Currently, monitoring during general anesthesia maintained with a volatile anesthetic includes real-time measurement of its end-tidal partial pressure (FET), displayed on the workstation as concentration and often also as fraction of minimum alveolar concentration (fMAC) or age-adjusted fMAC. The current review explains how proper understanding of the minimum alveolar concentration (MAC) and fMAC concept will help the clinician to titrate volatile anesthetics. Table 1 lists the most frequently used abbreviations and acronyms. Figures and dosing examples are mainly used to explain concepts; we clearly mention whether a figure or part of a figure is based on patient data.

Table 1.

Definitions, Abbreviations, and Acronyms

Definitions, Abbreviations, and Acronyms
Definitions, Abbreviations, and Acronyms

MAC has been defined by Ted Eger and Lawrence Saidman1,2  as the steady-state minimal alveolar concentration that results in immobility in 50% of animals and humans after application of a noxious stimulus. In animals, to determine MAC, they are anesthetized with the study drug in the absence of any other drug while keeping the FET constant for at least 15 min. A strong stimulus (tail clamp or electrical current) is applied for up to 1 min; the head, torso, and limbs are observed for movement, resulting in a quantal response, i.e., movement or no movement. Stiffening, coughing, and hyperventilation are not considered to be movement. If no movement occurs, the FET is decreased by 20%, but if movement does occur, the FET is increased by 20%, and the process is repeated once or twice. Smaller up and down changes in FET allow for more accuracy but will prolong the study. Eventually, the highest FET that does not prevent movement and the lowest one that does prevent movement are determined, and the FET “midway” (the term used by Eger) between the brackets is the MAC in that individual animal. This process is called the “bracketing technique.” Studying a group of animals or humans this way allows the determination of the median end-tidal concentration that results in immobility in 50% of the subjects of this species, or MAC. At the same time, this technique gives us an estimate of the variability of MAC.

In humans, usually only one observation is made in each patient during initial skin incision after FET has been held constant for 15 min. If a patient shows no response to the noxious stimulus, the next patient receives a lower FET; if the patient does respond, then the next patient receives a higher FET (“up-and-down” method). Each response is plotted as 0 (movement) or 1 (no movement) versus FET (quantal concentration – response curve). Applying logistic regression to this data set yields an S-shaped graph that displays the probability of no response versus the equilibrated FET in the population (fig. 1). The median point on the graph represents the FET that corresponds to the 50% probability of no movement; this specific FET was called the minimal alveolar concentration (often abbreviated as MAC) by Eger but could also be called the effective concentration that results in a 50% probability of the clinical endpoint being attained in a population, or EC50. This method is called the “quantal technique,” although both bracketing and the quantal technique use quantal data. The two analyses result in the same MAC values.3 

Fig. 1.

Quantal concentration–response curve for desflurane. The target response is no movement. During general anesthesia in mice (n = 370), a tail clamp is applied, and movement is observed. Movement in each animal is plotted as 0, and no movement is plotted as 1. The data are fit by logistic regression, resulting in a sigmoid curve. Minimum alveolar concentration (MAC; more correctly called MACimmobility) is defined as the median of the concentration–response curve and can also be called the 50% effective concentration (EC50). The figure is based on the work of Sonner.3  (Sonner JM: Issues in the design and interpretation of minimum alveolar anesthetic concentration (MAC) studies. Anesth Analg 2002; 95:609–14. Adapted with permission.)

Fig. 1.

Quantal concentration–response curve for desflurane. The target response is no movement. During general anesthesia in mice (n = 370), a tail clamp is applied, and movement is observed. Movement in each animal is plotted as 0, and no movement is plotted as 1. The data are fit by logistic regression, resulting in a sigmoid curve. Minimum alveolar concentration (MAC; more correctly called MACimmobility) is defined as the median of the concentration–response curve and can also be called the 50% effective concentration (EC50). The figure is based on the work of Sonner.3  (Sonner JM: Issues in the design and interpretation of minimum alveolar anesthetic concentration (MAC) studies. Anesth Analg 2002; 95:609–14. Adapted with permission.)

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MAC thus is inherently probabilistic: the EC50 of the quantal concentration–response curve generated from a sample of the population cannot be used to predict an all or none response in the individual patient. It is only possible to estimate the probability of an individual to display no response at a certain fMAC. It has been determined that the probability of no response at a certain fMAC in the population can be converted into Pno-response in the individual patient: if, at a certain fMAC, 40% of the patients move on incision, then the probability that the individual patient will move is also 40%.3 

The term “MAC” is plagued with semantic issues. First, there is significant debate on whether the “M” in MAC should refer to “minimal” or “median.” When using the bracketing technique in a group of subjects or patients, the “M” in MAC does not represent “minimal”; instead, it is the median of a collection of MAC values, each determined in individual subjects or patients. When using the quantal technique, MAC is calculated by logistic regression as the EC50 value resulting in 50% of the population affected (fig. 1). In either technique, it is the “median” alveolar concentration that is determined, and therefore MAC should be (re)defined as the “median alveolar concentration.” If one wants to avoid the issue of minimal versus median completely, then MAC could be defined as “the alveolar concentration of a volatile anesthetic at 1 atm at equilibrium that results in a 50% probability of movement in subjects exposed to a standardized noxious stimulus.” Second, the term “partial pressure” might be preferred instead of “concentration.” For example, the partial pressure at sea level and at high altitude to anesthetize the same patient will be the same, but the concentration will differ because atmospheric pressure will differ. However, because they are related via Henry’s law and for uniformity, “concentration” will still be used throughout this article. Third, it is not an alveolar concentration but an end-tidal concentration: “ideal alveolar concentration” and end-tidal concentration differ due to dead space ventilation and other factors.4  This, however, does not invalidate the MAC concept. Fourth, MAC should specify its endpoint (MACimmobility). When MAC was initially used as an indicator of anesthetic potency, the only response that was looked for was movement after a noxious stimulus. In addition, the clinical “no response” is not used consistently: MACawake should be MACunconsciousness.

