The Effects of Volatile Aromatic Anesthetics on Voltage-Gated Na⁺ Channels Expressed in Xenopus Oocytes

Abstract

BACKGROUND: 

Many inhaled anesthetics inhibit voltage-gated sodium channels at clinically relevant concentrations, and suppression of neurotransmitter release by these anesthetics results, at least partly, from decreased presynaptic sodium channel activity. Volatile aromatic anesthetics can inhibit N-methyl-d-aspartate (NMDA) receptor function and enhance γ-amino butyric acid A receptor function, but these effects depend strongly on the chemical properties of the aromatic compounds. In the present study we tested whether diverse aromatic anesthetics consistently inhibit sodium channel function.

METHODS: 

We studied the effect of eight aromatic anesthetics on Na_v1.2 sodium channels with β₁ subunits, using whole-cell, two-electrode voltage-clamp techniques in Xenopus oocytes.

RESULTS: 

All aromatic anesthetics inhibited I_Na (sodium currents) at a holding potential which produce half-maximal current (V_1/2) (partial depolarization); inhibition was modest with 1,3,5-trifluorobenzene (8% ± 2%), pentafluorobenzene (13% ± 2%), and hexafluorobenzene (13% ± 2%), but greater with benzene (37% ± 2%), fluorobenzene (39% ± 2%), 1,2-difluorobenzene (48% ± 2%), 1,4-difluorobenzene (31 ± 3%), and 1,2,4-trifluorobenzene (33% ± 1%). Such dichotomous effects were noted by others for NMDA and γ-aminobutyric acid A receptors. Parallel, but much smaller inhibition, was found for I_Na at a holding potential which produced near maximal current (−90 mV) (V_H-90), and hexafluorobenzene caused small (6% ± 1%) enhancement of this current. These changes in sodium channel function were correlated with effectiveness for inhibiting NMDA receptors, with lipid solubility of the compounds, with molecular volume, and with cation-π interactions.

CONCLUSION: 

Aromatic compounds vary in their actions on the kinetics of sodium channel gating and this may underlie their variable inhibition. The range of inhibition produced by minimum alveolar anesthetic concentration concentrations of inhaled anesthetics indicates that sodium channel inhibition may underlie the action of some of these anesthetics, but not others.

In Brief

IMPLICATIONS: Aromatic anesthetics can block N-methyl-d-aspartate receptors and enhance γ-aminobutyric acid A receptor responses. The present report finds various effects of these compounds on sodium channels. Although volatile aromatic anesthetics are not used clinically, exploring their effects on ion channels may aid in understanding the mechanisms of clinical inhaled anesthetic actions.

Voltage-gated sodium channels have an important role in the action potential initiation and propagation in excitable cells of nerve and muscle. They are established targets of local anesthetics, but have been considered to be resistant to general anesthetics.¹ However, recent reports suggest that clinical concentrations of volatile anesthetics significantly suppress sodium channel function in neurons,^2,3 and in recombinant mammalian sodium channels.^4–6 Moreover, blocking of presynaptic sodium channels provides a mechanism for suppression of neurotransmitter release by volatile anesthetics.^7–10

N-methyl-d-aspartate (NMDA) and γ-aminobutyric acid A (GABA_A) receptors are targets for general anesthetics.^11–14 Although not used as clinical anesthetics, volatile aromatic compounds have industrial applications, are drugs of abuse, and have anesthetic effects.¹⁵ They inhibit NMDA receptor function,¹⁶ and enhance GABA_A receptor function,¹⁷ doing so in a reciprocal manner: the aromatic anesthetics which inhibit NMDA receptors best enhance GABA_A receptor function the least. The importance of aromatic structure to an effect on sodium channels is unknown and such knowledge might be important to an understanding of potential targets and mechanisms of volatile anesthetics.

Nine distinct pore-forming α subunits of sodium channels have been identified.^18,19 Each α subunit has a different pattern of development and localization and demonstrates subtle differences in electrophysiological characteristics.²⁰ We examined the effect of several structurally distinct volatile aromatics on Na_v1.2, a sodium channel expressed primarily in the central nervous system, including the spinal cord, a major site of inhaled anesthetic action.²¹ We used the oocyte expression system to explore the mechanism of effect by volatile anesthetics on Na_v1.2.

