Pharmacokinetic-Pharmacodynamic Model for the Reversal of Neuromuscular Blockade by Sugammadex

In this study, a parsimonious (i.e. , the simplest model that could adequately describe the data) PK-PD interaction model was developed to describe data from different clinical trials exploring the pharmacokinetic and pharmacodynamic profile of rocuronium and sugammadex alone and in combination. Part of the data were used to estimate the model parameters; other data were used for external validation by fixing all model parameters and simulating the validation dataset. Resemblance between simulated and observed data were used to confirm the accuracy and validity of the model.

Table 1summarizes the studies used for model development (calibration) and validation. Calibration study 1 and validation studies 1, 2, and 3 (table 1) have been published previously and were conducted after institutional review board approval as described by Gijsenbergh et al. ,4Sorgenfrei et al. ,7Sparr et al. ,6and Suy et al.  9, respectively. The protocol of calibration study 2 (table 1) was approved by the institutional review boards of the Surugadai Hospital (Tokyo, Japan), Keio University (Tokyo, Japan), Tokyo Women’s Medical University (Tokyo, Japan), and Kyorin University (Tokyo, Japan). The institutional review board of the Columbia University (New York, New York) approved the protocol for calibration study 3 (table 1). All patients gave written informal consent according to the Declaration of Helsinki.

The analysis was performed by means of nonlinear mixed-effects modeling using NONMEM version V, release 1.1 (University of California at San Francisco, San Francisco, CA).14The pharmacokinetic and pharmacodynamic data were analyzed sequentially. The first order conditional method with interaction was used for estimation.

Model performance was validated using a visual predictive check, which evaluated whether the identified model was able to predict the observed variability in the pharmacokinetic and/or pharmacodynamic observations for 50% of the population.15As the number of observations3–8was small it was decided to use a smaller prediction interval, as compared with the generally applied interval of 90%.15The outcome of the trial was simulated by drawing random samples from the distributions for the interindividual and residual variability for 1,000 hypothetical patients. Resemblance between simulated (median, 25th and 75th percentiles) and original distributions indicated the accuracy of the model (i.e. , 50% of the observed data should fall within the predicted range for 50% of the variability).

The PK-PD interaction model was composed of several submodels, including the PK-PD model for rocuronium and the pharmacokinetic-interaction model. The former described the relationship between the plasma concentrations of rocuronium and NMB, and the latter described the plasma concentration of sugammadex and rocuronium after concomitant administration. The full PK-PD interaction model is shown in figure 1.

The rocuronium and sugammadex concentration data were described by a three-compartment model with first-order elimination from the central compartment, parameterized in terms of volume of distribution of the central (V1 ), first (V2 ), and second peripheral compartment (V3 ), intercompartmental clearance from the central to the first (Q2 ) and from the central to the second (Q3 ) peripheral compartment, and clearance from the central compartment (Cl ). Hysteresis between arterial and venous plasma sugammadex concentration was modeled by adding a compartment to the model for the venous concentration, with a first-order rate constant (k^vo ) linking the venous concentration to the arterial concentration.

It was assumed that equilibrium of the interaction between rocuronium and sugammadex was not achieved instantaneously. Therefore, the kinetics of the complex formation were described by equation 1, in which [Roc^free ] is the free concentration of rocuronium, [Sug^free ] is the free concentration of sugammadex, [Cplx ] is the concentration of the complex, K¹  is the association rate constant, and K²  is the dissociation rate constant.

The K^d  is defined as the ratio between K²  and K¹  (equation 2).

As only total rocuronium and sugammadex concentration data were available, the pharmacokinetics of the complex could not be determined independently. It was assumed that the pharmacokinetic profile of the complex was identical to that of free sugammadex. The model was simplified further by setting the volume of all compartments equal to V1  of free sugammadex. Equation 3describes the kinetics of the complex. CL^cplx  is the clearance of the complex from the plasma, V1^cmplx  is the apparent volume of distribution of the central compartment, and k^1x  and k^x1  are the rate constants for distribution between the central and the two peripheral compartments. C^cplx,x  is the complex concentration in the compartments, and C^roc,1  and C^sug,1  are the free rocuronium and sugammadex concentration in the central compartment, respectively.

