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Pain Medicine  |   July 2003
Differential Uptake of Volatile Agents into Brain Tissue In Vitro  : Measurement and Application of a Diffusion Model to Determine Concentration Profiles in Brain Slices
Author Affiliations & Notes
  • Michael A. Chesney, B.S.
    *
  • Misha Perouansky, M.D.
  • Robert A. Pearce, M.D., Ph.D.
  • *Graduate Student, Department of Biochemistry, †Visiting Associate Professor of Anesthesiology, ‡Betty J. Bamforth Research Professor of Anes-thesiology.
  • Received from the Department of Anesthesiology, University of Wisconsin, Madison.
Article Information
Pain Medicine
Pain Medicine   |   July 2003
Differential Uptake of Volatile Agents into Brain Tissue In Vitro  : Measurement and Application of a Diffusion Model to Determine Concentration Profiles in Brain Slices
Anesthesiology 7 2003, Vol.99, 122-130. doi:
Anesthesiology 7 2003, Vol.99, 122-130. doi:
INVESTIGATIONS of anesthetics have revealed that these drugs affect numerous molecular and cellular processes. 1 Separating effects that are relevant to the mechanism of anesthesia from irrelevant ones is therefore of fundamental importance. One strategy to achieve this aim calls for comparing the effects of anesthetics with those of drugs that have anesthetic-like physicochemical characteristics but that fail to produce the full spectrum of anesthetic actions in vivo  . Such compounds were initially termed nonanesthetics  . 2 The finding that some agents do cause amnesia but do not prevent movement in response to noxious stimulus 3 has now led to their classification as nonimmobilizers  .
The nonimmobilizer that has been studied most extensively to date is the compound 1,2-dichlorohexafluorocyclobutane (F6, also termed 2N  in the literature). Unlike conventional anesthetics, it does not produce immobility even at high concentrations, 2 it is not analgesic, 2,4 it does not depress breathing, 5 and it does not affect thermoregulation. 6 However, it does produce amnesia at a concentration of approximately one third the predicted minimum alveolar concentration (MACpred). 2,7 In addition, it produces convulsions at concentrations slightly higher than MACpred. 8 Thus, as a compound that produces only a subset of anesthetic actions, this drug has been of particular interest.
To investigate the cellular mechanisms by which conventional anesthetics and nonimmobilizers produce their effects in the central nervous system, we and others have used hippocampal brain slices to study their effects on electrophysiologic processes. These studies have demonstrated that anesthetics alter a number of cellular processes, most prominent among them being decreases in excitatory synaptic transmission 9,10 and increases in inhibitory synaptic transmission. 11,12 The combination of these effects leads to decreases in evoked responses. 12–14 In contrast, a recent study of F6 reported no effects on the evoked population spike (PS) and inconsistent effects on the population excitatory postsynaptic potential (EPSP) at concentrations up to twice MACpred. 15 
A crucial aspect of performing studies using brain slices is assuring that drug delivery to tissue sites of action is sufficiently rapid that equilibration occurs during the time course of the study. For conventional anesthetics such as halothane and isoflurane, onset of action has been found to be rapid, and drug actions are readily reversible. 16,17 However, for drugs such as diazepam and propofol, which have high lipid solubility but low aqueous solubility, extremely slow onset of action has been noted. 18,19 Here, in consideration of the highly nonpolar nature of F6, we have performed electrophysiologic studies of the effects of F6 using long equilibration times (40 min) and aqueous drug concentrations equal to or greater than MACpred. Further, to ascertain whether our experimental conditions produced tissue concentrations comparable to those obtained in vivo  , we measured the rate at which F6 diffuses into the brain slice and used the information to reconstruct concentration profiles through the tissue as a function of time and depth. We found that at tissue concentrations corresponding to approximately 0.87 MACpred, F6 did not alter electrophysiologic responses in the CA1 region of the hippocampus.
Materials and Methods
All experiments were conducted according to the guidelines laid out in the Guide for the Care and Use of Laboratory Animals and were approved by the University of Wisconsin Animal Care and Use Committee (Madison, Wisconsin).
Solutions
Experiments were conducted using artificial cerebrospinal fluid (ACSF) of the following composition: 127 mm NaCl, 1.21 mm KH2PO4, 1.87 mm KCl, 26 mm NaHCO3, 2.17 mm CaCl2, 1.44 mm MgSO4, 10 mm glucose, saturated with “carbogen” gas (95% O2–5% CO2). Solutions of ACSF containing halothane and F6 were prepared in Chemware Teflon FEP gas sampling bags (North Safety Products, Cranston, RI) fitted with three-way stopcocks. F6 solutions were prepared by partially filling Teflon bags with ACSF that had been preequilibrated with carbogen and adding to the headspace appropriate quantities of F6-saturated carbogen and pure carbogen to achieve the desired F6 concentration. Halothane solutions were prepared similarly except that halothane-saturated ACSF was added to the Teflon bag. For electrophysiologic experiments, solutions were equilibrated by shaking manually for approximately 1 min and then allowed to stand for at least 1 h. For uptake experiments, solutions were equilibrated on a shaker table for 1 h (0.5-l bag) or 2 h (3-l bag). F6-saturated carbogen stock was prepared in a separate Teflon bag by first evacuating the bag and then adding carbogen, water, and an excess of F6 liquid and shaking for 1 h to equilibrate. Control ACSF solutions were prepared similarly in Teflon bags. Appropriate aqueous oxygen concentrations in control and anesthetic solutions were confirmed using an oxygen detector (YSI, Marion, MA).
