Minimum alveolar anesthetic concentration (MAC), first described in 1963, has been used extensively since then to determine the potency of inhaled anesthetics (1,2). The initial method, as described in a laboratory setting, exposed an animal to multiple anesthetic concentrations and tested for movement to a noxious stimulus (1,3). If the animal moved at the initial concentration, the anesthetic partial pressure was increased incrementally, and the noxious stimulus was reapplied. These incremental changes were repeated until the animal did not move. If the animal did not move initially, the anesthetic concentration was decreased until movement occurred. A bracketing design was used whereby MAC was defined as the average of the largest concentration permitting movement and the smallest concentration preventing movement. Incremental changes in anesthetic concentration were in the range of approximately 20% of MAC, and while making incremental changes, the anesthetic concentration crossed over from the concentration immediately less than MAC to the concentration immediately more than MAC once in each animal.
The method as modified for clinical use involves a quantal design rather than a bracketing design (4). Each patient is exposed to an anesthetic concentration, a noxious stimulus (usually skin incision) occurs, and movement or lack thereof is recorded. If a patient moves with incision, the anesthetic concentration is increased in the next patient before incision. If a patient does not move with incision, the anesthetic concentration is decreased in the next patient before incision. A logistic or sigmoid Emax equation is used to fit the resulting quantal (categorical; all-or-none) data. Quantal analysis gives the dose at which there is a 50% probability of no movement.
Computer simulations have been used to evaluate methodologic variables that may affect MAC as estimated by the quantal technique generally used in patients (5). One “delivered” inhaled anesthetic concentration was compared with one randomly generated (from a normal distribution) “MAC” in each “subject.” Increasing the incremental concentration change of inhaled anesthetic increased the range of MAC estimates, and increasing the number of “crossovers” (“delivered” concentration more than and then less than, or less than and then more than, “MAC” in two successive “subjects”) improved the accuracy of MAC estimates.
We hypothesized that these variables may also affect the estimation of MAC with the bracketing technique generally applied to laboratory animals. Specifically, we hypothesized that using increments of <20% of MAC and more than one crossover may decrease the range of MAC estimates and improve accuracy. One aim of our study was to test this hypothesis by determining MAC in rats, first when the classic increment size and one crossover were used and then again when both increment size and the number of crossovers were altered.
Our aim could have been achieved by determining MAC in a single group of rats. However, we chose to use 2 cohorts of rats because we also were interested to know whether using incremental changes of approximately 20% of MAC and one crossover, as compared with smaller increments and several crossovers, might mask differences in MAC between groups in which MAC might be expected to differ. As a model of a condition in which MAC between groups was expected to differ, we chose to study pregnant (P) and nonpregnant (NP) rats (6). Four previous studies reported smaller MAC during pregnancy (7–10).
The protocol for this study was approved by the Animal Care Committee of Ben-Gurion University of the Negev, Beer Sheva, Israel. Sixty-one adult Sprague-Dawley rats, 250–350 g, from a colony maintained by the university and deriving from rats originally supplied by Arlen (Jerusalem, Israel), were used in this study. All rats were anesthetized in a small chamber with halothane 3.5% (inspired concentration). The halothane vaporizer was calibrated before each experiment by using a mass spectrometer (Perkin-Elmer 1100). A rapid fresh-gas flow of air 10 L/min was used to ensure rapid equilibration of the inspired halothane concentration with that in the chamber. Anesthesia was judged adequate once corneal reflexes were abolished. A tracheotomy was performed and a tracheotomy tube inserted, and rats breathed spontaneously. A catheter was inserted into the tail artery for determination of systolic and diastolic blood pressures and for blood sampling to obtain measurements of arterial blood gas tensions and serum sodium concentrations. Mean arterial blood pressure (MAP) was determined by electronic integration of the systolic and diastolic blood pressures. Rectal temperature was monitored and maintained at 37.0°C ± 0.5°C with a heating pad and heat lamps. The fresh gas flow was decreased to 2 L/min, and the inspired concentration of halothane was decreased to achieve an expired (end-tidal) concentration of halothane of 0.50% (0.48%–0.52%). Expired concentrations of halothane were measured by using an infrared gas analyzer (Capnomac Ultima; Datex-Ohmeda Inc., Madison, WI) (11–13). This analyzer measures halothane with an accuracy of 2% of the anesthetic concentration, i.e., approximately 0.01%–0.03% halothane for the range of halothane concentrations used in this study, reporting to the nearest 0.01%. The expired halothane concentration was maintained at 0.50% for 20 min before the determination of MAC was begun. No neuromuscular blocking drugs were given. The protocol included a provision to increase the concentration of halothane if, during the 20-min equilibration period, rats moved or demonstrated any signs of distress (i.e., hypertension, tachycardia, or tachypnea).
