A mathematical model of angiogenesis and tumor growth: analysis and application in anti-angiogenesis therapy.

The purpose of this paper is to develop a new coupled mathematical model of angiogenesis (new blood vessel growth) and tumor growth to study cancer development and anti-angiogenesis therapy. The angiogenesis part assumes the capillary to be a viscoelastic continuum whose stress depends on cell proliferation or death, and the tumor part is a Darcy's law model regarding the tumor mass as an incompressible fluid where the nutrient-dependent growth elicits volume change. For the coupled model, we provide both an inviscid analysis and a parameter sensitivity analysis of the angiogenesis model in response to a stationary hypoxic tumor, and a steady state analysis of the tumor growth in response to a fixed and long blood capillary. The analysis shows that the stable steady state tumor with an invading blood capillary exists if and only if the nutrient release rate divided by the decay rate is less than the tumor viable limit, and the full tumor encloses one part of the capillary in this steady state. Afterwards, we use the coupled model to simulate vascularized tumor growth and anti-angiogenesis therapy. The simulations show that the tumor tends to maximize the nutrient transfer by blood vessel co-option and the anti-angiogenesis treatment by using growth factor neutralizing antibodies would regress the neovasculature and shrink the tumor size. However, the shrunken tumor mass could survive by feeding on mature blood vessels that resist the treatment. This implies the limited efficacy of the anti-angiogenesis monotherapy and its effect on vessel normalization.