EDITORIAL
Does it matter how you get from D (drug dose) to E (clinical effect)? Not that long ago, when one of us was a boy, his parents owned a car that developed intermittent mechanical problems. One day, while returning from a short trip, the driver noted that the steering pulled slightly to the right. While the occupants speculated as to the cause— the steering, the brakes, or something else—the driver found that the car could be controlled reasonably by carefully compensating for the tendency to pull to the right. Right turns could be taken rather easily but left turns required more effort. Luckily, they were close to home and arrived safely. The problem turned out to be with the right front brake disk. This knowledge, while obviously useful for repairing the car, was not essential to navigate the car home safely. An analogous situation can arise when one tries to produce a combined pharmacokinetic/pharmacodynamic (PK/PD) model. The aim of such a model is to predict the time course of clinical drug effect arising from a drug administration regimen. Ideally, the set of PK parameters (predicting the relationship over time between administered dose profile and plasma concentration) and the linked set PD parameters (predicting the relationship over time between plasma concentrations and clinical effect) should be estimated from a single study in which plasma concentrations and clinical effects are measured simultaneously in each subject during and after drug administration. Such an approach is time-consuming, expensive, and complex. What is commonly done in studies is to use an existing PK model to estimate plasma drug concentrations associated with the drug doses administered, and to accept as valid the estimates, and then develop a PD model to predict the relationship between these estimated plasma concentrations and clinical effect. It turns out that although the PK model might be making (moderately or even significantly) inaccurate plasma concentration estimates, it is possible that the new PD component can compensate for the imperfect PK component to such a degree that the overall model provides a realistic estimate of the relationship between drug dose and clinical effect (1). Of course, no PK model, and for that matter no PK/ PD model, is perfect. Clinical practice and available literature shows us that it is possible to base either manual or computerized target-controlled anesthetic drug administration on inaccurate PK and PD models, and still achieve an acceptable state of sedation or anesthesia. However, this can cause an additional mental load 544
for the anesthesiologist. He or she must divert some of their attention to compensating for the deficiencies of the model predictions. For example, if a PK–PD model suggests that drug effect is expected to be inadequate while the patient shows clinical signs of deeper anesthesia then this may be attributed to a general “sensitive patient” phenomena. Target concentrations or drug doses are likely to be reduced and the anesthesiologist may make a mental note to reduce future drug doses as well. It is not important whether the inaccuracy lies with the PK or PD models or both. If a PK model is biased and the PD model has a sufficient compensatory bias, then the overall PK–PD predictions can still be of good quality. The anesthesiologist may not even be aware that the individual components of the PK/PD model are deficient. In this issue, Fuentes and colleagues report an investigation in which they determined appropriate age-related effect-site target concentrations when using the Kataria PK model expanded with a ke0 parameter (the PD time constant parameter used to estimate rate of plasmaeffect-site equilibration) in a group of their patients (2). They found a strong negative correlation between the Ce50 (effective effect-site concentration in 50% of patients, a PD sensitivity parameter) and age. The question is whether this reflected a true increase in pharmacodynamic sensitivity to a given effect-site propofol concentration with increasing age among their patients, or a misspecification in the PK part of their PK/PD model. If the PK component overestimates the plasma concentration, then the PK/PD model will also overestimate the effect-site concentration, particularly at steady state conditions, when the plasma and effect-site concentrations are the same. Although the Kataria PK model is commonly used in studies, and is widely known and used clinically, it is by no means perfect, as it was developed long before the deep insights of allometric scaling started to be applied to PK models (3). In the Kataria model, all parameters scale linearly with weight, while allometric theory suggests that clearances scale to the 3/4 power of body size. This difference suggests that when the Kataria PK model is used to control propofol administration in older, larger children, it will likely have a tendency to overestimate clearance. This may thus result in administration of more propofol than is necessary for a given target plasma concentration, and achieve higher actual
© 2015 John Wiley & Sons Ltd Pediatric Anesthesia 25 (2015) 544–545
Editorial
plasma concentrations than those estimated. With the approach used by Fuentes et al., where no actual measurements of plasma propofol concentrations are available, we cannot be certain whether the lower Ce50 values in older children are the result of PK or PD differences or both. Nonetheless, selection of a lower effect-site target concentration in older larger children will result in lower administered doses. In this case, it is possible that a PD misspecification (older children may not have a lower Ce50) will be compensated for by a PK misspecification (actual plasma concentrations may be higher than estimated concentrations in older children). An aspect of the approach used by Fuentes is an inherent (potential) source of confusion for scientific research. The terminology used to describe the parameters of their PD model is the same as that used to describe the underlying target of anesthesia—the anatomical and physiological characteristics of the brain— even though they potentially describe two very different things. In circumstances where the PK model is inaccurate, the parameters ke0, Ce50, and those derived from predicted drug effects (i.e., effect compartment concentrations) mentioned by Fuentes et al. will have no strict relationship with the underlying biological systems. Rather they are also dependant on the characteristics (and problems!) of the Kataria PK model used for predictions of plasma concentration over time. The fact that Fuentes et al. found that the estimated target propofol Ce required to induce anesthesia decreases with age does not necessarily mean that older individuals require lower propofol concentrations to induce anesthesia. This is confusing, even for experts in the PK–PD field. One can only imagine how opaque such language must be for novices in the field.
