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Anesth Analg 2002;95:588-596
© 2002 International Anesthesia Research Society

ANESTHETIC PHARMACOLOGY

Pharmacokinetic/Pharmacodynamic Modeling of Rocuronium in Myasthenic Patients Is Improved by Taking into Account the Number of Unbound Acetylcholine Receptors

Ann De Haes, MD*, Johannes H. Proost, PharmD PhD*, Jan B. M. Kuks, MD PhD{dagger}, David C. van den Tol, MD{ddagger}, and J. Mark K. H. Wierda, MD PhD*

*Research Group for Experimental Anesthesiology and Clinical Pharmacology and {dagger}Department of Neurology, University Hospital Groningen, Groningen, The Netherlands; and {ddagger}Department of Anesthesiology, Lievensberg General Hospital, Bergen op Zoom, The Netherlands

Address correspondence and reprint requests to Ann De Haes, MD, Department of Anesthesiology, University Hospital Groningen, PO Box 30001, 9700 RB Groningen, The Netherlands. Address e-mail to a.de.haes{at}anest.azg.nl


   Abstract
Top
 Abstract
Introduction
 Methods
 Results
 Discussion
 References
 
Patients with myasthenia gravis are more sensitive than healthy patients to nondepolarizing neuromuscular blocking drugs. We performed a pharmacokinetic/pharmacodynamic modeling study of rocuronium in eight myasthenic patients and eight matched control patients. Patients were anesthetized with propofol and sufentanil and a mixture of nitrous oxide/oxygen. Mechanomyographical monitoring of the adductor pollicis was applied. Rocuronium was infused at a rate of 25 µg · kg-1 · min-1 in myasthenic patients and 116.7 µg · kg-1 · min-1 in control patients and was terminated at 70% neuromuscular block. Arterial blood samples were drawn during onset and offset of the block and for 4 h after the administration of rocuronium. Plasma concentrations were determined by high-performance liquid chromatography. Pharmacokinetic/pharmacodynamic modeling was performed by using the Sheiner model and the unbound receptor model (URM), which takes into account the number of unbound acetylcholine receptors. The effective concentration at 50% effect and the steepness of the concentration-effect relationship were significantly decreased in myasthenic patients. Both the URM and the Sheiner model provided an adequate fit in myasthenic patients. The acetylcholine receptor concentration was significantly decreased in myasthenic patients. The URM explains the observed differences in time course and potency, whereas the Sheiner model does not.

IMPLICATIONS: We performed a pharmacokinetic/pharmacodynamic modeling study in myasthenic patients and control patients. The unbound receptor model, which takes into account the number of unbound acetylcholine receptors in the biophase, was introduced and compared with the model proposed by Sheiner.


   Introduction
Top
 Abstract
 Introduction
Methods
 Results
 Discussion
 References
 
Myasthenia gravis is an autoimmune disease that attacks the acetylcholine receptors (AChRs) at the neuromuscular junction, resulting in fewer receptors (1,2). Some of the remaining AChRs are blocked by antibodies (3,4). Patients with myasthenia gravis are more sensitive to nondepolarizing neuromuscular blocking drugs (NMBDs), as reflected in the decreased dose required to achieve a 90% neuromuscular block (ED90) and a prolongation of neuromuscular block (2,5–7). The increased sensitivity of myasthenic patients to NMBDs has been ascribed to the decreased number of AChRs in the synaptic cleft (2,5). As a result, the margin of safety for NMBDs is decreased, and smaller doses are needed to obtain a certain degree of neuromuscular block. Therefore, an optimal individual dose adjustment is needed for myasthenic patients.

Although the alteration in potency and time course of action can be understood from the pathophysiological changes, the pharmacokinetic/pharmacodynamic (PK-PD) models developed until now do not explain the observed alterations in potency and time course of action. In simulations, the PK-PD model proposed by Sheiner et al. (8) may predict the increased sensitivity to and the longer recovery time of NMBDs in myasthenic patients (6) on the basis of a smaller 50% effective concentration (EC50) and the steepness of the concentration-effect relationship ({gamma}). The Sheiner model gives, however, no insight as to why these variables are changed in this group of patients (5,9–13). Therefore, we developed a novel PK-PD model, the unbound receptor model (URM), which takes into account the number of unbound AChRs and which may thus explain the altered potency and time course of NMBDs in myasthenic patients. In a previously conducted PK-PD modeling study, we tested this more physiologically based model in myasthenic pigs (14) and found that the URM provided a good fit of the time course of effect after a bolus dose of rocuronium in myasthenic animals. The differences in sensitivity and time course of effect between myasthenic and control pigs could be accounted for by a decreased receptor concentration only.

