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Cerebral and lung kinetics of morphine in conscious sheep after short intravenous infusions
British Journal of Anaesthesia 90 (6): 750±8 (2003)
DOI: 10.1093/bja/aeg131
LABORATORY INVESTIGATIONS Cerebral and lung kinetics of morphine in conscious sheep after short intravenous infusions R. N. Upton1*, G. L. Ludbrook1, A. M. Martinez1, C. Grant1 and R. W. Milne2 1
Department of Anaesthesia and Intensive Care, Royal Adelaide Hospital, University of Adelaide, SA 5005 Adelaide, Australia. 2Centre for Pharmaceutical Research, School of Pharmacy and Medical Sciences, University of South Australia, Adelaide, Australia *Corresponding author. E-mail: [email protected]
Methods. Sheep were given short i.v. infusions of morphine (30 mg over 4 min). Cerebral kinetics were inferred from arterio±sagittal sinus concentration gradients and cerebral blood ¯ow, and lung kinetics from the pulmonary artery±aortic gradient and cardiac output. These data were ®tted to ¯ow- and membrane-limited models of the kinetics in each organ. Results. Morphine had minimal cardiovascular effects, did not alter cerebral blood ¯ow and caused insigni®cant respiratory depression. Lung kinetics were best described by a single distribution volume (2036 ml) with a ®rst-order loss (1370 ml min±1), which was attributed to deep distribution. The cerebral kinetics of morphine were characterized by a signi®cant permeability barrier. Permeability across the barrier (7.44 ml min±1) was estimated with good precision, and was approximately one-®fth of the nominal cerebral blood ¯ow. The distribution volume of morphine in the brain was estimated with less precision, but was described by a brain:blood partition coef®cient of approximately 1.4. The time required for 50% equilibration between brain and blood concentrations was approximately 10.3 min. Conclusion. The cerebral equilibration of morphine was relatively slow, and was characterized by signi®cant membrane limitation. Br J Anaesth 2003; 90: 750±8 Keywords: analgesics opioid, morphine; brain; lung, function; pharmacokinetics; sheep Accepted for publication: February 10, 2003
The time course of the cerebral effects (e.g. analgesia, changes in the EEG) of many clinically used opioids lag behind their concentration in blood.1 As this lag is similar in magnitude to the time required for equilibration of the central nervous system (CNS) concentrations with blood concentrations, it has been proposed that CNS equilibration is a major component of the lag.2 Furthermore, differences in the rate of CNS equilibration between opioids appear to correspond to their clinically observed duration of action
after i.v. bolus administration.2 This delayed equilibration becomes of particular clinical signi®cance in postoperative patients in whom multiple doses of parenteral opioids are titrated against pain levels, such as when patients are `loaded' with opioid in the recovery ward, or during subsequent patient-controlled analgesia. Simulations of CNS opioid concentrations in these settings were found to be more consistent with clinical experience than simulations of blood concentrations.2 While many aspects of this type of
Ó The Board of Management and Trustees of the British Journal of Anaesthesia 2003
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Background. The analgesic effects of morphine are delayed relative to its concentration in blood. The rate of equilibration of morphine between blood and brain may contribute to this delay, but the kinetics of this process have not been modelled. This was determined in conscious instrumented sheep. The lung kinetics of morphine were also determined given their importance in de®ning systemic kinetics after i.v. bolus administration.
Cerebral kinetics of morphine in sheep
Methods Animal preparation All experimental procedures were approved by the Animal Ethics Committee of the University of Adelaide. Female Merino sheep of similar ages and body mass (approximately 50 kg) were used, and were instrumented under general anaesthesia as reported previously.3 Catheters were chronically implanted via the femoral vessels in the abdominal aorta (for sampling of arterial blood), in the right atrium (for drug administration), in the pulmonary artery (for blood sampling and thermodilution measurement of cardiac output), and in the dorsal sagittal sinus (the appropriate site for sampling cerebral venous blood in sheep13). A Doppler transducer was placed over the sagittal sinus using a previously validated method to provide an index of cerebral blood ¯ow.13 14 After recovery from anaesthesia, the sheep were housed in metabolic crates and their catheters maintained with a saline/heparin lock (0.9%/50 i.u. ml±1).
Study design Six sheep were studied. For each study, instrumented sheep were placed in non-weight-bearing slings inside metabolic crates and were prepared for physiological measurements and blood sampling. After a period of baseline measurements, an i.v. morphine infusion (morphine sulphate injection, David Bull Laboratories, Mulgrave, Victoria, Australia) was begun at time zero at a rate of 7.5 mg min±1 for 4 min. The sheep were not intubated, and breathed room air spontaneously throughout. For each study, the following data were collected. Pharmacokinetic measurements
Cerebral pharmacokinetics were determined from simultaneous measurements of arterial and sagittal-sinus drug concentrations and cerebral blood ¯ow, as performed previously in this preparation.3 Arterial and sagittal-sinus blood samples (0.5 ml) were taken at 0, 0.5, 1, 1.5, 2, 3, 4, 4.5, 5, 5.5, 6, 8, 10, 15, 20, 30, 45, 60 and 75 min after the start of the infusion. Lung pharmacokinetics were determined in an analogous manner, from pulmonary arterial samples taken at the same times as the arterial samples. Whole-blood samples were stored frozen (±20 °C) before assay. Morphine is stable for up to 2 years at this temperature.15 Although some studies of drug uptake into organs have used concurrent intravascular markers, no such marker was used in the present study as previous experience and computer simulations suggested that intravascular transit times for both organs were too rapid to be resolved using the proposed blood sampling schedules.
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kinetic analysis based on global CNS concentrations of opioids are speculative, it is clear that future kinetic± dynamic analysis of opioids will require, in part, suf®cient understanding of the cerebral kinetics of each opioid so that the time course of global CNS concentrations can be predicted in various circumstances. This requires identi®cation of a structural model of the cerebral kinetics of the opioid, with suf®cient data to reliably estimate parameter values for the model. Such models have been developed for alfentanil and pethidine.3 An understanding of the cerebral kinetics of morphine is of particular interest because its clinical use is characterized by a relatively long time to onset of peak effect, and a relatively long duration of action.4 However, a kinetic± dynamic explanation of this behaviour is complicated by a number of factors. Kinetic factors include: (i) the low lipophilicity of morphine, as given by its octanol:buffer partition coef®cient, compared with other opioids;4 this may cause a rate limitation in its movement across the blood± brain barrier (BBB) not present for other opioids, which are generally characterized by ¯ow-limited kinetics; (ii) the active transport of morphine out of the BBB by P-glycoprotein, which appears to be more signi®cant for morphine than other opioids5 and may alter its effective permeability across the BBB. Dynamic issues include: (i) the possibility of slower dissociation of morphine from opioid receptors in the CNS compared with other opioids;6 (ii) the potential presence of agonist (e.g. morphine-6glucuronide) and antagonist (e.g. morphine-3-glucuronide) metabolites that can enter the CNS. The extent of metabolite formation is highly dependent on the route and duration of morphine administration, and is species dependent.7 Given the complexity of these factors, it is not surprising that only two papers appear to have reported models of the cerebral kinetics of morphine.8 9 Unfortunately, both these papers related cerebral kinetics to venous rather than arterial blood concentrations, which introduces an artefact that makes the rate of cerebral (or effect) equilibration appear more rapid.10 Furthermore, it is unlikely that any one study would provide enough information to develop a comprehensive kinetic±dynamic model for morphine incorporating all the above factors. As a ®rst step in developing such a model, the aim of this study was to measure the cerebral kinetics of morphine after a short infusion in conscious chronically instrumented sheep. Kinetics were inferred from the time course of the morphine concentration across the brain (arterial-sagittal sinus). Studies were performed in a comparable manner to earlier studies of the cerebral kinetics of alfentanil and pethidine3 so that direct comparisons between opioids could be made. The kinetics of morphine in the lungs was examined concurrently. Lung kinetics can also play an important part in dictating the initial concentrations and effects of some drugs, particularly after i.v. bolus or short infusion.11 Unfortunately, opioids are poor analgesics in sheep, which precludes dynamic measurements for comparison with cerebral kinetic data.12
Upton et al.
Cardiovascular and blood gas measurements
distribution volume and cerebral blood ¯ow; (iii) a single ¯ow-limited compartment with an apparent ®rst-order loss representing either deep distribution or metabolism; (iv) a two-compartment membrane-limited model with a permeability term representing distribution into a deep compartment. The basic forms of the equations describing these models have been published previously,18 and are given below in a general form where Cin and Cout are the afferent and efferent drug concentrations of an organ, respectively, and Q is organ blood ¯ow. Cout Cm
Morphine was assayed using high-pressure liquid chromatography. A method for liquid±liquid extraction from whole blood was modi®ed from that of McLean and colleagues.16 Whole-blood samples (with hydromorphone as an internal standard) were extracted into dichloromethane at pH 9 (0.2 M bicarbonate buffer) followed by evaporation to dryness and reconstitution in mobile phase. The use of an organic solvent (dichloromethane) ensured red cell lysis. The chromatographic conditions were based on those reported by Evans and Shanahan17 with UV detection (210 nm). The mobile phase consisted of acetonitrile 7.5%, methanol 2.5% in 70 mM phosphate buffer (adjusted to pH 3) and was pumped through a C18 column (Alphabond, Alltech, Illinois, USA) at a ¯ow rate of 1 ml min±1. All assays were calibrated using six-point standard curves prepared in blood taken from the same animal before drug administration. The average r2 value of these standard curves was 0.998 (SD 0.002). The limit of quantitation of the assays was 0.04 mg ml±1. The coef®cient of variation of the assay was 5.5% at 0.25 mg ml±1, and 3.3% at 2 mg ml±1. Thus, ®ve replicates would have reduced the contribution of assay variability of the mean data to less than 2.5%. It would be expected that the extraction phase would exclude the glucuronide metabolites of morphine, and normorphine was shown not to co-chromatograph with morphine.