Does this potential problem really matter? If an anesthesiologist administers propofol by effect-site TCI and the only PK–PD model available is the Kataria PK model expanded with the ke0 described by Fuentes et al., then the advice of Fuentes et al. should be heeded: decrease the target Ce in older children, and this will result in a lower D (drug) which will generate a more appropriate E (clinical effect). In the case of the car anecdote above, the efforts of the driver to compensate for the tendency of the car to pull to the right should not have been performed in any other cars, or once the brakes had been repaired. Likewise anesthesiologists should be cautioned that the advice of Fuentes et al. is specific to the PK/PD model used in their study. This advice does not apply, and may even be wrong, when other PK or PD models are used. If another PK model is used, and it specifies the effect of age on clearance differently, then choosing lower target (effect or plasma) concentrations may or may not be appropriate. What works in one specific situation may steer you in the wrong direction under different conditions!
Disclosures The authors report no conflict of interest. Douglas J. Eleveld & Anthony R. Absalom Department of Anesthesiology, University Medical Center Groningen, University of Groningen, Groningen, The Netherlands Email: [email protected] doi:10.1111/pan.12665
References 1 Coppens MJ, Eleveld DJ, Proost JH et al. An evaluation of using population pharmacokinetic models to estimate pharmacodynamic parameters for propofol and bispectral index in children. Anesthesiology 2011; 115: 83–93.
© 2015 John Wiley & Sons Ltd Pediatric Anesthesia 25 (2015) 544–545
2 Fuentes R, Cortínez I, Ibacache M et al. Effective propofol concentration to induce general anesthesia in children aged 3–11 years with the Kataria effect-site model. Pediatr Anesth 2015; 25: 544–545.
3 Anderson BJ, Holford NH. Mechanistic basis of using body size and maturation to predict clearance in humans. Drug Metab Pharmacokinet 2009; 24: 25–36.
545
Does it matter how you get from D (drug dose) to E (clinical effect)? Not that long ago, when one of us was a boy, his parents owned a car that developed intermittent mechanical problems. One day, while returning from a short trip, the driver noted that the steering pulled slightly to the right. While the occupants speculated as to the cause— the steering, the brakes, or something else—the driver found that the car could be controlled reasonably by carefully compensating for the tendency to pull to the right. Right turns could be taken rather easily but left turns required more effort. Luckily, they were close to home and arrived safely. The problem turned out to be with the right front brake disk. This knowledge, while obviously useful for repairing the car, was not essential to navigate the car home safely. An analogous situation can arise when one tries to produce a combined pharmacokinetic/pharmacodynamic (PK/PD) model. The aim of such a model is to predict the time course of clinical drug effect arising from a drug administration regimen. Ideally, the set of PK parameters (predicting the relationship over time between administered dose profile and plasma concentration) and the linked set PD parameters (predicting the relationship over time between plasma concentrations and clinical effect) should be estimated from a single study in which plasma concentrations and clinical effects are measured simultaneously in each subject during and after drug administration. Such an approach is time-consuming, expensive, and complex. What is commonly done in studies is to use an existing PK model to estimate plasma drug concentrations associated with the drug doses administered, and to accept as valid the estimates, and then develop a PD model to predict the relationship between these estimated plasma concentrations and clinical effect. It turns out that although the PK model might be making (moderately or even significantly) inaccurate plasma concentration estimates, it is possible that the new PD component can compensate for the imperfect PK component to such a degree that the overall model provides a realistic estimate of the relationship between drug dose and clinical effect (1). Of course, no PK model, and for that matter no PK/ PD model, is perfect. Clinical practice and available literature shows us that it is possible to base either manual or computerized target-controlled anesthetic drug administration on inaccurate PK and PD models, and still achieve an acceptable state of sedation or anesthesia. However, this can cause an additional mental load 544
for the anesthesiologist. He or she must divert some of their attention to compensating for the deficiencies of the model predictions. For example, if a PK–PD model suggests that drug effect is expected to be inadequate while the patient shows clinical signs of deeper anesthesia then this may be attributed to a general “sensitive patient” phenomena. Target concentrations or drug doses are likely to be reduced and the anesthesiologist may make a mental note to reduce future drug doses as well. It is not important whether the inaccuracy lies with the PK or PD models or both. If a PK model is biased and the PD model has a sufficient compensatory bias, then the overall PK–PD predictions can still be of good quality. The anesthesiologist may not even be aware that the individual components of the PK/PD model are deficient. In this issue, Fuentes and colleagues report an investigation in which