College of Natural & Agricultural Sciences

Skye 284

Bjorn Birnir, UCSB

Angiogenesis is a multiscale process by which a primaryblood vessel issues secondary vessel sprouts that reach regions lackingoxygen. Angiogenesis can be a natural process of organ growth anddevelopment or a pathological one induced by a cancerous tumor.A mean-field approximation for a stochastic model of angiogenesisconsists of a partial differential equation (PDE) for the density of activevessel tips. Addition of Gaussian and jump noise terms to this equationproduces a stochastic PDE that defines an infinite-dimensional Lévyprocess and is the basis of a statistical theory of angiogenesis.The associated functional equation has been solved and the invariantmeasure obtained. The results of this theory are compared to directnumerical simulations of the underlying angiogenesis model. The invariantmeasure and the moments are functions of a Korteweg–de Vries-like soliton,which approximates the deterministic density of active vessel tips.

Contact Information
Qi Zhang
Target Audience
General Public
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