  Using geometrical arguments it is shown that Cancer Stem Cells (CSC) must be
confined inside solid tumors under natural situations. Aided by an agent-based
model and percolation theory, the probability for a CSC to be at the border of
a colony is estimated. This probability is estimated as a function of the CSCs
self-renewal probability $p_s$, i.e. the chance that an CSC become
non-differentiate after mitosis. In the most common situations, $p_s$ is small
and CSCs are mostly destined to produce differentiated cells at a very low
rate. The results presented here show that CSCs form a small core in the center
of the cancer cell colony, becoming quiescent due to the lack of space to
proliferate, which stabilizes their population size. This result provides a
simple explanation for the CSC niche size that dispenses with the need of
quorum sensing or other proposed signalling mechanisms. It is also supports the
hypothesis that metastases are likely to start at the very beginning of the
tumoral development.
