Context-sensitive decrement times can help us understand why one anesthetic may differ greatly from another in time to recovery from anesthesia (1,2). Duration of anesthesia can play a large distinguishing effect, and this effect is the focus of the present essay.
For inhaled anesthetics, context-sensitive decrement times connect two values: a) anesthetic duration (nominally at a constant alveolar concentration)—the “context” and b) the time needed to decrease the alveolar or vital tissue (e.g., brain, heart, kidney and liver, collectively called the vessel rich group of tissues or VRG) (3) concentration by some fractional “decrement” of the starting concentration (e.g., an 80% decrement time would be the time needed to reach 20% of the starting concentration. After only a few minutes of anesthesia, the VRG is thought to be in equilibrium with the alveolar concentration. Both alveolar (or plasma) and effect-site decrement times might be of interest (4). The present report focuses on VRG decrement times while noting the difference from alveolar decrement times. Times to achieve a particular decrement in the VRG are a more appropriate focus than the alveolar concentrations because the central nervous system contains the effect-site for depressant drugs such as opioids, hypnotics, and inhaled anesthetics (5). However, as we will show, the times for a given decrement in the alveoli closely approximate those for the VRG.
Some things intuitively follow from the above description. An anesthetic of short duration produces a shorter time to a specific decrement (say, 95%) because a longer anesthetic duration increases anesthetic accumulation in tissue depots. This accumulation limits the decrease in drug concentration at the conclusion of anesthesia. Similarly, a greater anesthetic solubility in tissues promotes a greater accumulation of anesthetic in tissues, an accumulation that will linger during recovery from anesthesia. More soluble drugs also equilibrate slower and this can affect recovery in a complex manner. The greater accumulation over time and the slower equilibration are two views of the same fact: the body stores more molecules of a highly soluble drug in tissue than a poorly soluble drug at the same partial pressure of drug (e.g., the same “free” drug) in the brain.
Anesthetic solubility is a prime determinant of recovery from anesthesia. The blood/gas partition coefficient or λ (e.g., λ = 0.45 for desflurane and 0.65 for sevoflurane) (6) defines the solubility in blood and describes the affinity or capacity of blood to hold anesthetic (note that determinations of solubility differ slightly from laboratory to laboratory; for example, the value for desflurane is given as anything between 0.42 and 0.49). Thus, the affinity or capacity of desflurane for blood is 0.45 times (45% of) the affinity for the gas phase. By definition
It is assumed that equilibrium (the same partial pressure of anesthetic) exists between the two phases—blood and gas.
For the same duration of anesthesia, the decrease in the alveolar anesthetic concentration will be greater at a specific time of recovery (e.g., 10 min after discontinuation of anesthetic administration) with a less soluble anesthetic. This follows from the fraction of anesthetic (F) cleared from the blood as it passes through the lungs. F may be calculated from equation 2 (7):
where Q is cardiac output and VA is alveolar ventilation. Note that when λ is zero, F = 100%.
The extremes of solubility illustrate its importance to context-sensitive decrement times (see the Appendix for details). For anesthetic X with minimal solubility, nearly all of X is cleared at the lungs (test this by inserting a very small value for λ in equation 2). So the time to almost any decrement must be short regardless of the extent of equilibration. For anesthetic Y with enormous solubility, only a trivial fraction is cleared at the lungs (test this by putting in a very large number for λ in equation 2). Furthermore, with anesthetic Y, equilibration becomes a vital determinant of decrement time because the decrement will be to whatever degree of equilibration has occurred. That is, if the blood returning to the lungs were half equilibrated with the inspired partial pressure of Y, then the concentration could only decrease very slowly from this level.