By definition, the only factor that affects MAC is age (and possibly genetic factors) because MAC is determined in healthy subjects not receiving any other drugs. In humans, MAC increases by 30% from birth until 1 to 6 months of age and then decreases by about 6 to 7% every decade after 20 years. fMAC or age-adjusted fMAC is now displayed on many anesthesia workstation screens (Eger called this “multiples of MAC”).5  After reviewing the algorithms for age correction of MAC by several different anesthesia machine manufacturers, we have concluded that these result in differences as high as 23%.6  Hereafter in the article, MAC and fMAC are always presumed to be age-adjusted.

Most anesthesiologists currently define general anesthesia as a drug-induced reversible state of unconsciousness while providing appropriate surgical conditions (immobility) with blunting of excessive autonomic responses (BAR) to noxious stimuli.7,8  Each of these components is mediated by different neural circuits in the central nervous system (CNS). For example, volatile anesthetics mediate immobility mainly at the level of the spinal cord and unconsciousness at the cortical level and the thalamus.8,9  Analgesia and amnesia are not separate goals of general anesthesia: the unconscious state in and by itself prevents not just the perception of pain (which requires consciousness) but also the formation of memory.8  It is important to distinguish nociception from pain: nociception is the activation of certain neuronal pathways through the sensory system, while pain is the conscious subjective experience of this “nociceptive information.”8,10  Because all three components of the anesthetic state (unconsciousness, immobility, and blunting of adrenergic responses) can be achieved by volatile anesthetics alone at different but clinically relevant concentrations, these drugs are considered to be complete anesthetics.

While immobility and blunting of adrenergic responses are straightforward to monitor, determining whether the patient is unconscious during general anesthesia is more complex.11  If unconsciousness is defined as absence of intraoperative awareness, the literature will offer the clinician little dosing guidance because existing, underpowered studies on the incidence of intraoperative awareness mostly rely on postoperative interviews or surveys and thus reflect the incidence of intraoperative awareness with explicit recall. The low incidence of recall in these studies is not unexpected because memory is more sensitive to general anesthetics than consciousness. Clinicians actually see this every day: patients are clearly conscious during or just after extubation but often have no recall of this event when interviewed later.

Investigators have attempted to determine the presence of “intraoperative awareness” with the isolated forearm test (or technique).11,12  After induction of anesthesia but before administering neuromuscular blocking drugs, a forearm is isolated with a tourniquet to avoid paralysis of the forearm. The patient is then asked to squeeze the unparalyzed hand. The main advantage of the isolated forearm test is that it does not depend on memory and thus allows us to study the state of consciousness during general anesthesia. In a prospective study of 260 patients, positive responses were reported in 12 patients (4.6%), indicating “perceptive awareness” at that moment.12  Most positive responders do not move their hand without being instructed (“spontaneously unresponsive”),13  but very few of those who move have recall for the event.12,13  It is possible that several of the nonresponders simply lack motivation to obey the verbal command during the isolated forearm test, and therefore “perceptive awareness” may have a higher incidence than these studies suggest. The neuromuscular blocking state increases the probability of a positive response to a verbal command, and volatile anesthetics may reduce it.12,14,15  Positive responders have a higher incidence of sympathetic activation.12 

Other observations during these isolated forearm test studies may be very relevant. Bispectral Index (BIS) values are poorly predictive of the isolated forearm test response: even though slightly higher in responders, BIS values of less than 40 occurred in both responders and nonresponders.12  There is also no difference in the electroencephalogram (EEG) patterns of the frontal lobe between responders and nonresponders.14  Unfortunately, in these studies, the anesthetic management was not standardized, and very little information about anesthetic technique was provided.

While the clinical relevance of a positive isolated forearm test remains unclear, it corroborates the view held by many cognitive neuroscientists that consciousness versus unconsciousness is not a binary phenomenon.11,13  There may be several degrees of wakefulness and unconsciousness: a patient may be “somewhat” conscious but sufficiently impaired to tolerate surgery yet still be able to respond to a command, all followed by absence of explicit recall.16  Whether intraoperative awareness without explicit recall harms the patient remains unclear.12  The isolated forearm test has been applied in a very small number of patients, and in routine clinical care, it is at present impossible to know with certainty whether the fully paralyzed patient is conscious or not. By extension, we cannot know with a high degree of certainty the partial pressure that prevents intraoperative awareness in the individual patient.

This discussion makes it clear that the definition of general anesthesia needs to be adjusted as scientific progress is being made in understanding unconsciousness. With our current understanding, anesthesia can be defined as a drug-induced reversible state of unconsciousness or altered consciousness without explicit recall while providing appropriate surgical conditions (immobility) with blunting of excessive autonomic responses (BAR) to noxious stimuli. In other words, the majority of patients are unconscious, but a minority (4.6 to 6.7%) has reduced consciousness without explicit recall.12,14  We apparently cannot use frontal EEG parameters or BIS to differentiate between the two groups, and we also do not know whether this reduced conscious state is the result of insufficient anesthesia.

