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Original Article

Is time to peak effect of neuromuscular blocking agents dependent on dose? Testing the concept of buffered diffusion

Proost, J. H.1; Houwertjes, M. C.1; Wierda, J. M. K. H.1

Author Information
European Journal of Anaesthesiology: July 2008 - Volume 25 - Issue 7 - p 572-580
doi: 10.1017/S0265021508004079

Abstract

Introduction

The time course of action of a neuromuscular blocking agent (NMBA) is governed by its pharmacokinetic and pharmacodynamic properties [1-4]. It is well recognized that the duration of neuromuscular block and the rate of recovery of the muscle response are dependent on the rate of decay of the plasma concentration. Also, it has been demonstrated that the time to peak effect of a submaximal blocking dose (Tpeak) is governed by the rate of decay of the plasma concentration profile [5]. The predominant role of pharmacokinetics on the time course of action of NMBAs can be explained by pharmacokinetic–pharmacodynamic (PK-PD) modelling [6-8]. The transport from plasma to the receptor site (also denoted effect compartment or biophase; for NMBAs, these terms refer to the neuromuscular junction or synaptic cleft) is also an important factor determining Tpeak. The role of this transport process can be inferred from the observed relationship between the rate constant characterizing this process (usually denoted ke0) and time to peak effect [9]. Pharmacokinetics also affects the dose needed to achieve a certain peak effect of neuromuscular block (NMBpeak), e.g. ED90, and thus affects the ‘apparent potency' of NMBAs [2,5,8].

It is less obvious whether or not the pharmacodynamic properties of a NMBA, i.e. the concentration–effect relationship (characterized by EC50, or ‘intrinsic potency') play a significant role in the time course of action of NMBAs. A possible mechanism for an influence of receptor affinity is a process called ‘buffered diffusion' [10-12]. The presence of a very high concentration of acetylcholine receptors (AChR) in the synaptic cleft causes repeated binding and release of NMBA molecules to these receptors, thus slowing down the rate of the diffusion of NMBA between the synaptic cleft and plasma. In vitro iontophoretic studies at the postsynaptic membrane of frog skeletal muscle fibres demonstrated the involvement of buffered diffusion in the kinetics of the action of NMBAs [13,14]. However, these findings do not prove that buffered diffusion plays a role in the time course of action of NMBAs when administered in vivo.

The aim of the present study was to determine whether the essential characteristics of buffered diffusion are recognizable in the time course of action of NMBAs, in particular in the time to peak effect. If buffered diffusion does play a significant role, PK-PD modelling predicts that Tpeak decreases with increasing dose, and that this effect of dose is more pronounced for potent NMBAs and less pronounced or absent for less potent NMBAs [7,8]. This can be explained as follows. After injection of the NMBA the drug diffuses from the plasma into the synaptic cleft. Part of the drug molecules in the synaptic cleft binds to the postsynaptic AChR. The driving force for diffusion of NMBA molecules between plasma and effect compartment is the unbound NMBA concentration gradient between plasma and effect compartment. The peak effect is reached if the concentrations of unbound NMBA in plasma and effect compartment are equal. Binding of NMBA molecules to AChR results in a lower unbound NMBA concentration in the effect compartment, and thus increases the time point at which the concentration in the effect compartment equals the concentration in plasma, i.e. increasing Tpeak. If a lower dose is given, i.e. if NMBpeak is lower, this increase in Tpeak will be more pronounced, because the number of free binding sites on AChR for NMBA is higher. Similarly, Tpeak will decrease with increasing dose. This effect of dose on Tpeak will be more pronounced for a potent NMBA than for a less potent NMBA. For a less potent NMBA, the binding of NMBA molecules to AChR hardly affects the unbound concentration, since the effective concentration needed to reach the same degree of NMB is higher, whereas, according to receptor theory, the number of drug molecules bound to AChR is likely to be independent of the potency of the NMBA for the same degree of block. On the other hand, for a potent NMBA, the number of drug molecules bound to AChR will be high compared to the number of unbound drug molecules, and the effect of dose on Tpeak will be more pronounced.

