Sugammadex selectively binds steroidal neuromuscular blocking drugs, leading to reversal of neuromuscular blockade. The authors developed a pharmacokinetic-pharmacodynamic model for reversal of neuromuscular blockade by sugammadex, assuming that reversal results from a decrease of free drug in plasma and/or neuromuscular junction. The model was applied for predicting the interaction between sugammadex and rocuronium or vecuronium.

Noninstantaneous equilibrium of rocuronium-sugammadex complex formation was assumed in the pharmacokinetic-pharmacodynamic interaction model. The pharmacokinetic parameters for the complex and sugammadex alone were assumed to be identical. After development of a pharmacokinetic-pharmacodynamic model for rocuronium alone, the interaction model was optimized using rocuronium and sugammadex concentration data after administration of 0.1-8 mg/kg sugammadex 3 min after administration of 0.6 mg/kg rocuronium. Subsequently, the predicted reversal of neuromuscular blockade by sugammadex was compared with data after administration of up to 8 mg/kg sugammadex at reappearance of second twitch of the train-of-four; or 3, 5, or 15 min after administration of 0.6 mg/kg rocuronium. Finally, the model was applied to predict reversal of vecuronium-induced neuromuscular blockade.

Using the in vitro dissociation constants for the binding of rocuronium and vecuronium to sugammadex, the pharmacokinetic-pharmacodynamic interaction model adequately predicted the increase in total rocuronium and vecuronium plasma concentrations and the time-course of reversal of neuromuscular blockade.

Model-based evaluation supports the hypothesis that reversal of rocuronium- and vecuronium-induced neuromuscular blockade by sugammadex results from a decrease in the free rocuronium and vecuronium concentration in plasma and neuromuscular junction. The model is useful for prediction of reversal of rocuronium and vecuronium-induced neuromuscular blockade with sugammadex.

IDEALLY, neuromuscular blocking agents should have a rapid onset and offset of neuromuscular blockade (NMB).1Of the nondepolarizing neuromuscular blocking agents used in clinical practice, rocuronium shows the most rapid onset of NMB and has an intermediate to long duration of action. To decrease its duration of action, a cyclodextrin has been designed to specifically bind rocuronium, thereby reversing rocuronium-induced NMB. The effectiveness and safety of this cyclodextrin, sugammadex, for the reversal of rocuronium-induced NMB has been reported in several preclinical2–3and clinical studies4–11; these studies have investigated sugammadex administered at a variety of time points, including administration 3 min after a rocuronium dose and at reappearance of the second twitch (T^{2}) of train-of-four (TOF) stimulation.

Pharmacokinetic studies consistently show decreased rocuronium clearance and increased total rocuronium concentrations shortly after sugammadex administration. As discussed by others,1,4,6rocuronium bound by sugammadex is eliminated by renal excretion with a total clearance that is approximately one-third that of unbound rocuronium. As a result, higher total rocuronium concentrations are observed after sugammadex administration, as compared with administration of rocuronium alone.4–6However, it is hypothesized that the free rocuronium concentration decreases after sugammadex administration, resulting in decreased availability of rocuronium at the nicotinic receptors.1,4,6As a result, a more rapid reversal of NMB is observed. Although consensus exists about the proposed mechanism of action for the reversal of rocuronium-induced NMB after sugammadex administration, this hypothesis has not been confirmed by measuring the actual free rocuronium concentration. The absence of an analytical method to separate free rocuronium from sugammadex-bound rocuronium prevents testing of this hypothesis.3However, mechanism-based pharmacokinetic–pharmacodynamic (PK-PD) modeling and simulation can serve as an alternative method to evaluate the proposed mechanism of action of sugammadex. Mechanism-based PK-PD modeling involves the description of the processes in the causal path between drug administration and effect in a strictly quantitative manner.12Adequate prediction of the observed data using a mechanism-based PK-PD model based on the proposed pharmacology and (patho) physiology should support the underlying hypotheses. The validity and accuracy of the model and its underlying mechanism can be improved if the model is based on prior knowledge from different sources (*i.e.* , preclinical, *in vitro* bioassays) and is derived under different experimental circumstances.

The affinity of rocuronium and a variety of other compounds for sugammadex has been measured *in vitro* by isothermal microcalorimetry, providing a measure of the equilibrium dissociation constant (*K ^{d}* ).13Using the

*K*the free rocuronium concentration can be calculated on the basis of the total rocuronium and sugammadex concentration. Under the assumptions that only the free rocuronium concentration is cleared

^{d},*via*the rocuronium clearance pathway (

*i.e.*, excretion

*via*urine and bile) and that the complex is cleared

*via*the sugammadex pathway (most likely renal clearance, since the sugammadex clearance is close to the glomerular filtration rate4), the effect of sugammadex administration on the overall clearance of total rocuronium can be predicted. In addition, according to the free drug hypothesis, NMB is related to the free rocuronium concentration, and reversal of rocuronium-induced NMB is a measure of the change in free rocuronium concentration in the biophase. Consequently, if the underlying assumptions are valid, the observed reversal of NMB should be adequately predicted by a PK-PD model, linking the free rocuronium concentration to NMB.

In the current study, we tested the hypothesis that the *in vitro K ^{d}* can be used to predict the observed change in the total rocuronium concentration after sugammadex administration to humans. The other model parameters were estimated using pharmacokinetic and pharmacodynamic data from healthy Caucasian volunteers and Japanese and Caucasian patients. PK-PD modeling implicitly requires making assumptions about the model structure. As it is not always possible to justify these assumptions

*a priori*, (

*e.g.*, is the

*in vitro K*valid

^{d}*in vivo*?), it is essential to validate these assumptions by evaluating the ability to predict data from other studies, which were performed under different circumstances (e.g., administration of sugammadex at reappearance of T

^{2}) and were not used to estimate the model parameters.

