Basic pharmacodynamic models for agents that alter production of natural cells

Basic indirect pharmacodynamic models for agents which alter the generation of natural cells based on a life-span concept are introduced. It is assumed that cells (R) are produced at a constant rate (k(in)), survive for a specific duration T(R), and then are lost. The rate of cell loss must equal the production rate but is delayed by T(R). A therapeutic agent can stimulate or inhibit the production rate according to the Hill function: 1 ± H(C(t)) where H(C(t)) contains capacity (S(max)) and sensitivity (SC₅₀) constants and C(t) is a pharmacokinetic function. Thus an operative model is dR/dt = k(in)·[1 ± H(C(t))]-k(in)·[1 ± H(C(t-T(R))] with the baseline condition R₀ = k(in)·T(R). One- and two-compartrnent catenary cell models were examined by simulation to describe the role of pharmacokinetics and cell properties. The area under the effect curve (AUCE) was derived. The models were applied to literature data to describe the stimulatory effects of single doses of hematopoietic growth factors such as granulocyte colony-stimulating factor (G-CSF) on neutrophils, thrombopoietin (TPO) on platelets, and erythropoietin (EPO) on reticulocytes in blood. The models described experimental data adequately and provided cell life-spans and SC(50) values. The proposed cell production/loss models can be readily used to analyze the pharmacodynamics of agents which alter cell production yielding realistic physiological parameters.