Convergence of direct and indirect pharmacodynamic response models

The article by Verotta and Sheiner (1) provides a cogent extension of the indirect response models (IRM) of Dayneka et al. (2) to accommodate a linear "effect compartment" as a biophase for the drug and a nonlinear transformation of an endogenous mediator (R) to produce an effect (E). An example of the considerable utility of this conceptual approach can be found in the pharmacoimmunodynamic model of Mishina and Jusko (3) which employed a biophase to account for methylprednisolone available to the spleen from liposomes, measurement of corticosteroid receptor-binding as an indirect biosensor process, and employment of the Hill function for transduction of steroid-receptor occupancy to inhibition of splenocyte immunosuppression. More complex, multistep transduction functions are needed to account for the gene-mediated induction of enzymes by corticosteroids (4). On the other hand, various clinical drug effects can be accommodated by the basic four IRM models if it is assumed that E= R (5). A scheme that may more aptly reflect the state-of-the-art in pharmacokinetic/pharmacodynamic (PK/PD) modeling is depicted in Fig. 1. This diagram summarizes our progression in evolving IRM models to accommodate both the biophase and transduction elements and pictorially extends the "general model" of Verotta and Sheiner. The biosensor process can be the Hill function or other equation that produces inhibition or stimulation of k~n or kou t (e.g., ref. 2). The scheme may be helpful in reminding an investigator to consider that there may be at least four intermediary components between drug in blood and the measured response which, depending