Introduction

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According to World Health Organization recommendations, pharmacologic treatment with morphine is considered the standard in alleviating moderate to severe pain associated with neoplastic disease (WHO, 1986). Morphine can be administered to cancer patients via different modes and routes, such as p.o. (as a solution or as fast-acting or sustained-release tablets), i.v. (continuous infusion and/or multiple i.v. boluses), intrathecally and epidurally. Tolerance, manifested clinically as an increase in the dose required over time to maintain a pain-free state, develops to the analgesic effect of morphine (Säwe et al., 1983; Portenoy et al., 1986; Gourlay et al., 1991). Investigations of morphine analgesia during chronic therapy, and in particular quantitative studies of the kinetics of tolerance development in cancer patients, are difficult to conduct because of interindividual variations in perception of and reaction to pain, the absence of precise assessments of pain relief and changes in dose requirements that result from progression of the underlying disease. Thus quantitative information on the rate and extent of tolerance development is limited despite the prevalence of this phenomenon.

Animal studies investigating tolerance to morphine have focused on the tolerant and/or dependent state rather than on the kinetics of tolerance development. Tolerance to morphine antinociception in rats has been shown to develop rapidly, i.e., within 8 to 12 hr during continuous i.v. infusion (Ling et al., 1989; Kissin et al., 1991; Ouellet and Pollack, 1995a). A longer period (7-10 days) is required for tolerance development during administration of morphine as multiple s.c. or i.p. bolus doses (Yamamoto et al., 1988; Trujillo and Akil, 1991). It is not known whether these results reflect different underlying mechanisms of tolerance (i.e., acute vs. chronic) between prolonged and repeated exposure to morphine or are an artifact of the experimental design. PK-PD models are used to predict the intensity and duration of pharmacologic effect in relation to the systemic concentrations of the drug (Holford and Sheiner, 1982; Dingemanse et al., 1988). However, only a few models have been developed to examine how the decrease in pharmacologic response over time that results from tolerance development is related to the systemic disposition of the drug (Porchet et al., 1988; Kroboth et al., 1988; Ekblom et al., 1993). Although PK-PD models are empirical in nature, defining the link between the kinetics of tolerance development and the kinetics of morphine disposition with different modes of administration may provide some indication of the underlying mechanism(s) involved. Recently, a PK-PD model of tolerance was constructed to describe both the development of tolerance to morphine-induced antinociception during a 12-hr continuous i.v. infusion and the kinetics of tolerance offset after cessation of drug administration (Ouellet and Pollack, 1995a). However, the applicability of this model to alternative modes of morphine administration remains to be evaluated.

The objectives of the experiments reported herein were 1) to evaluate morphine-induced antinociception, including the intensity and duration of the pharmacologic response, after the administration of multiple increasing i.v. bolus doses within a 12-hr period or over 13 days; 2) to characterize the rate and extent of tolerance development during each treatment regimen; and 3) to evaluate the PK-PD model of tolerance defining the link between the systemic disposition of morphine and the time course of antinociception.

	Materials and Methods

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Animals. Experiments were conducted in male Sprague-Dawley rats (Hilltop Laboratory Animals Inc., Scottdale, PA) weighing between 300 and 370 g. All rats were housed in temperature-controlled rooms with a 12-hr light/dark cycle and were acclimated a minimum of 5 days before experimentation. Implantation of a silicone rubber cannula in the right jugular vein was performed under light ether anesthesia the day before the study period.

Materials. Morphine (as the sulfate salt; Research Biochemicals Inc., Natick, MA) was dissolved in sterile normal saline for drug administration. Nalorphine hydrochloride and M3G were purchased from Sigma Chemical Co. (St. Louis, MO). All other reagents and solvents were obtained from commercial sources and were of the highest purity standard available.