In the first cohort, the method for determining MAC was similar to that described by White et al. (14) for rats. This cohort included 31 rats. There were 4 male rats and 27 female rats. Females comprised three groups: NP, early P, and late P. The four male rats were included for comparison with the NP female rats, but data from the males were not subjected to statistical analysis. Early P was defined as 9–11 days of pregnancy, and late P was defined as 18–21 days of pregnancy (the average duration of pregnancy in rats is 21 days). The number of rats needed in the female groups for statistical analysis with a two-sided test with a significance level of 0.05 and a power of 0.85 was calculated (15). Assuming a mean MAC for halothane of 0.95% (the average of 5 recently published studies of halothane MAC in rats) (11,12,16–18), a difference between the null and alternative hypotheses of 0.08%, and the average of the standard deviations (sd) of the mean in the 5 aforementioned studies (0.08%), the sample size calculation yielded 9 rats per group. A supramaximal stimulus was delivered by application of a hemostat to the tail. It was clamped to a full ratchet lock for 60 s, and animals were observed for purposeful movement. Movement was assessed by a blinded observer, and tail flick accompanied by either twisting of the back or hips or kicking of the legs was defined as purposeful. If movement occurred, the expired concentration of halothane was increased by approximately 0.20% (0.18%–0.22%) and was maintained at that concentration for 20 min before application of the tail clamp was repeated. Each successive tail clamp was made at a progressively more proximal site. The halothane concentration continued to be changed in 0.20% increments depending on the presence or absence of movement. If the rat responded to the clamp, the concentration was increased, and if the rat did not respond, the concentration was decreased. After each change in anesthetic concentration 20 min was allowed for stabilization of alveolar gas concentration. MAC was defined as the halothane concentration midway between the largest concentration allowing movement and the smallest concentration preventing movement. The concentration of halothane was allowed to cross over from the concentration immediately less than MAC to the concentration immediately more than MAC just once in each rat.
In the second cohort, the method for determining MAC was similar to that used in the first cohort, with the following exceptions. The second cohort included 30 female rats, the incremental change in halothane was approximately 0.10% (0.09%–0.11%), and 4 crossovers were made. In both cohorts, blood samples were obtained at the end of the first 20 min at 0.50% expired halothane (before the first application of the tail clamp) and at the end of the experimental period. Systolic and diastolic blood pressures and MAP were determined at each halothane concentration.
The central tendency and variance of MAC data for each group were calculated both as the mean and sd and as the median and range. Mean values were calculated to provide comparison with previously reported values because historically most studies of MAC have reported values as mean and sd or se(1,7,8,14,17,19–21). In addition, studies using infrared gas analysis have reported data in that form (11). Median values were calculated to provide comparison with previously reported values from authors who considered the data to be not normally distributed, considered the incremental changes in halothane concentration used during the determination of MAC to represent an ordinal scale, or determined values by using logistic regression (9,10,12). Measures of central tendency and variance were expressed to 0.01%, as was reported in previous studies with infrared gas analysis (11–13). Mean values were compared between groups by using two-way analysis of variance (21). Median values were compared between groups using the Kruskal-Wallis test. Blood sample values (Paco2, Pao2, and serum sodium concentration) and blood pressures were compared between groups by using two-way repeated-measures analysis of variance. P < 0.05 was considered significant.
