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Modeling of Tumor Induced Angiogenesis

Modeling of Tumor Induced Angiogenesis. Heather Harrington, Marc Maier & Lé Santha Naidoo Faculty Advisors: Panayotis Kevrekidis & Nathaniel Whitaker. Biological Background Important terms.

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Modeling of Tumor Induced Angiogenesis

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  1. Modeling of Tumor Induced Angiogenesis Heather Harrington, Marc Maier & Lé Santha Naidoo Faculty Advisors: Panayotis Kevrekidis & Nathaniel Whitaker

  2. Biological BackgroundImportant terms • Angiogenesis: The process of formation of capillary sprouts in response to external chemical stimuli which leads to the formation of blood vessels. • Tumor Angiogenic Factors (TAFs): Stimuli secreted by Tumors • Extra Cellular Matrix (ECM): The area in which cells interact with the Fibronectin(F). • Haptotaxis: The attraction of cells to ECM. • Proteases (P): Secreted by tumor to attract cells and destroy Inhibitors. Promotes Angiogenesis. • Inhibitors: Prevent Cells from getting to tumor. Generated by fibronectin cells in the ECM to inactivate proteases.

  3. Cells: Diffuse in the ECM, get generated and die. They are driven to the TAF gradient (chemotaxis), as well as the ECM concentration gradient and are “repelled” from inhibitor gradients TAFs: We assume TAF gradient is fixed ECM: Secretion of Proteases by the tumor gradually degrades the ECM; proteases involved in the angiogenic process bind to the Fibronectin depleting it allowing the cells to be driven to the tumor Proteases: Neutralized by inhibitors Inhibitor: Mutually Neutralizes with Protease. More Bio

  4. (1) Ct = DcΔC – ∂/∂x(fF* ∂F/∂x) - ∂/∂x(fT* ∂T/∂x) + ∂/∂x(fI* ∂I/∂x) + k1C(1-C) (2)T = e(-(x-L)²/ε) (3) Ft = -k2PF (4) Pt = -k3PI + k4TC + k5T – k6P (5) It = -k3PI fT term represents chemotactic attraction of cells to tumor fF term represents haptotactic response to the Fibronectin fI term represents the “repulsive” effect of inhibitor gradients Dc = Diffusion Coefficient fF = a1C fT = a2C/(1 + a3T) fI = a4C 5 “Species” Dynamical Evolution Model

  5. What’s Next? • 1-Dimensional Model with “random walker cells” • 2-Dimensional Model of Angiogenesis • Modelling Angiogenesis in the Cornea (ignoring inhibitors) • (If Time Permits) Angiogenesis in the Cornea with Inhibitors

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