Effect-plasma drug concentration state space for tolerance

Using the approach of Sheiner and Verotta [452], a large number of pharmacodynamic models can be considered as hierarchical models composed of a series of submodels. These submodels are linear or nonlinear, static or dynamic input-output, elementary models. Several possible combinations of such submodels have been considered, but they have systematically associated the linear with dynamic features, and the nonlinear with static ones. Is there hesitation or fear of using nonlinear dynamics in the traditional pharmacokinetic-dynamic modeling context  

The most interesting case arises by removing assumption HI, i.e., when the reaction between drug and receptor is not at equilibrium [428]. This happens when relatively slow rates of association and dissociation of the complex are observed. Under these conditions, a slow dynamic receptor-binding model is most applicable. By maintaining the proportionality between the effect and the concentration of the drug-receptor complex, (10.4) can be written in terms of the effect 

A very general scheme for relating effects to concentration, of which both the effect-compartment and the indirect-effect models are special cases, was outlined by Sheiner and Verotta [452], The models presented in the study can be considered to be a special case of that unified scheme. As judiciously presented by these authors, both direct-response and indirect-response models are composed of one nonlinear static submodel and one dynamic submodel, but the placement of the submodels in the global model differs  

All these models introducing the prereceptor and postreceptor events have an interesting appeal with respect to physiologically implied mechanisms. Sheiner and Verotta [452] pointed out the importance of knowing where the rate-limiting step is located in a series of events from pre- to postreceptor drug interactions. 

The fundamental assumption and equations governing the effect-concentration relationship for each one of the models considered are listed in Table 10.1. The presence or not of an hysteresis loop in the effect-plasma concentration plot of each model is also quoted in Table 10.1. At present, the methodology for performing efficient pharmacokinetic-dynamic modeling is well established [405,456,457], 

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Figure 10.4 Normalized effect-plasma drug concentration state space for tolerance phenomena. As time flows (indicated by arrows) a clockwise hysteresis loop is formed.

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