TABLE 1.

Theoretical mathematical relationships among cancer cells in tumors.

Tabular representation of what is proposed in Figure 1. Theoretical mathematical relationships among CCs in a tumor process could be obtained for each cell typology (CSCs and non-CSCs), as reported in the formulae at the top of Table 1. These formulae can be obtained following the sequence of arrows, as shown. Regarding the total number of CCs, a discrepancy between theoretical (column h) and presumed (column i) values is the result of missing CDCs (column g) arising at the sixth division (*) and increasing progressively in subsequent divisions. The mCDCs might be a natural occurrence if CDCs cannot proliferate, whereas they might be the result of apoptotic death if CDCs are still proliferating; however, in this case, it would not be explainable how a mathematical model might foresee it. The data in Table 1 allow us to determine the presumed ratio between CSCs and total CCs (**), progressively decreasing during tumor progression, as experimentally detected in mammary tumors. Note the high convergence between presumed and experimental CSC percentages (about 18%) at the n = 10 division number (***).