The pharmacokinetics of rocuronium and sugammadex were described with equation 4, in which CL^drug  is the clearance of rocuronium or sugammadex from plasma, k^1x,drug  and k^x1,drug  are the rate constants for distribution between the central and the two peripheral compartments for rocuronium and sugammadex, and A^drug,x  is the amount of rocuronium or sugammadex in one of the compartments.

The pharmacokinetic parameters for sugammadex were optimized to data from part I and II of calibration study 1 (table 1), whereas the pharmacokinetic parameters of rocuronium were fixed to the individual specific (post hoc ) parameters of the pharmacokinetic model for rocuronium alone. The parameter K²  was estimated, whereas K¹  was calculated using a K^d  value of 0.1 μm, which was derived in vitro  by isothermal microcalorimetry.13 

In vitro  binding studies showed that sugammadex does not bind to human plasma proteins (data on file, N.V. Organon; Oss, The Netherlands). In the absence of sugammadex, approximately 37% of rocuronium is bound to plasma proteins (data on file, N.V. Organon;  Oss, The Netherlands). The extent of protein binding declines when sugammadex is added until all rocuronium is captured by sugammadex and, consequently, no rocuronium is bound to plasma proteins. It was concluded that the binding affinity of rocuronium for sugammadex is much greater than that for plasma proteins. As a result, protein binding was ignored in the interaction model.

The relationship between the rocuronium plasma concentration and NMB was described by a hypothetical effect-compartment to link the rocuronium concentration in plasma or one of the peripheral compartments (C^roc,x ) to the concentration at the effect site (Ce^{ro  c}) using a first-order rate constant (ke0 )16–18(equation 5).

The concentration-effect relationship was described by equation 6with parameters for the baseline TOF ratio (E⁰ ), the maximum effect (E^max ), the Ce^roc  resulting in an effect of 50% of E^max  (EC⁵⁰ ), and a sigmoidicity parameter (γ ). Data from part II of calibration study 1 were used to estimate the pharmacodynamic parameters for rocuronium. The pharmacokinetic parameters were fixed to individual-specific estimates, which were obtained using the pharmacokinetic model for rocuronium alone.

We evaluated whether the observed change in NMB can be described by linking the concentration in the effect compartment to the free rocuronium concentration. In addition, we evaluated the hypothesis that both rocuronium and sugammadex distribute to the neuromuscular junction where both compounds instantly form a complex. As a result, rocuronium-induced NMB decreases because of a reduction in the free and pharmacologically active fraction. As the neuromuscular junction was represented by the effect compartment in the PK-PD model, the free rocuronium concentration (Ce^free ) in the effect compartment was calculated from the total concentration of rocuronium and sugammadex in the effect compartment using equation 7, in which Ce^roc,tot  and Ce^sug,tot  are the total concentrations of rocuronium and sugammadex, respectively. As there was no information on the rate of distribution of sugammadex to the effect compartment, the same ke0  value was assumed for rocuronium and sugammadex.

For external validation of the PK-PD interaction model, it was determined whether the effect of sugammadex administration on vecuronium pharmacokinetics and pharmacodynamics could be predicted also with the same model structure, but with vecuronium-specific pharmacokinetic and pharmacodynamic parameter values. By assuming the K¹  parameter representing the probability that two molecules meet to form a complex, this parameter is considered compound-independent. Hence, by assuming the same K¹  for vecuronium and rocuronium, the K²  was derived from equation 2using a vecuronium-specific K^d  of 0.175 μm (data on file, N.V. Organon; Oss, The Netherlands). The remaining vecuronium pharmacokinetic and pharmacodynamic parameters were identified by fitting the model to the data. The pharmacokinetic profile of vecuronium was described by a two-compartment model with first-order elimination.19 

The interindividual variability in most model parameters was modeled using equation 8, where θⁱ  is the individual specific parameter value for the subject, i, θ^mean  is the population mean, and ηⁱ  is the difference of the logarithm between the individual value of the subject i  and the population mean. ηⁱ  is normally distributed with a mean of zero and a variance ω  ².

The residual variability was described by the general equation 9, in which Y^ij  is the jth observation of individual i, PRED^ij  is the jth model prediction for individual i , and ϵ^prop,ij  and ϵ^add,ij  are the proportional and additive residual errors for the jth prediction of individual i . ϵ^prop,ij  and ϵ^add,ij  are normally distributed with mean 0 and a variance ς².