To summarize, the clinician is left with having to titrate drugs to attain unconsciousness or an altered state of consciousness without explicit recall. At present, the marker most often used to help target this state in clinical studies and for which dose–response curves have been constructed is the loss of response to verbal command, discussed in the following section. In what follows, “unconsciousness” is therefore functionally defined as “loss of response to verbal command.” However, it is important to realize that any functional definition of “unconsciousness” as mediated by volatile anesthetics will be hampered by our current lack of understanding of unconsciousness itself. Obviously much more research including a much larger number of subjects is needed in this area. This may include the use of more advanced EEG analyses.

The concentration–response relationships between the steady-state fMAC (or FET) of volatile anesthetics and each clinical effect (unconsciousness, immobility, and blunting of adrenergic responses) can only be constructed after defining each clinical endpoint in terms of a stimulus–response pair indicative of that clinical effect: loss of response to verbal command, loss of movement after incision, and attenuation of heart rate and blood pressure increase after laryngoscopy. The resulting concentration–response relationships are analogous to the concentration–response relationship of intravenous drugs: each curve is described by the effective concentration that results in a 50% probability of the clinical endpoint being attained in a population, called EC50 (fig. 2), and by its slope (Hill coefficient). For volatile anesthetics, the FET in a population at which there is a 50% chance of no response to a verbal command (Punconsciousness = 50%), no movement after surgical incision (Pimmobility = 50%), and achieving blunting of adrenergic responses (PBAR = 50%) have been defined as MACawake, MAC, and MACBAR by Ted Eger and Larry Saidman, Robert Stoelting, and Mike Roizen, respectively (fig. 2A).2,17–20  Compared to IV anesthetics, the FET–response curves have a steep slope with a small variability (SD approximately 0.1).3,21,22  A SD of 0.1 (or 10%) is less than what is frequently stated (approximately 15%), meaning that the concentration–response curves are actually steeper than often assumed. The other consequence is that approximately 97.5% of patients are immobile with fMAC of 1.2 (steady state). While the reason for this small variability remains a mystery,23  this distinct important property results in the usefulness of fMAC as an indicator of probability of no response, which is distinctly different from IV anesthetics. The concentration–response curves for unconsciousness, immobility, and blunting of adrenergic responses are often presumed to run parallel, even though this has never been studied in great detail; this is an area that requires more research.

Fig. 2.

The quantal concentration–response curves of the steady-state end-tidal partial pressure (FET) of volatile anesthetics. All curves are meant to explain concepts and are not directly based on patient data, except when specifically mentioned. (A) As the concentration (expressed as a fraction of minimum alveolar concentration [fMAC]) is increased, the probability of rendering patients unconscious (blue), immobile (green), and blunting autonomic responses (BAR) (red) increases and reaches 50% at MACawake, minimum alveolar concentration (MAC), and MACBAR, respectively (colored circles on the x-axis). (B) We propose that anesthesia requires a 99.99% or greater, 95%, and 85% probability of unconsciousness, immobility, and blunting of adrenergic responses, respectively. The corresponding required steady-state fMAC can be back-extrapolated to the x-axis. (C) Effect of a 2-ng/ml effect-site fentanyl concentration on fMAC required to ensure the three different clinical endpoints. Opioids do not reduce MAC (a fixed point in the x-axis) but reduce the steady-state FET (or fMAC) needed to attain the same no-response probability (Pno-response). This graph is adapted from data by Katoh et al.,30–32  with the percentages being only approximate changes used for illustrative purposes. (D) If a 2-ng/ml effect site fentanyl (or equivalent) concentration is maintained, 0.7 fMAC can ensure that all three clinical goals are achieved. Although based on patient data (in the work of Katoh et al.30–32 ), this cartoon only illustrates the general concept. (Katoh T, Ikeda K: The effects of fentanyl on sevoflurane requirements for loss of consciousness and skin incision. Anesthesiology 1998; 88:18–24; and Katoh T, Kobayashi S, Suzuki A, Iwamoto T, Bito H, Ikeda K: The effect of fentanyl on sevoflurane requirements for somatic and sympathetic responses to surgical incision. Anesthesiology 1999; 90:398–405. Adapted with permission.)

Fig. 2.

The quantal concentration–response curves of the steady-state end-tidal partial pressure (FET) of volatile anesthetics. All curves are meant to explain concepts and are not directly based on patient data, except when specifically mentioned. (A) As the concentration (expressed as a fraction of minimum alveolar concentration [fMAC]) is increased, the probability of rendering patients unconscious (blue), immobile (green), and blunting autonomic responses (BAR) (red) increases and reaches 50% at MACawake, minimum alveolar concentration (MAC), and MACBAR, respectively (colored circles on the x-axis). (B) We propose that anesthesia requires a 99.99% or greater, 95%, and 85% probability of unconsciousness, immobility, and blunting of adrenergic responses, respectively. The corresponding required steady-state fMAC can be back-extrapolated to the x-axis. (C) Effect of a 2-ng/ml effect-site fentanyl concentration on fMAC required to ensure the three different clinical endpoints. Opioids do not reduce MAC (a fixed point in the x-axis) but reduce the steady-state FET (or fMAC) needed to attain the same no-response probability (Pno-response). This graph is adapted from data by Katoh et al.,30–32  with the percentages being only approximate changes used for illustrative purposes. (D) If a 2-ng/ml effect site fentanyl (or equivalent) concentration is maintained, 0.7 fMAC can ensure that all three clinical goals are achieved. Although based on patient data (in the work of Katoh et al.30–32 ), this cartoon only illustrates the general concept. (Katoh T, Ikeda K: The effects of fentanyl on sevoflurane requirements for loss of consciousness and skin incision. Anesthesiology 1998; 88:18–24; and Katoh T, Kobayashi S, Suzuki A, Iwamoto T, Bito H, Ikeda K: The effect of fentanyl on sevoflurane requirements for somatic and sympathetic responses to surgical incision. Anesthesiology 1999; 90:398–405. Adapted with permission.)