A key element of mechanism-based PK-PD modeling is the explicit distinction between drug-specific and biologic system-specific properties.12Hence, if the system is adequately described, the model should allow predicting the effects of other drugs of the same class after adjusting the drug-specific parameters. We evaluated whether the PK-PD interaction model could be used to predict the pharmacokinetic and pharmacodynamic parameters of vecuronium, another steroidal neuromuscular blocking drug, which also binds specifically to sugammadex, albeit with a somewhat lower affinity than that of rocuronium.9For this purpose, we evaluated if the same model structure as applied for rocuronium, but with vecuronium-specific pharmacokinetic and pharmacodynamic model parameters, could also predict the observed changes in the pharmacokinetic and pharmacodynamic parameters of vecuronium (administered as a 0.1 mg/kg intubating dose) after administration of sugammadex at reappearance of T^{2}.9

## Materials and Methods

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.

### Study Data

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.

### Data Analysis

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.

### Visual Predictive Check

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).

### PK-PD Interaction Model

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.

### Pharmacokinetic Model

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*] is the free concentration of sugammadex, [

^{free}*Cplx*] is the concentration of the complex,

*K*is the association rate constant, and

^{1}*K*is the dissociation rate constant.

^{2}The *K ^{d}* is defined as the ratio between

*K*and

^{2}*K*(equation 2).

^{1}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*is the apparent volume of distribution of the central compartment, and

^{cmplx}*k*and

^{1x}*k*are the rate constants for distribution between the central and the two peripheral compartments.

^{x1}*C*is the complex concentration in the compartments, and

^{cplx,x}*C*and

^{roc,1}*C*are the free rocuronium and sugammadex concentration in the central compartment, respectively.

^{sug}^{,1}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*and

^{1x,drug}*k*are the rate constants for distribution between the central and the two peripheral compartments for rocuronium and sugammadex, and

^{x1,drug}*A*is the amount of rocuronium or sugammadex in one of the compartments.

^{drug,x}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 *K ^{2}* was estimated, whereas

*K*was calculated using a

^{1}*K*value of 0.1 μm, which was derived

^{d}*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.

### Pharmacodynamic 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 (*E ^{0}* ), the maximum effect (

*E*), the

^{max}*Ce*resulting in an effect of 50% of

^{roc}*E*(

^{max}*EC*), and a sigmoidicity parameter (

^{50}*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*and

^{roc,tot}*Ce*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

^{sug,tot}*ke0*value was assumed for rocuronium and sugammadex.

### PK-PD Interaction Model for Vecuronium

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 *K ^{1}* parameter representing the probability that two molecules meet to form a complex, this parameter is considered compound-independent. Hence, by assuming the same

*K*for vecuronium and rocuronium, the

^{1}*K*was derived from equation 2using a vecuronium-specific

^{2}*K*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

^{d}### Statistical Model

The interindividual variability in most model parameters was modeled using equation 8, where *θ ^{i}* is the individual specific parameter value for the subject,

*i, θ*is the population mean, and

^{mean}*η*is the difference of the logarithm between the individual value of the subject

^{i}*i*and the population mean.

*η*is normally distributed with a mean of zero and a variance

^{i}*ω*

^{2}.

The residual variability was described by the general equation 9, in which *Y ^{ij}* is the jth observation of individual i,

*PRED*is the jth model prediction for individual

^{ij}*i*, and

*ϵ*and

^{prop,ij}*ϵ*are the proportional and additive residual errors for the jth prediction of individual

^{add,ij}*i*.

*ϵ*and

^{prop,ij}*ϵ*are normally distributed with mean 0 and a variance ς

^{add,ij}^{2}.

In the pharmacokinetic model for rocuronium, both *ϵ ^{prop,ij}* and

*ϵ*were identified, whereas for the sugammadex pharmacokinetic model only

^{add,ij}*ϵ*was identified. The residual error in the PK-PD models was described by

^{prop,ij}*ϵ*only.

^{add,ij}## Results

### Model Development

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 *K ^{2}* of 0.00216 min

^{−1}(dissociation half-life = 5.3 h) and a

*K*value fixed to 0.1 μm, the pharmacokinetic interaction model adequately predicted the observed increase in total rocuronium concentration after sugammadex administration (fig. 2).

^{d}As *E ^{0}* and

*E*could not be distinguished using the available NMB data,

^{max}*E*was set to the individual estimate of

^{max}*E*. 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).

^{0}### Model Validation

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 T^{2}(fig. 5). The time to reappearance of T^{2}(*i.e.* , T^{2}twitch height ≥ 1%) was simulated using a PK-PD model for the effect of rocuronium on the T^{2}twitch height (fig. 5A). The parameter values were estimated using T^{2}data from calibration study 1 (parameters not shown). Subsequently, the effect of sugammadex administration, at the simulated time of reappearance of T^{2}, 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

*K*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 T

^{1}^{2}. 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.

### Application

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 T^{2}after 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.

## Discussion

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^{−1}and *V1* value of 44.8 ml/kg were very close to previously reported values of 3.2 ml · min^{−1}· kg^{−1}and 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*(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.

^{ss}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 *EC ^{50}* 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

*EC*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 T

^{50}^{2}(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.

## References

*NONMEM users guides.*Ellicott City, Maryland; Icon Development Solutions; 1989–2006

*versus*sequential analysis for population PK/PD data II: Robustness of methods. J Pharmacokinet Pharmacodyn 2003; 30:405–16