A model with ‘growth retardation’ for the kinetic heterogeneity of tumour cell populations

In the present paper we propose a continuous cell population model based on Shackney’s idea of growth retardation. Cells are characterized by two state variables: the cell maturity x, 0 ⩽ x ⩽ 1, and a state variable T that identifies the rate of maturation along cell cycle. During their life span, cells can change T at random by jump transitions to T values corresponding to slower maturation rates, while at each jump the maturity x is conserved. Both the time evolution of the population and the exponential stationary solution are numerically computed. The distribution of the cell cycle transit time in asynchronous exponential growth is investigated by Monte Carlo simulation. An approximated formula for the distribution of cell cycle time is also provided.