Transport theory for growing cell populations.

The partial differential equation that describes the growth of cell populations whose maturation rate is random is developed. The equation resembles that used in classical transport theory but mitotic boundary conditions and the restriction of the maturation rate to non-negative values brings out new features and new problems. This is a generalization of a previously published formulation in which cells could make transitions at random between only two maturation velocities: a characteristic velocity and zero. Growth rates, cycle time distributions and pulsed labeled mitotic curves are calculated for a simple choice of parameters. A numerical algorithm that is suited to the solution of the transport equation is given.