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Anesth Analg 2007;104:1440-1446 © 2007 International Anesthesia Research Society doi: 10.1213/01.ane.0000263274.62303.1a
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Abstract |
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 Top Abstract IntroductionMETHODSRESULTSDISCUSSIONAPPENDIX: CALCULATION OF...REFERENCES |
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BACKGROUND: There are two recognized methods of estimating the brain concentrations of IV anesthetic drugs: (i) use of pharmacokinetic/pharmacodynamic (PK/PD) modeling of drug effect, from arterial concentrations and electroencephalogram changes, and (ii) direct measurement of the uptake of drug in the brain, by simultaneously measuring arterial and jugular concentrations and cerebral blood flow (mass-balance method). These two methods have not been directly compared. Because an accurate estimate of the time taken for transfer of anesthetic drug from arterial blood to its effect-compartment in the brain is critical for accurate effect-compartment dosing in IV anesthesia, we compared the PK/PD and mass-balance methods for propofol, methohexital, and ketamine in a sheep model.
METHODS: After instrumentation with arterial and sagittal-sinus cannulae, electrocorticogram, and sagittal sinus Doppler flow measurement seven adult sheep were given a random sequence of short anesthetic infusions with methohexital, ketamine, and propofol. Multiple blood samples were taken for measurement of the time course of the drug concentrations, and the electrocorticogram processed (approximate entropy, for propofol and methohexital and percentage high frequency time, for ketamine) to numerically quantify drug effect.
RESULTS: Using the PK/PD method the t
Keo was 2.0 ± 0.4 min for ketamine, 2.7 ± 1.1 min for propofol, and was significantly shorter (0.3 ± 0.1 min) for methohexital. PK/PD and the mass-balance methods did not differ in the times to peak effect.
CONCLUSIONS: Both methods of calculating the delay in transfer of drug from arterial blood to brain give similar values. Methohexital crosses into the brain much faster than either propofol or ketamine.
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Introduction |
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TopAbstractIntroductionMETHODSRESULTSDISCUSSIONAPPENDIX: CALCULATION OF...REFERENCES |
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The pharmacokinetic (PK) profiles of the IV anesthetics propofol, ketamine, and methohexital drugs are well described (1) and are used to formulate dose regimens to optimize anesthetic depth. Because of the equilibration delay between plasma and brain compartments, some of the currently available pharmacologic models directly target brain concentration by incorporating plasma effect-compartment kinetics (2). The utility of these models for targeting effect-compartment concentrations and for optimizing anesthetic depth is dependent upon the accuracy of the incorporated PK/pharmacodynamic (PK/PD) data.
The kinetics of propofol uptake into the brain has been a matter of some debate. Animal and human studies using mass-balance principles have suggested that propofol exhibits a large and prolonged (tKeo 
6 min) disequilibrium between blood and target-site (brain) concentrations (3,4), resulting in a postinduction delay of 15–20 min before a constant level of anesthesia is achieved (5). On the other hand, PK/PD modeling of propofol uptake into the brain, using a variety of parametric and nonparametric methods, give tKeo values of only 2–3 min (6–8).
The primary aim of the present study was to directly compare the brain uptake kinetics of propofol using these two different methods: mass-balance and PK/PD modeling. The former method is based on calculation of the net flux of the drug into the brain from the difference in arteriovenous concentrations and the cerebral blood flow. PK/PD analysis is a well-established method for linking the measured blood concentration profile with drug effect, from which an estimate of effect-compartment (brain) concentration can be derived.
The PD characteristics of ketamine and methohexital have been less well studied than those of propofol. In the only previous article that has investigated the PK/PD of induction of anesthesia with ketamine, Keo and effect-compartment concentrations were not calculated (9). Similarly, we are not aware of any previous studies that have modeled the PK/PD characteristics of methohexital induction. The second aim of this study, therefore, was to compare the PD profiles of ketamine and methohexital with that of propofol.
