Physical Mathematics Seminar
Tuesday, October 19, 2021 at 2:30pm to 3:30pmVirtual Event
Speaker: Luis L. Bonilla (Universidad Carlos III de Madrid, SPAIN)
Title: Stochastic modeling and analysis of blood vessel growth
Angiogenesis is a multiscale process by which blood vessels grow from existing ones and carry oxygen to distant organs. Angiogenesis is essential for normal organ growth and wounded tissue repair but its imbalance contributes to many diseases such as age related macular degeneration (AMD) and cancer. I will present stochastic models of angiogenesis at the cellular level and at the mesoscale. Numerical simulations of stochastic models at the cellular level help understanding angiogenesis and may offer clues on ameliorating exudative AMD. Simpler mesoscale models track the motion of blood vessel tips advancing toward a region lacking oxygen. I derive a deterministic integrodifferential description of the vessel tip density from the stochastic model and show that the density advances as a soliton (similar to the Korteweg-de Vries soliton) whose shape and velocity change slowly. Analyzing these collective coordinates paves the way for controlling angiogenesis through the soliton, the engine that drives this process.
Meeting ID: 955 9772 1876