General relationship between transit compartments and lifespan models

Transit compartment models (TCM) are important tools in pharmacokinetic/pharmacodynamic (PKPD) modeling. In this work we investigate the relationship between TCMs with arbitrary initial values and lifespan models (LSM) with non-constant past and constant lifespan. We show that the total population in all transit compartments converges to a LSM, if the number of compartments n tends to infinity. The key to obtain this result is to establish a relationship between the initial values of the TCM and the non-constant past of the LSM. We apply the result to two already published PKPD models.