Pharmacokinetic analysis All kinetic analyses were based on the time course of the mean concentrations. Model parameters therefore represent estimates of the behaviour of the average sheep, which is optimal for discriminating between various models of organ kinetics. Four different kinetic models of the brain were ®tted to the data: (i) a null model that tested the hypothesis that there was no concentration gradient across the organ; (ii) a single ¯ow-limited compartment de®ned by a single
dCout Q: Cin ÿ Cout dt
2
dCout Q: Cin ÿ Cout ÿ PSloss :Cout dt
3
V1 :
Morphine analysis
V1 :
1
dCout Q: Cin ÿ Cout PS: C2 ÿ Cout dt dC2 PS: Cout ÿ C2 V2 : dt
V1 :
4
V1 is the volume of the ®rst compartment of the organs, and V2 and C2 are the volume of, and concentration in, the second compartment of the organ (if appropriate). PS is the permeability term for loss or exchange from the ®rst compartment. For the cerebral kinetic models, these parameters were appended with the subscript `brn', Cin was the arterial concentration, Cout the sagittal-sinus concentration and Q was cerebral blood ¯ow. For the lung kinetic models, these parameters were appended with the subscript `lng', Cin was the pulmonary arterial concentration, Cout the arterial concentration and Q was cardiac output. A hybrid modelling approach was used (i.e. where one part of the model is physiologically realistic, and the remainder is empirical descriptions of available data).19 To illustrate the principle, note that Equation 2 can be used to predict Cout as a function of time only if Cin and Q are known. As both Cin and Q are time-dependent variables, an algebraic solution for the equation is virtually impossible. However, Eqn 2 can be solved using a differential equation solving program (e.g. via the Runge±Kutta algorithm) if continuous mathematical functions describing Cin and Q with time are included in the system of equations to be solved. In hybrid modelling, these functions are derived by curve ®tting the available experimental data, which consist of measurements of Cin and Q at discrete time points. The form of these interpolation or `forcing' functions (e.g. sums
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Immediately before morphine infusion, cardiac output was measured three times using a thermodilution method. The values were averaged to yield baseline cardiac output. Arterial pressure was recorded continuously via a pressure transducer on one of the arterial catheters. Cerebral blood ¯ow was measured using the Doppler ¯ow probe and a ¯ow meter (Bioengineering, University of Iowa, USA). Both were recorded for 5 min before the start of drug infusion (baseline), and throughout the infusion, using an analogueto-digital card (Metrabyte DAS 16-G2) and a personal computer (486 based IBM compatible). Additional arterial blood samples for blood gas analysis were taken immediately before the infusion and at 4, 10 and 30 min after the start of the infusion (ABL System 625, Radiometer, Sweden). Arterial oxygen tension (PaO2), carbon dioxide tension (PaCO2), and arterial oxygen saturation (SaO2) were also recorded.
Cerebral kinetics of morphine in sheep
0P n
ÿ 2 1 wi Yobs i ÿ Yobs Bi1 C 2p Cÿ MSC lnB n @P A n 2 wi Yobs i ÿ Ycal i
5
i1
where wi is a weighting term and p is the number of parameters. No weighting scheme was used. Calculated variables
Fig 1 (A) Mean (symbols) and 95% con®dence intervals (dotted lines) of the index of cerebral blood ¯ow (CBF) expressed as a percentage of baseline values in six sheep. (B) Equivalent data for the measured mean arterial pressure (MAP) and (C) arterial carbon dioxide tension (PaCO2). The solid lines are the baseline values. Statistically signi®cant changes from baseline were inferred if the 95% con®dence intervals for a subsequent measurement did not include the mean baseline value. This did not occur for any of the measurements.
of exponentials or polynomials) is not important, provided the resultant curve closely matches the experimental data for Cin and Q. In essence, these functions can be used to `force' Cin and Q in Eqn 2 to follow the time course of the observed data.20 In practical terms, this means that the time
Model parameters were used to calculate secondary variables to facilitate comparison with other opioids and literature values. Cerebral equilibration times for morphine (and other opioids) were calculated by using the ®nal cerebral kinetic model to simulate the time course of the brain concentrations for a step increase in the arterial concentration from 0 to 1. The times required for the cerebral concentration to reach 50% and 95% of the arterial concentration were recorded. The former is equivalent to the half-time of cerebral equilibration only for a ¯ow-limited (single-compartment) model. The apparent permeability of the BBB (PS) was compared with a nominal cerebral blood ¯ow of 40 ml min±1.13 The apparent brain:blood partition coef®cient was calculated from Vb and a nominal real volume of 65 ml for the region of the brain drained by the sagittal-sinus catheter.13 Total arterial (AUCart) and sagittal-sinus (AUCss) area under the blood morphine concentration±time curves to 30 min were calculated using the trapezoidal rule. Drug retention (R%) in the brain was calculated as follows: R% 1 ÿ
AUCss :100 AUCart
6
This indicates the amount of morphine that had entered the brain via the arterial blood but had not left the brain via the
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course of Cout predicted by the equation now depends only on the one remaining unknown of the equation (V1), which can be estimated from Cout by curve ®tting. The advantage of this approach is that organ kinetics (e.g. V1) can be estimated without having to develop models for the many factors that affect Cin and Q in vivo. In the present study, the input concentrations were interpolated using exponential forcing functions. The measured changes in blood ¯ow were interpolated using polynomial forcing functions, but with the baseline value based on previous measurements.13 The output concentrations were curve ®tted to determine model parameters using modelling software (Scientist for Windows, version 2, Micromath, Utah, USA). The best ®t was determined by maximising the model selection criterion (MSC) of this software, which has been described in detail previously.19 The MSC is essentially the Akaike information criterion scaled to compensate for data sets of different magnitudes, and is calculated from the following formula:
Upton et al.
Cardiovascular and blood gas data
Pharmacokinetic data
Fig 2 (A) Measured pulmonary artery (triangle) and arterial concentrations (circle) of morphine in four sheep. (B) Measured arterial (circle) and sagittal-sinus (inverted triangle) concentrations of morphine in ®ve sheep. Data are shown as the mean at each time point. The variability of the data can be deduced from Figure 3. Solid lines are the best ®t of the kinetic model with the highest model selection criteria. These were the `¯ow limited with loss' model for the lungs (Table 1), and the membrane-limited model with V1 ®xed for the brain (Table 2).
sagittal sinus by the end of the study period. Retention in the brain could be the result of metabolism or deep distribution. An analogous calculation was also performed for the lung using arterial and pulmonary artery AUC values.
Results Deviations from the protocol were as follows. In one study, the measured arterial concentrations were found to be approximately half of the concurrent pulmonary artery and sagittal-sinus concentrations. A partially extravascular catheter that re-sampled catheter ¯ush solution was postulated to account for this apparent dilution, and the data were excluded. In another study, it was not possible to sample pulmonary artery blood because of catheter failure. The total number of studies of arterial±sagittal sinus gradients across the brain was therefore ®ve, and of pulmonary artery±arterial gradients across the lungs was four.
Mean observed blood morphine concentrations are shown in Figure 2. Peak arterial morphine concentration was 2.11 mg ml±1 (95% CI 0.91±3.30 mg ml±1), and this occurred for the last sample taken during the infusion. The concentration differences of morphine across the lungs and brain were small, and the differences were most obvious in the intrainfusion period (Fig. 2). Concentration gradients were therefore only analysed until 30 min after the infusion. If the arterio±venous concentration difference is small, a large number of replicates may be required to resolve the contribution of organ kinetics from that of assay variability.21 However, for the present data, the time course of the arterio±venous difference showed a consistent non-random pattern, with uptake occurring into both organs during the infusion, and with limited elution from the organ in the postinfusion period (Fig. 3), suggesting that the number of replicates was suf®cient for this purpose. As a further precaution against this phenomenon, the null model (Cout=Cin) was included for all modelling analysis. For both the lungs and brain, the null model was a poor alternative to structural models of organ kinetics (Tables 1 and 2). Lung kinetics
Parameter estimates for the various models of lung kinetics are summarized in Table 1. All models concurred that the volume of the ®rst compartment of the lungs was of the order of 2 litre. This is a relatively small volume of distribution for the lung in sheep, and produces reversible pulmonary artery±arterial gradients across the lung only after rapid i.v. administration.11 For the baseline cardiac output of 6 litre min±1, the half-life of equilibration of morphine through this component of the lung was 0.23 min. However, the improved ®ts of the `¯ow with loss' and membrane-limited models suggested that there was a deeper
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Morphine had minimal effects on cerebral blood ¯ow, arterial carbon dioxide tension and mean arterial pressure (Fig. 1). Arterial oxygen tension and haemoglobin saturation were unchanged from baseline. Thus, although the dose of morphine used was relatively high, it was not associated with signi®cant respiratory or cardiovascular side-effects. A ®xed baseline cerebral blood ¯ow of 40 ml min±1 was assumed in subsequent modelling of cerebral kinetics, in keeping with previous measurements in this preparation.13 Mean baseline cardiac output was 6210 ml min±1 (95% con®dence interval [CI] 4740±7680 ml min±1). This baseline value was used in subsequent modelling of lung kinetics. In all sheep, morphine was noted to produce a mild degree of dysphoria (agitation, mouthing of crate, nystagmus).
