snowball rolling down a hill (citation needed). One model used to describe tumor growth is the exponential growth model. V(t)=V_(0 ) e^(-∠t) in which