We performed a PK-PD modeling study in myasthenic patients and matched controls to test the adequacy of the URM to describe the time course of action of rocuronium in myasthenic patients and compared the results with the results obtained with the Sheiner model.


   Methods
Top
 Abstract
 Introduction
 Methods
Results
 Discussion
 References
 
After approval of the Medical Ethical Committee of the University Hospital of Groningen, The Netherlands, and after written, informed consent was obtained, eight myasthenic patients scheduled for thymectomy and eight matched controls scheduled for elective otorhinolaryngology or general surgery not requiring additional relaxation after intubation were enrolled in the study. Age, height, weight, sex, and underlying diseases of the control group were matched with those of the myasthenic patients. Clinical assessment of myasthenic patients was performed with a six-point disability score as developed by Oosterhuis (15). Information about the disease state of the myasthenic patients is depicted in Table 1. [[16]]Patients with cardiovascular disease and those receiving any medication interacting with rocuronium were excluded.


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  		Table 1. Table 1. Patient Characteristics; Values Are Median (Range)
 
The last dose of pyridostigmine was administered the evening before the day of surgery. Therefore, perioperative measurements were performed without anticholinesterases for more than 12 h. Premedication consisted of an oral dose of midazolam 7.5 mg if required. Standard monitors were used. Anesthesia was induced with sufentanil 0.1–0.5 µg/kg and propofol 2–4 mg/kg and was maintained with sufentanil increments of 5–10 µg and a constant propofol infusion, starting at 10 mg · kg-1 · h-1 and increased or decreased by 2 mg · kg-1 · h-1, all according to the patient’s needs. The patients were ventilated with a nitrous oxide/oxygen mixture (fraction of inspired oxygen, 33%; fraction of inspired nitrous oxide, 67%), and the end-tidal PCO2 was kept between 30 and 35 mm Hg. Arterial blood samples were drawn from the radial artery of the arm not used for neuromuscular monitoring or from the dorsal pedal artery.

The arm was wrapped to keep its temperature stable and >32.5°C and was immobilized in a splint. After the induction of anesthesia, measurement of the twitch height was started. The ulnar nerve was stimulated at the wrist through two surface electrodes with single twitches of 200-µs duration at 0.1 Hz. The isometric contraction of the adductor pollicis muscle was measured by a force transducer and recorded; preload was kept between 200 and 400g. Monitoring was continued until the twitch height returned to its control value.

After the neuromuscular monitoring equipment was calibrated, rocuronium was administered in a fast-running infusion. The myasthenic patients received rocuronium at a rate of 25 µg · kg-1 · min-1, and the control group received rocuronium at a rate of 116.7 µg · kg-1 · min-1 until the infusion was discontinued at 70% twitch depression. If, after completion of the pharmacodynamic data sampling, additional relaxation was needed, vecuronium had to be used because this drug and its putative metabolites do not interfere with the detection of rocuronium in plasma. The interval 75%–25% is defined as the time elapsed from 75% to 25% twitch height during the onset of neuromuscular block and, for the interval 25%–75%, vice versa.

Just before the administration of rocuronium, a blank sample was drawn from the arterial line. Samples were taken both during the onset and offset of neuromuscular block at 80%, 60%, 40%, and 20% twitch height and on maximum block. Additional samples were taken 25, 40, 60, 90, 120, 150, 180, and 240 min after the start of rocuronium administration. Each sample contained 3 mL of blood and was collected in standard heparinized blood tubes (glass). They were centrifuged for 10 min at 4000 rpm, and the plasma was pipetted from the centrifuge tubes into clean glass tubes with a plastic stopper within 4 h after collection. The plasma samples were stored at -20°C until high-performance liquid chromatography was performed for the quantitative determination of rocuronium and its putative derivatives (17).