To test the hypothesis that buffered diffusion plays a role in the time to peak effect, we investigated the influence of dose on Tpeak of a submaximal blocking dose in the pig for four NMBAs which vary in potency. In addition, we performed PK-PD simulations to support the expected relationships between potency, dose, NMBpeak and Tpeak.

Methods

Following approval of the Animal Care Committee of the University of Groningen, 21 male pigs (body weight 20–28 kg) were studied. After a fasting period of 16 h with free access to water, the pigs were anaesthetized with 500 mg ketamine followed by 15 mg midazolam, given intramuscularly. The animal was weighed, and ear veins were cannulated to allow infusions of pentobarbital (2 mg kg−1 h−1) and fentanyl (2–4 μg kg−1 h−1), adjusted if needed to maintain an adequate depth of anaesthesia. The trachea was intubated and the lungs were artificially ventilated with an air/oxygen mixture, using a Cameco UV 705 (Cameco, Sweden) respirator, with a frequency of 19 breaths per minute, and 20 cm water pressure. The end tidal carbon dioxide level was maintained between 4 and 5 kPa (Godart Capnograph Mark II; E. Jaeger, Wuerzburg, Germany). Heart rate and blood pressure were measured continuously (Pressure Transducer, HP 78342A, Hewlett Packard, Boeblingen, Germany). Rectal temperature was measured continuously and maintained at 38°C with the use of a heating blanket. The axillary vein was cannulated for infusion of glucose 2.5% in saline 0.45%, and for administration of the NMBAs. The axillary artery was catheterized for continuous blood pressure measurements and for sampling of blood. The left peroneal nerve was exposed and attached to two silver stimulation electrodes. To prevent repetitive backfiring, the nerve was ligated proximal to the electrodes. The overlying skin was closed and the nerve was stimulated supramaximally with square wave stimuli of 0.2 ms at a frequency of 0.1 Hz (Grass S88; Grass Instruments, Quincy, MA, USA). The response of the tibialis anterior muscle was registered mechanomyographically using a force transducer (LB 8000 25N, Maryland Instruments Corp., Baltimore, MD, USA) connected to a muscle relaxation monitor MK II and to a recorder (MT 9000, Astro-Med, West Warwick, RI, USA). Preload was measured continuously and kept constant at approximately 75 g. The muscle response was allowed to stabilize before administration of a NMBA. After the experiment the animals were terminated by an overdose of pentobarbital.

The initial dose in the first animal of each NMBA group (rocuronium, vecuronium, pipecuronium or d-tubocurarine) was equal to the ED90 (dose needed to achieve a peak effect of 90% block) estimated from earlier studies, i.e. 600 μg kg−1 for rocuronium bromide (molecular weight (MW) 609.69), 100 μg kg−1 for vecuronium bromide (MW 637.74), 77 μg kg−1 for pipecuronium (MW 762.71) and 30 μg kg−1 for d-tubocurarine (MW 681.85). From NMBpeak obtained after this dose, the dose needed to achieve 20%, 40%, 60%, 75% and 90% block were estimated, assuming a relationship between NMBpeak and dose as described under data analysis, using a Hill coefficient of 4. This initial dose was adjusted in the next animals treated with the same NMBA if NMBpeak of this initial dose was not close to 90%.

Subsequently, five different doses of the same NMBA were administered to each animal, i.e. the estimated doses aiming at 20%, 40%, 60%, 75% or 90% block, in a random order. Each dose was given 45 min after complete recovery of the twitch response had been obtained. Each NMBA was studied in 5 or 6 animals.

The time to peak effect (Tpeak), defined as the time interval between the time of injection and the peak effect, was recorded after each dose.