We have been simplistic in the previous explanations. We assumed that we could treat the body as a single bag of gloop wherein all tissues equilibrate equally. Not so. In fact, some tissues equilibrate quickly (the brain, heart, liver, kidney), some slower (muscle and skin), and some slower still (fat). Thus, when anesthetic administration ceases, the alveolar anesthetic concentration decreases in a multiexponential manner. That is, the concentration decreases very rapidly at first, then slower, then still slower until at last it decreases at a rate dictated by the slowest component, the elimination of anesthetic vapor from fat. Using overpressure, the anesthesiologist may force anesthetic into quickly equilibrating tissues (especially the brain) to rapidly reach anesthetizing concentrations. Because these tissues equilibrate quickly, this does not take much time. Yasuda et al. (8,9) estimated time constants of 3–6 minutes for the VRG. Similarly, it does not take much time to eliminate anesthetic from the rapidly equilibrating tissues, although it does take more time to get drug out of the VRG than into the VRG because there is no equivalent of overpressure during washout of drug. Thus, initially the washout from the rapidly equilibrating VRG dictates blood and alveolar concentration during recovery. Subsequently, elimination from muscles and fat also determines the alveolar concentration during recovery from anesthesia. A longer anesthesia will cause more anesthetic to accumulate in muscle and fat, and, as the duration of anesthesia increases, the final part of the elimination curve moves higher and higher, increasing the time for recovery from anesthesia. However, as indicated in the previous discussion, for a nearly insoluble anesthetic the increase must be trivial, whereas for an extremely soluble anesthetic the increase must be considerable.
The most commonly used potent anesthetic vapors, isoflurane, sevoflurane, and desflurane, have solubility characteristics between the extremes of anesthetics X or Y. As a result, we have intermediate effects on decrement times.
Context-sensitive decrement times vary as a function of the duration of anesthesia (a “context”) as well as the solubility of the anesthetic. The particular decrement selected (e.g., 50%, 80%, 90%, 95%) will also influence the separation among anesthetics. If we chose a smaller decrement (say 50%), anesthetics will differ minimally in the time to reach that decrement; the time to reach a 50% decrement is small for isoflurane, sevoflurane, and desflurane regardless of anesthesia duration (2). But at smaller decrements, separations among anesthetics arise. At a 90% decrement, moderately soluble anesthetics like isoflurane will show a considerable increase in decrement times with increasing duration of anesthesia (2), and this increase occurs after relatively brief anesthetics. Sevoflurane also shows an increase but only after longer anesthetics. As we will show, at a 95% decrement, sevoflurane would also show an increase after a brief anesthetic.
We tested these concepts using simulations performed by Gas Man® (Version 3.1.8) (10). Gas Man® is a physiologically based model of inhaled anesthetic uptake and distribution. It is a commercially available computer program used for education (11,12) and can accurately predict expired anesthetic concentrations during induction and emergence from anesthesia (13). Gas Man® assumes several things. Inhaled anesthetic kinetics may be described with a flow-limited 4 compartment mammillary model (lungs, VRG, muscle group [MG], fat group [FG]) attached to another compartment, the breathing circuit. Each compartment equilibrates instantly with the anesthetic brought to it, and, except for the concentration effect, the equilibration follows first-order kinetics. Solubility in blood and tissues, gas and blood flows, and compartment volumes determine the rate of equilibration. The model allows the user to fix the essential elements: anesthetic solubility in blood and tissues, gas and blood flows, and tissue volumes. It does not correct for intertissue diffusion of anesthetics, anesthetic metabolism, or ventilation/perfusion abnormalities. The particular (Euler) integration used stabilizes the behavior of the model under extreme conditions of fresh gas flow, ventilation, and cardiac output.
For comparisons among desflurane, isoflurane and sevoflurane, we used an alveolar ventilation of 4 L/min and a cardiac output of 6 L/min. Solubility settings were those available in Gas Man® (Table 1). By using the largest anesthetic concentrations that could be delivered and an open system, we rapidly (4–7 min of simulated time) achieved alveolar target concentrations of 10% desflurane, 4% isoflurane, and 5% sevoflurane. The actual concentrations are not relevant to this exercise except that they allowed accurate determinations of the time to various decrements.
