What is the k e0 and what does it tell me about propofol?

Propofol is now the ‘gold standard’ intravenous anaesthetic drug and is commonly used as the hypnotic component of total intravenous anaesthesia (TIVA) as it has a relatively fast onset and short duration of action, making it easy to titrate. Like most anaesthetics, it has a narrow therapeutic ratio and significant dose-dependent adverse effects. A precise control of the anaesthetic effect requires a good understanding of the dose-effect relationship and rational dose schemes. Effect-compartment models are empirical models that relate the dose of a drug to its concentration (pharmacokinetic) and the concentration to the effect (pharmacodynamic), thereby assisting in titration of the drug and its effects. These models are being increasingly used in target controlled infusion (TCI) devices to facilitate administration of a number of drugs used in intravenous anaesthesia. Since the concentration of propofol in the brain cannot be measured, effect-site models are derived using repeated measurements of propofol's hypnotic effect. One of the major problems of this approach is that propofol's hypnotic effect is not easily measured 1. Most studies have used indices based on EEG activity as surrogate measures of propofol's hypnotic effect. However, discrepancies in these indices have resulted in markedly different effect-site elimination rate constant (ke0) values 2, with different descriptions of propofol's effect-time profile. In currently available TCI pumps, it is possible to find two very different Marsh effect-site models: one with a slow ke0 (0.26 min−1) incorporated in the Diprifusor™ (AstraZeneca, London, UK); and one with a fast ke0 (1.21 min−1) used by the Base Primea system (Fresenius-Kabi, Brezins, France). The Schnider model, also available in the base Primea system, uses yet another ke0. This has created confusion among anaesthetists who must understand the implications of these differences in TCI model predictions. In addition, there is ongoing discussion regarding the adequacy of available effect compartment models to characterise propofol's effect-time profile 3, 4. In this scenario, two studies by Thomson et al., published in this issue of Anaesthesia, add new relevant information to this topic 5, 6. The principles of pharmacokinetic/pharmacodynamic modelling have been explained in detail by Rigby-Jones and Sneyd in this journal 7. The aim of this editorial is to help clinicians to understand some important differences between currently available propofol effect-site models, focusing on the relevance of the ke0. Since the ke0 is critically dependent on the pharmacokinetic model, I will use the same model (the Marsh model) with two different ke0s in the simulated scenarios (manual bolus dose and TCI). I will first use a simulated manual bolus dose of propofol (2 mg.kg−1) to analyse the time profile of propofol effect and the predictions of the two currently available Marsh effect-site models (Fig. 1). In this scenario, plasma propofol concentrations and propofol effect-site concentrations are predicted by the Marsh pharmacokinetic model 8 using the slow and the fast ke0s. The predicted effect will range from 10 (awake) to 0 (maximum propofol hypnotic effect). Figure 1 shows that after the bolus dose, predicted plasma concentration of propofol and the course of the predicted effect do not follow the same pattern. While the Marsh pharmacokinetic model predicts an initial peak plasma concentration followed by a monotonic decay, the hynotic effect reaches its maximum (lowest values) shortly after the bolus dose and shows a faster profile with the fastest ke0 of 1.21 min−1. The delay between the peak plasma concentration and the peak effect is called hysteresis and can be observed as a hysteresis loop in a concentration-vs-effect plot (not shown). The reason for this delay between concentration and effect is that plasma is not the site of action of propofol and additional time is required for the drug to transfer to the brain (effect site). It is clear, therefore, that, during non-steady state conditions, plasma concentrations do not adequately characterise the time profile of propofol's effect. Figure 1 also shows that there are important pharmacokinetic model misspecifications during the initial distribution period, where the model erroneously assumes an instantaneous mixing of propofol within the central compartment (peak concentration at time zero). Early drug distribution after a bolus dose is not well characterised by traditional compartment models and important discrepancies exist between current propofol pharmacokinetic models. While the Marsh model has a large initial volume of distribution (V1) of 0.228 × weight (kg) litres, the Schnider model has a small fixed V1 of 4.27 litres. This is important to understand since erroneous plasma concentration predictions during this initial period will reduce the capacity of all currently available effect-compartment models adequately to characterise propofol's effect-time profile during the first 1–2 minutes after a bolus dose 9. In steady-state conditions, the plasma concentrations of a drug can be directly related to the drug response using a pharmacodynamic model. In the absence of equilibrium, when the drug response is not apparently related to plasma concentration, a link model (effect-compartment model) can be used to remove the hysteresis. Since drug concentration is not measured in the effect-site organ, effect compartment models are constructed adding a virtual compartment that does not affect drug distribution. This virtual effect compartment is structurally linked to the central compartment by a first-order rate constant (ke0). The ke0 is calculated based on an analysis of plasma concentrations and the corresponding time profile of the measured effect. With this parameter the pharmacokinetic model can be used to predict the dose-concentration relationship and the course of the effect. The ke0 can be expressed as a half-time ke0 (ln(2)/ke0), which is directly correlated with the time of equilibration between the central compartment and the effect site. If plasma concentration is maintained stable, as in the case