METHODS

The Animal Care and Use Committees of the University of Texas approved this study.

Adult female Xenopus laevis frogs were obtained from Xenopus Express, Inc. (Plant City, FL). All aromatic anesthetics were purchased from Sigma-Aldrich (St. Louis, MO). We thank the following researchers for providing the subunit clones: cDNA for rat Na_v1.2 α subunit (Dr. W. A. Catterall, University of WA, Seatle, WA), cDNA for human β₁ subunit (Dr. AL George, Vanderbilt University).

Linearized cDNA templates with ClaI (Na_v1.2 α subunit), EcoRI (β₁ subunit) were transcribed using T7 (Na_v1.2 α subunit), T6 (β₁ subunit) RNA polymerase of mMESSAGE mMACHINE kit (Ambion, Ausin, TX). Preparation of Xenopus laevis oocytes and microinjection of the cRNA were performed as described previously.⁵ Stage IV-VI oocytes were manually isolated from an ovary. Oocytes were treated with collagenase (0.5 mg/mL) for 10 min and Na_v1.2 α subunit cRNA was co-injected with the β₁ subunit cRNA at a ratio of 1:10 (total volume was 20 approximately 40 ng/50 nL). Injected oocytes were incubated in modified Barth’s solution (88 mM NaCl, 1 mM KCl, 2.4 mM NaHCO₃, 10 mM HEPES, 0.82 mM MgSO₄, 0.33 mM Ca(NO₃)₂, 0.91 mM CaCl₂, adjusted to pH 7.5) supplemented with 10,000 U of penicillin, 50 mg of gentamicin, 90 mg of theophylline, and 220 mg of sodium pyruvate per liter (incubation medium) at 19°C.

Two to 6 days after injection, electrophysiological recordings were performed at room temperature (23°C) using the whole-cell, two-electrode, voltage-clamp technique. Oocytes were placed in a 100 μL recording chamber and impaled with recording electrodes prepared with borosilcate glass using a puller (P-97; Sutter Instruments Company, Novato, CA) and filled with 3M KCl/0.5% low melting point agarose and with resistances between 0.3 and 0.5 M[Omega]. The oocytes were perfused at 2 mL/min with frog Ringer’s solution containing NaCl 115 mM, KCl 2.5 mM, HEPES 10 mM, CaCl₂ 1.8 mM, pH 7.2 using a peristaltic pump (Cole-Palmer Instrument CO, Chicago, IL). The whole-cell voltage clamp was achieved through these two electrodes using a Warner Instruments model OC-725C (Hamden, CT). Currents were recorded and analyzed using pCLAMP software (Axon Instruments, Foster City, CA). The sodium current amplitudes were typically 2 to 15 μA. Transients and leak currents were subtracted using the P/N procedure.

The voltage dependence of activation was determined by 50-ms depolarizing pulses from a holding potential of −90 mV (V_H-90) or from a holding potential causing half-maximal current (V_1/2) (approximately from −50 mV to −60 mV) to 60 mV in 10-mV increments. V_1/2 value was determined individually for each oocyte in each experiment. Normalized activation data were fitted to a Boltzmann equation: G/G_max = 1/(1 + exp(V_1/2 – V)/k), where G is the voltage-dependent sodium conductance, G_max is the maximal sodium conductance, G/G_max is the normalized fractional conductance, V_1/2 is the potential at which activation is half maximal, k is the slope factor. G values for each oocyte were calculated using: G = I/(Vt – Vr), where I is the peak sodium current, Vt is the test potential, and Vr is the reversal potential. Vr for each oocyte was estimated by extrapolating the linear ascending segment of the current voltage relationship (I–V) curve to the voltage axis. To measure steady-state inactivation, currents were elicited by a 50-ms test pulse to −20 mV after 200-ms prepulses ranging from −140 mV to 0 mV in 10-mV increments from a holding potential of −90 mV. Steady-state inactivation curves were fitted to a Boltzmann equation: I/I_max = 1/(1 + exp(V_1/2 – V)/k), where I_max is the maximal sodium current, I/I_max is the normalized current, V_1/2 is the voltage of half-maximal inactivation, and k is the slope factor.