Data analysis and statistics

The relationship between dose and NMBpeak was analysed by an iterative two-stage Bayesian population fitting procedure [15,16], using the program MultiFit (developed by J. H. Proost) for each NMBA separately, according to the following equation:

where ED50 is the calculated dose producing 50% NMBpeak and γ is the exponent or Hill coefficient. Data were unweighted, i.e. it was assumed that the difference between the measured and calculated NMBpeak was independent of the degree of block.

The relationship between NMBpeak and Tpeak was analysed by standard multiple linear regression analysis (Excel 1997, Microsoft Corp, Redmond, WA, USA), with NMBpeak, sequential dose number (between 1 and 5), and the individual animals as regressors, for each NMBA separately, according to the following equation:

where Tpeak(50) is the intercept, i.e. the time to peak effect for 50% NMBpeak (individual value for each animal), slopeNMB is the slope of the relationship between Tpeak and NMBpeak, and slopeN is the slope of the relationship between Tpeak and sequential dose number. The values 50 and 3 refer to the midrange value of the regressors NMBpeak and N, respectively. The mean value and SD of Tpeak(50) was obtained from the individual values.

The relationship between dose and Tpeak was analysed by standard multiple linear regression analysis, with the logarithm of dose, sequential dose number, and the individual animals as regressors, for each NMBA separately, according to the following equation:

where slopedose is the slope of the relationship between Tpeak and the logarithm of the dose (in μmol kg−1). The values log10(ED50) and 3 refer to the midrange values of the regressors log10(dose) and N, respectively.

The first dose administered to each animal was not taken into account in the data analysis, unless stated otherwise. Differences between NMBAs were tested using the U-test; a P value <0.05 was considered significant. Data are presented as mean ± SD.

PK-PD simulations

To investigate the expected effect of buffering on Tpeak, computer simulations were performed using the PK-PD model and data for rocuronium in pigs described by De Haes and colleagues [17,18]. In this model, buffering is taken into account by including the binding of NMBA to AChR in the effect compartment, similar to earlier models [7,8]. In these earlier models, the neuromuscular blocking effect was related to the unbound NMBA concentration in the effect compartment, which is questionable from a mechanistic point of view. In the Unbound Receptor model (URM) of De Haes and colleagues [17,18], the degree of neuromuscular block is related to the concentration of unbound AChR available for acetylcholine to bind, resulting in muscle contraction. The URM and the model parameters for rocuronium in pigs are described in the Appendix.

To investigate the influence of the dose and NMBpeak on Tpeak, the following simulations were performed. First, the dose producing x% NMBpeak (EDx) was calculated for x varying between 1% and 99% by an iterative procedure, and Tpeak was determined for each EDx. Then, ED50 and γ (Eq. (1)), Tpeak(50), slopeNMB and slopeN (Eq. (2)), and slopedose and slopeN (Eq. (3)) were estimated from the calculated values for x = 20%, 40%, 60%, 75% and 90%, similar to the experimental data as describe above. The simulations were performed with a study design similar to the experiments in pigs, i.e. an ED90 dose, followed by five consecutive doses ED20, ED40, ED60, ED75 and ED90 in a random order. This procedure was performed five times, simulating five animal studies. Similar to the experiments in pigs, the results following the first dose were not used in the data analysis.

In addition to rocuronium, two additional hypothetical NMBAs were investigated, i.e. a more potent NMBA simulated by a tenfold decrease of the dissociation constant Kd (0.04 μM), and a less potent NMBA simulated by a tenfold increase of Kd (4 μM).

Results

Totally, 21 experiments were performed (Table 1). In two experiments (one with rocuronium and one with vecuronium), the last scheduled dose could not be administered for technical reasons. In three cases, the first dose resulted in 100% block, but NMBpeak was less than 100% in all the subsequent doses used for the data analysis.

Table 1
Table 1:
Number of animals, number of doses, potency (ED50), Hill coefficient (γ) and time to peak effect of 50% block (Tpeak(50)).