We manipulated the vaporizer settings to rapidly achieve and maintain the target concentrations. At 30, 60, 90, 120, 150, 180, 210, and 240 min after the start of anesthesia, anesthetic administration was abruptly discontinued (the vaporizer setting decreased to zero) and the circuit was flushed. A nonrebreathing system continued to be used. We noted the minutes of washout needed to decrease the alveolar and VRG concentrations by 50%, 60%, 70%, 80%, 88%, 90%, 92%, and 95%.
We also simulated the effect of different cardiac outputs on decrement times for sevoflurane. In addition to the 6 L/min used in a comparison of the anesthetics, we used 4 L/min and 8 L/min. Each cardiac output was applied throughout the simulation.
Finally, to mimic the effect of “tapering” at the end of anesthesia, we simulated the effect of decreasing the alveolar concentration by half during the last 30 min of anesthesia (e.g., isoflurane might be maintained at 4% for 60 min, then at 2% for the last 30 min (before discontinuing anesthetic administration). Decrements examined were from the primary concentration used (e.g., from 4% isoflurane).
As predicted, the time to an 80% decrement is relatively short for desflurane, isoflurane, and sevoflurane (Fig. 1A), particularly for anesthesia in the usual clinical range of up to 120 min duration. For anesthesia shorter than 90 min, the times to an 80% decrement would likely be clinically indistinguishable among the three drugs. For anesthesia longer than 90 min, accumulation of isoflurane in tissue increasingly delays the time to an 80% decrement. These delays might be clinically appreciable. For sevoflurane and desflurane, accumulation of drug in tissue does not appreciably influence 80% decrement times for anesthesia of less than 240 min duration.
The time to an 88% decrement shows the delay in recovery produced by accumulation of sufficient anesthetic in muscle and fat to make the slow terminal washout from these tissues rate limiting (Fig. 1B). For isoflurane anesthesia exceeding 90 min in duration, the rapid washout from the VRG cannot produce an 88% decrease in concentration because the slower washout of drug from the muscle and fat increasingly prolongs the time to an 88% decrement compared with sevoflurane and desflurane. The times for sevoflurane and desflurane also show the influence of drug accumulation on recovery, with the effect more pronounced for sevoflurane than for desflurane.
These trends progress with increasing decrements. At a 90% decrement (Fig. 1C), the graph for sevoflurane draws away from that for desflurane after a 120-min anesthesia. At a 92% decrement (Fig. 1D), the difference between times for sevoflurane and desflurane to achieve a particular decrement increases, and the rise in the sevoflurane curve occurs at an earlier time. At a 95% decrement (Fig. 1E), the rise occurs at a still earlier time. In addition, although the effect is much greater and earlier with sevoflurane, we now see an increase with desflurane. In each case, the primary cause of the increase in time with larger decrements and longer anesthesia is that the rapid washout from the VRG by itself cannot produce the required decrement and recovery increasingly depends on washout from more slowly equilibrating tissues.
The effect of increasing duration of anesthesia on decrement times can be illustrated for individual anesthetics. As indicated in Figure 2A (desflurane) and B (sevoflurane), an increasing duration lengthens the time to a given decrement and shortens the time to an appreciable increase in time to reach that decrement. Solubility influences both effects: the lengthening is greater with the more soluble sevoflurane, and increasing the duration of anesthesia produces an earlier increase with sevoflurane. Decreasing the anesthetic concentration by half for the last 30 min of anesthesia shortens the times to a specific decrement (compare Figs. 2, A and C; and compare Figs. 2, B and D), but the qualitative relationship between anesthetics (e.g., desflurane versus sevoflurane) remains the same. This approach to tapering anesthesia during the last 30 min of anesthesia does not cause anesthesia with isoflurane to allow the rapid attainment of longer decrement times (compare Fig. 2E with any of the remaining graphs in Fig. 2).