In the pharmacokinetic model for rocuronium, both ϵ^prop,ij  and ϵ^add,ij  were identified, whereas for the sugammadex pharmacokinetic model only ϵ^prop,ij  was identified. The residual error in the PK-PD models was described by ϵ^add,ij  only.

The pharmacokinetics of rocuronium administered alone to Japanese and Caucasian patients could be described by the three-compartment model (fig. 2). Cl, V1, Q2, V3,  and Q3  values for rocuronium differed between Japanese and Caucasian patients (table 2). This difference could not be explained by observed differences in body weight, height, and age between the Japanese and Caucasian subpopulation. In addition, at the lowest rocuronium dose, tested only in Japanese patients (0.3 mg/kg), a different value for V1  was identified (table 2).

The pharmacokinetics of sugammadex differed according to whether sugammadex was administered with anesthesia and rocuronium or without anesthesia, with higher Q3  and V3  values and lower V2  and Q2  values reported with sugammadex plus rocuronium, as compared with sugammadex alone (table 2).

With a K²  of 0.00216 min⁻¹(dissociation half-life = 5.3 h) and a K^d  value fixed to 0.1 μm, the pharmacokinetic interaction model adequately predicted the observed increase in total rocuronium concentration after sugammadex administration (fig. 2).

As E⁰  and E^max  could not be distinguished using the available NMB data, E^max  was set to the individual estimate of E⁰ . The fit of the observed rocuronium-induced NMB considerably improved by linking the concentration in the effect compartment to the first peripheral compartment (data not shown). Using this assumption, the population PK-PD model adequately described the time course of response after administration of 0.6 mg/kg rocuronium alone (table 2; fig. 3, dashed line). After fixing all individual specific pharmacokinetic and pharmacodynamic parameters for rocuronium, the PK-PD interaction model could not predict the observed rapid reversal of NMB (fig. 3, short-dashed line). However, assuming that sugammadex also distributes to the effect compartment, thereby lowering the free rocuronium concentration, resulted in an adequate prediction of the observed rapid reversal of NMB after sugammadex administration (fig. 3, solid line).

The observed recovery time (time from sugammadex administration to recovery of the TOF ratio to 90%) after sugammadex administration at 3, 5, or 15 min after administration of 0.6 mg/kg rocuronium closely resembled the predictions by the PK-PD interaction model (fig. 4). The predicted recovery time closely resembled the observed data for most scenarios, since the predicted median was within the 95% CI of the (bootstrapped) observed median (fig. 4, A and C). However, the observed reversal time after 1 and 2 mg/kg sugammadex administered 5 min after rocuronium was underpredicted (fig. 4B). When 1 mg/kg was administered 3 min after rocuronium, 0.1% of the 1,000 simulated patients showed a rebound in NMB, such as actually observed by Eleveld et al.  20, with a temporary increase in NMB after recovery to a TOF ratio of 90%. The maximum rebound was a decrease to a TOF ratio of 20%. However, none of the simulated patients showed rebound after 2 mg/kg. Also, the probability for rebound decreased to 0.04% when 1 mg/kg was administered 5 min after rocuronium.

The model could also adequately predict the observed recovery times from rocuronium and vecuronium-induced blockade after sugammadex administration at reappearance of T²(fig. 5). The time to reappearance of T²(i.e. , T²twitch height ≥ 1%) was simulated using a PK-PD model for the effect of rocuronium on the T²twitch height (fig. 5A). The parameter values were estimated using T²data from calibration study 1 (parameters not shown). Subsequently, the effect of sugammadex administration, at the simulated time of reappearance of T², on the TOF ratio was simulated for the same patients. Although the observed 95% CI did not include the predicted median after administration of 2 mg/kg, this observation seems to be inconsistent, since the model adequately predicted the observed recovery time for a 1 mg/kg lower and higher dose (fig. 5A).

Vecuronium pharmacokinetics without sugammadex was adequately described by a two-compartment model (fig. 6). The time course of response was described with the same model structure as applied for rocuronium, but with vecuronium-specific pharmacokinetic and pharmacodynamic model parameters. As with rocuronium, the concentration in the effect compartment was linked to the vecuronium concentration in the first peripheral compartment. After replacing the rocuronium pharmacokinetic and pharmacodynamic parameters for those of vecuronium (table 3) and using a K^d  value of 0.175 μm, while fixing the K¹  value to the value of the rocuronium model, the PK-PD interaction model described the pharmacokinetics (fig. 6) and pharmacodynamics (fig. 5B) of vecuronium after sugammadex administration at reappearance of T². However, the model appeared to underpredict the observed reversal time after administration of 0.5 mg/kg sugammadex, since all observations were greater than the predicted median.