Analgesia assessment. Antinociception was evaluated with the standard hot water-induced tail flick. Briefly, rats were placed in Plexiglas restraining cages 30 min before tail-flick testing. The distal 5 cm of the tail was immersed in water (50°C), and the time to withdrawal of the tail was measured in duplicate immediately before the first morphine dose and at timed intervals during the remainder of the study. A cutoff time of 15 sec was used to minimize tissue damage. Antinociception was expressed as % MPR):

(1)

Analysis of the data in this manner allows for (1) expression of the degree of response relative to a fixed maximum and (2) correction of antinociceptive response data for interanimal variability in the response to the nociceptive stimulus. In a separate validation experiment (G. Pollack, S. Letrent and M. Bush, unpublished results), duplicate base-line tail-flick responses were measured in a group of 32 rats identical in strain and size to those in the present study. Using analysis of variance techniques to partition the source of variance, we found the between-animal coefficient of variation to be 32.3%; the within-animal coefficient of variation was estimated as 8.5%. Thus incorporation of the base-line measurement in the expression of morphine-induced antinociception should improve between-animal reproducibility substantially.

Morphine administration. Morphine was administered i.v. as a bolus according to two different dosing regimens: a 12-hr TXT, in which multiple increasing doses of morphine were administered within a 12-hr period, and a 13-day TXT, in which morphine was administered once a day for 13 days. These dosing intervals were selected on the basis of predictions derived from a previously published PK-PD model for tolerance development during continuous morphine infusion (Ouellet and Pollack, 1995a). Rats (n = 4) included in the 12-hr TXT received a total of 24 mg/kg in 7 doses (1.85 [at time 0 hr], 2.15 [1 hr], 3 [2 hr], 3.5 [4 hr], 4 [6 hr], 4.5 [8 hr] and 5 mg/kg [10 hr]). Antinociceptive effect was assessed at base line (0 hr); at timed intervals after dose 1 (0.125, 0.25, 0.5 and 1 hr); at peak effect, i.e., at 0.25 hr after doses 2 to 6 (1.25, 2.25, 4.25, 6.25 and 8.25 hr); and before and at timed intervals after dose 7 (10, 10.125, 10.25, 10.5, 11 and 12 hr). Control rats (n = 3) received injections of normal saline according to the same schedule. Blood (0.1-0.3 ml) was withdrawn from the jugular vein immediately after pharmacologic assessment, and an additional sample was obtained before the administration of each of doses 2 to 6. In the 13-day TXT, rats (n = 5) received i.v. bolus doses of morphine every morning (1.85 [days 1 and 2], 2.35 [days 3 and 4], 3.5 [days 5 and 6], and 6 [days 7-13] mg/kg). Antinociception was evaluated at base line and at timed intervals (0.125, 0.25, 0.5, 1 and 2 hr after dose) on days 1, 3, 5, 7, 9, 11 and 13, and at peak effect (0.25 hr after dose) on alternate days. Rats (n = 3) that received injections of normal saline were included as controls. Blood (0.1 ml) was withdrawn from the jugular vein immediately after pharmacologic assessment. Samples were centrifuged for 10 min, and the serum was harvested and stored at 20°C pending analysis.

Morphine and M3G assay. Serum concentrations of morphine and its major metabolite, M3G, were quantitated by a sensitive and specific HPLC method with fluorescence detection. Chromatographic separation was achieved by constant-flow (1 ml/min) gradient elution after extraction of the sample with a solid-phase procedure. The method was modified from procedures described by Glare et al. (1991) and Venn and Michalkiewicz (1990) and is explained in detail by Ouellet and Pollack (1995b). Detection limits for morphine and M3G were 25 ng/ml and 37.5 ng/ml, respectively.

Pharmacokinetic-pharmacodynamic modeling. The scheme depicting the PK-PD model of tolerance to morphine-induced analgesia is presented in figure 1. Morphine disposition after administration of multiple i.v. bolus doses can be described by either one or two pharmacokinetic compartments, with elimination occurring from the central compartment according to the first-order rate constant k₁₀. Two hypothetical compartments, linked to the central compartment of volume V_c by first-order rate constants, are used to model pharmacologic response and tolerance development; this scheme is similar to the model described by Porchet et al. (1988). The measured analgesic effect results from the interaction between drug in the effect compartment (C_e), which is assumed to produce the desired pharmacologic effect, and drug in the tolerance compartment (C_t), which is assumed to attenuate the effect mediated by C_e, according to equation 2:

