Fig. 2. Schematic representation of the pharmacokinetic–pharmacodynamic model. The model has three distinct parts. Part I is the remifentanil pharmacokinetic part, consisting of the distribution of remifentanil through the body, including the effect site (i.e.,  the respiratory controller in the brainstem) (via  a rate constant, k^e0). Part II is the respiratory controller in the brainstem. Effect of remifentanil on the ventilatory control system results in a reduction of ventilation (via  a delay, τ). Part III is the part that describes carbon dioxide kinetics. Carbon dioxide production determines together with ventilation the arterial carbon dioxide concentration. Because remifentanil causes the reduction of ventilation and carbon dioxide production is minimally affected, the ability of the system to clear carbon dioxide has diminished, and arterial carbon dioxide concentrations increase. This will have a stimulatory effect on the respiratory controller (part II). The main effect of adding propofol on top of propofol is shown as an effect on the gain factor G. CL = clearance; C^REM= remifentanil concentration in plasma; C⁵⁰= concentration remifentanil causing 50% respiratory depression; G = gain of the ventilatory control system or slope of the hypercapnic ventilatory response; k^e0= blood effect site rate constant; P^E= end-tidal carbon dioxide partial pressure; P^E_0= baseline (predrug) end-tidal carbon partial pressure; Q̇= cardiac output; τ= time constant of the ventilatory control system; V̇= inspired minute ventilation; V̇⁰ = baseline (predrug) inspired minute ventilation; V̇^CO2 = carbon dioxide production; V^AL= alveolar volume; V^TS= tissue volume; V^1–3= volumes of compartments 1–3 of the kinetic remifentanil model.