With all other factors held constant, our simulations show that cardiac output can considerably influence the times to a given decrement (Fig. 3). An increase in cardiac output increases time to reach a given decrement and causes an earlier increase in the time to reach a given decrement. A decrease in cardiac output does the reverse. This is, of course, to be expected from equation 2. We can rewrite our definition of F, the fraction of anesthetic cleared from the blood as it passes through the lungs, as F = 100%* 1/[1 + (λ*Q)/VA]. Note that Q and λ are multiplied. Thus, each enters the equation for F in an identical form, and an increase in Q has the same effect as a proportional increase in λ.
The simulations showed little difference (approximately 2 to 3 min) between the average values for the decrement times for the VRG versus the alveolar concentrations regardless of duration of anesthesia (data not shown). The difference was slightly smaller with desflurane than with sevoflurane because of the greater tissue/blood partition coefficients of sevoflurane. An increase in cardiac output (presuming the VRG shares in the increase in blood flow) narrowed the difference between alveolar and VRG decrement times whereas a decrease in cardiac output did the reverse (data not shown).
These results confirm and enlarge upon the predictions concerning context-sensitive decrements for inhaled anesthetics made by Bailey (2), detailing the effect of the choice of decrement on decrement times. Our simulations describe a larger range of decrement times and apply a test of “tapering.” They use a readily available tool (Gas Man®) to determine decrement times. Finally, we demonstrate the importance of cardiac output as a determinant of decrement times.
But which decrement time is important to recovery from anesthesia? In part there is no simple answer to this question because the concentration reached is not indicated by the decrement time. If we chose 90%, we must ask “90% of what?” If we had chosen 2 MAC, then a 90% decrement would mean a decrease to 0.2 MAC, but if we had chosen 1 MAC, then a 90% decrement would mean a decrease to 0.1 MAC. Neither of these examples considers the impact of drugs given concurrently (e.g., midazolam or opioids). Administration of fentanyl may markedly decrease the alveolar concentration required to prevent movement (14,15). Thus, the patient given typical doses of fentanyl may receive 0.5 MAC during surgery. Such administration will decrease the separation of awakening times among anesthetics because a smaller decrement allows emergence from anesthesia. That is a major reason to use adjuvant drugs in combination with inhaled anesthetics. Parenthetically, we note that the pharmacokinetics of all anesthetic adjuvants (e.g., fentanyl) determine their deposition and thereby add to the complexity of interpretation of the present article’s simulations.
The concepts underlying context-sensitive decrement times were first developed for IV anesthetics (1,5). As in the present essay, these reports made use of multicompartmental uptake and elimination, noting the importance (as do we) of blood and tissue solubility. What we have outlined in the present essay applies, with several modifications, to IV anesthetics and anesthetic adjuvants. First, inhaled anesthetics enter and leave the body via the lungs whereas injected compounds usually enter via a vein and require the liver and kidneys for their removal (and thus, in contrast to inhaled anesthetics, by increasing blood flow to the liver, an increase in cardiac output may accelerate rather than retard recovery from anesthesia with injected drugs). Second, a constant inspired concentration of inhaled anesthetic closely (but not exactly) mimics a constant rate IV infusion. In both cases, drug transfer follows first-order principles, except that the gas transfer must deal with the concentration and second gas effects. The different routes of administration and elimination also may produce opposite effects. For example, increasing cardiac output will increase hepatic blood flow, thereby accelerating the clearance of an IV drug but minimally affecting recovery from an inhaled anesthetic. Third, inhaled anesthetics passively and easily traverse all membranes, lipid and aqueous. But some injected anesthetics are actively transported (e.g., note the role of p-glycoprotein in morphine plasma-brain equilibration), whereas other drugs (e.g., neuromuscular blocking drugs) do not pass through the blood-brain barrier at all.
Further, we must ask, “what MAC-fraction is important regarding recovery?” MACawake for desflurane or isoflurane is a third of MAC (16,17). By definition, such a level must be attained to have 50% of patients respond appropriately to command. Thus, although there will be a difference among anesthetics because of solubility, the differences cannot be great because all will allow an 80% decrement to be reached in a short period of time, particularly for the most common durations of anesthesia, under 120 minutes (Fig. 1,A).
