title: Explicit solutions for a class of indirect pharmacodynamic response models.
abstract: Explicit solutions for four, ordinary differential equation (ODE)-based, types of indirect response models are presented. These response models were introduced by Dayneka et al. in 1993 [J. Pharmacokinet. Biopharm. 21 (1993) 457] to describe pharmacodynamic responses utilizing inhibitory or stimulatory E(max) type functions. The explicit solutions are expressed in terms of hypergeometric 2F1 functions and their analytical continuations. A practical application is demonstrated for modeling the kinetics of drug action for ibandronate, a potent bisphosphonate that suppresses bone turnover resulting in a reduction in the markers of bone turnover. Ten times shorter model evaluation times, with the explicit solution compared with the differential equation implementation, may enhance situations where a large number of model evaluations are needed, such as clinical trial simulations and parameter estimation.
authors.affiliation: Pharma Development, Clinical Science, F. Hoffmann-La Roche Ltd., PDMB, B74/3.OG-W, CH-4070 Basel, Switzerland. paul.jordan@roche.com
authors.forename: P
authors.initials: P
authors.lastname: Jordan
authors.forename: R
authors.initials: R
authors.lastname: Gieschke
mesh_terms: D016723:Bone Remodeling; D001842:Bone and Bones / Q000187:drug effects*; D004164:Diphosphonates / Q000493:pharmacokinetics / Q000494:pharmacology*; D004305:Dose-Response Relationship, Drug; D006801:Humans; D000077557:Ibandronic Acid; D008954:Models, Biological
chemical_list: D004164:Diphosphonates; D000077557:Ibandronic Acid