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Using geometrical arguments it is shown that Cancer Stem Cells (CSC) must beconfined inside solid tumors under natural situations. Aided by an agent-basedmodel and percolation theory, the probability for a CSC to be at the border ofa colony is estimated. This probability is estimated as a function of the CSCsself-renewal probability $p_s$, i.e. the chance that an CSC becomenon-differentiate after mitosis. In the most common situations, $p_s$ is smalland CSCs are mostly destined to produce differentiated cells at a very lowrate. The results presented here show that CSCs form a small core in the centerof the cancer cell colony, becoming quiescent due to the lack of space toproliferate, which stabilizes their population size. This result provides asimple explanation for the CSC niche size that dispenses with the need ofquorum sensing or other proposed signalling mechanisms. It is also supports thehypothesis that metastases are likely to start at the very beginning of thetumoral development.

Radial percolation reveals that Cancer Stem Cells are trapped in the core of tumorspheres