The presence of a lag between the observed effect and plasma concentrations that cannot be accounted by the presence of an effect compartment alone is indicative of a mechanism that involves indirect effects. In this case, the overall effect can be thought of as the result of the interaction between a compound and one or more physiological processes at steady state that produce mediators (for example, biomarker, hormones, signaling proteins, etc.) that modulate the effect (Figure 5.7). The production of these mediators is a zero-order process, whereas the output is a first-order process dependent on the mediator concentration S.
where kin and kout are the specific input and output rate constants of the mediator, respectively. In the absence of drug and at steady state, the baseline level
Figure 5.7 general scheme of an indirect effect model. at the top, the plasma concentration is related to the concentration at the site of action (Ce), which in turn modulates the rate of change of the concentration of a mediator, either by stimulating (+) or inhibiting (-) the production (or input, kin) or consumption (output, kout) of a biosignal. The thick blue arrows represent pharmacodynamic signal transduction leading to the final response.
of S (S0) is S0 = kin/kout, and the baseline effect (E0) is proportional to S0. Compounds can act by increasing or decreasing the input (kin) or the output (kout) of those mediators via the functions H(t) and G(t), respectively:
For example, the oral hypoglycemic tolbutamide stimulates the release of insulin, which causes a decrease in blood glucose levels, whereas atorvasta- tin inhibits the production of mevalonic acid by HMG-coA reductase, resulting in a decrease in blood cholesterol.
Notice that in contrast to direct models, where there is a direct effect of the concentration of the compound in the concentration of the mediator (S), in indirect models the concentration of drug affects the rate of change of the concentration of the mediator (dS/dt), and because of that, the effect takes longer to occur.
Indirect models can be refined by describing the signal transduction processes that occur between the pharmacokinetics and the final effect. These additional processes can be modeled by the use of transit compartments between the activation of the receptor and the observed final effect, and can be described by additional differential equations. these transit compartment models have been used successfully in anticancer drugs and in describing the time course of myelosuppresion in clinical studies.36’37
A feature of indirect models is the effect of dose on the time of the observed maximum effect. In contrast to direct-effect models, the time of the observed maximum effect is shifted to later times as the dose is increased.