Cerebral kinetics of morphine in sheep Table 1 Models of lung kinetics ± goodness of ®t of the models of morphine kinetics in the lung. The MSC is the model selection criteria ± the higher the number, the better the ®t. Parameters are apparent distribution volume of the shallow compartment that includes blood (V1,lng), membrane permeability (PSlng) and deep compartment volume (V2,lng) in the lung. Data are mean (SD) returned by the curve-®tting program
compartment in the lung, for which uptake was essentially irreversible on the time scale of the study. The loss to this compartment was better described as a unidirectional loss term (PSloss), as the volume of the deep compartment of the membrane-limited model tended to very small values during ®tting, essentially defaulting to the `¯ow with loss' model. There was good agreement that the effective clearance of this loss was approximately 1.4 litre min±1. For a cardiac output of 6 litre min±1, this amounts to an effective extraction of 23% across the lung during the study. The retention of morphine in the lungs after 30 min was 12.3% (95% CI ±30.8% to 55.4%). Cerebral kinetics
Parameter estimates for the various models of cerebral kinetics are summarized in Table 2. The ¯ow-limited and null model were equally poor descriptions of the data, suggesting that the cerebral kinetics of morphine were not compatible with ¯ow-limited uptake. Data were better described by models where there was a permeability term describing loss from the ®rst volume of the brain. In contrast to the lungs, this permeability term was better described by transfer of morphine into a deeper compartment
MSC
V1,lng (ml)
PSlng (ml min±1)
V2,lng (ml)
Null model Flow Flow plus loss Membrane
1.49 1.93 3.36 3.23
2032 (598) 2036 (407) 2060 (485)
1370 (231) 1352 (268)
>105 (>105)
(membrane-limited model) rather than a ®rst-order loss term (`¯ow with loss' model). When the data were used to estimate both volumes of the membrane-limited model, the ®rst volume tended to a small number and was therefore constrained to be greater than 10±3 ml. As an alternative, this volume was ®xed at the nominal volume of the vascular compartment of the brain in sheep (5% of 90 ml, or 4.5 ml). This volume is remarkably similar to the volume of the ®rst compartment estimated by ®tting the other models (Table 2). This model was felt to be consistent with the notion of rate limitation for the movement of morphine across the BBB, and produced good parameter estimates. These were used for subsequent calculations. The permeability value of morphine was 7.4 ml min±1, and approximately one-®fth of the nominal blood ¯ow (40 ml min±1). The ®nal volume of the deep compartment was 92 ml. Given the nominal real volume of the region of the brain drained by the sagittalsinus catheter (70% of 90 ml13), this equates to a brain:blood partition coef®cient of approximately 1.4 (Table 3). Retention of morphine in the brain after 30 min was 8.4% (95% CI ±17.5% to 34.4%).
Discussion Cardiovascular and blood gas changes These data (Fig. 1) are in general agreement with the literature in that morphine had minimal effects on the cardiovascular system4 and cerebral blood ¯ow.22 Slight and transient respiratory depression was evident, as suggested by the small rise in carbon dioxide partial pressure but this was not statistically signi®cant. There was no associated hypoxia.
Lung kinetics A number of in vitro and in vivo studies have con®rmed that morphine is not metabolized by the lung.7 However, in agreement with the present data, a number of studies suggest retention of morphine in the lung, which can manifest as extraction or clearance across the lung in short-term studies. In rabbits, the lung retention of morphine was reported to be 33% following bolus administration.23 The value of 23%
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Fig 3 Mean (symbols) and 95% con®dence intervals (dotted lines) of the individual concentration differences across the lungs (pulmonary artery±arterial) in four sheep (A) and of the individual concentration differences across the brain (arterial±sagittal sinus) in ®ve sheep (B).
Model
Upton et al.
calculated from the present data in sheep is comparable. Importantly, the gradient of morphine across the lungs of sheep was reported to be minimal after 5 h of a constant-rate infusion.24 25 Therefore, it can be assumed that deep distribution was complete by 5 h. Assuming the process is ®rst order, a half-life of less than 1 h can be calculated. In man, ®rst-pass retention of morphine in the lungs has been reported as 7%26 and 4%.27 Low ®rst-pass uptake is consistent with membrane-limited uptake into the lungs, as suggested by the present data.
the half-time of the delay between morphine effects and blood concentrations reported previously for opioids of approximately 13 min,28 17 min29 and 34 min.30 Thus, while acknowledging potential differences in species and methodology, it may be that there is a component to this pharmacodynamic delay in addition to the time required for cerebral equilibration. Potential factors contributing to this delay were given in the introduction.
Concentration±effect relationships and active metabolites
Cerebral kinetics
Table 2 Models of cerebral kinetics ± goodness of ®t of the models of morphine kinetics in the brain. MSC is the model selection criteria ± the higher the number, the better the ®t. Parameters are apparent distribution volume of the shallow compartment that includes blood (V1,brn), membrane permeability (PSbrn) and deep compartment volume (V2,brn) in the brain. Data are mean (SD) returned by the curve-®tting program Model
MSC
V1,brn (ml)
Null model Flow Flow plus loss Membrane Membrane (V1 ®xed)
2.47 2.46 3.56 3.72 3.71
4.41 (2.38) 4.51 (1.76) 0.001 constrained 4.5 ®xed
PSbrn (ml min±1)
5.98 (1.19) 9.97 (1.92) 7.44 (1.60)
V2,brn (ml)
50.4 (33.4) 92.4 (59.2)
Morphine-6-glucuronide is active at the m-opioid receptor, while morphine-3-glucoronide may antagonize analgesia.7 While it is clear that a kinetic±dynamic analysis of morphine must account for the systemic and cerebral kinetics of parent morphine, and also the systemic and cerebral kinetics of its glucuronide metabolites, the latter was not performed in the present study. Some understanding of kinetic±dynamic relationships for morphine alone can be inferred from studies in the rat, which produces no morphine-6-glucuronide. In this species, the time course of parent morphine concentrations in the whole brain31 and brain extracellular ¯uid9 showed a good relationship with the time course of analgesia. In contrast, earlier work using vocalization as an analgesic end-point suggested that analgesia lagged behind brain morphine concentrations.32
Global vs regional brain concentrations The model presented here can be used to predict the global brain concentration of morphine. This will be useful if the global concentration is representative of the concentration surrounding opioid receptors. This is not to imply that opioid concentrations in all regions of the brain (and spinal cord) are equal, but rather that they change in parallel and this is consistent with the literature on morphine distribution throughout the brain. Positron emission tomography studies of morphine distribution in the brain of monkeys showed homogenous distribution.33 Direct measurements of the concentrations of morphine in different brain regions (including the spinal cord) showed a signi®cant difference in absolute concentration between regions, but are super®cially consistent with the notion that regional concentrations changed in parallel.8 34
Table 3 Comparison of model parameters for morphine with those of other opioids. Models were ®tted to cerebral kinetic data for different opioids collected under the same experimental conditions in conscious instrumented sheep. Data for alfentanil and pethidine have been published previously and could be described using a ¯ow-limited model.3 PS is the apparent permeability of the blood±brain barrier, Vb is the apparent distribution volume of the brain, R is the apparent brain:blood partition coef®cient. The times required for 50% and 95% equilibration (tequil50% and tequil95%, respectively) of the deep compartment of the brain determined by simulation are also shown. Where possible data are mean (SD) Opioid
PS (ml min±1)
Vb (ml)
R
tequil50% (min)
tequil95% (min)
Morphine Alfentanil Pethidine
7.4 (1.6) >1000 >1000
92 (59) 47 (8) 364 (17)
1.4 (0.9) 0.72 (0.12) 5.6 (0.26)
10.3 0.83 6.3
44.3 3.5 27.3
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The parameters of the model estimated from the present morphine data are shown in Table 3, together with parameters estimated for other opioids in the same experimental preparation.3 Alfentanil and pethidine were shown to have no rate limitation across the BBB, and cerebral kinetics were therefore ¯ow limited and dictated by their cerebral distribution volumes. As these differed markedly, their cerebral equilibration half-times also differed. In keeping with the literature, note that the permeability of morphine across the BBB was low compared with these other opioids, as was its cerebral distribution volume. The data unequivocally show that the cerebral kinetics of morphine could not be described by a ¯ow-limited (or venous-equilibrium) model. The permeability of morphine across the BBB was estimated relatively precisely, and was approximately one-®fth of cerebral blood ¯ow. While the calculated brain:blood partition coef®cient was relatively uncertain, it was evident that the time required for 50% equilibration was longer than for the other opioids (10.3 min, Table 3). However, this was shorter than the values for
Cerebral kinetics of morphine in sheep
Contribution of P-glycoprotein An analysis of the cerebral kinetics of morphine is complicated by the fact that morphine is a P-glycoprotein substrate, and is actively pumped out of the BBB. Abolishing this transport produces brain concentrations and analgesia 3±4 times higher than normal, in the face of minimal changes in systemic kinetics.5 9 As sheep also express the gene for P-glycoprotein,35 the permeability term estimated for morphine in the brain in the present model is therefore a composite of the permeability resulting from diffusion and the effective ef¯ux from the membrane by P-glycoprotein. This should be accounted for when correlating permeability with physicochemical properties.
