Modeling Sprouting Angiogenesis by Drift Forces with the Usage of Fokker-Planck Equation

Abstract

One of the first phases of cancer is known as angiogenesis by the which are created new blood vessels from the pre-existing one. In this paper, the well-known equation of Fokker-Planck is used to describe the time evolution of the new vessels since their creation until the time that them acquire certain stability. In particular, emphasis is done to the term of drift that encompasses the stochastic character of angiogenesis. Once the theory is proposed, computational simulations are carried out. For this, the Gaussian approach with a time-dependent width is employed. This yields a oscillating scenario of ions due to the repulsion and attraction forces at the events of permeability.