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MAC is probabilistic, and thus if we desire to guide clinical use of anesthetics based on fMAC monitoring, we must choose target probabilities for the different clinical endpoints. It is a priority to achieve unconsciousness or altered consciousness without explicit recall with near certainty—it is part of the contract we make with patients when we inform them that they will receive a general anesthetic. If not detrimental (e.g., eye or intracranial surgery), occasional mild movement is acceptable. Finally, some degree of short-lived hypertension and tachycardia is acceptable with some exceptions. To illustrate how the probabilistic nature of MAC can guide the clinician to titrate volatile anesthetics, we propose that general anesthesia in probability space requires a 99.99% or higher, 95%, and 85% likelihood of having attained unconsciousness, immobility, and blunting of adrenergic responses, respectively (fig. 2B). While it could be argued that a probability of unconsciousness of greater than or equal to 99.99% is extremely high and not achievable, Pandit et al.24  have reported an incidence of intraoperative awareness of 0.005%. While this number may underestimate the true incidence because it was obtained through an audit, it does support the order of magnitude of P ≥ 99.99 as clinically relevant and achievable.24  Determining target probabilities is what the clinician does intuitively when targeting an fMAC or FET of the volatile anesthetic. It also allows us to introduce the concept of isoboles that are nothing but lines of equal no-response probability in the presence of certain drug combinations (see “Drug Interactions: Opioids”). The higher the fMAC, the more reassurance the clinician has that a response will be suppressed.

With the current state of knowledge, determining the specific threshold for unconsciousness remains impossible for reasons explained under “Definition and Description of General Anesthesia.” In addition, we do not have enough data to construct high-resolution concentration–response curves, especially not at their “tails.” Still, thresholds have been recommended that can serve as lower limit alarms in an attempt to at least minimize the occurrence of awareness with explicit recall. Avidan et al. in 201125  reported that FET monitoring with the intention to maintain age-adjusted fMAC of 0.7 or higher resulted in a lower incidence of intraoperative awareness than when using an EEG-based monitor (0.07% vs. 0.24%, respectively). The incidence of awareness could even have been lower because fMAC greater than or equal to 0.7 was achieved only a median of 84.8% of the time. Although this study was underpowered, it serves as a guidance for the clinician. While Eger and Sonner recommended 0.5 fMAC to virtually guarantee unconsciousness,26  they also noticed that learning of emotionally charged information is suppressed at anesthetic concentrations of 1.5 to 2 times MACawake (0.6 to 0.7 fMAC) and that fMAC greater than 0.6 suppresses explicit and implicit learning.27,28  Our preference is to err on the higher side (greater than or equal to 0.7 MAC) because it is well tolerated, without hemodynamic compromise in most patients, and without affecting neurologic outcome (i.e., no evidence exists that lowering fMAC from 0.7 to 0.5 would convey a clinically meaningful difference in postoperative outcome). Immobility and blunting of adrenergic response can be achieved at much higher levels of fMAC, but when opioids are coadministered, fMAC needs to be only slightly higher than 0.7 (see “Drug Interactions: Opioids”). However, when immobility or blunting of adrenergic response is critical for an optimal outcome, other drugs (neuromuscular blocking or vasoactive drugs) should be used. fMAC monitoring will help the clinician in avoiding the use of excessive concentrations by applying proper age correction and by correlating the prevailing fMAC with the individual patient response.

In summary, we pragmatically propose that we should aim to achieve probabilities for unconsciousness, immobility, and blunting of adrenergic response of 99.99% or higher, 95%, and 85%, respectively. We also propose that a high probability of unconsciousness may be obtained by administering an fMAC of greater than or equal to 0.7 (age-adjusted, steady-state). Based on the currently available literature, about 5% of our patients during “general anesthesia” may not be completely unconscious but are in a state of altered consciousness without explicit recall, and it is currently impossible to say how this state of altered consciousness should be managed. Consequently, the goals we proposed will likely change when more clinical studies have improved our knowledge.

In clinical practice, unconsciousness, immobility, and blunting of adrenergic responses are most often obtained through a combination of volatile anesthetics, neuromuscular blocking drugs, and opioids. The use of opioids has profound implications for the predictive value of fMAC because opioids shift each fMAC/Pno-response curve to the left (fig. 2C).29–31  While it is often claimed that opioids “reduce MAC,” they do not—the fMAC to attain a certain Pno-response is reduced, but MAC remains unaltered (it only depends on age).