10
11 12 13
The present data suggest that the delay in cerebral equilibration of morphine contributes to the slow onset and long duration of action for morphine. However, the quantitative role of other contributing factors to this clinical behaviour has yet to be determined. Nevertheless, the present model is a building block for these more complicated models of cerebral kinetic±dynamic relationships for morphine.
15
16
17
Acknowledgement Supported by the National Health and Medical Research Council of Australia (Project Grant 9936988).
References 1 Shafer SL, Varvel JR. Pharmacokinetics, pharmacodynamics and rational opioid selection. Anesthesiology 1991; 74: 53±63 2 Upton RN, Semple T, Macintyre P. The pharmacokinetic optimisation of opioid treatment in acute pain therapy. Clin Pharmacokinet 1997; 33: 225±44 3 Upton RN, Ludbrook GL, Gray EC, Grant C. The cerebral pharmacokinetics of meperidine and alfentanil in conscious sheep. Anesthesiology 1997; 86: 1317±25 4 Wood M. Opioid agonists and antagonists. In: Wood M, Wood AJJ, eds. Drugs and Anesthesia. Pharmacology for Anesthesiologists, 2nd Edn. Baltimore: Williams and Wilkins,1990; 129±78 5 Thompson SJ, Koszdin K, Bernards CM. Opiate-induced analgesia is increased and prolonged in mice lacking P-glycoprotein. Anesthesiology 2000; 92: 1392±9 6 Leysen JE, Gommeren W. Drug±receptor dissociation time, new tool for drug research. Receptor binding af®nity and drug receptor dissociation pro®les of serotonin-S2, dopamine-D2, histamine-H1 antagonists, and opiates. Drug Dev Res 1986, 8: 119±31 7 Milne RW, Nation RL, Somogyi AA. Disposition of morphine and its 3- and 6-glucuronide metabolites in humans and animals, and the importance of the metabolites to the pharmacological effects of morphine. Drug Metab Rev 1996; 28: 345±472 8 Dahlstrom BE, Paalzow LK. Pharmacokinetics of morphine in plasma and discrete areas of rat brain. J Pharmacokinet Biopharm 1975; 5: 293±303 9 Letrent SP, Pollack GM, Brouwer KR, Brouwer KL. Effects of a
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14
Conclusion
potent and speci®c P-glycoprotein inhibitor on the blood-brain barrier distribution and antinociceptive effect of morphine in the rat. Drug Metab Dispos 1999; 27: 827±34 Tuk B, Herben VMM, Mandema JW, Danhof M. Relevance of arteriovenous concentration differences in pharmacokineticpharmacodynamic modeling of midazolam. J Pharmacol Exp Ther 1998; 284: 202±7 Upton RN, Doolette DJ. Kinetic aspects of drug disposition in the lungs. Clin Exp Pharmacol Physiol 1999; 26: 381±91 Grant C, Upton RN, Kuchel TR. An assessment of the ef®cacy of intramuscular analgesics for acute pain in the sheep. Aust Vet J 1996; 73: 129±32 Doolette DJ, Upton RN, Grant C. Agreement between ultrasonic Doppler venous out¯ow and Kety Schmidt estimates of cerebral blood ¯ow. Clin Exp Pharmacol Physiol 1999; 26: 736±40 Upton RN, Grant C, Ludbrook GL. An ultrasonic Doppler venous out¯ow method for the continuous measurement of cerebral blood ¯ow in conscious sheep. J Cereb Blood Flow Metab 1994; 14: 680±8 Milne RW, Nation RL, Reynolds GD, Somogyi AA, Van Crugten JT. High performance liquid chromatographic determination of morphine and its 3- and 6-glucuronide metabolites: improvements to the method and application to stability studies. J Chromatogr B Biomed 1991; 565: 457±64 McLean CF, Mather LE, Odontiadis J, Sloan PA. Improved method for morphine determination in biological ¯uids and tissues: rapid; sensitive and selective. J Pharm Pharmacol 1990; 42: 669±71 Evans AM, Shanahan K. The disposition of morphine and its metabolites in the in-situ rat isolated perfused liver. J Pharm Pharmacol 1995; 47: 333±9 Huang YF, Upton RN, Zheng D, McLean C, Gray EC, Grant C. The enantiomer speci®c kinetics and dynamics of verapamil after rapid intravenous administration to sheep ± physiological analysis and modeling. J Pharmacol Exp Ther 1998; 284: 1048±57 Upton RN, Ludbrook GL, Grant C, Doolette DJ. The effect of altered cerebral blood ¯ow on the cerebral kinetics of thiopental and propofol in sheep. Anesthesiology 2000; 93: 1085±94 Rainville ED, Bedient PE. Elementary Differential Equations, 5th Edn. New York: Macmillan Publishing Co., 1974; 207 Upton RN. An analysis of errors arising from the direct use of mass balance principles to describe regional drug uptake and elution. J Pharmacokinet Biopharm 1994; 22: 309±21 Bjorkman S, Akeson J, Helfer M, Fyge A, Gustafsson LL. Cerebral uptake of morphine in the pig calculated from arterio-venous plasma concentration gradients: an alternative to tissue microdialysis. Life Sci 1995; 57: 2335±45 Abdallah C, Besner JG, Du Souich P. Presystemic elimination of morphine in anesthetized rabbits. Contribution of the intestine, liver, and lungs. Drug Metab Dispos 1995; 23: 584±9 Sloan PA, Mather LE, McLean CF, et al. Physiological disposition of i.v. morphine in sheep. Br J Anaesth 1991; 67: 378±86 Milne RW, Sloan PA, McLean CF, et al. Disposition of morphine and its 3- and 6-glucuronide metabolites during morphine infusion in the sheep. Drug Metab Dispos 1993; 21: 1151±6 Boer F, Bovill JG, Burm AG, Mooren RA. Uptake of sufentanil, alfentanil and morphine in the lungs of patients about to undergo coronary artery surgery. Br J Anaesth 1992; 68: 370±5 Roerig DL, Kotrly KJ, Vucins EJ, Ahlf SB, Dawson CA, Kampine JP. First pass uptake of fentanyl, meperidine, and morphine in the human lung. Anesthesiology 1987; 67: 466±72 Bragg P, Zwass MS, Lau M, Fisher DM. Opioid pharmaco-
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dynamics in neonatal dogs: differences between morphine and fentanyl. J Appl Physiol 1995; 79: 1519±24 29 Kramer TH, d`Amours RH, Buettner C. Pharmacodynamic model of the effects of morphine and morphine-6-glucuronide during patient controlled analgesia. Clin Pharmacol Ther 1996; 59: 132 30 Gardmark M, Ekblom M, Bouw R, Hammarlund-Udeaes M. Quantitation of effect delay and acute tolerance development to morphine in the rat. J Pharmacol Exp Ther 1993; 267: 1061±7 31 van Crugten JT, Somogyi AA, Nation RL, Reynolds G. Concentration-effect relationships of morphine and morphine6 beta-glucuronide in the rat. Clin Exp Pharmacol Physiol 1997; 24: 359±64
32 Dahlstrom BE, Paalzow LK, Segre G, Agren AJ. Relation between morphine pharmacokinetics and analgesia. J Pharmacokinet Biopharm 1978; 6: 41±53 33 Hartvig P, Bergstrom K, Lindberg B, et al. Kinetics of 11C-labeled opiates in the brain of rhesus monkeys. J Pharmacol Exp Ther 1984; 230: 250±5 34 Bhargava HN, Villar VM, Rahmani NH, Larsen AK. Time course of the distribution of morphine in brain regions, spinal cord and serum following intravenous injection to rats of differing ages. Pharmacology 1993; 47: 13±23 35 Longley M, Phua SH, van Stijn TC, Crawford AM. Isolation and mapping of the ®rst ruminant multidrug resistance genes. Anim Genet 1999; 30: 207±10
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758
DOI: 10.1093/bja/aeg131
LABORATORY INVESTIGATIONS Cerebral and lung kinetics of morphine in conscious sheep after short intravenous infusions R. N. Upton1*, G. L. Ludbrook1, A. M. Martinez1, C. Grant1 and R. W. Milne2 1
Department of Anaesthesia and Intensive Care, Royal Adelaide Hospital, University of Adelaide, SA 5005 Adelaide, Australia. 2Centre for Pharmaceutical Research, School of Pharmacy and Medical Sciences, University of South Australia, Adelaide, Australia *Corresponding author. E-mail: [email protected]
Methods. Sheep were given short i.v. infusions of morphine (30 mg over 4 min). Cerebral kinetics were inferred from arterio±sagittal sinus concentration gradients and cerebral blood ¯ow, and lung kinetics from the pulmonary artery±aortic gradient and cardiac output. These data were ®tted to ¯ow- and membrane-limited models of the kinetics in each organ. Results. Morphine had minimal cardiovascular effects, did not alter cerebral blood ¯ow and caused insigni®cant respiratory depression. Lung kinetics were best described by a single distribution volume (2036 ml) with a ®rst-order loss (1370 ml min±1), which was attributed to deep distribution. The cerebral kinetics of morphine were characterized by a signi®cant permeability barrier. Permeability across the barrier (7.44 ml min±1) was estimated with good precision, and was approximately one-®fth of the nominal cerebral blood ¯ow. The distribution volume of morphine in the brain was estimated with less precision, but was described by a brain:blood partition coef®cient of approximately 1.4. The time required for 50% equilibration between brain and blood concentrations was approximately 10.3 min. Conclusion. The cerebral equilibration of morphine was relatively slow, and was characterized by signi®cant membrane limitation. Br J Anaesth 2003; 90: 750±8 Keywords: analgesics opioid, morphine; brain; lung, function; pharmacokinetics; sheep Accepted for publication: February 10, 2003