The mean difference in MAC between the 2 cohorts (17%; 0.14% halothane) was larger than expected for the magnitude of incremental change in halothane concentration used here to estimate MAC. To determine the theoretical maximum contribution of the incremental changes used here (0.1% and 0.2%), 78 simulated determinations of MAC were performed. For the first three simulations, we chose 0.91 to be the mean “real” MAC. There were 10 subjects in each group. In the first group we assumed minimal variance. The MAC of five subjects was −0.004% from the mean, and the MAC of the other five subjects was +0.004% from the mean. In the second group we assumed large variance. The MAC of five subjects was −2 sd from the mean, and the MAC of the other five subjects was +2 sd from the mean. For sd we used 0.08%, based on previous studies (11,12,16–18). In the third group we assumed intermediate variance. The MAC of two subjects was −2 sd from the mean, the MAC of two subjects was −1 sd from the mean, the MAC of two subjects was the mean value (0.91%), the MAC of two subjects was +1 sd from the mean, and the MAC of two subjects was +2 sd from the mean. For each group, estimated MAC was determined by assuming that the halothane concentration began at 0.5% and was increased in increments of 0.2%. Estimated MAC determination was then repeated by assuming an initial halothane concentration of 0.5% and an incremental change of 0.1%. Thus, six simulations were performed for the mean real MAC of 0.91% by using two sizes of incremental change (0.1% and 0.2%) for each of three variances of subject MAC values within each group. We chose the three variances to represent the two opposite extremes of variance and one intermediate variance. This simulation process was then repeated for 12 additional mean real MAC values: 0.92%, 0.93%, 0.94%, 0.95%, 0.96%, 0.97%, 0.98%, 0.99%, 1.00%, 1.01%, 1.02%, and 1.03%. As summarized previously, six simulations were performed for each mean real MAC value. This range of mean real MAC values was selected on the basis that it would be sufficient to illustrate the pattern of effect produced by increments of 0.1% and 0.2% for small, intermediate, and large variance of MAC values within each group of subjects.
In the first cohort, the mean MAC for halothane in males was 0.92 ± 0.06 (mean ± sd). In the female groups, the mean MAC values were NP, 0.95 ± 0.06; early P, 1.01 ± 0.09; and late P, 0.93 ± 0.13 (Table 1). Corresponding median values for females were NP, 0.90 (range, 0.70–1.12); early P, 0.90 (range, 0.72–1.30); and late P, 0.90 (range, 0.69–1.10). MAC values did not differ among the female groups. In the second cohort, the mean MAC values were NP, 1.16 ± 0.12; early P, 1.14 ± 0.10; and late P, 1.07 ± 0.10. Corresponding median values were NP, 1.15 (range, 1.10–1.41); early P, 1.15 (range, 0.98–1.40); and late P, 1.05 (range, 0.90–1.21). MAC values did not differ among groups or between time periods (the four crossovers) within each group. However, MAC for each condition (NP, early P, and late P) in the second cohort was significantly different from that for the same condition in the first cohort.
There were no differences in MAP between time periods within groups, but there was one between-group difference (the average MAP in the NP group in the first cohort was increased compared with the early P and late P groups). There were no differences in Paco2, Pao2, or serum sodium concentrations either between groups or between time periods within groups. Values for Paco2 ranged from 46 ± 2 mm Hg to 54 ± 10 mm Hg, values for Pao2 ranged from 189 ± 77 mm Hg to 303 ± 68 mm Hg, and values for serum sodium concentrations ranged from 129 ± 4 mEq/L to 139 ± 2 mEq/L.
The simulation data are shown in Table 2. Increment size affected the estimated MAC most when the variance of MAC values within a group was minimal. The largest difference in estimated MAC with 0.2% increments as compared with 0.1% increments was 0.05% (i.e., half the size of the smaller increment). With the largest variance of MAC values within a group, increment size had no effect for most MAC values, but it produced maximal difference for one of the MAC values within the range of mean real MAC values studied. Increment size had the least effect with intermediate distribution of MAC values within a group. Only an increment size of 0.1% consistently accurately estimated MAC and did so only when the distribution of MAC values within the group was not extremely small or large.
Our in vivo findings confirmed our hypothesis that the estimation of MAC in rats was affected when increment size was altered. In the second cohort, we found that MAC determined on any one of the crossovers was not different from MAC determined on each of the other three of four crossovers. This finding indicates that, for an increment size of approximately 10% of MAC, multiple crossovers did not significantly alter the estimation of MAC. Because our findings in the second cohort may be attributable to our design (starting with a small concentration of halothane and increasing in steps), it should not be concluded from our data that decreasing increment size and multiple crossovers will always increase estimated MAC. It is possible that if the initial concentration of halothane were much more than MAC and then decreased in steps, we would have found that using decreased increment size and multiple crossovers decreased MAC. Our conclusion that the increase in the number of crossovers probably did not contribute to the increased MAC determined in each group in the second cohort remains unproven because we have no data on MAC estimates for use in a design with an increment size of approximately 20% of MAC and multiple crossovers.
