Theory of cell age distribution in suspension culture with feed and/or drain

A mixed problem for the M'Kendrick-von Foerster equation satisfied by the number density function in terms of the age of the viable cells in a suspension culture with feed and/or drain is solved, and a method of calculating the number density function and time-dependent generation time from observed data of cell number and cell mass is presented. This theory is adequate to analyze the growth of cells that undergo binary fission. The equation of mass balance follows as a natural consequence of this treatment. The equation of substrate balance in consideration of the effect of cell volume is derived rigorously.