The relationship between dose and NMBpeak was analysed using Eq. (1), and the results have been summarized in Table 1. The four NMBAs showed a 20-fold range in potencies, expressed in their molar ED50 values. The steepness of the dose–response relationship, expressed in the Hill coefficient γ, was not significantly different between the four compounds.

The relationship between NMBpeak and Tpeak is depicted in Figure 1 for each of the four NMBAs, and was analysed using Eq. (2). The results are summarized in Tables 1 (Tpeak(50)) and 2. The time to peak effect at 50% block (Tpeak(50)) for d-tubocurarine was significantly longer than for the other NMBAs, but the differences between rocuronium, vecuronium and pipecuronium did not reach statistical significance. However, statistical analysis of the measured Tpeak pooled for each NMBA revealed significant differences in Tpeak between any of the four NMBAs (rocuronium < vecuronium < pipecuronium < d-tubocurarine). The mean values of the measured Tpeak for all doses were close to the Tpeak(50) values listed in Table 1.

Figure 1.
Figure 1.:
Relationship between NMBpeak and Tpeak for rocuronium, vecuronium, pipecuronium and d-tubocurarine. Each line represents the data of an individual animal (n = 6 for vecuronium and n = 5 for rocuronium, pipecuronium and d-tubocurarine).

For rocuronium and pipecuronium, a significant positive correlation between NMBpeak and Tpeak was observed; for vecuronium and d-tubocurarine the slope of relationship between Tpeak and NMBpeak was close to zero, and no significant correlation was found (Table 2). Similar results were obtained by plotting Tpeak against the administered dose using Eq. (3) (Table 3).

Table 2
Table 2:
Slope of the relationship between NMBpeak and time to peak effect (slopeNMB), slope of the relationship between the sequential dose number and time to peak effect (slopeN), and the P values for the hypothesis that the slopes are zero.
Table 3
Table 3:
Slope of the relationship between the logarithm of the dose and time to peak effect (slopedose), slope of the relationship between the sequential dose number and time to peak effect (slopeN), and the P values for the hypothesis that the slopes are zero.

For vecuronium, pipecuronium and d-tubocurarine, a significant positive correlation between the sequential dose number and Tpeak was observed, both for the analysis of NMBpeak (Table 2) and dose (Table 3).

The relationship between ED50 and Tpeak(50) for the four NMBAs is shown in Figure 2.

Figure 2.
Figure 2.:
Relationship between ED50 and Tpeak(50) for rocuronium, vecuronium, pipecuronium and d-tubocurarine. The symbol represents the data of an individual animal (n = 6 for vecuronium and n = 5 for rocuronium, pipecuronium and d-tubocurarine).

PK-PD simulations

In a first series of simulations, Tpeak of rocuronium was calculated for different doses producing a peak effect of 1–99%, and the resulting relationship between NMBpeak and Tpeak is shown in Figure 3.

Figure 3.
Figure 3.:
Relationship between NMBpeak and Tpeak predicted by PK-PD simulation for three NMBAs with different potencies, i.e. Kd = 0.04, 0.4 (rocuronium) and 4 μM, respectively.

The predicted values of ED50 and γ were 0.385 μmol kg−1 and 2.81, respectively. These values agree well with the values obtained from the experimental data (Table 1). The predicted time to peak effect (Tpeak(50)) was 91 s, and was markedly higher than the observed value of 53 s. The predicted values for the slopes were slopeNMB = −0.21 s, slopeN = 0.06 s (Eq. (2)), slopedose = −28 s and slopeN = 0.07 s (Eq. (3)).

In addition to the simulations for rocuronium, this relationship was investigated in two hypothetical NMBAs, i.e. a more potent NMBA simulated by a tenfold decrease of the dissociation constant Kd (0.04 μM), and a less potent NMBA simulated by a tenfold increase of Kd (4 μM) compared with rocuronium (Kd 0.4 μM). For the more potent NMBA, Tpeak is markedly longer than for rocuronium, and is more affected by the degree of NMB (Fig. 3). For the less potent NMBA, Tpeak is shorter than for rocuronium, and is hardly dependent on the degree of NMB.

