1. Chaos in Tumor Growth Elliotte Flaum

2. Background: Cancer

3. Gene Mutation Theory vs. Aneuploidy Theory ●Risk progression with age ●Carcinogens ●Aneuploidy is induced ●Patterns of aneuploidy found ●Aneuploidy contributes to cancer’s survival ●Cancer cells morph faster than genes

4. Background: Mitosis

5. Background: Aneuploidy

6. Background: Cancerous Cells

7. Tumors and Chaos Improper chromosome segregation can lead to different outcomes for the cell Difficult to predict when mitosis will go wrong Different severities of aneuploidy

8. Logistic Equation Φ n+1 = r Φ n (1 - Φ n ) = r Φ n - r Φ n 2

9. Probability Map

10. Applications New therapies to cancer may be developed New research methods may be developed to further understand cancer May lead to further understanding other types of cancer that are not tumorous, such as leukemia

11. Research Proposal Although tumor growth can be described by chaos theory, not all forms of cancer are characterized by tumors. For example, leukemia is cancer of the white blood cells. I am interested in studying whether development of cancerous cells in cancers such as leukemia can also be described by chaos theory.

12. Questions?

13. Sources "Biology Vocabularies." : Marzo 2011. Blogger.com, 29 Mar. 2011. Web. 11 Feb. 2016. "Cell Division Mitosis Diagram 32143 | TECHDATAI." Cell Division Mitosis Diagram 32143 | TECHDATAI. N.p., n.d. Web. 11 Feb. 2016. Duesberg, Peter. "Chromosomal Chaos and Cancer." Sci Am Scientific American 296.5 (2007): 52-59. Web. 31 Jan. 2016. Ivancevic, Tijana T., Murk J. Bottema, and Lakhmi C. Jain. "Models of Growth and Decay." Empirical Model Building Wiley Series in Probability and Statistics (n.d.): 6-43. Web. Rasnick, David. "Aneuploidy Theory Explains Tumor Formation, the Absence of Immune Surveillance, and the Failure of Chemotherapy." Cancer Genetics and Cytogenetics 136.1 (2002): 66-72. Web. 30 Jan. 2016.