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METHODS |
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TopAbstractIntroductionMETHODSRESULTSDISCUSSIONAPPENDIX: CALCULATION OF...REFERENCES |
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After approval by the Animal Ethics Committee of the University of Adelaide 7 adult Merino sheep, each weighing approximately 50 kg, were studied during anesthesia with propofol, ketamine, and methohexital. Under halothane anesthesia, the sheep were instrumented as previously described (10). This included insertion of a sagittal-sinus Doppler flowprobe for cerebral blood flow measurements, a femoral arterial intravascular cannula for arterial blood sampling, a sagittal-sinus catheter for sampling of cerebral effluent blood and a parasagittal linear array of stainless steel electrodes for quantifying the approximate entropy of the electrocorticogram (ECoG). The electrodes were spaced 2 mm apart, and penetrated 1–2 mm into the outer layers of the cortical gray matter. The ECoG was obtained using two electroencephalogram (EEG) monitors (A1000, Aspect Medical Systems, Natick, MA) with the output voltage from the cortical surface reduced electronically, so that the input into the EEG monitors was similar in magnitude to that observed with scalp electrodes. The signal was digitally sampled at 256/s, and downloaded without further filtering to a computer for further analysis. After allowing at least 24 h for the animal to recover and to check the stability of the recording apparatus, the sheep were given a series of short IV anesthetics. Propofol (200 mg), ketamine (300 mg) and methohexital (150 mg) were administered over 2 min in random order and the sheep were then allowed to recover fully (at least 2 h) before the administration of the next drug. The relatively short recovery time allowed all anesthetics to be delivered on the same day, eliminating deterioration in Doppler flow data quality over successive days. All variables were recorded for 20 min after induction of anesthesia. Arterial and sagittal sinus blood samples (1 mL) were taken at intervals of 15 s for 3 min, and then every minute up to 20 min, heparinized (25 IU) and stored at –5°C. The concentration of each drug was later assayed using high performance liquid chromatography (HPLC) and the fluorescence detection method. Sample sizes were 500 µL for each drug. Propofol concentrations in whole blood were assayed using a modification of a technique described by Mather et al. (11) based on solvent (n-hexane) extraction of samples and HPLC. A silica column was used, and the buffer was acetonitrile: 0.5% acetic acid (55:45). Fluorescence detection was used with excitation and emission wavelengths of 274 and 300 nm, respectively. Thymol was the internal standard and the limit of sensitivity was approximately 0.02 µg/mL. Ketamine was assayed using solvent (n-hexane) extraction of samples and HPLC with a C18 column and using an acetonitrile-phosphate buffer (42:58), pH-8, with UV detection (210 nm). Lidocaine was used as an internal standard, and the limit of sensitivity was approximately 0.1 µg/mL. Methohexital was assayed using solvent (n-hexane) extraction and HPLC with a C18 column and acetonitrile-phosphate buffer (38:62), pH-5.5, with UV detection (230 nm). Pentobarbital was used as an internal standard, and the limit of sensitivity was approximately 0.15 µg/mL. The linear calibration ranges were 1.25–40 µg/mL for propofol, 0.5–4 µg/mL for ketamine and 10–50 µg/mL for methohexital.
MA-Balance Measurement of Brain Concentration
The brain concentration of each anesthetic was calculated as previously described (10) using mass-balance principles. This is equivalent to the Fick Principle used in other physiological applications. Briefly, the net flux of each drug into the brain was calculated from the difference in concentration between arterial and sagittal sinus blood and the cerebral blood flow rate. We assumed a brain mass of the area drained by the sagittal sinus of 75 g. Arteriovenous transit time was not accounted for in the mass balance method. Although transit times can affect calculations of drug concentrations, in practice the small size of transit time compared with sampling intervals means any errors are small. From here on, this method will be referred to as the "mass-balance" method of calculating the brain concentration.
Quantification of Anesthetic Effect on the ECoG
All ECoG analysis was done using Matlab software (Matlab 7.0 Mathworks, Natick, MA). The effect of anesthesia on the ECoG was quantified using two algorithms: 1) approximate entropy (for propofol and methohexital) and 2) the proportion of high frequency activity (for ketamine). The latter method was necessary because ketamine did not have a consistent effect on approximate entropy.
The approximate entropy of the ECoG was calculated from non-overlapping 5 s ECoG segments in the standard manner, as described by Bruhn et al. (12), using a sample rate of 128/s, an embedding of m = 2, and noise threshold r = 0.2 x SD. Because the algorithm incorporates a lower threshold for noise, approximate entropy has been shown to seamlessly decrease as burst suppression increases.
