Generalization of the Greenspan MCS model to n-dimensional case

In tumour dynamics there is a well known model of spherical growth underthe diffusion of nutrient. The basic concept of multicellular spheroid (MCS) in 3-D was proposed by Greenspan. I'll show the formal generalization of this concept in n-dimensional case. I'll focus on the dependence of the model dynamics on the dimension parameter n, especially in comparison of two standard cases - for n=3 and n=2.