It has been established in several types of cancers, that the growth and maintenance of many cancers is due to a (typically small) sub-population of cells with stem-like properties:
cells which are capable of indefinite self-renewal and of giving rise to all the different types of
cells present in the cancer. The origins of these stem-like cancer cells are not entirely clear, and
it has not been established if they originate from healthy stem-cells, healthy self-sustaining subpopulations
of progenitor cells or even from mature, fully dierentiated cells by way of dedierentiation.
In this paper we investigate some mathematical problems which arise when one considers
the possibility of cancer stem-cells arising from healthy progenitor cells (normally possessing limited
division potential) which have been perturbed in some way, such as through mutation. For
example, glial progenitors have been previously proposed as a possible source of gliomas. We
model the progression from stem cell to mature cell where at each cell division we include a
probability of a cell either advancing or regressing in maturity. Whereas in normal, healthy cell
populations, cells will be more likely to advance in maturity, we suggest that the tendency to
advance or regress in maturity may be altered by changes in the cell population such as mutation,
and that this may cause the subpopulation of progenitor cells to become self-sustaining, leading to
uncontrolled growth of this subpopulation. The conditions, according to our model, under which
a population of progenitor cells is self-sustaining are then discussed.