The aromatic anesthetics were examined at the concentrations that are equivalent to 1 MAC (minimum alveolar anesthetic concentration) or 2 MAC in rats.^16,22 (MAC is the minimum anesthetic concentration needed to produce immobility in response to noxious stimulation in 50% of rats; it is equivalent to the EC₅₀ for producing surgical immobility). All aromatic anesthetics were directly dissolved in the frog Ringer’s solution, and were infused for 3 min to produce equilibrium. The loss of concentration from vial to bath was approximately 60% to 80% for all aromatic anesthetics, as determined by gas chromatography. Bath/vial concentrations of the four compounds that were tested were 1.1/2.5 mM (benzene), 0.40/1.4 mM (1,3,5-trifluorobenzene), 0.65/2.1 mM (pentafluorobenzene), and 0.12/0.58 mM (hexafluorobenzene).

Data Analysis

All values are presented as the mean ± sem. The n values refer to the number of oocytes studied. Each experiment was performed with oocytes from at least two frogs. Statistical analyses were performed using a one-way analysis of variance for multiple comparisons and a t-test using GraphPad Prism software (GraphPad Software Inc., San Diego, CA).

RESULTS

Effects of Aromatic Anesthetics on the Peak Na⁺ Inward Currents Elicited from Two Different Holding Potentials

All eight aromatic anesthetics suppressed I_Na (sodium currents) at the V_1/2 holding potential, and the magnitudes of these effects varied widely (Figs. 1B and D and Fig. 2). At V_1/2, these anesthetics reduced I_Na by 37% ± 2% (benzene), 39% ± 2% (fluorobenzene), 48% ± 2% (1,2-difluorobenzene), 31% ± 3% (1,4-difluorobenzene), 33% ± 1% (1,2,4-trifluorobenzene), 8% ± 2% (1,3,5-trifluorobenzene), 13% ± 2% (pentafluorobenzene), and 13% ± 2% (hexafluorobenzene) (Fig. 2). Effects on I_Na at V_H-90 were smaller than at V_1/2holding potential, and the magnitudes of the effects varied widely, with inhibitions of 8% ± 1% (benzene), 10% ± 1% (fluorobenzene), 15% ± 2% (1,2-difluorobenzene), 6% ± 0.5% (1,4-difluorobenzene), and 3% ± 0.7% (1,2,4-trifluorobenzene) (Fig. 1A, Fig. 2). 1,3,5-trifluorobenzene did not affect these currents. In contrast, pentafluorobenzene and hexafluorobenzene enhanced I_Na at V_H-90 by 2% ± 1%, 6% ± 1%, respectively (Fig. 1C, Fig. 2). Thus, there are two effects of aromatic anesthetics on sodium channels: all produced inhibitory effects at V_1/2 holding potential, albeit by widely varying amounts. At V_H-90, benzene, fluorobenzene, 1,2-difluorobenzene, 1,4-difluorobenzene, and 1,2, 4-trifluorobenzene produced inhibition but pentafluorobenzene and hexafluorobenzene caused slight enhancement.

Figure 1.: Effects of benzene and hexafluorobenzene on sodium currents at different holding potentials in oocytes expressing Na_v1.2 with β₁. (A) The effect of benzene at −90 mV (V_H-90) holding potential. Left panel; traces of sodium currents evoked by a 50-ms depolarizing pulse to −20 mV from a holding potential of V_H-90 in the absence and presence of benzene. Right panel; time course figure of benzene effect at V_H-90 holding potential on sodium currents. Currents were elicited by a 50-ms depolarizing pulses to −20 mV applied every 10 s from −90 mV. Normalized current is shown. Filled circles represent control and washout, open circles represent currents during 3 min benzene treatment. (B) The effect of benzene at a holding potential which induced half maximal current (V_1/2). Left panel; traces of sodium currents evoked by a 50-ms depolarizing pulse to −20 mV from V_1/2 holding potentials in the absence and presence of benzene. Right panel; time course of benzene action at V_1/2 holding potential. Currents were elicited by a 50-ms depolarizing pulses to −20 mV applied every 10 s from V_1/2 holding potential. (C) Effect of hexafluorobenzene at V_H-90 holding potential. (D) Effect of hexafluorobenzene at V_1/2 holding potential. Concentrations of anesthetics were equivalent to 1 minimum alveolar anesthetic concentration.