they determined appropriate age-related effect-site target concentrations when using the Kataria PK model expanded with a ke0 parameter (the PD time constant parameter used to estimate rate of plasmaeffect-site equilibration) in a group of their patients (2). They found a strong negative correlation between the Ce50 (effective effect-site concentration in 50% of patients, a PD sensitivity parameter) and age. The question is whether this reflected a true increase in pharmacodynamic sensitivity to a given effect-site propofol concentration with increasing age among their patients, or a misspecification in the PK part of their PK/PD model. If the PK component overestimates the plasma concentration, then the PK/PD model will also overestimate the effect-site concentration, particularly at steady state conditions, when the plasma and effect-site concentrations are the same. Although the Kataria PK model is commonly used in studies, and is widely known and used clinically, it is by no means perfect, as it was developed long before the deep insights of allometric scaling started to be applied to PK models (3). In the Kataria model, all parameters scale linearly with weight, while allometric theory suggests that clearances scale to the 3/4 power of body size. This difference suggests that when the Kataria PK model is used to control propofol administration in older, larger children, it will likely have a tendency to overestimate clearance. This may thus result in administration of more propofol than is necessary for a given target plasma concentration, and achieve higher actual
© 2015 John Wiley & Sons Ltd Pediatric Anesthesia 25 (2015) 544–545
Editorial
plasma concentrations than those estimated. With the approach used by Fuentes et al., where no actual measurements of plasma propofol concentrations are available, we cannot be certain whether the lower Ce50 values in older children are the result of PK or PD differences or both. Nonetheless, selection of a lower effect-site target concentration in older larger children will result in lower administered doses. In this case, it is possible that a PD misspecification (older children may not have a lower Ce50) will be compensated for by a PK misspecification (actual plasma concentrations may be higher than estimated concentrations in older children). An aspect of the approach used by Fuentes is an inherent (potential) source of confusion for scientific research. The terminology used to describe the parameters of their PD model is the same as that used to describe the underlying target of anesthesia—the anatomical and physiological characteristics of the brain— even though they potentially describe two very different things. In circumstances where the PK model is inaccurate, the parameters ke0, Ce50, and those derived from predicted drug effects (i.e., effect compartment concentrations) mentioned by Fuentes et al. will have no strict relationship with the underlying biological systems. Rather they are also dependant on the characteristics (and problems!) of the Kataria PK model used for predictions of plasma concentration over time. The fact that Fuentes et al. found that the estimated target propofol Ce required to induce anesthesia decreases with age does not necessarily mean that older individuals require lower propofol concentrations to induce anesthesia. This is confusing, even for experts in the PK–PD field. One can only imagine how opaque such language must be for novices in the field.
Does this potential problem really matter? If an anesthesiologist administers propofol by effect-site TCI and the only PK–PD model available is the Kataria PK model expanded with the ke0 described by Fuentes et al., then the advice of Fuentes et al. should be heeded: decrease the target Ce in older children, and this will result in a lower D (drug) which will generate a more appropriate E (clinical effect). In the case of the car anecdote above, the efforts of the driver to compensate for the tendency of the car to pull to the right should not have been performed in any other cars, or once the brakes had been repaired. Likewise anesthesiologists should be cautioned that the advice of Fuentes et al. is specific to the PK/PD model used in their study. This advice does not apply, and may even be wrong, when other PK or PD models are used. If another PK model is used, and it specifies the effect of age on clearance differently, then choosing lower target (effect or plasma) concentrations may or may not be appropriate. What works in one specific situation may steer you in the wrong direction under different conditions!
Disclosures The authors report no conflict of interest. Douglas J. Eleveld & Anthony R. Absalom Department of Anesthesiology, University Medical Center Groningen, University of Groningen, Groningen, The Netherlands Email: [email protected] doi:10.1111/pan.12665
References 1 Coppens MJ, Eleveld DJ, Proost JH et al. An evaluation of using population pharmacokinetic models to estimate pharmacodynamic parameters for propofol and bispectral index in children. Anesthesiology 2011; 115: 83–93.
© 2015 John Wiley & Sons Ltd Pediatric Anesthesia 25 (2015) 544–545
2 Fuentes R, Cortínez I, Ibacache M et al. Effective propofol concentration to induce general anesthesia in children aged 3–11 years with the Kataria effect-site model. Pediatr Anesth 2015; 25: 544–545.
3 Anderson BJ, Holford NH. Mechanistic basis of using body size and maturation to predict clearance in humans. Drug Metab Pharmacokinet 2009; 24: 25–36.
545