To illustrate the application of the PK-PD model in clinical development, the possible effect of residual sugammadex in the circulation at the onset time of a subsequent (second or repeat) dose of rocuronium was simulated with the model. The onset time was defined as the time from administration of rocuronium until 90% NMB was reached (TOF = 10%). NMB was simulated after readministration of rocuronium (0.6 or 1.2 mg/kg) after earlier administration of 2 mg/kg sugammadex at reappearance of T²after a first rocuronium dose of 0.6 mg/kg. Figure 7shows the percentage of the population reaching more than 90% NMB within a specified time frame of 2 to 10 min.

The pharmacokinetic interaction model, which assumes that binding of rocuronium in the central compartment decreases the free rocuronium concentration, could predict the observed increase in total plasma rocuronium concentrations after sugammadex administration. In addition, the PK-PD interaction model assumes that sugammadex decreases the free rocuronium concentration in the effect compartment (i.e.,  the neuromuscular junction). Using these assumptions, the rapid reversal of rocuronium-induced NMB after sugammadex administration could be predicted. This is consistent with the proposed mechanism of action of sugammadex. Obviously, measuring the actual free rocuronium concentration would be the ultimate test, but as these data are currently unavailable, mechanism-based modeling is a valid alternative. This is further supported by showing that the same mechanism of action also applies to another steroidal neuromuscular blocking drug, vecuronium, since the PK-PD interaction model with vecuronium-specific parameter values could also predict the change in vecuronium pharmacokinetics and pharmacodynamics after sugammadex administration.

The model assumes three types of interaction (binding), with increasing complexity: no binding (in the peripheral compartments), binding with instantaneous equilibrium (in the biophase) and noninstantaneous equilibrium (in plasma). It would have been more consistent to assume the same type of interaction (e.g.,  interaction with noninstantaneous equilibrium) in all compartments. However, this would have resulted in a very complex model. It was preferred to select a parsimonious model by evaluating, for each compartment, whether including a more complex interaction resulted in a better prediction, assuming that noninstantaneous binding in plasma resulted in a better prediction, whereas the assumption of complex formation in the peripheral compartments did not (results not shown). The rapid reversal of NMB could not be predicted without the assumption of complex formation in the biophase (fig. 3). No direct information was available about the rate of distribution of sugammadex to the biophase. Therefore, we assumed this rate to be equal to that of rocuronium. Using this assumption in addition to the simplest assumption of instantaneous equilibrium in the biophase, the observed reversal of NMB could be adequately predicted (fig. 3). Using the assumption of noninstantaneous equilibrium in the biophase, it will take some time to reach equilibrium resulting in a higher free rocuronium concentration in the biophase. This would result in slower reversal, as compared with the assumption of instantaneous equilibrium, which was not observed.

The identified pharmacokinetic parameters for rocuronium are consistent with previously published values.18Using a mean body weight of 80 kg for Caucasian patients, the rocuronium Cl  value of 3.1 ml · min⁻¹· kg⁻¹and V1  value of 44.8 ml/kg were very close to previously reported values of 3.2 ml · min⁻¹· kg⁻¹and 42 ml/kg,18respectively. Also, the pharmacokinetic parameters of vecuronium identified in this study are consistent with previously published values.19 

The pharmacokinetics of rocuronium appeared to be different in Japanese and Caucasian patients. This difference could not be explained by observed differences in body weight, height, and/or age between the Japanese and Caucasian subpopulation. The estimated values for Cl  (0.252 l/min) and V^ss  (10.2 l) for Japanese patients are close to previously reported Cl  (0.266–0.315 l/min) and V^ss  (10.2–12.7 l) values.21The estimated differences in pharmacokinetic parameters between Japanese and Caucasians correspond to a mean difference in total exposure to rocuronium of 17% between Japanese and Caucasians, which is considered not clinically relevant, requiring no dose adjustment.