of plasma TCI, the time required for the effect-site concentration to reach 50%, 75% or 87.5% of plasma concentration can be estimated by 1, 2 or 3 × half-time ke0, respectively . Figure 1 shows that effect-site concentration predicted by both Marsh effect-site models (slow and fast ke0s) allows a much better characterisation of propofol's effect-time profile than plasma concentration. However, important differences between effect-site predictions are observed. While the small ke0 predicts a slower effect-time profile, with a time to peak effect-site concentration (Tpeak) of 3.9 min, the ke0 of 1.21 predicts a more rapid onset and offset of propofol response with a predicted Tpeak of 1.6 min. It should be noted that Tpeak depends not only on the ke0 but also on the pharmacokinetic profile of the drug. As an example, the Schnider pharmacokinetic model requires a much slower ke0 of around 0.4 min−1 to predict a Tpeak of 1.6 10, 11. The slower ke0 compensates for the faster decay in plasma concentrations predicted by the Schnider model, which has a much smaller V1 than that present in the Marsh model. In Fig. 1, it is also possible to see that the magnitude of the effect-site concentration reached and its corresponding predicted effect are markedly different with these ke0s, reaching higher peak effect-site concentrations and a more pronounced predicted effect with the fast ke0. The explanation for this is that equilibrium between the effect-site and central compartment occurs more rapidly with a fast ke0 when less propofol has been distributed or eliminated from the central compartment. If propofol is administered using plasma TCI, the amount of drug given to reach and maintain a constant plasma concentration will depend exclusively on the pharmacokinetic parameters of the drug and the desired target. Since we know the plasma is not the site of effect of propofol, in this modality it is usual to set a higher initial target (plasma overshoot) to reach the desired effect more rapidly. In the case of targeting the effect site, peak plasma concentration will always reach higher values than the target concentration and the magnitude of plasma overshoot will depend on the ke0 value. It should be noted that the Diprifusor only allows propofol administration by plasma target mode and therefore the slow ke0 incorporated in this system is only used to predict effect-site concentrations. Figure 2 shows propofol concentration and effect-time profiles when the Marsh model with fast and slow ke0s is used to administer the drug using effect-site TCI (target =3 μg.ml−1). It can be seen that the slow ke0 determines a greater bolus dose (1.9 mg.kg−1) to achieve the target effect-site concentration as fast as possible. Since the model assumes a slow equilibration rate between the effect-site and the plasma, a large plasma overshoot is calculated in the bolus dose given, to obtain the desired effect-site concentration rapidly. In contrast, a faster ke0 of 1.21 min−1 will result in a smaller bolus dose (1.0 mg.kg−1) that results in less plasma overdose for the same effect-site target. Since both models use the same pharmacokinetic parameters, the final predicted effect will be of the same magnitude but will be reached faster with the fast ke0. The question now is: which of these models better predict propofol's effects? In the current issue of Anaesthesia, Thomson and colleagues derived a new ke0 for the Marsh propofol model using an alternative clinical measure of propofol effect to avoid the use of surrogate EEG indices 5. Their method was based on a validated clinical sign of sedation called visual reaction time 12, which is classified as stable, deepening, or lightening. Using effect-site propofol TCI with the Marsh model and different ke0 values, the authors assumed that the best ke0 should be the one with the greater probability of obtaining stable reaction times when the target was kept stable. In their results, Thomson et al. show that a ke0 of 0.6 min−1 was best for the Marsh model. Thomson et al.'s use of a previously validated clinical marker to derive the ke0 is a clear strength of this study, which also used a very nice and novel modelling approach. In the follow-up study 6, the authors tested the adequacy of this new ke0 in terms of speed of induction and side-effects when compared with other currently available models. Unfortunately, since they used speed of induction and side-effects as the measured outcomes, both of which are critically dependent on the target selected, it is my opinion that they cannot discriminate between models but only test the adequacy of the predefined selected target. To understand the possible implications of Thomson et al.'s findings better, let us now assume that the ke0 of 0.26 min−1 and 1.21 min−1 incorporated in the Marsh model are both wrong, and that the real propofol effect-time profile is better described using this new proposed ke0 of 0.6 min−1. In this hypothetical scenario, the ‘real effect’ is represented in Fig. 2 with a dashed green line. In the case of using propofol TCI with the Marsh 0.26 model, the bolus given would be too large and, consequently, the real effect would be more pronounced and faster than that predicted by the Marsh 0.26 model. In contrast, if using the Marsh 1.21 model, the initial bolus dose would be too small and would take more time to reach the desired effect than that predicted by the Marsh 1.21 model. In both cases, differences between the models should be expected to occur only during the first few minutes after setting the target. It is not the purpose of this editorial to decide on which is the best model to use, but to provide tools to assist the interpretation of the models’ predictions. It is possible that in the future, new integrated pharmacokinetic/pharmacodynamic models derived from larger populations might allow a better characterisation of the propofol dose-effect relationship and its variability. In the meantime, the most important message for clinicians is the need to understand the limitations of currently available models and use them with good clinical judgment and careful titration to clinical effect. No external funding and no competing interests declared.