The degree to which opioids reduce fMAC required to attain a certain Pno-response differs quantitatively for the different clinical endpoints and are described by isobolograms (fig. 3). An isobologram visualizes all possible effect site concentration and/or partial pressure combinations (that are at steady state by definition) of one or more hypnotics or volatile anesthetics with one or more opioids that result in the same Pno-response (fig. 3).29–32  Of the many possible combinations, we select one in this review to illustrate how opioids differentially affect fMAC for the different clinical endpoints, namely the interaction between sevoflurane and a commonly used fentanyl effect site concentration (Ce) of 2 ng/ml (based on data from Katoh et al.).30–32  At 2 ng/ml Ce fentanyl, the fMAC needed to attain Punconsciousness, Pimmobility, and PBAR at 50% is reduced by about 10 to 15%, 50%, and 75%, respectively, causing the three curves to move fairly close together (fig. 2, C and D). An equipotent concentration of another opioid has the same effect: 1.67 ng/ml fentanyl = 0.14 ng/ml sufentanil = 28.8 ng/ml alfentanil = 1.37 ng/ml remifentanil.33  If for illustrative purposes we continue to define anesthesia in probability space as a 99.99%, 95%, and 85% likelihood of having attained unconsciousness, immobility, and blunting of autonomic responses, isobolographic analysis informs us that combining an fMAC of 0.7 of a volatile anesthetic (yellow circle) with a Ce of 2 ng/ml fentanyl can achieve these goals (fig. 3).30–32,34  Clinical responses (movement, autonomic responses) in the individual patient will inform the clinician that fMAC or the opioid Ce may have to be increased or decreased, or whether alternatively additional intravenous hypnotics, muscle relaxants, and vasoactive drugs can be used to achieve the desired effects. The probabilistic nature of fMAC implies that it cannot be used with certainty to predict stimulus-response suppression in the individual but can allow the clinician to get an idea of where in the population the individual patient is located and can provide a reference value to guide future dosing.

Fig. 3.

Differential synergistic effects between opioids and volatile anesthetics. Isoboles describe the same probabilities of response suppression when different concentrations of volatile anesthetics and opioids are simultaneously administered. (A1 and A2) The isoboles representing 50% and 95% probability of unconsciousness are colored light blue (thin line) and dark blue (thick line), respectively (95% probability only shown in A1). (B) The isoboles representing 50% and 95% probability of immobility are colored light green (thin line) and dark green (thick line), respectively. (C) The isoboles representing 50% and 95% probability of hemodynamic stability are pink (thin line) and red (thick line), respectively. For example, at a plasma concentration of ≈2 ng/ml fentanyl (the yellow-shaded area represents the 0 to 2 ng/ml range), fentanyl reduces the FET required to achieve 50% probability of unconsciousness, immobility, and blunting of adrenergic responses by about 10 to 15%, 50%, and 75%, respectively (thick black arrows). The combination of 1.4% end-tidal partial pressure (FET) sevoflurane and 2 ng/ml fentanyl has a 95% probability of providing immobility (light green circle), an 85% probability of providing heart rate and blood pressure control (red circle), and 99.99% or higher probability of providing unconsciousness (only shown in A1). Note the different scaling of the x- and y-axes in the different panels. This drug combination during steady state thus results in a very high likelihood of having attained Punconsciousness, Pimmobility, and PBAR of 99.99% or higher, greater than 95%, and greater than 85%, respectively. Because MACawake is only minimally influenced by the presence of opioids, we can predict that fraction of minimum alveolar concentration (fMAC) is a very valuable indicator of Punconsciousness at any time. See text for details. The figure was modified after the work of Katoh et al.30–32  (Katoh T, Ikeda K: The effects of fentanyl on sevoflurane requirements for loss of consciousness and skin incision. Anesthesiology 1998; 88:18–24; and Katoh T, Kobayashi S, Suzuki A, Iwamoto T, Bito H, Ikeda K: The effect of fentanyl on sevoflurane requirements for somatic and sympathetic responses to surgical incision. Anesthesiology 1999; 90:398–405. Adapted and reprinted with permission.)

Fig. 3.

Differential synergistic effects between opioids and volatile anesthetics. Isoboles describe the same probabilities of response suppression when different concentrations of volatile anesthetics and opioids are simultaneously administered. (A1 and A2) The isoboles representing 50% and 95% probability of unconsciousness are colored light blue (thin line) and dark blue (thick line), respectively (95% probability only shown in A1). (B) The isoboles representing 50% and 95% probability of immobility are colored light green (thin line) and dark green (thick line), respectively. (C) The isoboles representing 50% and 95% probability of hemodynamic stability are pink (thin line) and red (thick line), respectively. For example, at a plasma concentration of ≈2 ng/ml fentanyl (the yellow-shaded area represents the 0 to 2 ng/ml range), fentanyl reduces the FET required to achieve 50% probability of unconsciousness, immobility, and blunting of adrenergic responses by about 10 to 15%, 50%, and 75%, respectively (thick black arrows). The combination of 1.4% end-tidal partial pressure (FET) sevoflurane and 2 ng/ml fentanyl has a 95% probability of providing immobility (light green circle), an 85% probability of providing heart rate and blood pressure control (red circle), and 99.99% or higher probability of providing unconsciousness (only shown in A1). Note the different scaling of the x- and y-axes in the different panels. This drug combination during steady state thus results in a very high likelihood of having attained Punconsciousness, Pimmobility, and PBAR of 99.99% or higher, greater than 95%, and greater than 85%, respectively. Because MACawake is only minimally influenced by the presence of opioids, we can predict that fraction of minimum alveolar concentration (fMAC) is a very valuable indicator of Punconsciousness at any time. See text for details. The figure was modified after the work of Katoh et al.30–32  (Katoh T, Ikeda K: The effects of fentanyl on sevoflurane requirements for loss of consciousness and skin incision. Anesthesiology 1998; 88:18–24; and Katoh T, Kobayashi S, Suzuki A, Iwamoto T, Bito H, Ikeda K: The effect of fentanyl on sevoflurane requirements for somatic and sympathetic responses to surgical incision. Anesthesiology 1999; 90:398–405. Adapted and reprinted with permission.)