The time course of the cerebral effects (e.g. analgesia, changes in the EEG) of many clinically used opioids lag behind their concentration in blood.1 As this lag is similar in magnitude to the time required for equilibration of the central nervous system (CNS) concentrations with blood concentrations, it has been proposed that CNS equilibration is a major component of the lag.2 Furthermore, differences in the rate of CNS equilibration between opioids appear to correspond to their clinically observed duration of action
after i.v. bolus administration.2 This delayed equilibration becomes of particular clinical signi®cance in postoperative patients in whom multiple doses of parenteral opioids are titrated against pain levels, such as when patients are `loaded' with opioid in the recovery ward, or during subsequent patient-controlled analgesia. Simulations of CNS opioid concentrations in these settings were found to be more consistent with clinical experience than simulations of blood concentrations.2 While many aspects of this type of
Ó The Board of Management and Trustees of the British Journal of Anaesthesia 2003
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Background. The analgesic effects of morphine are delayed relative to its concentration in blood. The rate of equilibration of morphine between blood and brain may contribute to this delay, but the kinetics of this process have not been modelled. This was determined in conscious instrumented sheep. The lung kinetics of morphine were also determined given their importance in de®ning systemic kinetics after i.v. bolus administration.
Cerebral kinetics of morphine in sheep
Methods Animal preparation All experimental procedures were approved by the Animal Ethics Committee of the University of Adelaide. Female Merino sheep of similar ages and body mass (approximately 50 kg) were used, and were instrumented under general anaesthesia as reported previously.3 Catheters were chronically implanted via the femoral vessels in the abdominal aorta (for sampling of arterial blood), in the right atrium (for drug administration), in the pulmonary artery (for blood sampling and thermodilution measurement of cardiac output), and in the dorsal sagittal sinus (the appropriate site for sampling cerebral venous blood in sheep13). A Doppler transducer was placed over the sagittal sinus using a previously validated method to provide an index of cerebral blood ¯ow.13 14 After recovery from anaesthesia, the sheep were housed in metabolic crates and their catheters maintained with a saline/heparin lock (0.9%/50 i.u. ml±1).
Study design Six sheep were studied. For each study, instrumented sheep were placed in non-weight-bearing slings inside metabolic crates and were prepared for physiological measurements and blood sampling. After a period of baseline measurements, an i.v. morphine infusion (morphine sulphate injection, David Bull Laboratories, Mulgrave, Victoria, Australia) was begun at time zero at a rate of 7.5 mg min±1 for 4 min. The sheep were not intubated, and breathed room air spontaneously throughout. For each study, the following data were collected. Pharmacokinetic measurements
Cerebral pharmacokinetics were determined from simultaneous measurements of arterial and sagittal-sinus drug concentrations and cerebral blood ¯ow, as performed previously in this preparation.3 Arterial and sagittal-sinus blood samples (0.5 ml) were taken at 0, 0.5, 1, 1.5, 2, 3, 4, 4.5, 5, 5.5, 6, 8, 10, 15, 20, 30, 45, 60 and 75 min after the start of the infusion. Lung pharmacokinetics were determined in an analogous manner, from pulmonary arterial samples taken at the same times as the arterial samples. Whole-blood samples were stored frozen (±20 °C) before assay. Morphine is stable for up to 2 years at this temperature.15 Although some studies of drug uptake into organs have used concurrent intravascular markers, no such marker was used in the present study as previous experience and computer simulations suggested that intravascular transit times for both organs were too rapid to be resolved using the proposed blood sampling schedules.
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kinetic analysis based on global CNS concentrations of opioids are speculative, it is clear that future kinetic± dynamic analysis of opioids will require, in part, suf®cient understanding of the cerebral kinetics of each opioid so that the time course of global CNS concentrations can be predicted in various circumstances. This requires identi®cation of a structural model of the cerebral kinetics of the opioid, with suf®cient data to reliably estimate parameter values for the model. Such models have been developed for alfentanil and pethidine.3 An understanding of the cerebral kinetics of morphine is of particular interest because its clinical use is characterized by a relatively long time to onset of peak effect, and a relatively long duration of action.4 However, a kinetic± dynamic explanation of this behaviour is complicated by a number of factors. Kinetic factors include: (i) the low lipophilicity of morphine, as given by its octanol:buffer partition coef®cient, compared with other opioids;4 this may cause a rate limitation in its movement across the blood± brain barrier (BBB) not present for other opioids, which are generally characterized by ¯ow-limited kinetics; (ii) the active transport of morphine out of the BBB by P-glycoprotein, which appears to be more signi®cant for morphine than other opioids5 and may alter its effective permeability across the BBB. Dynamic issues include: (i) the possibility of slower dissociation of morphine from opioid receptors in the CNS compared with other opioids;6 (ii) the potential presence of agonist (e.g. morphine-6glucuronide) and antagonist (e.g. morphine-3-glucuronide) metabolites that can enter the CNS. The extent of metabolite formation is highly dependent on the route and duration of morphine administration, and is species dependent.7 Given the complexity of these factors, it is not surprising that only two papers appear to have reported models of the cerebral kinetics of morphine.8 9 Unfortunately, both these papers related cerebral kinetics to venous rather than arterial blood concentrations, which introduces an artefact that makes the rate of cerebral (or effect) equilibration appear more rapid.10 Furthermore, it is unlikely that any one study would provide enough information to develop a comprehensive kinetic±dynamic model for morphine incorporating all the above factors. As a ®rst step in developing such a model, the aim of this study was to measure the cerebral kinetics of morphine after a short infusion in conscious chronically instrumented sheep. Kinetics were inferred from the time course of the morphine concentration across the brain (arterial-sagittal sinus). Studies were performed in a comparable manner to earlier studies of the cerebral kinetics of alfentanil and pethidine3 so that direct comparisons between opioids could be made. The kinetics of morphine in the lungs was examined concurrently. Lung kinetics can also play an important part in dictating the initial concentrations and effects of some drugs, particularly after i.v. bolus or short infusion.11 Unfortunately, opioids are poor analgesics in sheep, which precludes dynamic measurements for comparison with cerebral kinetic data.12
Upton et al.
Cardiovascular and blood gas measurements
distribution volume and cerebral blood ¯ow; (iii) a single ¯ow-limited compartment with an apparent ®rst-order loss representing either deep distribution or metabolism; (iv) a two-compartment membrane-limited model with a permeability term representing distribution into a deep compartment. The basic forms of the equations describing these models have been published previously,18 and are given below in a general form where Cin and Cout are the afferent and efferent drug concentrations of an organ, respectively, and Q is organ blood ¯ow. Cout Cm
Morphine was assayed using high-pressure liquid chromatography. A method for liquid±liquid extraction from whole blood was modi®ed from that of McLean and colleagues.16 Whole-blood samples (with hydromorphone as an internal standard) were extracted into dichloromethane at pH 9 (0.2 M bicarbonate buffer) followed by evaporation to dryness and reconstitution in mobile phase. The use of an organic solvent (dichloromethane) ensured red cell lysis. The chromatographic conditions were based on those reported by Evans and Shanahan17 with UV detection (210 nm). The mobile phase consisted of acetonitrile 7.5%, methanol 2.5% in 70 mM phosphate buffer (adjusted to pH 3) and was pumped through a C18 column (Alphabond, Alltech, Illinois, USA) at a ¯ow rate of 1 ml min±1. All assays were calibrated using six-point standard curves prepared in blood taken from the same animal before drug administration. The average r2 value of these standard curves was 0.998 (SD 0.002). The limit of quantitation of the assays was 0.04 mg ml±1. The coef®cient of variation of the assay was 5.5% at 0.25 mg ml±1, and 3.3% at 2 mg ml±1. Thus, ®ve replicates would have reduced the contribution of assay variability of the mean data to less than 2.5%. It would be expected that the extraction phase would exclude the glucuronide metabolites of morphine, and normorphine was shown not to co-chromatograph with morphine.