Our simulation findings confirm that increment size can affect the estimation of MAC. The magnitude of this effect is related to the variance of MAC values within the experimental group and to the MAC values themselves. The effect of increment size is maximal for tightly distributed data, may be minimal or maximal for data with large variance, and is minimal for data with intermediate variance. Our simulation findings indicate that up to 36% of the difference between Cohorts 1 and 2 in our in vivo studies may have been due to increment size, with the remainder being due to other factors, such as the use of two cohorts of outbred rats, interaction between increment size and number of crossovers, and measurement error.
The halothane MAC values for the NP rats in the 2 cohorts of our study, 0.95% ± 0.06% and 0.90% (0.70%–1.12%) in the first cohort and 1.16% ± 0.12% and 1.15% (1.00%–1.41%) in the second cohort, are in good agreement with recently reported halothane MAC values for rats (Table 3) (11,12,16,18). Those studies examined male Sprague-Dawley rats or Wistar rats, used a tail clamp or tail electrodes as the stimulus, changed the halothane concentration in 0.1% to 0.2% increments, allowed 12 to 40 minutes between each concentration change, and used one crossover. MAC values ranged from mean values of 0.76% ± 0.08% to 1.26% ± 0.08% and median values of 0.88% (0.82%–0.93%) to 1.00% (0.94–1.06%), where range was expressed as the 95% confidence interval. Although Sprague-Dawley rats were used in four of the five studies, vendor differences may have contributed to between-study variance.
An additional methodologic issue is the number of noxious stimuli delivered when multiple crossovers are performed. Performing multiple crossovers increases the number of tail-clamp applications. Within such a series of stimulations, later responses may be altered by earlier stimuli. Our finding that MAC determined on any one of the four crossovers in the second cohort was not different from MAC determined on each of the other three of four crossovers suggests that with allowing at least 20 minutes between applying the tail clamp and applying each successive tail clamp at a progressively more proximal site, neither sensitization/recruitment nor desensitization/fatigue of sensory or motor pathways occurred. This conclusion remains unproven because we have no data using a design either 1) with longer or shorter recovery times or 2) without repeated stimulation.
An unexpected finding of this study was that within each cohort (i.e., within each method of determining MAC), the MAC for NP rats was not significantly different from that for early P and late P. We had assumed that there was a difference that might be masked in the first cohort but would be demonstrable in the second cohort. Our results are consistent with two studies that reported no difference in MAC between P and NP subjects (19,22). It was previously speculated that the failure to demonstrate a difference in MAC in one of these two studies was due to the use of too large an incremental change in halothane (20%–25% of MAC) (9,19). The results of our study do not support that criticism. Review of the previous studies on the effects of pregnancy on halothane (or isoflurane) MAC do not reveal an obvious reason for the difference between our results and those of the several studies reporting decreased halothane (or isoflurane) MAC during pregnancy (Table 4). Factors that do not correlate with demonstrating or not demonstrating a decrease include species, endotracheal tube versus tracheostomy, mechanical versus spontaneous ventilation, skin clamp versus transcutaneous electrical stimulation, duration of stimulus, equilibration time at anesthetic concentration before stimulation, starting anesthetic concentration more than or less than the MAC concentration, incremental change in anesthetic concentration, and number of crossovers. A factor that may correlate with demonstrating or not demonstrating a decrease of MAC during pregnancy is the site of subsequent stimulus when repeated noxious stimulation is applied. This cannot be stated with certainty because of lack of information about the methods used in some early studies (Table 4). High progesterone levels were proposed as one possible explanation for decreased MAC during pregnancy. This proposal was based in part on a study in which halothane MAC was decreased in rabbits given exogenous progesterone (23). However, studies of halothane MAC in NP, P, and lactating rats revealed no correlation between decreased MAC and progesterone concentrations (8).
In summary, the results of our study confirmed our hypothesis that increment size affects estimates of MAC in rats with the bracketing technique. Our simulation studies indicate that up to 36% of this effect may be due to increment size per se. Lack of difference of MAC values among NP, early P, and late P groups cannot be explained as false-negative findings attributable to too-large increments or too few crossovers during the determination of MAC.
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