But recovery means more than simply responding to command. The threshold for measurable impairment of cognitive function equals 0.1 MAC (18,19). Thus, if we were at 1 MAC during anesthesia, we would wish to get below 0.1 MAC during recovery—further if other depressant drugs (midazolam) have been given. An approach to complete recovery probably demands that the patient be at 0.05 MAC or less. If we began with 1.0 MAC, that would require a 95% decrement. The patient who gets isoflurane might be “awake” after a prolonged anesthetic, but would not feel “awake.” That is, an 80% decrement might be reached reasonably quickly (Fig. 2E), but a prolonged period of time would be required to reach a 90% or more decrement, particularly after more than 1 hour of anesthesia. The same is true to a lesser extent with sevoflurane. Desflurane would allow the earliest return to a sense of “normally awake” (20).
Numerous studies indicate the importance of solubility to various end-points of recovery. Consistent with the present analysis, a lesser solubility produces an earlier recovery to a given end-point. Recovery is quicker with sevoflurane than with isoflurane (21–25), and recovery is quicker with desflurane than with either sevoflurane (20,26–29) or isoflurane (30–36). Variability in patient responses and the use of adjuvant drugs may obscure these differences, and the most accurate estimates of differences may be found in studies of volunteers where anesthetic duration and concentration can be precisely controlled. The use of volunteers also avoids the confounding effects of surgery and other medications. Volunteers given desflurane awaken sooner than those given sevoflurane (27).
Moreover, the effect of increasing anesthetic duration has a greater effect on the more soluble sevoflurane (i.e., increasing duration of anesthesia results in a longer time to a given end-point than is the case with desflurane.) This appears to be true for both short-term end-points (response to command) and long-term end-points (recovery of normal judgment and cognition as assessed by recovery of normal digit symbol substitution results.) It may underlie the demonstration by McKay et al. (37) that recovery of pharyngeal function requires that the patient reach effect-site concentrations well below MACawake and that this differentiates the effects of desflurane from sevoflurane (pharyngeal dysfunction persists longer after anesthesia with sevoflurane.) Such observations are part of what distinguishes the present from previous reports: we have new data such as those presented by McKay et al. and we have extended the analysis of context-sensitive decrement times to greater decrements.
The clinician may rightly argue that we cannot assume a constant alveolar or VRG delivery of anesthetic to the end of anesthesia; that is not how clinical anesthesia is delivered. The clinician may taper the delivery towards the end of anesthesia, ending with a smaller concentration that allows a faster recovery from anesthesia. A faster recovery would occur because of the unloading of part of the anesthetic contained by the VRG. However, decreasing the alveolar concentration would have only a modest effect on anesthetic stored in muscles or fat, and thus the acceleration of recovery would be limited. This possibility was simulated by decreasing the alveolar concentration by half for the last 30 minutes of anesthesia (compare Fig. 2, A and B with Fig. 2, C and D). Although this maneuver shortened times to particular decrements, the effect was limited, particularly at larger decrements (e.g., 95%). Note that with isoflurane, even with a terminal 30 minutes at half the maintenance concentration, times to reach specific decrements still are prolonged relative to desflurane and sevoflurane without such a “tapering” (compare Figs. 2, C and D with Fig. 2E).
In summary, many factors determine recovery from anesthesia. Solubility and anesthetic kinetics remain key to the time to recovery. Context-sensitive decrements provide a powerful approach to understanding the importance of solubility and kinetics to recovery.
We appreciate the several suggestions made by Dr. James H. Philip in the construction of the manuscript and his advice concerning the use of Gas Man®.