Pharmacokinetic analysis All kinetic analyses were based on the time course of the mean concentrations. Model parameters therefore represent estimates of the behaviour of the average sheep, which is optimal for discriminating between various models of organ kinetics. Four different kinetic models of the brain were ®tted to the data: (i) a null model that tested the hypothesis that there was no concentration gradient across the organ; (ii) a single ¯ow-limited compartment de®ned by a single
dCout Q: Cin ÿ Cout dt
2
dCout Q: Cin ÿ Cout ÿ PSloss :Cout dt
3
V1 :
Morphine analysis
V1 :
1
dCout Q: Cin ÿ Cout PS: C2 ÿ Cout dt dC2 PS: Cout ÿ C2 V2 : dt
V1 :
4
V1 is the volume of the ®rst compartment of the organs, and V2 and C2 are the volume of, and concentration in, the second compartment of the organ (if appropriate). PS is the permeability term for loss or exchange from the ®rst compartment. For the cerebral kinetic models, these parameters were appended with the subscript `brn', Cin was the arterial concentration, Cout the sagittal-sinus concentration and Q was cerebral blood ¯ow. For the lung kinetic models, these parameters were appended with the subscript `lng', Cin was the pulmonary arterial concentration, Cout the arterial concentration and Q was cardiac output. A hybrid modelling approach was used (i.e. where one part of the model is physiologically realistic, and the remainder is empirical descriptions of available data).19 To illustrate the principle, note that Equation 2 can be used to predict Cout as a function of time only if Cin and Q are known. As both Cin and Q are time-dependent variables, an algebraic solution for the equation is virtually impossible. However, Eqn 2 can be solved using a differential equation solving program (e.g. via the Runge±Kutta algorithm) if continuous mathematical functions describing Cin and Q with time are included in the system of equations to be solved. In hybrid modelling, these functions are derived by curve ®tting the available experimental data, which consist of measurements of Cin and Q at discrete time points. The form of these interpolation or `forcing' functions (e.g. sums
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Immediately before morphine infusion, cardiac output was measured three times using a thermodilution method. The values were averaged to yield baseline cardiac output. Arterial pressure was recorded continuously via a pressure transducer on one of the arterial catheters. Cerebral blood ¯ow was measured using the Doppler ¯ow probe and a ¯ow meter (Bioengineering, University of Iowa, USA). Both were recorded for 5 min before the start of drug infusion (baseline), and throughout the infusion, using an analogueto-digital card (Metrabyte DAS 16-G2) and a personal computer (486 based IBM compatible). Additional arterial blood samples for blood gas analysis were taken immediately before the infusion and at 4, 10 and 30 min after the start of the infusion (ABL System 625, Radiometer, Sweden). Arterial oxygen tension (PaO2), carbon dioxide tension (PaCO2), and arterial oxygen saturation (SaO2) were also recorded.
Cerebral kinetics of morphine in sheep
0P n
ÿ 2 1 wi Yobs i ÿ Yobs Bi1 C 2p Cÿ MSC lnB n @P A n 2 wi Yobs i ÿ Ycal i
5
i1
where wi is a weighting term and p is the number of parameters. No weighting scheme was used. Calculated variables
Fig 1 (A) Mean (symbols) and 95% con®dence intervals (dotted lines) of the index of cerebral blood ¯ow (CBF) expressed as a percentage of baseline values in six sheep. (B) Equivalent data for the measured mean arterial pressure (MAP) and (C) arterial carbon dioxide tension (PaCO2). The solid lines are the baseline values. Statistically signi®cant changes from baseline were inferred if the 95% con®dence intervals for a subsequent measurement did not include the mean baseline value. This did not occur for any of the measurements.
of exponentials or polynomials) is not important, provided the resultant curve closely matches the experimental data for Cin and Q. In essence, these functions can be used to `force' Cin and Q in Eqn 2 to follow the time course of the observed data.20 In practical terms, this means that the time
Model parameters were used to calculate secondary variables to facilitate comparison with other opioids and literature values. Cerebral equilibration times for morphine (and other opioids) were calculated by using the ®nal cerebral kinetic model to simulate the time course of the brain concentrations for a step increase in the arterial concentration from 0 to 1. The times required for the cerebral concentration to reach 50% and 95% of the arterial concentration were recorded. The former is equivalent to the half-time of cerebral equilibration only for a ¯ow-limited (single-compartment) model. The apparent permeability of the BBB (PS) was compared with a nominal cerebral blood ¯ow of 40 ml min±1.13 The apparent brain:blood partition coef®cient was calculated from Vb and a nominal real volume of 65 ml for the region of the brain drained by the sagittal-sinus catheter.13 Total arterial (AUCart) and sagittal-sinus (AUCss) area under the blood morphine concentration±time curves to 30 min were calculated using the trapezoidal rule. Drug retention (R%) in the brain was calculated as follows: R% 1 ÿ
AUCss :100 AUCart
6
This indicates the amount of morphine that had entered the brain via the arterial blood but had not left the brain via the
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course of Cout predicted by the equation now depends only on the one remaining unknown of the equation (V1), which can be estimated from Cout by curve ®tting. The advantage of this approach is that organ kinetics (e.g. V1) can be estimated without having to develop models for the many factors that affect Cin and Q in vivo. In the present study, the input concentrations were interpolated using exponential forcing functions. The measured changes in blood ¯ow were interpolated using polynomial forcing functions, but with the baseline value based on previous measurements.13 The output concentrations were curve ®tted to determine model parameters using modelling software (Scientist for Windows, version 2, Micromath, Utah, USA). The best ®t was determined by maximising the model selection criterion (MSC) of this software, which has been described in detail previously.19 The MSC is essentially the Akaike information criterion scaled to compensate for data sets of different magnitudes, and is calculated from the following formula:
Upton et al.
Cardiovascular and blood gas data
Pharmacokinetic data
Fig 2 (A) Measured pulmonary artery (triangle) and arterial concentrations (circle) of morphine in four sheep. (B) Measured arterial (circle) and sagittal-sinus (inverted triangle) concentrations of morphine in ®ve sheep. Data are shown as the mean at each time point. The variability of the data can be deduced from Figure 3. Solid lines are the best ®t of the kinetic model with the highest model selection criteria. These were the `¯ow limited with loss' model for the lungs (Table 1), and the membrane-limited model with V1 ®xed for the brain (Table 2).
sagittal sinus by the end of the study period. Retention in the brain could be the result of metabolism or deep distribution. An analogous calculation was also performed for the lung using arterial and pulmonary artery AUC values.
Results Deviations from the protocol were as follows. In one study, the measured arterial concentrations were found to be approximately half of the concurrent pulmonary artery and sagittal-sinus concentrations. A partially extravascular catheter that re-sampled catheter ¯ush solution was postulated to account for this apparent dilution, and the data were excluded. In another study, it was not possible to sample pulmonary artery blood because of catheter failure. The total number of studies of arterial±sagittal sinus gradients across the brain was therefore ®ve, and of pulmonary artery±arterial gradients across the lungs was four.
Mean observed blood morphine concentrations are shown in Figure 2. Peak arterial morphine concentration was 2.11 mg ml±1 (95% CI 0.91±3.30 mg ml±1), and this occurred for the last sample taken during the infusion. The concentration differences of morphine across the lungs and brain were small, and the differences were most obvious in the intrainfusion period (Fig. 2). Concentration gradients were therefore only analysed until 30 min after the infusion. If the arterio±venous concentration difference is small, a large number of replicates may be required to resolve the contribution of organ kinetics from that of assay variability.21 However, for the present data, the time course of the arterio±venous difference showed a consistent non-random pattern, with uptake occurring into both organs during the infusion, and with limited elution from the organ in the postinfusion period (Fig. 3), suggesting that the number of replicates was suf®cient for this purpose. As a further precaution against this phenomenon, the null model (Cout=Cin) was included for all modelling analysis. For both the lungs and brain, the null model was a poor alternative to structural models of organ kinetics (Tables 1 and 2). Lung kinetics
Parameter estimates for the various models of lung kinetics are summarized in Table 1. All models concurred that the volume of the ®rst compartment of the lungs was of the order of 2 litre. This is a relatively small volume of distribution for the lung in sheep, and produces reversible pulmonary artery±arterial gradients across the lung only after rapid i.v. administration.11 For the baseline cardiac output of 6 litre min±1, the half-life of equilibration of morphine through this component of the lung was 0.23 min. However, the improved ®ts of the `¯ow with loss' and membrane-limited models suggested that there was a deeper
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Morphine had minimal effects on cerebral blood ¯ow, arterial carbon dioxide tension and mean arterial pressure (Fig. 1). Arterial oxygen tension and haemoglobin saturation were unchanged from baseline. Thus, although the dose of morphine used was relatively high, it was not associated with signi®cant respiratory or cardiovascular side-effects. A ®xed baseline cerebral blood ¯ow of 40 ml min±1 was assumed in subsequent modelling of cerebral kinetics, in keeping with previous measurements in this preparation.13 Mean baseline cardiac output was 6210 ml min±1 (95% con®dence interval [CI] 4740±7680 ml min±1). This baseline value was used in subsequent modelling of lung kinetics. In all sheep, morphine was noted to produce a mild degree of dysphoria (agitation, mouthing of crate, nystagmus).