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The differential effect of opioids on the fMAC needed to attain the three different anesthetic endpoints has implications for the use of fMAC as a tool to guide drug dosing. The pronounced effect of opioids on the fMAC–response curves for immobility and blunting of adrenergic responses adds a great deal of uncertainty to appropriate anesthetic dosing for these endpoints. We speculate that this may cause the use of MACimmobility and MACBAR to be perceived as flawed or useless. In addition, immobility and blunting of adrenergic responses can be accomplished by other drugs like neuromuscular blocking drugs or antihypertensive drugs, making the use of fMAC to attain these goals moot. However, because opioids only minimally shift the fMAC–response curve for unconsciousness to the left, fMAC remains a very valuable indicator of Punconsciousness, even in the presence of opioids. The value of fMAC in predicting Punconsciousness is only degraded when other intravenous hypnotics are added (e.g., propofol, whose concentration cannot be measured routinely online) while fMAC is starting to decrease to less than 0.7. Whenever fMAC has to be decreased less than 0.7, determining depth of anesthesia by EEG- or EEG-derived indices may be advisable.

Steady State and Time Constant

For our purposes, hysteresis is defined as the delay between changes in FET and changes in the partial pressure of anesthetic drug in the target tissue, the CNS. Thus, during initial delivery (wash-in) of volatile anesthetics, FET is higher than the CNS partial pressure, and during wash-out of anesthetic, FET is lower than the CNS partial pressure. The physiologic basis for estimating the duration of hysteresis for different volatile anesthetics is described below.

The dose–response curves described assume that FET has been constant for 15 min (“steady state”). Why is there a requirement for this steady state? The 15-min interval dates back to the halothane era: it is the time it takes for the halothane partial pressure in the CNS (FCNS) to reach 95% equilibration (steady state) with that in the arterial blood (Fa; approximated by FET).

The time it takes for FCNS to equilibrate with Fa is different for each volatile anesthetic and can be calculated through the concept of the time constant (τ, expressed in units of time). τ describes the exponential rise and fall of the anesthetic partial pressure in the CNS after a step change in Fa. For example, during wash-in (fig. 4A), this is mathematically expressed as

Fig. 4.

Mathematical description of organ wash-in. (A) The time required to wash in a compartment is determined by the time constant (τ). This exponential process is 63%, 86%, and 95% complete after 1, 2, and 3τ. See text for details. (B) Central nervous system (CNS) time constant (τCNS) defines the exponential rise and fall of the partial pressure in the CNS after a step change in Fa. For example, during wash-in, FCNS at time t = Fa (1 – e–t/τ). Color coding: τCNS for isoflurane (Iso, pink), sevoflurane (Sevo, yellow), and desflurane (Des, blue). See text for details.

Fig. 4.

Mathematical description of organ wash-in. (A) The time required to wash in a compartment is determined by the time constant (τ). This exponential process is 63%, 86%, and 95% complete after 1, 2, and 3τ. See text for details. (B) Central nervous system (CNS) time constant (τCNS) defines the exponential rise and fall of the partial pressure in the CNS after a step change in Fa. For example, during wash-in, FCNS at time t = Fa (1 – e–t/τ). Color coding: τCNS for isoflurane (Iso, pink), sevoflurane (Sevo, yellow), and desflurane (Des, blue). See text for details.

Close modal
FCNS= Fa(1  et/τ)

This exponential process is 63%, 86%, and 95% complete after 1, 2, and 3τ. For many exponential processes, τ is calculated as volume divided by flow, but in this case, τCNS is calculated as the capacity of the CNS to hold volatile anesthetic divided by its transport toward the CNS with the arterial blood.

τCNS= capacity/(volatileanesthetictransport)

The capacity (amount of volatile anesthetic the CNS can hold) is determined by the Fa, tissue/gas partition coefficient (λCNS/G), and CNS volume (VCNS):

Capacity= Fa×λCNS/G×VCNS

The volatile anesthetic transport to the CNS is determined by the Fa, blood/gas partition coefficient (λB/G), and CNS blood flow (QCNS):

Volatileanesthetictransport=Fa×λB/G×QCNS

This allows us to calculate τCNS:

τCNS=(Fa×λCNS/G×VCNS)/(Fa×λB/G×QCNS) orτCNS=(λCNS/G×VCNS)/(λB/G×QCNS)

Because λCNS/G/ λB/G can be redefined as λCNS/B, the formula can also be written as

τCNS=(λCNS/B×VCNS)/QCNS

Using data readily available from the literature, τCNS for isoflurane, sevoflurane, and desflurane can be calculated to be 3.3, 3.5, and 2.6 min, respectively (exact numbers may vary depending on the data source). Because 95% equilibration requires three time constants, it will take the CNS 9.9, 10.5, and 7.8 min to equilibrate with the isoflurane, sevoflurane, and desflurane Fa, respectively (fig. 4B). Wash-out of volatile anesthetic during emergence is similarly affected by these time constants. It is important to realize that these are only concepts: for example, brain tissue is not a homogeneous tissue, and perfusion is not equally distributed. Nevertheless, the observed emergence times are compatible with the calculated time constants.35 

fMAC Use during Non–steady-state Conditions: Hysteresis-corrected fMAC

Through routine measurement of FET, displayed as fMAC value, we can estimate the Pno-response as long as there is a steady-state situation. However, when there is no steady state, fMAC values poorly reflect the concurrent probability of no response. To illustrate, consider two situations in which the same fMAC value is associated with two very different Pno-response values due to hysteresis (fig. 5). During anesthetic wash-in, fMAC poorly reflects the concurrent probability of no response, as it suggests a lower probability of movement in response to surgical stimuli than is clinically observed (in unparalyzed patients). The situation is reversed at the end of an anesthetic when fMAC falls below MACunconsciousness, yet most patients remain unconscious. This may give the uninformed user the (false) impression that the fMAC monitor is clinically useless.

