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The development of pharmacokinetic and pharmacodynamic (PK/PD) models allows for a better understanding of the anesthetic drugs.14 They provide clinicians with the ability to titrate drug administration by means of complex mathematical approaches and new concepts and to understand drug behaviour better. Some of the most used anesthetics such as propofol have commercially available Target Control Systems based on PK/PD models incorporated into infusion pumps. However, this is not the case for most of the anesthetic drugs. Nevertheless, it is important to understand the PK/PD of the drug (table 2) so that the clinician can adequately titrate it to achieve the adequate endpoint. Several PK/PD models available for the different anesthetic drugs are explored in this section.

 

Propofol

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Propofol is the most widely used intravenous anesthetic drug for induction and maintenance of anesthesia, there are several PK/PD models and integrated in commercially available Target Controlled Infusion systems. These TCI infusion pumps titrate the propofol infusion rate to achieve and maintain a plasma or effect-site concentration as set by the clinician. The usefulness of the PK/PD models for propofol is widely proven (incorporated in TCI pumps) as a facilitator of clinical practice and maintenance of intravenous anesthesia 15. 

Absalom and colleagues, clearly show the difference between the Marsh and the Schnider propofol PK/PD models (the two models incorporated in all commercially available TCI devices) 15. The Schnider PK/PD model should be used for effect-site targeting and its parameters are adjusted to age, height and lean body mass (LBM). The use of the LBM equation in the Schnider model is of great concern when considering obese patients.  The Marsh model is more suitable for plasma targeting. This work also addresses the importance of effect-site targeting implementation by the different algorithms, with different . They concluded that there is little conclusive evidence to demonstrate the superiority of any particular model or method of effect-site targeting implementation. In general, it is best for clinician to use the model and methods with which they are most familiar, and to only use a different model or method of effect-site implementation if they understand the differences of the new model or method 15. 

To better achieve and maintain a time course of drug effect with propofol, it is desirable to use effect-site targeting in the TCI devices. This was shown when using the Bispetral Index (BIS) of the EEG as a measure of effect in clinical practice 16.

Masui and colleagues, compared the performance of compartmental and physiologically based recirculatory pharmacokinetic models for propofol, using different infusion schemes including TCI 17. The general conclusion was that for TCI and PK/PD modelling (using advisor displays), the Schnider model was the recommended, although not perfect. 

 

Sevoflurane and Isoflurane

The pharmacokinetic models for inhalational anesthetic drugs are well described in the literature and have been widely explored. In 1991, Yasuda and colleagues compared the pharmacokinetics of sevoflurane and isoflurane, publishing one of the still used PK models for these two drugs 18.  In this work, they concluded that the volume of the central compartment of sevoflurane (2.10±0.62 L) was smaller than that of isoflurane (2.31± 0.71 L). The elimination rate constant from the central compartment for sevoflurane was greater than that for isoflurane; the pulmonary elimination clearances and the rate constants from the peripheral compartments to the central compartment did not differ between the two drugs. Sevoflurane mammillary time constants were smaller than those for isoflurane for the lungs, but did not differ from isoflurane for the other compartments. The data for sevoflurane gave a slightly greater estimate of blood flow to the fat group than the data for isoflurane. The recovery of sevoflurane and isoflurane did not differ from each other either as absolute or normalized values18.

The pharmacodynamics of isoflurane were studied by Gentilini and colleagues, already with an approach of incorporating a closed-loop controller 19. This PK model was developed using the Bispectral index (BIS) of the EEG as measure of effect on a set of 20 volunteers, and based on the Yasuda PK model. The overall PK/PD model showed an EC50 of 0.6 % with a =0.217min-1 , to be noted that alfentanil was used during the study 19.  The reported   is higher than the one published by previous studies, were isoflurane was used alone but with the same EC50 20.

The PK/PD models for sevoflurane and isoflurane are well determined by Olofsen and colleagues, using both BIS and the Spectral Edge Frequency (SEF) of the EEG 20. In this study, only the EC50 proved to be different between the two drugs for BIS and for SEF. When using BIS the EC50 of isoflurane was 0.6% while for sevoflurane it was 1.14%, while the value were 0.71% and 1.37% when using SEF 20.

Kreuer and colleagues also report that the   values for sevoflurane and isoflurane are the same 21. These two inhalational anesthetic drugs have very similar pharmacodynamic profiles.

Regarding sevoflurane, McKay and colleagues developed a PK/PD model using the response and state entropy as measure of effect 22. They reported  and EC50= 1.7% using state entropy, which are not far from the values obtained by Olofsen and colleagues using BIS and SEF 20, 22.