Cerebral kinetics of morphine in sheep Table 1 Models of lung kinetics ± goodness of ®t of the models of morphine kinetics in the lung. The MSC is the model selection criteria ± the higher the number, the better the ®t. Parameters are apparent distribution volume of the shallow compartment that includes blood (V1,lng), membrane permeability (PSlng) and deep compartment volume (V2,lng) in the lung. Data are mean (SD) returned by the curve-®tting program
compartment in the lung, for which uptake was essentially irreversible on the time scale of the study. The loss to this compartment was better described as a unidirectional loss term (PSloss), as the volume of the deep compartment of the membrane-limited model tended to very small values during ®tting, essentially defaulting to the `¯ow with loss' model. There was good agreement that the effective clearance of this loss was approximately 1.4 litre min±1. For a cardiac output of 6 litre min±1, this amounts to an effective extraction of 23% across the lung during the study. The retention of morphine in the lungs after 30 min was 12.3% (95% CI ±30.8% to 55.4%). Cerebral kinetics
Parameter estimates for the various models of cerebral kinetics are summarized in Table 2. The ¯ow-limited and null model were equally poor descriptions of the data, suggesting that the cerebral kinetics of morphine were not compatible with ¯ow-limited uptake. Data were better described by models where there was a permeability term describing loss from the ®rst volume of the brain. In contrast to the lungs, this permeability term was better described by transfer of morphine into a deeper compartment
MSC
V1,lng (ml)
PSlng (ml min±1)
V2,lng (ml)
Null model Flow Flow plus loss Membrane
1.49 1.93 3.36 3.23
2032 (598) 2036 (407) 2060 (485)
1370 (231) 1352 (268)
>105 (>105)
(membrane-limited model) rather than a ®rst-order loss term (`¯ow with loss' model). When the data were used to estimate both volumes of the membrane-limited model, the ®rst volume tended to a small number and was therefore constrained to be greater than 10±3 ml. As an alternative, this volume was ®xed at the nominal volume of the vascular compartment of the brain in sheep (5% of 90 ml, or 4.5 ml). This volume is remarkably similar to the volume of the ®rst compartment estimated by ®tting the other models (Table 2). This model was felt to be consistent with the notion of rate limitation for the movement of morphine across the BBB, and produced good parameter estimates. These were used for subsequent calculations. The permeability value of morphine was 7.4 ml min±1, and approximately one-®fth of the nominal blood ¯ow (40 ml min±1). The ®nal volume of the deep compartment was 92 ml. Given the nominal real volume of the region of the brain drained by the sagittalsinus catheter (70% of 90 ml13), this equates to a brain:blood partition coef®cient of approximately 1.4 (Table 3). Retention of morphine in the brain after 30 min was 8.4% (95% CI ±17.5% to 34.4%).
Discussion Cardiovascular and blood gas changes These data (Fig. 1) are in general agreement with the literature in that morphine had minimal effects on the cardiovascular system4 and cerebral blood ¯ow.22 Slight and transient respiratory depression was evident, as suggested by the small rise in carbon dioxide partial pressure but this was not statistically signi®cant. There was no associated hypoxia.
Lung kinetics A number of in vitro and in vivo studies have con®rmed that morphine is not metabolized by the lung.7 However, in agreement with the present data, a number of studies suggest retention of morphine in the lung, which can manifest as extraction or clearance across the lung in short-term studies. In rabbits, the lung retention of morphine was reported to be 33% following bolus administration.23 The value of 23%
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Fig 3 Mean (symbols) and 95% con®dence intervals (dotted lines) of the individual concentration differences across the lungs (pulmonary artery±arterial) in four sheep (A) and of the individual concentration differences across the brain (arterial±sagittal sinus) in ®ve sheep (B).
Model
Upton et al.
calculated from the present data in sheep is comparable. Importantly, the gradient of morphine across the lungs of sheep was reported to be minimal after 5 h of a constant-rate infusion.24 25 Therefore, it can be assumed that deep distribution was complete by 5 h. Assuming the process is ®rst order, a half-life of less than 1 h can be calculated. In man, ®rst-pass retention of morphine in the lungs has been reported as 7%26 and 4%.27 Low ®rst-pass uptake is consistent with membrane-limited uptake into the lungs, as suggested by the present data.
the half-time of the delay between morphine effects and blood concentrations reported previously for opioids of approximately 13 min,28 17 min29 and 34 min.30 Thus, while acknowledging potential differences in species and methodology, it may be that there is a component to this pharmacodynamic delay in addition to the time required for cerebral equilibration. Potential factors contributing to this delay were given in the introduction.
Concentration±effect relationships and active metabolites
Cerebral kinetics
Table 2 Models of cerebral kinetics ± goodness of ®t of the models of morphine kinetics in the brain. MSC is the model selection criteria ± the higher the number, the better the ®t. Parameters are apparent distribution volume of the shallow compartment that includes blood (V1,brn), membrane permeability (PSbrn) and deep compartment volume (V2,brn) in the brain. Data are mean (SD) returned by the curve-®tting program Model
MSC
V1,brn (ml)
Null model Flow Flow plus loss Membrane Membrane (V1 ®xed)
2.47 2.46 3.56 3.72 3.71
4.41 (2.38) 4.51 (1.76) 0.001 constrained 4.5 ®xed
PSbrn (ml min±1)
5.98 (1.19) 9.97 (1.92) 7.44 (1.60)
V2,brn (ml)
50.4 (33.4) 92.4 (59.2)
Morphine-6-glucuronide is active at the m-opioid receptor, while morphine-3-glucoronide may antagonize analgesia.7 While it is clear that a kinetic±dynamic analysis of morphine must account for the systemic and cerebral kinetics of parent morphine, and also the systemic and cerebral kinetics of its glucuronide metabolites, the latter was not performed in the present study. Some understanding of kinetic±dynamic relationships for morphine alone can be inferred from studies in the rat, which produces no morphine-6-glucuronide. In this species, the time course of parent morphine concentrations in the whole brain31 and brain extracellular ¯uid9 showed a good relationship with the time course of analgesia. In contrast, earlier work using vocalization as an analgesic end-point suggested that analgesia lagged behind brain morphine concentrations.32
Global vs regional brain concentrations The model presented here can be used to predict the global brain concentration of morphine. This will be useful if the global concentration is representative of the concentration surrounding opioid receptors. This is not to imply that opioid concentrations in all regions of the brain (and spinal cord) are equal, but rather that they change in parallel and this is consistent with the literature on morphine distribution throughout the brain. Positron emission tomography studies of morphine distribution in the brain of monkeys showed homogenous distribution.33 Direct measurements of the concentrations of morphine in different brain regions (including the spinal cord) showed a signi®cant difference in absolute concentration between regions, but are super®cially consistent with the notion that regional concentrations changed in parallel.8 34
Table 3 Comparison of model parameters for morphine with those of other opioids. Models were ®tted to cerebral kinetic data for different opioids collected under the same experimental conditions in conscious instrumented sheep. Data for alfentanil and pethidine have been published previously and could be described using a ¯ow-limited model.3 PS is the apparent permeability of the blood±brain barrier, Vb is the apparent distribution volume of the brain, R is the apparent brain:blood partition coef®cient. The times required for 50% and 95% equilibration (tequil50% and tequil95%, respectively) of the deep compartment of the brain determined by simulation are also shown. Where possible data are mean (SD) Opioid
PS (ml min±1)
Vb (ml)
R
tequil50% (min)
tequil95% (min)
Morphine Alfentanil Pethidine
7.4 (1.6) >1000 >1000
92 (59) 47 (8) 364 (17)
1.4 (0.9) 0.72 (0.12) 5.6 (0.26)
10.3 0.83 6.3
44.3 3.5 27.3
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The parameters of the model estimated from the present morphine data are shown in Table 3, together with parameters estimated for other opioids in the same experimental preparation.3 Alfentanil and pethidine were shown to have no rate limitation across the BBB, and cerebral kinetics were therefore ¯ow limited and dictated by their cerebral distribution volumes. As these differed markedly, their cerebral equilibration half-times also differed. In keeping with the literature, note that the permeability of morphine across the BBB was low compared with these other opioids, as was its cerebral distribution volume. The data unequivocally show that the cerebral kinetics of morphine could not be described by a ¯ow-limited (or venous-equilibrium) model. The permeability of morphine across the BBB was estimated relatively precisely, and was approximately one-®fth of cerebral blood ¯ow. While the calculated brain:blood partition coef®cient was relatively uncertain, it was evident that the time required for 50% equilibration was longer than for the other opioids (10.3 min, Table 3). However, this was shorter than the values for
Cerebral kinetics of morphine in sheep
Contribution of P-glycoprotein An analysis of the cerebral kinetics of morphine is complicated by the fact that morphine is a P-glycoprotein substrate, and is actively pumped out of the BBB. Abolishing this transport produces brain concentrations and analgesia 3±4 times higher than normal, in the face of minimal changes in systemic kinetics.5 9 As sheep also express the gene for P-glycoprotein,35 the permeability term estimated for morphine in the brain in the present model is therefore a composite of the permeability resulting from diffusion and the effective ef¯ux from the membrane by P-glycoprotein. This should be accounted for when correlating permeability with physicochemical properties.