Fig. 5.

Hysteresis-corrected fraction of minimum alveolar concentration (fMAC): use of fMAC during non–steady-state conditions. Most contemporary monitors display an age-adjusted fMAC value calculated directly from the measured end-tidal partial pressure (FET) (dark blue line). However, this fMAC value is also displayed when there is no steady state (A; at the beginning and at the end of the anesthetic, FET poorly reflects FCNS). The partial pressure in the CNS (FCNS, light blue line, expressed as fMAC) trails FET during wash-in (t1) and wash-out (t2), a phenomenon called hysteresis. This causes identical fMAC values (dark blue circles) to represent two different probabilities of no-responsiveness: B shows that FCNS is lower than suggested by FET at the beginning of the anesthetic, and C illustrates that FCNS is higher than suggested by FET after the anesthetic is discontinued. This may cause the clinician to get the impression that the fMAC concept does not work. See text for details.

Fig. 5.

Hysteresis-corrected fraction of minimum alveolar concentration (fMAC): use of fMAC during non–steady-state conditions. Most contemporary monitors display an age-adjusted fMAC value calculated directly from the measured end-tidal partial pressure (FET) (dark blue line). However, this fMAC value is also displayed when there is no steady state (A; at the beginning and at the end of the anesthetic, FET poorly reflects FCNS). The partial pressure in the CNS (FCNS, light blue line, expressed as fMAC) trails FET during wash-in (t1) and wash-out (t2), a phenomenon called hysteresis. This causes identical fMAC values (dark blue circles) to represent two different probabilities of no-responsiveness: B shows that FCNS is lower than suggested by FET at the beginning of the anesthetic, and C illustrates that FCNS is higher than suggested by FET after the anesthetic is discontinued. This may cause the clinician to get the impression that the fMAC concept does not work. See text for details.

Close modal

Hysteresis can be taken into account in clinical practice by including the time delay required to reach equilibration (3τ). Converting fMAC to hysteresis-corrected fMAC is mathematically straightforward. Figure 5 displays the course of the fMAC and the hysteresis-corrected fMAC, which is the calculated fMAC in brain tissue. Such a display, pioneered for volatile anesthetics by Kennedy et al.,36  has been commercialized as an individual parameter (MAC Brain, Getinge, Sweden), and the concept has been incorporated into the SmartPilot (Dräger, Germany) and the Navigator (GE Healthcare, USA). Such a display could also guide the clinician who is using an fMAC that is temporarily higher than the target FCNS to speed up the process of increasing FCNS (“overpressure technique”). Similarly, it could guide the tapering process in preparation for emergence.

Hysteresis-corrected fMAC converts fMAC derived from non–steady-state FET measurements into the real-time Pno-response. However, while time for equilibration between Fa and FCNS is an important factor affecting hysteresis, other factors such as neural inertia (a resistance to changes in neural state) play a role as well.37  In addition, abrupt transitions in brain activity at a constant anesthetic concentration have been observed as well, further confounding hysteresis.38  It is clear that more research is needed to confirm the findings by Kennedy et al.36  in a much larger and diverse patient population, while further development of the visual displays is ongoing.

There are several methods to help the clinician with drug dosing to achieve the anesthetic state. The main goal is to titrate drugs in such a manner that a very high probability of unconsciousness is obtained without overdosing because excessive concentrations can cause hypotension, reduced cardiac output, and excessive CNS depression with possibly increased incidence of postoperative delirium.39 

One anesthetic dose guiding tool is based on monitoring of drug-induced CNS depression, which results in unconsciousness. This can be done through raw EEG observation, EEG analysis such as BIS determination, or auditory evoked potential analysis. The advantage of these monitoring techniques is that they can be applied during inhaled anesthesia, as well as intravenous anesthesia, and with or without opioids or other intravenous anesthetics or adjuvants. Disadvantages include the proprietary algorithms, the processing delay, and the lack of exact thresholds that guarantee unconsciousness.

Although MAC itself is not quantal, it is a descriptive metric determined from quantal outcomes (endpoints) in a population. The quantal and probabilistic properties of fMAC, combined with consideration of hysteresis and drug interactions, guide the titration of volatile anesthetics to achieve the proper anesthetic state. With any volatile anesthetic, we propose that keeping fMAC greater than or equal to 0.7 helps to minimize the risk of consciousness or awareness with explicit recall while at the same time reducing the incidence of severe overdosing. Understanding the effect of hysteresis and drug interaction with opioids and intravenous hypnotics can help to avoid inadequate anesthesia immediately after anesthesia induction when the propofol concentration is decreasing and the partial pressure of the volatile anesthetics in the CNS is gradually rising, which otherwise could result in a “valley of potentially inadequate anesthesia.” Modern technology will assist us during this transition (see “The Future of MAC: Drug Advisory Displays”).