Figure 2.: Effects of aromatic anesthetics on sodium currents at different holding potentials. Percent inhibitions were calculated from time course figure. Open columns represent the effect at V_H-90 holding potential. Closed columns indicate the effect at V_1/2 holding potential. Concentrations of anesthetics were equivalent to 1 minimum alveolar anesthetic concentration. V_1/2 value was −53.5 ± 0.4 mV. Data were obtained from 6 oocytes and are mean ± sem (n = 6). *P < 0.05; **P < 0.01; ***P < 0.001 (one-way analysis of variance).

Effects of Aromatic Anesthetics on Activation of Sodium Currents

Because of the different effects of aromatic anesthetics noted above, we examined the actions of these two types of compounds on gating of sodium channels. We selected benzene and 1,2-difluorobenzene as compounds with potent inhibitory effects at V_1/2 holding potential plus smaller inhibitory effects at V_H-90, and hexafluorobenzene as the compound with a much smaller inhibitory effect at V_1/2 holding potential and slight enhancing effect at V_H-90. The voltage dependence of activation was determined by 50-ms depolarizing pulses from a holding potential of −90 mV to 60 mV in 10-mV increments or from a holding potential of V_1/2 to 60 mV in 10-mV increments. The activation curves were derived from the I–V curve (see Methods). Benzene and 1,2-difluorobenzene (2 MAC) reduced the peak I_Na at V_H-90 and V_1/2 (Figs. 3A and B). However, hexafluorobenzene (2 MAC) enhanced the peak I_Na at V_H-90, especially in the depolarizing region where channel opening begins (around −40 approximately −30 mV) and suppressed the sodium currents at V_1/2 more weakly than benzene or 1,2-difluorobenzene (Fig. 3C). Benzene and 1,2-difluorobenzene did not affect voltage dependence of activation at V_H-90 or V_1/2 (Figs. 4A and B, Table 1), but hexafluorobenzene shifted the midpoint of steady-state activation, V_1/2 in a hyperpolarizing direction by 4.9 and 2.2 mV at V_H-90 and V_1/2 (Fig. 4C, Table 1).

Figure 3.: Effects of benzene (A), 1,2-difluorobenzene (B), and hexafluorobenzene (C) on I–V relations of sodium currents at V_H-90 and V_1/2 holding potentials in oocytes expressing Na_v1.2 with β₁ subunits. Left panel; representative I_Na traces in absence and presence of aromatic anesthetics at a V_H-90 holding potential. Currents were elicited by 50-ms depolarizing steps between −80 and 60 mV in 10-mV increments from holding potentials of −90 mV. Center panel; the effects of aromatic anesthetics on I–V curves elicited from a V_H-90 holding potential (closed circles, control; open circles, aromatic anesthetics; cross, washout). The peak currents were normalized to the maximal currents which were observed at −20 or −30 mV. Right panel; the effects of aromatic anesthetics on I–V curves elicited from a V_1/2 holding potential. Currents were elicited by 50-ms depolarizing steps between −60 and 60 mV in 10-mV increments from a V_1/2 holding potential. Maximal currents were observed at −20 mV. Concentrations of anesthetics were equivalent to 2 minimum alveolar anesthetic concentration. V_1/2 value was −53.3 ± 0.4 mV. Data were obtained from 5 oocytes and shown as mean ± sem (n = 5).

Figure 4.: Effects of benzene (A), 1,2-difluorobenzene (B), and hexafluorobenzene (C) on channel activation in oocytes expressing Na_v1.2 with β₁ from a V_H-90 holding potential (upper) or V_1/2 holding potential (down). Closed circles represent control, open circles indicate the effect of aromatic anesthetics, and cross indicate washout. Data shown as mean ± sem (n = 5). Activation curves were fitted to a Boltzmann equation and V_1/2 are shown in Table 1. Concentrations of anesthetics were equivalent to 2 minimum alveolar anesthetic concentration.