There is no previously published EEG method of quantifying ketamine’s effect. On observation of the ECoG signals it was apparent that anesthesia with ketamine is characterized by an ECoG pattern in which short episodes of low frequency, high amplitude oscillations alternate with the preexisting high frequency, low amplitude activity (see Fig. A1 in Appendix). With increasing depth of anesthesia, the proportion and length of the high frequency episodes decrease. The reduction in the percentage of high frequency component of the ECoG was quantified for ketamine using wavelet analysis (see Appendix for a more detailed explanation). Because these episodes of low frequency activity are localized in time, a wavelet transform was applied to the ECoG using the MatLab® function cwt (continuous wavelet transform, Morlet wavelet). A scale (approximately "1/frequency") of 48 was heuristically chosen as the high-low frequency boundary. The proportion of high frequency in the ECoG was quantified as the percentage of time that the wavelet coefficients for scales <48 were above an arbitrary coefficient threshold of 13, calculated as a running 10 s average. This method of quantification of ketamine’s effect was found to track concentrations well and was consistent across different animals (Fig. 3). A Matlab function for this method may be found in the Appendix.
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(PK/PD) Modeling of Effect-Compartment Brain Concentration
Modeling of the effect-compartment (brain) IV anesthetic concentration was performed by relating the measured arterial concentrations of each anesthetic to the measured effect. Plotting ECoG effect versus arterial concentration produced the anticipated hysteresis loop (Fig. 1a), reflecting the lag between arterial and effect-compartment concentration. Effect-compartment concentration was estimated by minimizing the hysteresis between arterial concentration and entropy (Fig. 1b) using the classic first-order effect-compartment model:
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where Cart is the arterial concentration of the anesthetic, Ceff is the effect-compartment concentration of the drug, and Keo is the first order rate constant for efflux from the effect-compartment.
We estimated the effect-compartment concentration of each drug by iteratively running this model with a series of Keo steps. For each iteration, a nonlinear inhibitory sigmoid Emax curve was fitted to the data using the MatLab "nlinfit" function (nonlinear least-squares data fitting), defined as follows:
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where effect is the approximate entropy or high frequency component of the ECoG, the Emax and Emin are the maximum and minimum ECoG effects recorded for each animal, the EC50 is the drug concentration at which the ECoG effect is midway between this maximum and minimum, the Ceff is the concentration at the effect-compartment, and 
describes the slope of the concentration-response relationship. Keo was determined from the iteration yielding the greatest coefficient of determination (R2) for measured and modeled entropy for each subject. Values of the pharmacodynamic parameters, and EC50, were derived from the fitted inhibitory Emax curves.
Data Handling and Statistical Analysis
For the PK/PD analysis, the brain concentration was derived from Eq. 1 (Ceff), using the value of Keo calculated as described above. Both the absolute concentration and values with the peak concentration normalized to one were plotted for each method, and the peak absolute brain concentration and time to peak concentration compared using the paired t-test. The partition coefficient for each drug was calculated as the ratio of the peak brain concentration for the mass-balance method, and peak effect-compartment concentration derived from the PK/PD analysis. Partition coefficients and peak concentration times for each drug were compared using one-way ANOVA (Tukeys post hoc test) and the Kruskal-Wallis test (Dunn’s post hoc test), for normally and non-normally distributed data, respectively. Post hoc tests were corrected for multiple comparisons. Normality of data was assessed using the Kolmogorov-Smirnov test. A value of P < 0.05 was considered statistically significant. All data are presented as mean ± sem.
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RESULTS |
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TopAbstractIntroductionMETHODSRESULTSDISCUSSIONAPPENDIX: CALCULATION OF...REFERENCES |
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Brain Concentration Time-Course
The summary PK/PD parameters for each drug are shown in Tables 1–3. The time-course of concentration changes were similar for propofol and ketamine, as reflected in the similar lag times to peak brain concentration for both analysis methods (Table 2 and Fig. 2). This implies similar t
Keo values for each method, 2.7 ± 1.1 min for propofol and 2.0 ± 0.4 min for ketamine. For methohexital, peak concentration was reached slightly more rapidly for the PK/PD analysis (129 ± 3 s compared with 156 ± 7 s, P < 0.05). The tKeo for methohexital was rapid (0.3 ± 0.1 min) and significantly faster than both propofol and ketamine (P < 0.05). This was reflected in a relatively short latency to peak brain concentration (Table 2 and Fig. 2).