Discussion

The experimental results demonstrate that the time to peak effect of a submaximal blocking dose of NMBAs is not inversely related to dose, independent of the potency of the NMBA (Fig. 1). The PK-PD simulations of buffered diffusion predict a decrease of Tpeak with dose, and an increase of Tpeak with increasing potency (Fig. 3). These findings suggest that, even for the most potent NMBA in this study, buffered diffusion does not play a dominant role in the time to peak effect. Therefore it is unlikely that the observed inverse relationship between potency and Tpeak of NMBAs is due to buffered diffusion.

The PK-PD simulations were performed using a mechanism-based model taking into account buffered diffusion. This URM was developed to explain the changes in potency and time course of action of rocuronium in case of a decreased number of AChR, as observed in myasthenic patients and pigs [17,18]. This model is also suited to predict the changes in time course of action due to differences in potency, similar to the model proposed earlier by Donati and Meistelman [7] and Proost and colleagues [8]. Although the PK-PD model parameters were obtained from a different study, the predicted values of ED50 and γ were in good agreement with the values obtained from the experimental data. However, the predicted Tpeak (91 s) was markedly higher than the observed value (53 s). The anaesthetic and surgical procedures in both studies were comparable. The PK-PD model parameters were obtained after an infusion of rocuronium over 4–8 min, whereas in the present experiments rocuronium was administered as a bolus dose. Shortly after a bolus administration, mixing within the vascular system is the predominant distribution process, and compartmental models do not account for this process and assume an instantaneous mixing [19,20]. For this reason, short-lasting infusions are preferred in PK-PD studies [21]. The observed difference between the simulated and experimental values of Tpeak may be related to this phenomenon.

The relationship between dose and NMBpeak (Eq. (1)) was analysed by an iterative two-stage Bayesian population fitting procedure for each NMBA separately [15,16]. The use of a population analysis is nowadays standard practice in PK and PK-PD analysis, because it allows a robust and reliable estimation of the mean and SD of the model parameters, as well as individual parameter values of ED50 and Hill coefficient (γ). For the relationships between NMBpeak and Tpeak (Eq. (2)), and dose and Tpeak (Eq. (3)), we used standard multiple regression analysis, allowing the estimation of a single value for slopeNMB and slopeN, and slopedose and slopeN, respectively.

An initial dose of the estimated ED90 was administered to allow a better prediction of the individual doses needed to achieve the aimed levels of block. To avoid bias due to a possible difference between the first dose (aiming at 90% block) and subsequent doses given at 45 min after complete recovery of the twitch response (aiming at 20%, 40%, 60%, 75% or 90% block, in a random order) with respect to the degree of block or Tpeak, we excluded the data of the first dose from the analysis, ensuring similar starting conditions for each measurement, i.e. 45 min after complete recovery of the twitch response from a previous dose.

A possible difference between the first dose and subsequent doses was investigated for all NMBAs simultaneously by the following exploratory analysis. The mean ± SD Tpeak of the first dose was 79 ± 26 s (n = 18; in three animals Tpeak could not be measured because complete block was reached). Tpeak of the second dose in the same animals was significantly shorter: 70 ± 23 s (P = 0.012). This difference may be related to the observed dose effect on Tpeak, because the first dose was close to ED90, whereas the average of the second dose was close to the ED50. The time to the highest dose (dose comparable to the first dose) was 86 ± 25 s (P = 0.14, compared to first dose), an increase corresponding to the observed increase of Tpeak with subsequent doses. These results indicate that Tpeak after the first dose is not markedly different from that of subsequent doses. In addition, we compared the observed NMBpeak after the first dose with the calculated NMBpeak from Eq. (1), using the individual values of ED50 and γ obtained from the analysis of the data of the subsequent doses, as reported in Table 1. The mean ± SD observed NMBpeak after the first dose was 90 ± 9%; the calculated NMBpeak (mean ± SD 86 ± 9%) was slightly, but significantly lower (P < 0.001). This indicates that the neuromuscular junction may be less sensitive to NMBA at the first dose than at subsequent doses. If residual receptor occupancy plays a role, one would expect that the neuromuscular junction becomes more sensitive after an initial dose. This observation suggests that the interval between the experiments (45 min after complete recovery) was sufficiently long to ensure that residual receptor occupancy does not unduly influence the results of our experiments.