Table 1: Effects of Benzene, 1,2-fluorobenzene, and Hexafluorobenzene on Activation and Inactivation in Oocytes Expressing Na_v1.2 with β₁

Effects of Aromatic Anesthetics on Inactivation of Sodium Currents

The effects of benzene, 1,2-difluorobenzene and hexafluorobenzene on steady-state inactivation were also investigated. Benzene and 1,2-difluorobenzene shifted V_1/2 in the hyperpolarizing direction significantly by 7.4 and 8.9 mV, respectively and also reduced sodium currents in the hyperpolarizing potential range (Fig. 5, Table 1). Hexafluorobenzene also significantly shifted V_1/2 in the hyperpolarizing direction by 4.6 mV although the shift was smaller than that by benzene and 1,2-difluorobenzene, whereas hexafluorobenzene enhanced sodium current in the hyperpolarizing potential range slightly (Fig. 5, Table 1). The effects of benzene, 1,2-difluorobenzene and hexafluorobenzene in the hyperpolarizing range were consistent with the effects of these compounds on I_Na at V_H-90, and the effects on these compounds on activation curve at V_H-90.

Figure 5.: Effects of benzene (A), 1,2-difluorobenzene (B), and hexafluorobenzene (C) on inactivation in oocytes expressing Na_v1.2 with β₁. Left panel; representative I_Na traces in absence and presence of aromatic anesthetics. Currents were elicited by a 50-ms test pulse to −20 mV after 200-ms prepulses ranging from −140 to 0 mV in 10-mV increments from a holding potential of V_H-90. Right panel; the effects of aromatic anesthetics on inactivation curves (closed circles, control; open circles, aromatic anesthetics; cross, washout). Data shown as mean ± sem (n = 7). Inactivation curves were fitted to a Boltzmann equation and the V_1/2 values are shown in Table 1. Concentrations of anesthetics were equivalent to 2 minimum alveolar anesthetic concentration.

DISCUSSION

We found that structurally distinct aromatic anesthetics differently affected I_Na at V_H-90 and V_1/2 holding potentials. At V_1/2 holding potential, 1 MAC benzene, fluorobenzene, 1,2-difluorobenzene, 1,4-difluorobenzene, 1,2,4-trifluorobenzene suppressed I_Na by 30% to 50%. These inhibitory effects parallel those of other inhaled anesthetics. For example, clinically relevant concentrations (0.25–0.4 mM) of isoflurane suppress I_Na by 30% to 40% in several preparations: Chinese hamster ovary cells expressing Na_v1.2,⁴ isolated rat neurohypophysial nerve terminals,³ and an oocyte system expressing Na_v1.2, Na_v1.4, or Na_v1.6.⁵

Solt et al. separated these aromatic anesthetics into two groups based on the inhibition of NMDA receptors produced by 1 MAC.¹⁶ Fewer fluorinated compounds with the limited fluorination, benzene, fluorobenzene, and 1,2-difluorobenzene, inhibited strongly (Group 1), and compounds with greater fluorination, 1,4-difluorobenzene, 1,2,4-trifluorobenzene, 1,3,5-trifluorobenzene, pentafluorobenzene, hexafluorobenzene, inhibited weakly (Group 2). Solt et al. also studied the effect of these compounds on GABA_A receptors,¹⁷ and found that aromatic anesthetics which inhibit NMDA receptor currents most (Group 1) enhance GABA_A receptor currents least, and anesthetics that inhibit NMDA receptor currents least (Group 2) enhance GABA_A receptor currents most. These findings suggest that distinct molecular properties determine the action of anesthetics on NMDA and GABA_A receptors.

We found that benzene, fluorobenzene, and 1,2-difluorobenzene (Group 1 compounds), strongly inhibited sodium currents at V_1/2, whereas 1,3,5-trifluorobenzene, pentafluorobenezene, and hexafluorobenzene (Group 2 compounds), inhibited weakly. But we found that, unlike the NMDA results, 1,4-difluorobenzene and 1,2,4-trifluorobenzene (Group 2 compounds) inhibited sodium currents (Fig. 6A). Our previous study of isoflurane⁵ found similar sodium channel inhibition as for 1,4-difluorobenzene and 1,2,4-trifluorobenzene, and these three compounds are effective on both sodium channels and GABA_A receptors (Fig. 6B).