The pharmacokinetics of sugammadex administered alone and without anesthesia or in the presence of rocuronium with anesthesia was considerably different, with higher sugammadex plasma concentrations in the latter case. This difference is reflected in a 50% lower value for V2  and Q2 , in addition to a 2.4-fold higher value for Q3  and a 52% higher value for V3  for sugammadex in the presence of rocuronium, as compared with sugammadex alone. Although an effect of complex formation on the pharmacokinetics of sugammadex cannot be excluded, the differences in the distribution of sugammadex with and without rocuronium and anesthesia could also result from anesthesia effects. As regional blood flow is likely to be different in anesthetized patients, this can explain the observed differences in the distribution parameters. However, the observed difference in sugammadex pharmacokinetics does not have clinical implications, since sugammadex will always be administered in the presence of rocuronium and anesthesia.

The model explicitly states that once sugammadex appears in the effect compartment, reversal of NMB is rapid because of the assumption of instantaneous complex formation in the effect compartment. Hence, the distribution of sugammadex to the effect compartment, characterized by ke0 , is assumed to be the rate-limiting step in the reversal process. However, underprediction of the reversal time for lower sugammadex doses equal to or below 2 mg/kg (fig. 4B) might arise from not considering rate limiting receptor dissociation. The predictions for vecuronium seem to support this hypothesis. As indicated by a lower EC⁵⁰  value, vecuronium has a higher affinity for the nicotinic receptor, as compared with rocuronium. Since the onset of and spontaneous reversal of NMB are slower for vecuronium as compared with rocuronium, it is more likely that the lower EC⁵⁰  is a result of a lower dissociation rate for vecuronium. This would imply that not taking into account the rate of receptor dissociation affects the prediction of reversal of vecuronium-induced NMB to a greater extent than prediction of the reversal of rocuronium-induced NMB. This corresponds to the observation that the PK-PD model adequately predicts the time to reversal of rocuronium-induced NMB after administration of sugammadex 0.5 mg/kg at reappearance of T²(fig. 5A), whereas the reversal time is clearly underpredicted for vecuronium-induced NMB after administration of the same sugammadex dose (fig. 5B).

In their theoretical approach, based on simulations with a hypothetical NMB agent and a specific binding agent, Nigrovic et al.  22proposed a model that takes the association and dissociation of nicotinic receptor binding and thereby the fraction of rocuronium bound to the nicotinic receptor into consideration. Their hypothesis is that for predicting the observed fast reversal of NMB the binding agent should diffuse into the effect compartment is consistent with our finding based on actual data. Furthermore, Nigrovic et al.  22showed that a two- to fourfold higher molar dose of sugammadex is required for fast and complete reversal when a binding agent is administered 3 to 5 min after rocuronium. This is consistent with our observation of under-predicting observed reversal time of rocuronium induced NMB after sugammadex doses equal to or below 2 mg/kg (fig. 4B). Our attempts to use a comparable model to the one described by Nigrovic et al.  22suggest that a more complex model is not supported by the available data. Presumably, data after different rocuronium doses are required for identification of the association and dissociation rate constants for the rocuronium receptor binding.

Simulations show that with another rocuronium dose of 0.6 mg/kg administered 120 min after sugammadex, approximately 90% of patients would achieve 90% NMB within 4 min. To reduce the time after sugammadex administration, the rocuronium dose could be increased (e.g. , 15 min after sugammadex, reparalysis with rocuronium 1.2 mg/kg would result in 90% NMB within 4 min) or nonsteroidal NMB agents which do not bind to sugammadex (such as cis-atracurium or succinylcholine) could be used.

In conclusion, we used the data from several clinical studies demonstrating the efficacy and safety of sugammadex for reversal of rocuronium-induced NMB to describe the pharmacokinetics and pharmacodynamics of rocuronium after sugammadex administration, using one comprehensive model. Our model-based analysis is consistent with the hypothesis that reversal of rocuronium-induced NMB results from decreased availability of the free rocuronium concentration in plasma and the neuromuscular junction. We showed that the model adequately predicts observed data from other studies that were not used for model development. We were also able to use the same model to predict the observed reversal after vecuronium-induced NMB. Therefore, this model is useful to predict reversal of rocuronium and vecuronium-induced NMB for relevant clinical scenarios.

The authors thank Jan Freijer, Ph.D. (LAP&P Consultants BV, Leiden, The Netherlands), for his mathematical assistance.