Mathematical modeling of oxygen distribution in malignant tumors

Abstract

Tumors of different shapes, in particular, vary in the degree of convergence or divergence of oxygen diffusion flows in them. Following simple geometric considerations, it becomes obvious that the highest convergence degree of oxygen diffusion flows is characteristic of spherical tumors with oxygen coming from the surface, while the highest divergence degree is typical of cylindrical tumors surrounding a blood vessel coaxial with the tumor and supplying it with oxygen. Estimates were performed for two oxygen tension values of 3.32 kPa and 1.99 kPa, corresponding to oxygen concentration values c0 : c01 = 25 mm Hg and с02 = 15 mm Hg respectively.