Interestingly, we found a positive correlation between NMBpeak, or dose, and Tpeak for rocuronium and pipecuronium, whereas no correlation was found for vecuronium and d-tubocurarine. This discrepancy does not seem to be related to potency. The ‘buffering hypothesis' predicts a negative correlation between NMBpeak, or dose, and Tpeak for potent NMBAs, and a less negative or no correlation for less potent NMBAs. Therefore it can be concluded that buffered diffusion does not play a role in the time to peak effect of NMBAs in the studied potency range, which is comparable to the potency range of NMBAs in current or former clinical use, i.e. ED50 ranging from 0.02 μmol kg−1 for doxacurium to 2 μmol kg−1 for rapacuronium. In contrast, it has been published that the onset time of atracurium and vecuronium [22], and the highly potent doxacurium [23] decreases with dose, but these authors did not discriminate between submaximal peak effect and complete block. The latter situation is more likely with higher doses and results in a shorter onset time compared to Tpeak after a submaximal blocking dose; however, this does not reflect the time of maximal concentration in the biophase, or maximal receptor occupancy, as in the case of a submaximal peak effect. Therefore these data are insufficient to demonstrate that Tpeak decreases with dose.

If buffered diffusion can be excluded as a dominant factor, differences in pharmacokinetics are likely to be responsible for the observed inverse relationship between potency and Tpeak of a submaximal blocking dose [24-26], and confirmed in our study (Fig. 2) [5,7-9]. This finding is in agreement with earlier studies in the isolated perfused tibialis model in the rat [27]. We found that the rates of recovery of rocuronium and pancuronium were similar, in spite of a fourfold difference in potency, i.e. in the concentration needed to reach a stable 90% block. It should be noted that differences in ke0 are also responsible for differences in Tpeak [9]. An increase in ke0 results in a decrease of Tpeak, and a simultaneous decrease of ED90; therefore differences in ke0 do not explain the observed inverse relationship between potency and Tpeak [8].

We do not have an explanation for the apparent discrepancy between the positive values for slopeNMB of rocuronium and pipecuronium, and the values close to zero for vecuronium and d-tubocurarine. Bias due to a temporal effect was excluded by randomization of the sequence of the doses. Possibly rocuronium and pipecuronium affect the blood perfusion of the muscle by a local pharmacodynamic effect. It was demonstrated that several less potent NMBAs possess calcium channel blocking effects in vascular smooth muscle [28], possibly resulting in local vasodilatation, and thus a faster onset of block. Therefore this mechanism does not explain the observed increase of Tpeak with dose. However, a possible role of blood perfusion, e.g. due to a dose-dependent local vasoconstriction, is still likely, as this is the assumed mechanism for the decrease of onset time of rocuronium by ephedrine, and the increase by esmolol [29]. In the latter study, ‘onset time' was the time to reach complete block (disappearance of all four twitches of a train-of-four; data on the influence of these drugs on Tpeak of a submaximal blocking dose are not available.

The observed increase of Tpeak with dose of rocuronium and pipecuronium would imply that the value of ke0, the rate constant of transport between plasma and biophase, obtained from a PK-PD analysis, would decrease with dose. A decrease of ke0 (and increase of EC50) with increasing dose was found in man for cisatracurium, a NMBAs of intermediate potency [30], although this has been disputed [31]. We are not aware of other studies demonstrating any effect of dose on the PK-PD model parameters.