There has been also work studying the pharmacodynamic interaction between anesthetic drugs, in this case sevoflurane and propofol. How can a model help to titrate the simultaneous use of two hypnotics? Diz and colleagues, developed a response surface model using BIS as a measure of effect, to study the transition between a propofol induction and a sevoflurane maintenance 23. The knowledge of the additive effect that these two drugs have on BIS, maybe clinically helpful to provide a smooth transition between the two anesthesia techniques 23.

 

Ketamine

Ketamine is an unique pharmacological agent and has a turbulent history 24. But already in 1987, the PD effects of Ketamine on the median spectral frequency of the EEG in human were studied 25. This work, studied the pharmacodynamics of a racemic mixture of ketamine R, S(±)-ketamine and of each enantiomer, S(+)-ketamine and R(-)-ketamine, in five volunteers. The maximal decrease (mean ± SD) of the median frequency (Emax) for R(-)-ketamine was 4.4±0.5 Hz and was significantly different from R,S(±)-ketamine (7.6±1.7Hz) and S(+)- ketamine (8.3±1.9 Hz). The ketamine serum concentration that caused one-half of the maximal median frequency decrease (IC50) was 1.8±0.5 µg/mL for R(-)-ketamine; 2.0±0.5 µg/mL for R,S(±)-ketamine; and 0.8±0.4g/mL for S(+)-ketamine 25.

In 2007, there is another PK/PD model for ketamine but in sheep that aims at comparing the PK/PD characteristics of different anesthetics 26. The most clinically useful conclusion is that ketamine did not show a statistically significantly different time to peak effect or   than propofol (measured by the effect on the EEG).

Dahan and colleagues in 2011 publish the most recent work, on a PK/PD model for ketamine induced pain relief in humans 27. They developed a population PK/PD model to analyze the effect of S(+)-ketamine on pain scores, with a treatment that could last several days. It is a very interesting work, but the scope is not unconsciousness.

 

Dexmedetomidine

Dexmedetomidine is a selective and potent ?2-adrenoceptor agonist that is used for its anxiolytic, sedative, and analgesic properties, in beginning of 2017 a very extensive review of the existing PK models was published by Weerink and colleagues 28. In this work, they present a complete table of existing PK models for Dexmedetomidine, clearly showing its differences in population type and size, drug profile used, model structure and covariates 28.  This very complete research is followed by an extensive simulation study using the adult population models, which show the relationship between doses and plasma concentrations. They also show pharmacodynamic studies done with dexmedetomidine considering its sedative, analgesic, respiratory and cardiovascular effects. The work finishes with an important consideration “Nevertheless, at the moment, quantitative PK/PD models, which could help to delineate the variability in the observed effects, are not available.”

However, later in 2017 two papers are published considering PK/PD models for dexmedotomidine in volunteers. Colin and colleagues, published two papers, one presenting a PK/PD model for the hemodynamic effect profile and the other PK/PD model for arousal and the sedation of dexmedotomidine 29, 30.  The data of 18 volunteers was used to develop a PK/PD model using bispectral index (BIS) monitoring of processed EEG for sedation29. The same step-up technique was used to characterize the haemodynamic properties of dexmedetomidine by developing a PK/PD model for the changes in mean arterial blood pressure and heart rate30. These two new models still have to be tested in a clinical environment, but are the first quantitative PK/PD models that may allow for a better target controlled titration of dexmedotomidine.

 

Etomidate

Etomidate, a carboxylated imidazole ester, is a potent intravenous anesthetic used for anesthesia induction. In 2011, Kaneda and colleagues published the etomidate PK/PD model using the bispectral index (BIS) of the EEG  and the Observer’s Assessment of Alertness and Sedation (OAA/S) scale as a measure of effect 31. This work used twenty volunteers, all volunteers received an infusion of 5 mg/min of etomidate 0.2% until loss of eyelash reflexes, resulting in a mean etomidate dose of 24mg.  The plasma concentration data were best described by a 2-compartment PK model and no interindividual variability was incorporated 31. This PD model has for BIS and Emax of 67, EC50 of 0.526 µg/ml and  of 1.55 minutes.  This is a complete PK/PD model for etomidate, which needs to be tested in a clinical environment and may allow for a better target controlled titration.

In 2013, although not using PK/PD models, a study compares the pharmacodymanic effect of etomidate with propofol for induction of anesthesia guided by BIS. This study, in a clinical perspective shows that propofol was faster than etomidate for loss palpebral reflex, lowering BIS to 60 and allowed for shorter time to intubation 32.  

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