Plasma concentration-time data were analyzed by iterative two-stage Bayesian (ITSB) analysis (18,19) by using the program Multifit. Mean values and SDs of the pharmacokinetic population variables of a one-compartment model (CL, V1) (see Table 2 for variable definitions), a two-compartment model (CL10, V1, CL12, V2), and a three-compartment model (CL10, V1, CL12, V2, CL13, V3) and the residual SD (SDres) were estimated. A log-normal distribution for both pharmacokinetic population variables and plasma concentration measurement errors was assumed. The correctness of the latter assumption was tested by visual inspection of the graphs of the residuals plotted against time and against concentration. SDres was assumed to be the same for each individual and to be independent of the concentration (after logarithmic transformation). Goodness of fit was evaluated from visual inspection of the measured and calculated data points and of the residuals plotted against time and against concentration. The choice among a one-, two-, and three-compartment model was based on Akaike’s information criterion (AIC) (20). AIC was calculated as the sum of the AIC values of the individual patients and a value of 2 for each estimated population value (mean and SD of each variable, and SDres). The pharmacokinetic modeling procedure was performed separately for both patient groups.


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  		Table 2. Table 2. Results of the Pharmacokinetic Modeling Procedure and the PK-PD Modeling Procedures for Myasthenic Patients and Control Patients. Values are median (range).
 
Two PK-PD models were applied to the data. First, the Sheiner model, with an effect compartment linked to the plasma compartment, was applied to the data by using the actual plasma concentration data (21). Second, we applied the unbound-receptor PK-PD model, which takes into account the free AChR concentration (Appendix 1). The twitch height/time data were analyzed by an ITSB analysis by using the program PkPdFit. The goodness of the fit was evaluated by visual inspection of the measured and calculated data, by the degree of minimization of the hysteresis loop, by the SDres, and by the AIC value. Also, the PK-PD modeling procedure was performed separately for both patient groups.

Fitting of each model variable (rate constant between plasma and effect compartment, ke0; dissociation constant of drug receptor complex, Kd; total receptor concentration, Rtot; concentration of free receptors at which twitch height is 50% of the maximum twitch height, Rfree50; and exponential coefficient of twitch height-unbound receptor concentration relationship, ß) did not result in reliable variable estimates because of the strong correlation among variables, in particular among Kd, Rtot, and Rfree50. Because the aim of the PK-PD model was to investigate the influence of AChR concentration on potency and time course of effect, Rtot was assumed to be variable between individuals. The values for Kd and Rfree50, however, were assumed to be the same for each individual. Estimates for these values were obtained as follows: assuming that a neuromuscular block of 50% is reached at a receptor occupancy of 87.5% in case of normal AChR density (i.e., in controls), the value of Rfree50 is 12.5% of the normal Rtot (22). By using the Sheiner model, the median EC50 in control patients was 1650 µg/L, or 2.71 µM. Substituting this EC50 value for Cue in Equation 6 (Appendix 1), and because Rfree/Rtot = Rfree50/Rtot = 0.125, it follows that Kd = 0.35 µM. This value was used for all patients. The Rfree50 value of 0.20 µM was determined by minimization of AIC during simultaneous fitting of all patients.

Data are presented as median and range, unless otherwise stated. Comparison between myasthenic patients and control patients was performed by the Mann-Whitney U-test. Correlation between EC50 as calculated by the new model and diagnostic criteria and values was examined with Pearson’s correlation test. A P value of <0.05 was considered significant. The AIC was used for comparison between two PK-PD models; a lower value of the AIC represents a better fit (20).


   Results
Top
 Abstract
 Introduction
 Methods
 Results
Discussion
 References
 
The myasthenic group and the matched control group were similar with respect to sex, age, weight, height, and body mass index (see Table 1). Maximum neuromuscular block ranged from 77% to 99% in myasthenic patients and from 94% to 99% in control patients (see Fig. 1, A and B).



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  		Figure 1. Effect-time curve for all patients.

 
The median rocuronium dose was 194 µg/kg (80–322 µg/kg) in myasthenic patients, compared with 440 µg/kg (320–700 µg/kg) in control patients. In myasthenic patients, the interval 25%–75% (17.6 min [14.0–44.5 min]) was significantly longer (P = 0.035) than in the control group (11.6 min [11.1–21.0 min]).

