Modeling of Tumor Induced Angiogenesis

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Modeling of Tumor Induced Angiogenesis

• Heather Harrington, Marc Maier
• Lé Santha Naidoo
• Faculty Advisors Panayotis Kevrekidis
  Nathaniel Whitaker

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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.

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More Bio

• 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.

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5 Species Dynamical Evolution Model

• (1) Ct Dc?C ?/?x(fF ?F/?x)
• - ?/?x(fT ?T/?x)
• ?/?x(fI ?I/?x) k1C(1-C)
• (2) T e(-(x-L)²/e)
• (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

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Whats 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