(2)

This model, which involves the interaction between the agonist (concentration C_e) and a hypothetical partial agonist (concentration C_t), was selected according to standard statistical criteria based on its ability to describe both the onset of tolerance during a 12-hr i.v. infusion of morphine and the offset of tolerance occurring over approximately 20 days after cessation of the infusion (Ouellet and Pollack, 1995a). Analysis of the pharmacodynamic data obtained during and after continuous morphine infusion indicated that the values of  for agonist and hypothetical partial agonist concentrations were indistinguishable. Thus a single shape factor was used for both dynamic compartments in the present analysis.

View larger version (16K): [in this window] [in a new window]   Fig. 1.   Scheme describing the PK-PD model of tolerance. This scheme represents the disposition of morphine after i.v. bolus dosing with two pharmacokinetic compartments. The pharmacodynamic data are described with two hypothetical compartments linked to the central compartment by first-order rate constants. The measured analgesic effect results from the interaction between drug accumulating in the effect compartment and drug accumulating in the tolerance compartment.

Data analysis. The model describing systemic morphine disposition was fit to the serum morphine concentration vs. time profile of each rat to determine the relevant pharmacokinetic parameters. Using the individual pharmacokinetic parameter estimates, we fit the pharmacodynamic model (with or without a tolerance compartment, as appropriate) to individual effect vs. time profiles. All relevant parameters were obtained by nonlinear least-squares regression analysis (PCNONLIN version. 3.0, SCI, Apex, NC). Assessment of the goodness of fit of the model to the observed data was based on Akaike's Information Criterion (AIC), residual plots, coefficients of determination and standard error of the estimates. Because significant variability existed in individual pharmacodynamic profiles, simulations were performed with the pharmacokinetic parameters obtained from mean morphine concentration vs. time profiles and compared with mean dynamic data.

	Results

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In general, both treatments were tolerated well by the rats. Weight loss during the course of 13-day TXT was minimal; mean body weights at the beginning and the end of the treatment period were 335 and 325 g, respectively (P = .42, paired t test). Two out of 5 rats failed to complete the entire treatment period, and the experiment was terminated on days 8 and 10. The rat sacrificed on day 8 was excluded from the data analysis because of the short duration of treatment.

Representative morphine and M3G serum concentration vs. time profiles are presented in figures 2 and 3 for the 12-hr TXT and 13-day TXT, respectively. A two-compartment pharmacokinetic model was used to describe the serum concentration data in 3 out of 4 rats in each treatment group; a one-compartment model only could be supported in the remaining animals. The pharmacokinetics of morphine appeared to be constant over time and with increasing doses. Complete washout occurred within 24 hr; in 3 out of 4 rats, morphine was undetectable in serum samples obtained immediately pre-dose during the 13-day TXT. Morphine disposition was similar in the 12-hr TXT and 13-day TXT; the results are summarized in table 1. A large degree of interanimal variability was observed in M3G concentrations (more than 3-fold) after morphine administration. The metabolite accumulated to a greater extent than the parent compound, with significant concentrations being measured in predose samples during the 13-day TXT.

View larger version (22K): [in this window] [in a new window]   Fig. 2.   Morphine (panel A) and M3G (panel B) serum concentration vs. time profiles in a representative rat exposed to 12-hr TXT. Line represents the fit of the pharmacokinetic model to serum morphine data; lines for M3G (which was not included in the kinetic model) serve to emphasize temporal relationships.

View larger version (22K): [in this window] [in a new window]   Fig. 3.   Morphine (panel A) and M3G (panel B) serum concentration vs. time profiles in a representative rat exposed to 13-day TXT. Line represents the fit of the pharmacokinetic model to serum morphine data; lines for M3G (which was not included in the kinetic model) serve to emphasize temporal relationships. For clarity, only data from complete profiles (on odd days) are presented.