The results of the pharmacokinetic modeling are summarized in Table 2. There was a significantly faster plasma clearance in the myasthenic patients. A three-compartment model fitted the concentration-time data significantly better than a two- and a one-compartment model. The results of both PK-PD modeling procedures (Sheiner model and URM) are also summarized in Table 2. The AIC and SDres for control patients were smaller with the Sheiner model than with the URM (13,011 and 3.06% vs 13,245 and 3.20%, respectively). The AIC and SDres for myasthenic patients were larger with the Sheiner model than with the URM (14,947 and 4.16% vs 14,795 and 4.02%, respectively). When all patients were modeled together, the AIC and SDres were larger with the Sheiner model than with the URM (28,257 and 3.66% vs 28,196 and 3.64%, respectively). The EC50 and ke0 were not significantly different after modeling with either the Sheiner link model or the URM in both groups. Individual results are depicted in Tables 3 and 4.


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  		Table 3. Table 3. Individual Results of the PK-PD Fitting Procedure with the Sheiner Model
 

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  		Table 4. Table 4. Individual Results of the PK-PD Fitting Procedure with the Unbound Receptor Model
 
There was no significant correlation between disease variables (see Table 1) and the EC50, except for blocking of the muscle fiber potential at the neuromuscular junction during single-fiber electromyelogram (EMG) (Pearson correlation = 0.819; P = 0.024) (Fig. 2). In patients with little or no blocking activity during single-fiber EMG, the decrease in EC50 was very small compared with that in patients with blocking activity, who had a much larger decrease in EC50.



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  		Figure 2. Correlation (Pearson correlation = 0.819; P = 0.024) between blocking of the electric signal during single-fiber electromyelogram (EMG) (16) and the 50% effective concentration (EC50).

 

   Discussion
Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
References
 
Both the Sheiner model and the URM were able to give an adequate fit for the concentration-effect data of all patients. The longer interval 25%–75% in the myasthenic group (17.6 vs 11.6 minutes, respectively) has been described for vecuronium (6), rocuronium (5), and mivacurium (9,23). The longer interval 25%–75% is related to the increased sensitivity to NMBDs, because of the decrease of AChRs (1), caused by antibodies against the receptor inducing internalization and destruction of end plates (3,24). This decreased number of AChRs results in a decreased margin of safety (25). Only one-fifth of the AChRs are needed to ensure normal neuromuscular transmission; the other receptors form a safety margin. In myasthenic patients, neuromuscular transmission will fail at an earlier point, which explains the weakness observed in these patients. This also implies that a smaller amount of NMBDs is needed to induce a neuromuscular blocking effect. The prolonged offset can be understood if the effect compartment in myasthenic patients is seen as a space with fewer AChRs compared with controls. This means that fewer relaxant molecules are bound to AChRs to exert a certain neuromuscular block and that fewer molecules will be present in the biophase. To return to a higher twitch height, relatively more relaxant molecules have to be cleared from the effect compartment in a myasthenic patient (for example, 1 molecule from a total of 4) compared with a control patient (who would have to clear 1 molecule from a total of 10).

We have no explanation for the faster plasma clearance in myasthenic patients. It might be that pyridostigmine or other drugs such as azathioprine, cyclosporine, and prednisone, used in the treatment for myasthenia gravis, enhance liver uptake of rocuronium or change its rate of metabolism. Because this is the first PK-PD study with an NMBD in myasthenic patients, no comparison with other studies or data is available. Differences in other kinetic variables are clinically unimportant.

The modeling procedure with the link model proposed by Sheiner revealed that both EC50 and {gamma} were significantly decreased in myasthenic patients. Although the Sheiner model provided an acceptable fit, the model was not designed to give explanations as to why {gamma} and EC50 were decreased in myasthenic patients, contrary to the URM.