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Peak Brain Concentrations—Comparison of Analysis Methods
Peak brain concentrations for each drug differed significantly according to analysis method (Table 3). These differences reflect the blood:brain partition coefficients for each drug, which was 2.6 ± 0.7 for propofol, 2.8 ± 0.6 for ketamine and 0.6 ± 0.1 for methohexital. For propofol and ketamine the mass-balance method yielded consistently higher brain concentration estimates compared with PK/PD analysis. This was statistically significant for ketamine (2.7 ± 0.4 µg/mL compared with 0.6 ± 0.2 µg/mL for the PK/PD estimate, P < 0.05), but marginal for propofol (8.6 ± 2.2 µg/mL compared with 4.1 ± 1.1 µg/mL for the PK/PD estimate, P = 0.05). In contrast, the brain concentration of methohexital was consistently higher for the PK/PD-analysis compared with the mass-balance method (22.5 ± 5.1 µg/mL compared with 13.9 ± 4.2 for the mass-balance method, P < 0.05).
Anesthetic Effects on the ECoG
The changes in ECoG-measured anesthetic effect for each drug are shown in Figure 3. The time-course with increasing and decreasing anesthetic concentrations were similar for ketamine and propofol, even though different ECoG algorithms were used. This seems to verify the similar PK/PD characteristics of the two drugs. In comparison, the changes in approximate entropy with methohexital were smaller and more rapid, consistent with its very short tKeo.
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DISCUSSION |
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TopAbstractIntroductionMETHODSRESULTSDISCUSSIONAPPENDIX: CALCULATION OF...REFERENCES |
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Brain Concentration Time-Course
The brain uptake kinetics for the two measurement methods were compared in the present study by analyzing the brain concentration time-course for each method.
MA-balance analysis of brain concentration and PK/PD modeling gave similar brain uptake kinetics for propofol, with a tKeo value of 2.7 min. This lag time is shorter than previously published data from sheep (4.3 min) and humans (6.5 min) using a six-compartment kinetic and dynamic physiological model (3,4), but similar to that derived from previous PK/PD analyses (6–8). Although the agreement between methods in the present study suggests that short (2–3 min) lag times may be appropriate for effect-compartment dosing in IV anesthesia, the discrepancies between studies cannot be wholly ignored, especially when one examines drug offset. The differences probably lie in the complexity of the brain equilibration process. Propofol kinetics in the brain are best described using a two-compartment model, where kinetics in the brain are affected by propofol’s own effect on cerebral blood flow (13,14). This "complex" process can be approximated by a single compartment model, however it takes at least three parameters (for a two-compartment model) to accurately describe the cerebral equilibration of propofol. Approximation of this process with a single number is a simplification at best. Time to peak effect seems a relatively simple process, evidenced by the similarity between time to peak effect determined by PK/PD and mass balance techniques. The discrepancies between rates of offset for propofol and methohexital (Fig. 2) suggest that offset is a more complex process when it can be hypothesized that the drugs’ own depression of cerebral blood flow acts to delay drug elution from the brain. Interestingly, there is little discrepancy between techniques for ketamine, a drug with minimal effects on cerebral blood flow.
The similarity in the time-course for changes in brain concentration between the analysis methods for propofol suggests that the disequilibrium between propofol blood concentrations and effect is due largely to the physicochemical diffusion properties of the drug, rather than to drug-receptor interaction kinetics. If there were a significant lag due to drug-receptor interactions, one would have expected the PK/PD effect-compartment data to lag behind the mass-balance-measured concentration profile. The time resolution of the ECoG analysis in our study was 10 s (around the same order of magnitude as the drug sampling time); thus the analysis lag did not contribute significantly to total tKeo value.
Methohexital had a very short lag time and rapid elimination compared with the other two drugs. These results indicate that methohexital has faster induction and emergence characteristics than propofol, the current drug of choice for rapid IV anesthesia.
Peak Brain Concentrations
The estimated brain concentrations for all three drugs tested in the present study differed according to the method of analysis used. It is problematic to try to compare the actual magnitude of the effect-compartment concentration and the mass-balance brain concentration. The effect-compartment model is structured like "an apparent distribution volume." So, at steady-state, the effect-compartment concentration will equal the arterial concentration. The effect-compartment concentration is thus an apparent, not a real, concentration because of an assumption of a partition coefficient of one. The mass-balance method calculates a "real" brain concentration. The amount of anesthetic drug calculated to be in the brain is divided by the physiological volume of the brain to give the brain concentration. At steady-state, this brain concentration can be more or less than the arterial concentration, depending on the drug’s oil:water partition coefficient and the amount of protein binding. It is therefore valid to compare the time-course of brain and effect-compartment concentrations, and to make conclusions about the timing of the peak concentrations for the PK/PD and mass-balance methods; however the magnitude of the concentrations derived from the two methods will not necessarily equate.