Initial analysis of the pharmacologic response data was based on normalization of peak antinociceptive effect during each dosing interval for the morphine serum concentration at the time of pharmacologic measurement. This normalization scheme was selected to account for increasing morphine concentrations during dose escalation. This approach assumes that over the relatively limited range of peak morphine concentrations within a given animal (figs. 2 and 3), the relationship between antinociceptive response and concentration should be approximately linear. Concentration-normalized peak response decreased during the 13-day TXT from day 1 to 8 (ANOVA, P < .05) and remained stable thereafter until the end of the treatment period (fig. 4B). In contrast, normalized peak effect remained relatively constant during the 12-hr TXT, although an apparent decrease in response was evident over the final three dosing intervals. Overall, this result suggests that little or no tolerance developed (fig. 4A).

View larger version (17K): [in this window] [in a new window]   Fig. 4.   Morphine concentration-normalized peak analgesic effect (symbols [mean ± S.E.]; left axis) and dose (line; right axis) vs. number of doses administered during 12-hr TXT (panel A) and 13-day TXT (panel B). Absence of error bars indicates a standard error that falls within the size of the symbol.

A PK-PD model with an effect compartment only was used to fit the pharmacodynamic data during the 12-hr TXT because no apparent tolerance was incurred during the 12-hr morphine administration period; the results of this analysis are presented in table 2. Representative antinociceptive effect vs. time profiles for treated and control rats are presented in figure 5. Tail-flick latencies in control rats remained constant over the 12-hr period, a result that might be interpreted as indicating the absence of tolerance. However, it should be noted that the administered dose of morphine was increased with each dosing interval; the associated increase in morphine concentration (figs. 2 and 3) masked the development of tolerance. Using the entire effect vs. time profile to estimate the pharmacodynamic parameters tended to underestimate the duration of the pharmacologic response after administration of the first dose. To assess whether tolerance resulted in a change in the shape of the pharmacologic response profile rather than a change in the peak effect, the PK-PD model was fit to truncated data, i.e., the effect data measured after doses 1 to 3 vs. doses 4 to 7. The data were truncated after the third dose (administered at 2 hr) because tolerance has been shown to become significant starting at 2 to 3 hr during continuous i.v. infusion (Ouellet and Pollack, 1995a). Thus the data from doses 1 to 3 should represent a nontolerant state, whereas those from doses 4 to 7 should be associated with tolerance. No significant differences were observed in the estimates for EC₅₀ (P = .42, paired t test) and  (P = .50, paired t test) on the basis of the data from doses 1 to 3 vs. doses 4 to 7. However, the value of k_e0 was smaller in all rats when the truncated profile (doses 1-3) was used, with a mean difference of 155% (P = .032, paired t test) compared with doses 4 to 7. 

View larger version (25K): [in this window] [in a new window]   Fig. 5.   Analgesic effect vs. time profiles in representative rats exposed to morphine () or saline (+) during 12-hr TXT (panel A) or to morphine () or saline (+) during 13-day TXT (panel B). Lines represent the fit of the PK-PD model without (panel A) and with (panel B) a tolerance compartment.

The PK-PD model of tolerance depicted in figure 1 was used to fit the pharmacodynamic response during 13-day TXT. The effect vs. time profiles after morphine administration (odd days only) for representative treated and control animals are depicted in figure 5. Tail-flick latencies remained constant in the control condition. Mean parameter estimates for the PK-PD model of tolerance are summarized in table 2. The fit of the model to the data in general was good, although it underestimated the pharmacologic response after administration of the first dose of morphine. The model presented in figure 1 was developed to describe the onset and offset of tolerance to a 12-hr i.v. infusion of morphine (Ouellet and Pollack, 1995a). The pharmacodynamic parameter estimates obtained during morphine infusion are presented in table 2 to allow comparisons between studies. Parameter estimates for the pharmacologic effect of morphine appeared consistent among the three groups. Differences were noted in the parameters of the model describing tolerance development: k_t0 and IC₅₀ were somewhat larger and I_max was smaller with the 13-day TXT as compared with infusion. However, considering the difference in study design, the parameters recovered in the two experiments were comparable.