10
11 12 13
The present data suggest that the delay in cerebral equilibration of morphine contributes to the slow onset and long duration of action for morphine. However, the quantitative role of other contributing factors to this clinical behaviour has yet to be determined. Nevertheless, the present model is a building block for these more complicated models of cerebral kinetic±dynamic relationships for morphine.
15
16
17
Acknowledgement Supported by the National Health and Medical Research Council of Australia (Project Grant 9936988).
References 1 Shafer SL, Varvel JR. Pharmacokinetics, pharmacodynamics and rational opioid selection. Anesthesiology 1991; 74: 53±63 2 Upton RN, Semple T, Macintyre P. The pharmacokinetic optimisation of opioid treatment in acute pain therapy. Clin Pharmacokinet 1997; 33: 225±44 3 Upton RN, Ludbrook GL, Gray EC, Grant C. The cerebral pharmacokinetics of meperidine and alfentanil in conscious sheep. Anesthesiology 1997; 86: 1317±25 4 Wood M. Opioid agonists and antagonists. In: Wood M, Wood AJJ, eds. Drugs and Anesthesia. Pharmacology for Anesthesiologists, 2nd Edn. Baltimore: Williams and Wilkins,1990; 129±78 5 Thompson SJ, Koszdin K, Bernards CM. Opiate-induced analgesia is increased and prolonged in mice lacking P-glycoprotein. Anesthesiology 2000; 92: 1392±9 6 Leysen JE, Gommeren W. Drug±receptor dissociation time, new tool for drug research. Receptor binding af®nity and drug receptor dissociation pro®les of serotonin-S2, dopamine-D2, histamine-H1 antagonists, and opiates. Drug Dev Res 1986, 8: 119±31 7 Milne RW, Nation RL, Somogyi AA. Disposition of morphine and its 3- and 6-glucuronide metabolites in humans and animals, and the importance of the metabolites to the pharmacological effects of morphine. Drug Metab Rev 1996; 28: 345±472 8 Dahlstrom BE, Paalzow LK. Pharmacokinetics of morphine in plasma and discrete areas of rat brain. J Pharmacokinet Biopharm 1975; 5: 293±303 9 Letrent SP, Pollack GM, Brouwer KR, Brouwer KL. Effects of a
757
18
19 20 21 22
23 24 25 26 27 28
Downloaded from http://bja.oxfordjournals.org/ at UNIVERSITY OF PITTSBURGH on March 10, 2015
14
Conclusion
potent and speci®c P-glycoprotein inhibitor on the blood-brain barrier distribution and antinociceptive effect of morphine in the rat. Drug Metab Dispos 1999; 27: 827±34 Tuk B, Herben VMM, Mandema JW, Danhof M. Relevance of arteriovenous concentration differences in pharmacokineticpharmacodynamic modeling of midazolam. J Pharmacol Exp Ther 1998; 284: 202±7 Upton RN, Doolette DJ. Kinetic aspects of drug disposition in the lungs. Clin Exp Pharmacol Physiol 1999; 26: 381±91 Grant C, Upton RN, Kuchel TR. An assessment of the ef®cacy of intramuscular analgesics for acute pain in the sheep. Aust Vet J 1996; 73: 129±32 Doolette DJ, Upton RN, Grant C. Agreement between ultrasonic Doppler venous out¯ow and Kety Schmidt estimates of cerebral blood ¯ow. Clin Exp Pharmacol Physiol 1999; 26: 736±40 Upton RN, Grant C, Ludbrook GL. An ultrasonic Doppler venous out¯ow method for the continuous measurement of cerebral blood ¯ow in conscious sheep. J Cereb Blood Flow Metab 1994; 14: 680±8 Milne RW, Nation RL, Reynolds GD, Somogyi AA, Van Crugten JT. High performance liquid chromatographic determination of morphine and its 3- and 6-glucuronide metabolites: improvements to the method and application to stability studies. J Chromatogr B Biomed 1991; 565: 457±64 McLean CF, Mather LE, Odontiadis J, Sloan PA. Improved method for morphine determination in biological ¯uids and tissues: rapid; sensitive and selective. J Pharm Pharmacol 1990; 42: 669±71 Evans AM, Shanahan K. The disposition of morphine and its metabolites in the in-situ rat isolated perfused liver. J Pharm Pharmacol 1995; 47: 333±9 Huang YF, Upton RN, Zheng D, McLean C, Gray EC, Grant C. The enantiomer speci®c kinetics and dynamics of verapamil after rapid intravenous administration to sheep ± physiological analysis and modeling. J Pharmacol Exp Ther 1998; 284: 1048±57 Upton RN, Ludbrook GL, Grant C, Doolette DJ. The effect of altered cerebral blood ¯ow on the cerebral kinetics of thiopental and propofol in sheep. Anesthesiology 2000; 93: 1085±94 Rainville ED, Bedient PE. Elementary Differential Equations, 5th Edn. New York: Macmillan Publishing Co., 1974; 207 Upton RN. An analysis of errors arising from the direct use of mass balance principles to describe regional drug uptake and elution. J Pharmacokinet Biopharm 1994; 22: 309±21 Bjorkman S, Akeson J, Helfer M, Fyge A, Gustafsson LL. Cerebral uptake of morphine in the pig calculated from arterio-venous plasma concentration gradients: an alternative to tissue microdialysis. Life Sci 1995; 57: 2335±45 Abdallah C, Besner JG, Du Souich P. Presystemic elimination of morphine in anesthetized rabbits. Contribution of the intestine, liver, and lungs. Drug Metab Dispos 1995; 23: 584±9 Sloan PA, Mather LE, McLean CF, et al. Physiological disposition of i.v. morphine in sheep. Br J Anaesth 1991; 67: 378±86 Milne RW, Sloan PA, McLean CF, et al. Disposition of morphine and its 3- and 6-glucuronide metabolites during morphine infusion in the sheep. Drug Metab Dispos 1993; 21: 1151±6 Boer F, Bovill JG, Burm AG, Mooren RA. Uptake of sufentanil, alfentanil and morphine in the lungs of patients about to undergo coronary artery surgery. Br J Anaesth 1992; 68: 370±5 Roerig DL, Kotrly KJ, Vucins EJ, Ahlf SB, Dawson CA, Kampine JP. First pass uptake of fentanyl, meperidine, and morphine in the human lung. Anesthesiology 1987; 67: 466±72 Bragg P, Zwass MS, Lau M, Fisher DM. Opioid pharmaco-
Upton et al.
dynamics in neonatal dogs: differences between morphine and fentanyl. J Appl Physiol 1995; 79: 1519±24 29 Kramer TH, d`Amours RH, Buettner C. Pharmacodynamic model of the effects of morphine and morphine-6-glucuronide during patient controlled analgesia. Clin Pharmacol Ther 1996; 59: 132 30 Gardmark M, Ekblom M, Bouw R, Hammarlund-Udeaes M. Quantitation of effect delay and acute tolerance development to morphine in the rat. J Pharmacol Exp Ther 1993; 267: 1061±7 31 van Crugten JT, Somogyi AA, Nation RL, Reynolds G. Concentration-effect relationships of morphine and morphine6 beta-glucuronide in the rat. Clin Exp Pharmacol Physiol 1997; 24: 359±64
32 Dahlstrom BE, Paalzow LK, Segre G, Agren AJ. Relation between morphine pharmacokinetics and analgesia. J Pharmacokinet Biopharm 1978; 6: 41±53 33 Hartvig P, Bergstrom K, Lindberg B, et al. Kinetics of 11C-labeled opiates in the brain of rhesus monkeys. J Pharmacol Exp Ther 1984; 230: 250±5 34 Bhargava HN, Villar VM, Rahmani NH, Larsen AK. Time course of the distribution of morphine in brain regions, spinal cord and serum following intravenous injection to rats of differing ages. Pharmacology 1993; 47: 13±23 35 Longley M, Phua SH, van Stijn TC, Crawford AM. Isolation and mapping of the ®rst ruminant multidrug resistance genes. Anim Genet 1999; 30: 207±10
Downloaded from http://bja.oxfordjournals.org/ at UNIVERSITY OF PITTSBURGH on March 10, 2015
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