The calculated partition coefficients in our study differ from published values (15). This is because the latter are based solely on octanol:water partition coefficients, whereas our values are based on real brain concentrations, which are dependent on drug lipophilicity and the extent of protein binding. The slightly higher partition coefficient for ketamine compared with propofol is therefore explained on the basis of the low protein binding of ketamine (15). Similarly, the very low partition coefficient for methohexital may be explained by its comparatively high protein binding and modest lipophilicity.
An alternative explanation for the difference in calculated brain concentrations between the methods of analysis is that the PK/PD-derived effect compartment concentrations were not representative of the overall brain concentration. Total and regional brain concentrations of propofol have been measured previously in rats using HPLC (16,17). However, these studies showed a uniform regional distribution of propofol throughout the brain, with the possible exception of the midbrain, which showed increased concentrations at low infusion rates (17). Overall, these findings indicate that the differences observed in the present study are unlikely to be attributable to a regional distribution effect. This conclusion is further supported on grounds that both measurement methods were effectively sampling from the cerebral cortex, not the entire cerebrum.
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APPENDIX: CALCULATION OF KETAMINE EFFECTS ON THE ECoG |
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TopAbstractIntroductionMETHODSRESULTSDISCUSSIONAPPENDIX: CALCULATION OF...REFERENCES |
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As shown in Figure A1, at low levels of ketamine (left side), the "awake" (low-amplitude, mixed frequency) electrocorticogram (ECoG) pattern is interrupted by episodes of large amplitude slow waves (1–5 Hz), lasting about 1 s. At the peak of the ketamine effect these slow-wave episodes have increased to take up most of the ECoG (right side). This can be easily quantified in frequency and time using the Morelet wavelet transform - shown in the lower figures. A Matlab function to achieve this is: function [perc] = ket_wave_funct(x,Fs,thres);
% Does cwt and then determines percentage time that the ECoG ...
% signal is in "slow wave" mode (vs "awake/REM" mode)
% INPUTS:
% (1) ECoG signal (x)
% (2) Sampling frequency (set for Fs = 256/s)
% (3) Threshold for determining presence of slow wave episodes
% OUTPUTS percentage time (perc) that the ECoG is in slow-wave mode
% ——————————————————–
% Transforms to continuous wavelet - morlet - low frequencies only ...
% (i.e., scales 48 to 64)
coefs = cwt(x,[48:8:64],‘morl’);
zin = abs(coefs(3,:)); % Absolute magnitude of wavelets
len = length(zin);
% Make a smooth envelope of wavelet coeffs
zins = medfilt1(zin,40);
% Separate series into slow segments and fast segments
% The threshold may need optimization depending on the ECoG amplitude
a = find(zins > thres); %find the bits with lots of low frequency power
b = find(zins <= thres); %find the bits with no low frequency power
hi = x + 1;
lo = x;
hi(b) = 0; % set all no LF bits to zero
lo(a) = 0; % set all lots of LF bits to zero (just for testing graph)
% Go through whole file and identify low sections and %time low> 0
llo = length(lo);
perc = [];
seg = Fs*5; %five second running averages
kk = 1;
for i = 1:seg:seg*fix(llo/seg)-seg;
zzz = lo(i:i+seg); % 5 s segment
aa = find(zzz = 0);
perc(kk) = length(aa)/seg;
kk = kk + 1;
end
%% Do figure to check visually OK
% figure (9); plot(perc,‘k’);
% xlabel(‘Time (s)’);
% ylabel(’Percentage slow waves’);
return
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Footnotes |
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Supported by the Neurological Foundation of New Zealand.
Reprints will not be available from the authors.
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REFERENCES |
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TopAbstractIntroductionMETHODSRESULTSDISCUSSIONAPPENDIX: CALCULATION OF...REFERENCES |
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[Abstract/Free Full Text] - Ludbrook GL, Upton RN. A physiological model of induction of anaesthesia with propofol in sheep. II. Model analysis and implications for dose requirements. Br J Anaesth 1997;79:505–13.
[Abstract/Free Full Text] - Sewell JC, Sear JW. Can molecular similarity-activity models for intravenous general anaesthetics help explain their mechanism of action? Br J Anaesth 2002;88:166–74.
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- Larsson JE, Wahlstrom G. The influence of age and administration rate on the brain sensitivity to propofol in rats. Act Anaesthesiol Scand 1998;42:987–94.
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