	Discussion

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The development and offset of tolerance to morphine during and after a 12-hr infusion have been quantitated previously (Ouellet and Pollack, 1995a). Antinociceptive effect peaked between 2 and 3 hr after the start of the infusion and declined thereafter despite sustained morphine concentrations, which suggests the development of tolerance within this time period. One objective of the present experiment was to compare the rate and extent of tolerance development during intermittent (multiple i.v. bolus) exposure to morphine with that incurred during a continuous infusion. The dose of morphine given in the 12-hr TXT (total dose 24 mg/kg) was equivalent to the average dose administered previously by infusion (2 mg/kg/hr for 12 hr). Using this experimental design, we could detect no tolerance by examining the concentration-normalized peak effect. This observation was not unexpected and was consistent with the simulated effect vs. time profile generated from the infusion tolerance model; only a small decrease in the intensity of the pharmacologic response was predicted to occur during 12-hr TXT, and this difference became apparent only over the last three doses administered (fig. 6). Such a small difference would probably be masked by the variability in dynamic response. The 12-hr TXT data therefore are consistent with the model developed previously, a result that suggests that comparable rates and extents of tolerance development can be associated with different modes of morphine administration.

View larger version (20K): [in this window] [in a new window]   Fig. 6.   Mean ± S.E. effect vs. time profile during 12-hr TXT. Lines represent the simulated profiles generated with parameters estimated from the fit of the PK-PD model of tolerance during the infusion experiment with () and without (- - -) a tolerance compartment (panel A) or parameters obtained from the 13-d TXT experiment (- - -; panel B).

It was hypothesized that tolerance development was more apparent during continuous infusion because of the difference between k_e0 and k_t0. To explain the discrepancy in the appearance of tolerance, the effect and tolerance compartment concentration vs. time profiles during dosing with morphine as an infusion and as boluses (12-hr TXT) were simulated on the basis of the infusion PK-PD model (fig. 7). Because of the low rate constant for tolerance development (t_1/2 = 5.7 days based on the k_t0 value from the infusion model), the concentrations driving tolerance development (C_t) were almost superimposable whether morphine was infused or administered as repeated bolus doses. In contrast, the concentrations in the effect compartment more directly reflected morphine kinetics in serum, and a steady state was reached rapidly after the start of the infusion (t_1/2 ~ 10 min; k_e0). During the infusion study, the decrease in pharmacologic effect became apparent after 3 hr. During the 12-hr TXT, as the dose was increased continuously with each bolus administered, higher morphine concentrations were attained that presumably masked the development of tolerance, and no equilibrium was reached between the effect and tolerance compartments.

View larger version (17K): [in this window] [in a new window]   Fig. 7.   Predicted concentration vs. time profiles in the effect (panel A) and tolerance (panel B) compartments during the infusion (- - -) and the 12-hr TXT () experiments. The profiles were simulated on the basis of the model from the infusion experiment.

The underlying hypothesis of this study was that the rate and extent of tolerance development are a function of the kinetics of drug administration and disposition and that the same PK-PD model could be used to describe pharmacologic response and tolerance development with different modalities of drug administration. Similar estimates were obtained among the three groups (i.e., 12-hr TXT, 13-day TXT and infusion) for the pharmacodynamic parameters driving the pharmacologic response to morphine (table 2). However, when the tolerance model was fit to the 13-day TXT data, differences were observed in the estimates of the parameters governing tolerance development: a substantially larger k_t0 (6.7-fold) and a minor increase in IC₅₀ (1.6-fold) for 13-day TXT as compared with infusion. The overall predictability of each set of parameter estimates (infusion vs. 13-day TXT) was evaluated by estimating the analgesic effect during the alternative mode of administration (i.v. boluses over 12 hr and infusion or i.v. boluses over 13 days). The results are presented as a comparison between observed analgesic effect and predicted data for the two sets of parameters (fig. 8). The parameters obtained during the infusion experiment tended to describe all dynamic data better, although they overestimated somewhat the analgesic effect during 13-day TXT. The parameter estimates from the 13-day TXT data predicted a large and rapid decrease in pharmacologic response with multiple bolus doses administered within 12 hr (fig. 6). Comparisons between parameters from the infusion and the 13-day TXT data are difficult to draw, because the influence of an increase in IC₅₀ on the dynamic profile is offset by an increase in k_t0. Because of the larger number of animals used during the infusion studies (n = 4-6/group; five dose groups), the large range of concentrations obtained during administration of fixed infusion rates (200 to >600 ng/ml morphine), and because the model was able to describe the offset of tolerance data, more confidence was placed in the I_max and IC₅₀ estimates generated during the infusion experiment. Thus the value of k_t0 was estimated for 13-day TXT by holding I_max and IC₅₀ constant. The k_t0 value estimated using these restrictions was 0.00730 ± 0.00262 hr¹, which corresponds to a half-life for tolerance onset and offset of 3.9 days, a value similar to that obtained during the infusion experiment.