Imagine what happens at the extremes of solubility. Suppose that the blood/gas partition coefficient of anesthetic X is 0.001 and that the alveolar concentration is 70% (70 mL of anesthetic vapor per 100 mL of alveolar gas). The blood can hold very little anesthetic X, even at an alveolar concentration of 70%. Specifically, with the blood at equilibrium (i.e., at the same partial pressure of anesthetic) with the 70% alveolar concentration, the concentration in the blood (as defined by equation 1) equals 70*0.001 mL anesthetic vapor per 100 mL of blood, or 0.07 mL per 100 mL of blood. Suppose we stop the delivery of anesthetic X and that the alveolar ventilation and cardiac output are equal (say, 4 L/min, but the exact numbers do not matter). Assume also a bit of magic: that we instantaneously eliminate all residual anesthetic from the lungs. Now imagine that all (well, nearly all because F = 99.9% if λ = 0.001) anesthetic X in the blood traversing the lungs is transferred into the fresh alveolar ventilation gas. Because Q = VA, the concentration in the gas phase would be 0.07 mL per 100 mL of gas, or 0.07%. Thus, on discontinuing anesthetic administration and instantaneously washing out the residual anesthetic from the lungs, the alveolar concentration would immediately decrease from 70% to 0.07%. That is a 99.9% decrement.
But a very different change occurs at the other extreme. Suppose the blood/gas partition coefficient of anesthetic Y is 1000, a partition coefficient seen with alcohols (38). The blood can hold an enormous amount of anesthetic vapor Y. For example, at an alveolar concentration of 1%, equation 1 indicates that the concentration in blood equals 1%*1000 or 1000% (i.e., 1000 mL of anesthetic vapor per 100 mL of blood). That is, although 100 mL of blood would contain 1000 mL of anesthetic vapor, every 100 mL of alveolar gas would only contain 1 mL of anesthetic vapor. As with anesthetic X, suppose that we stop the delivery of anesthetic Y, that we instantaneously clear all of anesthetic Y from the alveoli, and that the alveolar ventilation and cardiac output are equal. Now if we transfer enough of Y from blood to the fresh alveolar gas to bring the concentration to 1% (actually 0.999%) in the alveoli, how much would be left in the blood? Answer: 999%. That is, bringing the alveolar gas concentration to equilibration with the anesthetic vapor in the blood would not materially decrease the concentration of anesthetic in the blood. Similarly, the alveolar concentration decreases from 1% to 0.999%, essentially a 0% decrement.
In the previous examples, the anesthetic concentrations were in equilibrium before removing anesthetic molecules from the air phase and then allowing re-equilibration to occur. However, let us suppose that the system is not at equilibrium. Assume that the concentration of X and Y in the blood phase is only half (50%) of the concentration that would be produced at equilibrium. This is somewhat closer to reality, in that “steady state” is typically not reached during anesthesia and the concentrations in the returning venous blood are less than those in the alveolus and the arterial blood leaving the lungs.
We now attempt to awaken the patient by removing all of the anesthetic molecules from the air phase, and permitting the remaining molecules in the blood phase to re-establish equilibrium. For anesthetic X, the concentration in the alveolus on re-equilibration will be minuscule because nearly all of the molecules were in the air phase initially, and those molecules were removed. So there is hardly any effect of the lack of equilibration; recovery is rapid regardless of the extent of disequilibration.
However, the situation differs for anesthetic Y. Suppose the concentration of Y in the alveoli equaled 1% (1 mL of vapor per each 100 mL of alveolar gas) but the blood returning to the lung had a concentration of 500% (500 mL of vapor per 100 mL of blood rather than the 1000 mL of vapor in the previous example). When we remove all the molecules of Y from alveolar air, we remove relatively few molecules. To re-establish equilibrium, 0.5 mL of vapor must move from blood into each 100 mL of alveolar gas. That leaves 499.5 mL of vapor per 100 mL of blood (499.5/0.5 = 1000, satisfying the blood/gas partition coefficient—see equation 1). Thus, the far larger number of molecules in the blood will establish a new equilibration that will reflect the concentration of Y that was in the blood before the Y molecules were removed from the air: half (50%) of the initial alveolar concentration of 1%. That is, we have a rapid decrease in alveolar concentration from 1% to 0.5%, a decrement of 50%. These observations indicate that the lack of equilibration had a big effect on Y and virtually no effect on X.
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