There is a significant difference among Rtot, EC50, and ß of myasthenic and control patients with respect to the URM. If the receptor concentration of an individual is compared with the median receptor concentration in controls, we find a ratio of 0.70–1.09 in control patients, and in myasthenic patients we find a median of 0.27 with a range of 0.09–0.65, which shows the relative decrease in receptor concentration. The use of the URM enables us to relate the clinical disease variables to the changes observed in the time course and potency of NMBDs in myasthenic patients. Beta was significantly different in myasthenic patients, which was contrary to our findings in myasthenic pigs, in which the receptor concentration alone was able to explain the observed differences in sensitivity and time course of effect. Our patients possibly represented a less homogenous group than our myasthenic pigs, because the pigs were all on the same diet and lived under the same circumstances and myasthenia gravis was induced in the same way.

The Sheiner model contains three variables, which can be assessed reliably. The URM model contains five variables. These five variables could not be uniquely identified, indicating that the model is overparameterized in relation to the available data. Therefore, we estimated two variables in a different way and used these estimates as fixed variables. Kd was estimated from the observed mean EC50 in control patients and from the assumption that in control patients receptor occupancy is 87.5% at 50% neuromuscular block (22). The variable Kd in the URM model is the dissociation constant of the rocuronium-receptor complex. Because it is likely that receptors are the same in all healthy patients, it follows that the value of Kd is the same in all healthy patients. In myasthenic patients, part of the AChR is blocked by antibodies or internalized. There is no a priori reason why the remaining functional receptors would be different, for the very reason that they are functional. In the URM model, Rtot reflects these functional receptors only. Similarly, we assumed that Rfree50 was the same in all patients.

To investigate the implications of the assumption of 87.5% receptor occupancy at 50% in control patients and the choice of Rfree50 on the presented results, we repeated the analysis with other values for Kd and Rfree50. Assuming that 50% block is reached at 75% receptor occupancy in control patients, Kd increased by a factor of 7:3 to 0.82 µM. The values of ke0 were hardly affected, and median ß was increased from 3.43 to 4.38 in myasthenic patients and from 4.91 to 5.66 in control patients, but median Rtot markedly decreased from 0.48 to 0.31 µM in myasthenic patients and from 1.75 to 0.86 µM in control patients. However, the ratio between the median value of both groups was only moderately affected, from 0.27 in the original analysis to 0.36, for a Kd value of 0.82 µM. The value of Rtot varied almost linearly with Rfree50, thus not affecting the ratio of Rtot in myasthenic and control patients, and ke0 and ß were hardly affected by the choice of Rfree50. From this analysis it can be concluded that the absolute values of Rtot are indeed dependent on the values for Kd and Rfree50 but that the ratio of Rtot in myasthenic patients and control patients, and the conclusions of the study, are not markedly affected by the assumptions with respect to Kd and Rfree50.

To demonstrate the differences between the PK-PD models, we performed a simulation for myasthenic and control patients by using median values from our fitting procedures (see Table 2) and prepared a time-effect plot. A short bolus dose of rocuronium was administered to obtain 90% block. For control patients, there were only small differences between the Sheiner model and the URM, the interval 75%–25% was virtually the same, and the same held for the interval 25%–75% (see Fig. 3 and Table 5).



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  		Figure 3. Simulation for the mean control patient and mean myasthenic patient showing the behavior of the link model proposed by Sheiner et al. (SM) (control SM and myasthenia gravis [MG] SM) and the unbound receptor model (URM) (control URM and MG URM). The bolus dose associated with this time course of effect can be found in Table 3; this is the log mean dose for control patients and myasthenic patients.

 

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  		Table 5. Table 5. Results of a Simulation (See Discussion)
 
In myasthenic patients, the interval 75%–25% is hardly influenced by the choice of the PK-PD model, but the interval 25%–75% is longer in the simulation of the URM. If the time course of effect after an ED90 bolus dose for each model is calculated, the Sheiner model predicts a shorter interval 75%–25% in myasthenic patients; this is in contrast to the observations made in myasthenic patients (5,12,26). In the URM, there is virtually no influence of the disease on interval 75%–25%. Both the URM and the link model proposed by Sheiner predict a prolonged offset time, as is seen in myasthenic patients (6,9,23,27), but the prolongation is more pronounced with the URM. There is a slight difference in ED90 for the control patients in the URM and the link model proposed by Sheiner, and this difference is caused by the model variable definitions.

