Indirect link model with bolus intravenous injection

Time is not an independent variable in the presented models. Dynamic behavior is either a consequence of the pharmacokinetics or the observed lag time by means of the effect compartment. Dynamic models from the occupancy theory and described by differential equations, such as (10.4), are scarce [428,429]. 

Neglecting dynamic models in pharmacodynamics [430] is perhaps due to the fact in that instant equilibrium relationships between concentration and effect appear to occur for most drugs. For some drugs, such as cytotoxic agents, this delay is often extremely long, and attempts to model it are seldom made. One can describe these relationships as time-dissociated or nondynamic because the temporal aspects of the effect are not linked to the time-concentration profile. 

The standard effect-compartment model, usually characterized as an atypical indirect-link model, also constitutes an example of what we will call a direct-response model in contrast to the indirect-response models. Globally, the standard direct-response models are models in which c(t) affects all dynamic processes only linearly. 

Ariens [432] was the first to describe drug action through indirect mechanisms. Later on, Nagashima et al. [433] introduced the indirect response concept to pharmacokinetic-dynamic modeling with their work on the kinetics of the anticoagulant effect of warfarin, which is controlled by the change in the prothrombin complex synthesis rate. Today, indirect-response modeling finds extensive 

In these expressions, g (t) is either gi (t) or ga (t), Smax s maximum stimulation rate, Jmax is maximum inhibition rate, Sc o and Ic q are the drug concentrations at which g (t) = 1 + Smax/2) and g (f) = 1 — (imax/2), respectively. Consequently, four basic models are formulated inhibition of inhibition of 

---

Figure 10.3 Indirect link model with bolus intravenous injection. (A) The classical time profiles of the two variables c(t) (solid line) and E (t) (dashed line) for dose qo = 0.5. (B) A two-dimensional phase space for the concentration c(t) vs. effect E (t) plot using three doses 0.5, 0.75, and 1 (solid, dashed, and dotted lines, respectively).

---