Figure 6.: (A) Relationship between inhibitory potencies on sodium channels at V_H-90 holding potential (open circle) or V_1/2 holding potential (closed circle) and that on N-methyl-d-aspartate (NMDA) receptors of aromatic anesthetics at 1 minimum alveolar anesthetic concentration. (B) Relationship between inhibitory potencies on sodium channels at V_H-90 holding potential (open circle) or V_1/2 holding potential (closed circle) and potencies of enhancement of aromatic anesthetics on γ-aminobutyric acid A (GABA_A) receptors. NMDA receptor inhibition are from Solt et al.,¹⁶ and GABA_A receptor enhancement are from Kelly et al.¹⁷ Data shown as mean ± sem (n = 6). Correlation between inhibitory potencies on sodium channels of aromatic anesthetics at V_H-90 holding potential (open circle) or V_1/2 holding potential (closed circle) and their abilities to oil/gas partition coefficient (C), molecular volumes (D), or cation-π interactions (E). The lines were derived from linear regression analysis. Oil/gas partition coefficients of aromatic anesthetics are from Fang et al.,²² molecular volume and cation-π binding energy of aromatic anesthetics are from Raines et al.,²³ In C, r ² = 0.88 and P = 0.0005 (V_1/2), r ² = 0.87 and P = 0.0006 (V_H-90); in D, r ² = 0.55 and P = 0.0353 (V_1/2), r ² = 0.68 and P = 0.0113 (V_H-90); in E, r ² = 0.52 and P = 0.0445 (V_1/2), r ² = 0.67 and P = 0.0135 (V_H-90).

Raines et al. showed that cation-π interactions predict the actions of aromatic anesthetics on NMDA receptors.²³ In order to explore the physical properties important for actions of these compounds on sodium channels, we correlated drug effects with several variables (Figs. 6C–E). Sodium channel inhibition was correlated with cation-π interactions, but this relationship was weaker than seen for cation-π interactions and NMDA receptor inhibition by Raines et al.²³ Inhibition of sodium channels was strongly correlated with oil/gas partition coefficients. These results suggest that aromatic anesthetics interact with different channels by distinct mechanisms. We recently reported that n-alcohols inhibit sodium channel function and their potency increase with carbon number up to a cut-off at nonanol,²⁴ suggesting that hydrophobic and steric interactions determine the potencies of n-alcohols. Hydrophobic and steric interactions might also be important for sodium channel inhibition by aromatic anesthetics, with a smaller contribution from cation-π interactions. Some fluorinated compounds are either not as potent anesthetics as would be predicted from their lipid solubility or do not produce anesthesia (nonimmobilizers).²⁵ The nonimmobilizing fluorinated cyclobutanes do not inhibit sodium channels,²⁶ indicating that factors other than lipid solubility are also important for channel inhibition by some compounds.

Analysis of gating variables revealed differences in the actions of benzene, 1,2-fluorobenzene, and hexafluorobenzene. Other volatile anesthetics generally enhance inactivation with no effect on activation.^5,6 We also found this to be true for benzene and 1,2-difluorobenzene. However, hexafluorobenzene enhanced peak I_Na at V_H-90, shifted activation in the hyperpolarizing direction and increased sodium currents in the hyperpolarizing range of inactivation. These changes indicate that hexafluorobenzene shifts channel gating equilibrium toward the open channel state. No other anesthetics have been reported to have an activating effect on sodium channels. This action of hexafluorobenzene on channel gating might offset the effects on the inactivated state and explain the small inhibition at V_1/2 holding potential relative to the other compounds. Pentafluorobenzene, another Group 2 compound, may shift GABA_A receptor gating toward the open channel state because pentafluorobenzene decreases the GABA EC₅₀ and activates GABA_A receptors directly.¹⁷ This observation suggests some commonalities in the action of aromatic compounds on sodium channels and GABA_A receptors.

In conclusion, we find that volatile aromatic anesthetics inhibit Na_v1.2 sodium channel function but that the magnitude of the inhibition varies widely among the compounds. Differences in the actions of these compounds on sodium channel gating are likely responsible for the range of inhibitory effects. Although numerous inhaled anesthetics and n-alcohols inhibit sodium channel function, some inhibit weakly and others strongly (Group 1 versus Group 2) at concentrations corresponding to MAC. We applied aromatic compounds in the present study because they reciprocally affect GABA_A and NMDA receptors; we tested whether the sodium channel might provide more consistent responses. However, neither the aromatics nor clinical anesthetics (e.g., halothane, isoflurane) provide consistent inhibition of sodium channels. This indicates that sodium channel inhibition may be important for some anesthetics but not others as a mediator of the capacity of inhaled anesthetics to produce immobility in the face of noxious stimulation.

ACKNOWLEDGMENTS

We thank Dr. Michael Laster for determining the concentrations of anesthetics used in this study.