Figure 1. Model schematic, showing key parameters governing the mathematical model based on the assumption that there exists a population of cells that have the capacity to self-renew (tumor initiating cells or cancer stem cells).
The tumor initiating cell population of size N0 is exclusively able to maintain the tumor due to occasional self renewal. Transit amplifying cells (N1, . . . , Nm) undergo m cell division before they enter cell senescence. Tumor initiating cells (TICs) proliferate with a rate S, self renew with probability p and die at a rate S d. Transit amplifying cells proliferate with rate D and die at a rate D d. The tumor initiating cell pool expands via symmetric stem cell divisions and the hierarchy is filled with transit amplifying cells via cell differentiation. Typically, the tumor is initiated with a single TIC in compartment 0.