View larger version (19K): [in this window] [in a new window]   Fig. 8.   Predicted vs. observed effect data across three modes of morphine administration. Predicted antinociceptive effects were based on the PK-PD parameters obtained during the infusion experiment (panels A and B) and the 13-day TXT experiment (panel C). Observed effect data were obtained from the 12-hr TXT experiment (panels A and C) and the 13-day TXT experiment (panel B). Symbols represent individual observations; the line represents the line of identity.

On the basis of the time required for tolerance to develop, a distinction has been made between acute and long-term tolerance to morphine analgesia (Gårdmark et al., 1993; Hovav and Weinstock, 1987; Rosenfeld and Burks, 1977). However, it is not clear whether this difference in the apparent rate of tolerance development reflects a difference in the underlying mechanism responsible for tolerance or differences in the method of quantifying tolerance development. The rate of tolerance development is dependent on several experimental factors, such as the dose and schedule of drug administration, the duration of drug exposure (e.g., constant infusion vs. bolus) and the method of assessment of pharmacologic response (e.g., peak effect vs. entire profile). The mathematical model used herein to describe the development of tolerance predicts that the loss of effect depends on both systemic drug concentrations and duration of exposure. Recently, a similar PK-PD model was published that described chronic tolerance development with morphine infusion and the rebound effect after morphine exposure (Ekblom et al., 1993). The same model was applied to describe the development of "acute" tolerance in a study in which very large doses of morphine were infused over a relatively short interval (10, 60 and 180 min), targeting a serum morphine concentration of 7100 ng/ml at the end of the infusion (Gårdmark et al., 1993). This model was based on a reverse agonist-agonist interaction to describe the loss of pharmacologic response due to tolerance development. Different rates of tolerance development were estimated, with corresponding half-lives of 48 min and 26 hr for the development of acute and chronic tolerance, respectively. A similar model was evaluated previously but failed to describe the offset of tolerance after a 12-hr morphine exposure (Ouellet and Pollack, 1995a). In the present study, a single PK-PD model was found to describe morphine pharmacodynamics during a continuous infusion and with repeated bolus doses.

Theoretically, PK-PD models can be used to optimize drug administration regimens by providing a better understanding of the factors that control the onset of pharmacologic response and the rate and extent of tolerance development in relation to the kinetics of drug exposure. For example, PK-PD models have been constructed to explain the pattern of use in relation to the intensity of pharmacologic effect and tolerance with nicotine and caffeine ingestion (Porchet et al., 1988; Shi et al., 1993). In both cases, the half-lives of tolerance onset and offset were short (35 min and 1 hr, respectively), which made possible the abatement or maintenance of tolerance during the course of the day, depending on the frequency of administration. The results presented herein suggest that optimization of the morphine dosing regimen to minimize tolerance development is not practical, because the half-life for tolerance onset and offset is too long to allow significant sensitization between intermittent doses. As shown in the 13-day TXT, increasing the interval between doses to 1 day does not reduce the magnitude of tolerance development. We therefore concluded that about the same degree of tolerance is achieved whether morphine is administered as a continuous infusion or as intermittent i.v. boluses.