Pharmacokinetic-pharmacodynamic modelling in anaesthesia

Abstract

Anaesthesiologists adjust drug dosing, administration system and kind of drug to the characteristics of the patient. They then observe the expected response and adjust dosing to the specific requirements according to the difference between observed response, expected response and the context of the surgery and the patient. The approach above can be achieved because on one hand quantification technology has made significant advances allowing the anaesthesiologist to measure almost any effect by using noninvasive, continuous measuring systems. On the other the knowledge on the relations between dosing, concentration, biophase dynamics and effect as well as detection of variability sources has been achieved as being the benchmark specialty for pharmacokinetic-pharmacodynamic (PKPD) modelling. The aim of the review is to revisit the most common PKPD models applied in the field of anaesthesia (i.e. effect compartmental, turnover, drug-receptor binding and drug interaction models) through representative examples. The effect compartmental model has been widely used in this field and there are multiple applications and examples. The use of turnover models has been limited mainly to describe respiratory effects. Similarly, cases in which the dissociation process of the drug-receptor complex is slow compared with other processes relevant to the time course of the anaesthetic effect are not frequent in anaesthesia, where in addition to a rapid onset, a fast offset of the response is required. With respect to the characterization of PD drug interactions different response surface models are discussed. Relevant applications that have changed the way modern anaesthesia is practiced are also provided.

Keywords: PKPD models; anaesthesia; clinical applications; pharmacometrics.

Figure 1

Time course of concentrations and effects. A) Time course of drug concentrations measured in plasma (C_p), and two response variables (Effect 1 and Effect 2). Sampling times, t₁ and t₂, show same values of C_p but correspond to very different levels of response. B and C) Effect vs C_p relationships. Arrows indicate time direction

Figure 2

Different interpretations of the relation between concentration and effect. Schematic representation of A) the effect compartment model proposed by Sheiner et al. [1] B) the interstitial ECm model (Schiere et al. [28]) and C) the two-compartments ECm (Björnsson et al. [29]). k_1e, k_e0, ke₁₂, ke₂₁, k_1p and k_pe, represent first order rate constants. C_p and C_e denote plasma and effect site drug concentrations, respectively

Figure 3

Pharmacodynamic models. Response vs. C_e profiles corresponding to the sigmoidal (red) and power (blue) models. Parameters used for the simulations: sigmoidal E_max model (E₀ = 100; I_max = 1; C₅₀ = 50 ng ml⁻¹; γ = 2), power model (E₀ = 100; C₅₀ = 50 ng ml⁻¹; γ = 2). In both simulations it is assumed that the drug induces an inhibitory effect

Figure 4

Schematic adaptation of the model published by Olofsen et al. [41], to describe respiratory effects of remifentanil and propofol. P_A and P_V are the arterial and venous carbon dioxide pressure, respectively; V_AL and V_TS correspond to the alveolar and tissue volumes, respectively; Q is the cardiac output; V₀ and V represent the inspired minute ventilation at baseline and during anaesthesia, respectively; VCO2 represents the carbon dioxide production; λ₁ and λ₂ are scaling parameters; G, gain of the ventilatory control system; P_{E_0}, and P_E, end-tidal P_CO2 at baseline and during anaesthesia, respectively; B, apneic threshold; τ, time delayed constant, E_Prop parameter accounting for the reducing effects of propofol on G [=1, in absence of propofol]; C_Rem and C_{e_Rem}, plasma and predicted effect site concentrations of remifentanil, respectively; k_e0, first order rate constant governing the elimination process from the effect site; C₁₀₀, effect site concentrations of remifentanil that elicits a 100% increase in B

Figure 5

A model explaining the relations between concentration and effect after epidural administration of a local anaesthetic drug. Schematic adaptation of the model developed by Olofsen et al. [44] to describe the anaesthetic effects of levobupivacaine and ropivacaine after epidural administration

Figure 6

Context sensitive decrement times for propofol according to the PKPD model of Schnider et al. [14]. The graph shows the time it would take for effect site propofol concentration to fall by an 80% as a function of infusion duration in a 80-year-old subject as compared with a 40-year-old. Also represented is the time it would take for a decrease of 50% in an 80-year-old vs. a 40-year-old

Figure 7

An example of the time course of plasma and effect site predicted concentrations when using a TCI system to administer remifentanil. The device is targeting the effect site, hence the relative overshooting in plasma to achieve faster the pseudoequilibrium at the biophase. Targeted concentrations are 1, 4, 3 5 and 0 ng ml^–1