For vecuronium, pipecuronium and d-tubocurarine, a significant positive correlation between the sequential dose number and Tpeakwas observed, both for the analysis of NMBpeak (Table 2) and dose (Table 3). This implies that Tpeak increased for subsequent doses; for pipecuronium and d-tubocurarine this increases was about 5 s for each dose. This effect of dose number seems to be uncorrelated to the effect of NMBpeak and dose on Tpeak, since these effects do not occur to the same extent in the four NMBAs. A possible explanation of the observed increase of Tpeak may be found in a decreasing muscle perfusion during the experimental period, e.g. due to decrease of cardiac output or local vasoconstriction.

In conclusion, time to peak effect of a submaximal blocking dose of NMBAs is not inversely related to dose. This finding suggests that buffered diffusion does not play a dominant role in the time to peak effect of NMBAs in the clinical range. Therefore it is unlikely that the observed inverse relationship between potency and time to peak effect of NMBAs is due to buffered diffusion.

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Appendix

Unbound receptor model

Usually, 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 [6-8]. However, this assumption is flawed from a mechanistic point of view, because the effect is the result of binding of the NMBA 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 NMBA. This hardly affects the model in a qualitative way, since the unbound concentration and the bound concentration are strongly correlated.

We developed a mechanism-based PK-PD model to explain the changes in potency and time course of action of rocuronium in case of a decreased number of AChR, as observed in myasthenic patients and pigs [17,18]. This model is also suited to predict the changes in time course of action due to differences in potency, similar to the model proposed earlier by Donati and Meistelman [7] and Proost and colleagues [8].

NMBAs 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):

where THmax is the maximum TH, i.e. TH in the case that 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 β is an exponential coefficient.

In the absence of NMBA, the concentration of free receptors equals the total receptor concentration; on substitution in Eq. (4) it follows:

where THc is the TH in the absence of NMBA (control) and Rtot is the total receptor concentration.

The neuromuscular blocking effect (E) of a NMBA is defined as

Substituting Eqs (4) and (5) in Eq. (6) yields

Eq. (7) describes the neuromuscular blocking effect as a function of the free AChR concentration. Total AChR concentration (Rtot), Rfree50 and β are system parameters, and are independent of the NMBA [32].

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

where Cue is the unbound concentration of NMBA 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 a NMBA molecule is bound.

Defining Rtot as the total concentration of AChR binding sites, it follows upon rearrangement:

The time course of the unbound concentration in the effect compartment (Cue) can be evaluated as described earlier [8]. Eq. (16) of that paper was simplified, not taking into account plasma protein binding and non-specific binding in the effect compartment, resulting in (10)

where C is the concentration in the central compartment (plasma concentration) and ke0 is the transport rate constant between the central compartment and effect compartment.

We assume that binding is very fast compared to the kinetic processes, so at any time equilibrium is assumed, i.e. Eq. (8)is valid at any time.

The PK-PD parameters were obtained from control animals of an earlier study [18]. The system parameters were Rtot = 1.47 μM, Rfree50 = 0.19 μM and β = 2.84. The PD and PK-PD link parameters for rocuronium were Kd = 0.40 μM and ke0 = 0.93 min−1, respectively. The pharmacokinetics of rocuronium was described by a two-compartment model with parameters clearance (CL) = 26 mL min−1 kg−1, volume of central compartment (V1) = 53 mL kg−1, distribution clearance (CL12) = 10.5 mL min−1 kg−1 and volume of peripheral compartment (V2) = 90 mL kg−1.

Keywords:

NEUROMUSCULAR BLOCKING AGENTS; PHARMACOKINETICS; PHARMACODYNAMICS; SWINE

© 2008 European Society of Anaesthesiology