Modeling Tumor Growth Jessie Xiao, Cindy Zhang, Jessica Zheng The model Tumor growth Lymphocyte growth Coupling tumor growth and NK cell growth Adding in chemotherapy Overview of Our Project Tumors An abnormal proliferation of tissues T = Population of tumor cells N = Population of NK (natural killer) cells C = Population of lymphocytes M = chemotherapy drug concentration in the bloodstream Variables Growth and death terms Cell-cell kill term (Tumor cells only) Cell recruitment (NK cells only) Inactivation terms (NK cells only) Chemotherapy term Explanation of Models The Model Logistic growth: Carrying capacity at (approximately 10 9 ) Tumor population at time t where A is a constant: A Tumor Cell By Itself Steady state: ( 6.25 x cells) A Lymphocyte By Itself NK Cells Setting to 0 to find nullclines: For T = : Coupling Tumor and NK cell growth Tumor Cells Setting to zero to find the nullclines: Coupling Tumor and NK cell growth cont. Tumor and NK Cell Nullclines Simulating Initial Conditions Tumor and NK Nullclines (zoomed in) Simulating Initial Conditions M was previously assumed to be zero Adding in the effect of chemotherapy v M (t) is assumed to be a constant Adding in Chemotherapy Solving for M gives: is a stable steady state Assume v M (t) is 5, so M is 5.56 Adding in Chemotherapy cont. Initial Conditions for M Solving for C : C was 6.25 x cells without chemotherapy Need to change C in the other equations Chemotherapy and Lymphocytes New C * value: Setting to 0: For : Chemotherapy and NK Cells Setting to zero : Chemotherapy and Tumor Cells Chemotherapy and Tumor-NK Nullclines Simulating Initial Conditions with Chemotherapy Simulating a System of Treatment Adding in Chemotherapy Adding Chemotherapy (zoomed in) Removing Chemotherapy Removing Chemotherapy (zoomed in) Limitations of our model Untreated tumors are unlikely to be eradicated by the immune system alone Chemotherapy kills tumor cells very effectively, but also kills immune cells effectively Conclusions and Discussion "Medical Diagnosis and Medicinal Plants." Medical Diagnosis and Medicinal Plants. N.p., n.d. Web. 30 July Pillis, L.g. De, W. Gu, and A.e. Radunskaya. "Mixed Immunotherapy and Chemotherapy of Tumors: Modeling, Applications and Biological Interpretations." Journal of Theoretical Biology (2006): Web. 30 July Pillis L.g. De, A.e. Radunskaya, and C.L. Wiseman. A Validated Mathematical Model of Cell-Mediated Immune Response to Tumor Growth. Web. 30 July "Tumor Doubling Defense : PA Cervical Cancer Misdiagnosis Attorneys." Meyers Evans & Associates, LLC. N.p., n.d. Web. 30 July Pillis, L.g. De, and A. Radunskaya. "A Mathematical Model of Immune Response to Tumor Invasion." Computational Fluid and Solid Mechanics 2003 (2003): Web. 30 July Sources Thank you to: Professors Tim Lewis, Sebastian Schreiber, and Bob Guy David and William Mr. Gonzalez Acknowledgements