Because we wanted to predict the dose of rocuronium needed in myasthenic patients and thus provide safer anesthesia, we looked for a correlation between disease variables and EC50, which will in turn influence ED90. Because blocking of the muscle fiber potential at the neuromuscular junction during single-fiber EMG was the only disease variable that showed a significant correlation with EC50, it seems of interest to study the blocking of the muscle-fiber potential at the neuromuscular junction in further studies on myasthenia gravis and NMBDs because this may serve as a predictor of sensitivity to rocuronium in myasthenic patients.

We used an ITSB method for the pharmacokinetic and PK-PD analysis. In the first stage, this method uses prior estimates of the population means and SDs, and the SDres of the measurements, to calculate the Bayesian maximum-likelihood variable estimates for each individual patient. In the second stage, the population mean values and SD are calculated from these individual estimates, and SDres is estimated. These new values are now used as prior estimates in the first stage, and the procedure is repeated until the calculated mean values for the variables and SDres converge to the prior estimates. We demonstrated previously that ITSB is a valuable technique for population pharmacokinetic analysis and is superior to the standard two-stage analysis, in particular for the estimation of interindividual SD (28,29).

Both the URM and the Sheiner model can fit the time course of effect of rocuronium in myasthenic patients satisfactorily. On the basis of the AIC, the URM performs better in these patients. The URM can, contrary to the model proposed by Sheiner, explain the observed changes in potency and time course of rocuronium in myasthenic patients by a decrease in receptor concentration at the neuromuscular junction, and this makes it a more suitable model to use for the development of a rational infusion regimen in myasthenic patients.

Appendix 1: URM
The existing PK-PD models assume that the neuromuscular blocking effect is related to the (unbound) concentration of the drug in the effect compartment, i.e., the neuromuscular junction (8,30). However, this assumption makes no sense from a mechanistic point of view, because the effect is the result of binding of the NMBD to the receptor and not just of the presence of free drug in the biophase. Alternatively, one might relate the effect to the concentration of bound NMBD. This hardly affects the model in a qualitative way, because the unbound concentration and the bound concentration are strongly correlated.

NMBDs are antagonists of acetylcholine, which is in turn responsible for neuromuscular transmission. Therefore, we postulated that the contractile force of a muscle after supramaximal stimulation, measured as twitch height (TH), is related to the free AChR concentration according to the sigmoid Emax model (Hill equation):

equation


where THmax is the maximum TH, i.e., TH in case the number of free receptors is infinitely high; Rfree is the concentration of free receptors; Rfree50 is the concentration of free receptors at which TH is 50% of THmax; and ß is the exponential coefficient.

In the absence of NMBD, the concentration of free receptors equals the total receptor concentration; on substitution in Equation 1, it follows that

equation


where THc is the TH in the absence of NMBD and Rtot is the total receptor concentration.

The neuromuscular blocking effect of a NMBD is defined as

equation


Substituting Equations 1 and 2 in Equation 3 yields

equation


Equation 4 describes the neuromuscular blocking effect as a function of the free AChR concentration. Total AChR concentration (Rtot), Rfree50, and ß are model variables.

Binding of the NMBD to the AChR binding sites is characterized by the equilibrium dissociation constant of the drug-receptor complex (Kd):

equation


where Cue is the unbound concentration of NMBD in the effect compartment, Rfree is the concentration of free binding sites of AChR, and Rbound is the concentration of AChR receptor sites to which an NMBD molecule is bound.

If Rtot is defined as the total concentration of AChR binding sites, it follows upon rearrangement that

equation


The time course of the unbound concentration in the effect compartment can be evaluated as described previously (31). Equation 16 of that article was simplified and did not take into account plasma protein binding and nonspecific binding in the effect compartment, resulting in

equation


where C is the concentration in the first compartment and ke0 is the transport rate constant.

We assume that binding is very fast compared with the kinetic processes, so at any time equilibrium is assumed, i.e., Equation 5 is valid at any time.


   References
Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 

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Accepted for publication May 10, 2002.





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Lippincott, Williams & Wilkins Anesthesia & Analgesia® is published for the International Anesthesia Research Society® by Lippincott Williams & Wilkins with the assistance of Stanford University Libraries' HighWire Press®. Copyright 2006 by the International Anesthesia Research Society. Online ISSN: 1526-7598   Print ISSN: 0003-2999 HighWire Press