Increasing fMAC to greater than or equal to 1 to prevent or treat movement or excessive adrenergic responses to nociceptive stimulation is rarely necessary because these goals can be accomplished by additional opioid administration or the use of other drugs (neuromuscular blocking drugs, β-antagonists, vasodilators, among others). Intraoperative opioid administration is still the mainstay of our anesthetic management40  and is very effective in achieving a high probability of no movement (even without neuromuscular blocking drugs) and blunting of adrenergic responses.

MAC is useful because it describes the potency of the different volatile anesthetics in a unifying manner. Because MAC reflects the probability of movement after a noxious stimulus, MAC is forever linked to probability of immobility.41  However, this is not the main reason fMAC is useful: the main benefit from the MAC concept is that the available evidence suggests that maintaining fMAC greater than or equal to 0.7 is currently our single best line of defense against intraoperative consciousness with explicit recall when using volatile anesthetics, a topic that warrants further study.3  In clinical practice, at steady state (or with hysteresis correction) and in the absence of other drugs, fMAC also provides us with a reference value against which the response of the individual patient can be benchmarked against that of the population and be used as the patient’s own reference to guide future drug dosing. In the presence of opioids, we now understand that the fMAC to attain these probabilities needs to be adjusted. Displaying fMAC on the anesthesia machine thus has significant advantages over displaying only FET.

Should we abandon the use of the acronym “MAC” and use a new denotation that is conceptually and semantically more correct and aligns our clinical pharmacology terminology with that of intravenous drugs? Would doing so add any real clinical value? In our opinion, at this moment, the term “MAC” should not be not replaced by EC50, mainly because the displayed fMAC applies to all volatile anesthetics, thereby reassuring the clinician with one look at the monitor that the risk of postoperative explicit recall becomes very small if the volatile anesthetic is titrated to a hysteresis-adjusted fMAC of 0.7 or higher.42,43  fMAC also allows the same lower alarm limit to be applied to all volatile anesthetics. Showing the hysteresis-corrected fMAC provides the same information when there is no steady state. As a result, the presentation of the fMAC value on the anesthesia machine, a drug advisory display avant la lettre, will continue to serve us for a while to come.

In the presence of opioids, fMAC monitoring continues to be helpful to ensure unconsciousness but is much less valuable to determine the probability of immobility and blunting of adrenergic responses. In addition, if intravenous hypnotics (e.g., propofol) are added to the anesthetic mix, then even estimating the probability of unconsciousness becomes problematic. This is where advanced drug advisory displays (SmartPilot and Navigator) may become useful. The first generation of these devices calculates probabilities and their time course when a mixture of volatile anesthetic, propofol, and the most readily available opioids are used. The first clinical studies with the SmartPilot are encouraging and ongoing.44,45  Future versions will very likely also handle other intravenous drugs such as ketamine, dexmedetomidine, and lidocaine. Until these smarter drug advisory displays are available, EEG-based monitors may be advisable when an intravenous hypnotic drug is used. The use of a combination of drug dosing advisory displays and EEG-based monitors in particular deserves further study.

Conclusions

Volatile anesthetics, combined with opioids, continue to be the most widely used drugs to maintain general anesthesia. The most important value of displaying fMAC lies in minimizing the incidence of awareness with explicit recall by ensuring unconsciousness or altered consciousness without explicit recall with a very high probability. While there is no absolute lower cutoff value that guarantees unconsciousness or altered consciousness without explicit recall, based on the limited available evidence, we propose a steady-state fMAC greater than or equal to 0.7, and in the absence of steady state, a computer-calculated hysteresis-corrected fMAC can be used. fMAC is less useful to titrate volatile anesthetics to obtain immobility and blunting of the autonomic nervous system response because of pronounced drug interactions with opioids (and other drugs). Advanced drug advisory displays require more development and research on how they could be helpful to titrate volatile anesthetics, opioids, and other drugs to ensure unconsciousness and immobility without neuromuscular blocking drugs. Whether more sophisticated EEG-based depth-of-anesthesia monitors will completely replace or rather supplement hysteresis-corrected fMAC and advanced drug advisory displays is unclear at this moment.

Acknowledgments

The authors thank Larry Saidman, M.D. (Department of Anesthesia, Stanford University, Stanford, California), coinventor of the MAC concept, for his critical review of this work.

Research Support

Support was provided solely from institutional and/or departmental sources.

Competing Interests

Dr. Hendrickx has received lecture support, travel reimbursements, equipment loans, consulting fees, and/or meeting organizational support from AbbVie (North Chicago, Illinois), Acertys (Aartselaar, Belgium), Air Liquide (Paris, France), Allied Healthcare (St. Louis, Missouri), Armstrong Medical (Coleraine, United Kingdom), Baxter (Deerfield, Illinois), Dräger (Lübeck, Germany), General Electric Healthcare (Madison, Wisconsin), Getinge (Gothenburg, Sweden), Hospithera (Anderlecht, Belgium), Heinen und Lowenstein (Bad Ems, Germany),Intersurgical (Wokingham, United Kingdom), MDoloris Medical Systems (Loos, France), MEDEC (Aalst, Belgium), Micropore (Elkton, Maryland), Molecular Products (Harlow, United Kingdom), Philips (Brussels, Belgium), Piramal (Mumbai, India), and Quantium Medical (Barcelona, Spain). Dr. Hendrickx is the current chair of the Industry Liaison Task Force of the European Society of Anaesthesiology and Intensive Care (Brussels, Belgium). Dr. De Wolf declares no competing interests.

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