Brain Slice Tissue Preparation
Male Sprague-Dawley rats (weight, 200–300 g) were decapitated under halothane or isoflurane anesthesia, and the brain was quickly removed and immersed in cold (4°C) ACSF saturated with carbogen. A block of tissue containing the hippocampus was glued to a tissue tray using cyanoacrylate glue. Tissue slices (500 μm) were prepared using a vibrating microtome, incubated at 35°C for 1 h, and then kept in carbogen-saturated ACSF at room temperature until use.
Electrophysiologic Recordings
Individual slices were transferred to a submersion-style recording chamber and superfused at 2.5 ml/min with carbogen-saturated ACSF at room temperature (22°C). The drip chamber that we typically use in the perfusion line to monitor and control solution flow rates was removed so that accumulation of F6 in the gas space would not delay delivery to the recording chamber. Extracellular PSs and EPSPs were recorded in CA1 stratum pyramidale  in response to electrical stimulation of Schaffer collateral fibers. Stimuli (0.1 ms, 50–300 μA) were delivered every 20 s using Tungsten electrodes (AM Systems, Sequim, WA). Recording electrodes were fabricated from 1.2 mm borosilicate glass, filled with 2 m NaCl, and broken to achieve tip resistance of 1–2 MΩ. Recordings were obtained using an Axoclamp 2A amplifier, Digidata 1200 interface, and pClamp data acquisition software (Axon Instruments, Union City, CA). Data were filtered at 3 KHz, sampled at 10 KHz, and stored on a Pentium-based personal computer. Responses were recorded for a 40-min control period, followed by 40 min of application of the anesthetic solution and a 40-min wash period. In most cases, F6 was applied during the first drug period, and the first wash was immediately followed by a 40-min application of halothane and a second wash period.
Concentrations of F6 and halothane in ACSF were measured from the Teflon bags and from the brain slice chamber to determine the fraction of loss and the concentrations that were actually applied to slices. Approximately 10% loss from the bag to the chamber was observed, so the F6 concentration to which brain slices were exposed was 24 ± 2.5 μm (mean ± SD, n = six measurements) and the halothane concentration was 270 ± 30 μm (n = five measurements). Aqueous concentrations were converted to MAC-equivalent values according to the method described by Franks and Lieb. 20 For these calculations, we used a MACpredvalue for F6 of 0.042 atm, based on the assumption that (MAC) × (oil/gas partition coefficient) = 1.82. 2 Based on these calculations, aqueous concentrations delivered to tissues slices were equivalent to 1.5 × MACpredfor F6 and 1.1 × MAC for halothane.
Data were analyzed using ClampFit (Axon Instruments), Microcal Origin (Microcal Software, Inc., Northampton, MA), and MS Excel (Microsoft, Redmond, WA). PS amplitude was defined as the difference between the peak negativity and the voltage at the same time point on a line connecting the positive peaks that preceded and followed the spike. EPSP slope was measured by fitting the rising phase of the population EPSP with a straight line between 20% and 80% of peak amplitude.
Aqueous Phase Drug Concentration Measurements
Aqueous samples (2 ml) were collected from Teflon bags or the brain slice perfusion chamber using a gas-tight glass syringe (Hamilton Co., Reno, NV) fitted with a Teflon stopcock (Hamilton Co.) Samples were transferred to 3.7-ml glass vials capped with Mininert valves (Alltech, Nicholasville, KY), and aqueous and gas phases within the vial were equilibrated by shaking for 1 h. Drug concentrations in the vial headspace were determined by gas chromatography using gas phase calibration standards for F6 or halothane. Concentrations in aqueous samples (Caq,sample) were calculated based on saline/gas partition coefficients (λsaline/gas) and the relative volumes of aqueous and gas phases within the vial (Vgas,vialand Vaq,vial), according to the equation:MATH
Gas phase concentrations (Cgas,vial) were measured using a Varian 3700 gas chromatograph (Varian Inc., Walnut Creek, CA) with a flame ionization detector. Separation was achieved by on-column injection into a 3.05-m × 3.2-mm stainless steel column packed with 5% SP-2100 100/120 Supelcoport (electrophysiology experiments) or a 1.83-m × 3.2-mm stainless steel column packed with 80/100 Poropak Q (uptake experiments).
Saline/Gas Partition Coefficient
The saline/gas partition coefficient of F6 at room temperature (22°C) was measured by a two-stage reequilibration method. A small volume of gas phase F6 was transferred from the saturated headspace of a stock vial to a sealed vial containing known volumes of saline and air. The F6 was allowed to distribute from air to saline by shaking for 1 h, which preliminary experiments had demonstrated was a sufficient duration to achieve equilibration. The gas phase concentration of F6 was then measured by GC. Next, the headspace in this vial was replaced with fresh gas containing no F6, residual F6 in the saline was allowed to redistribute between the saline and gas phases for 1 h, and the gas phase measurement was repeated. From the ratio of the two gas phase concentrations (Cgas,1and Cgas,2) and taking into account the volumes of air (Vgas,vial) and saline (Vaq,vial) in the vial, the air/saline partition coefficient was calculated according to the equation:MATH
The saline/gas partition coefficient λsaline/gasmeasured by this method yielded a value of 0.026. This is similar to the value of 0.024 at 23°C that was reported previously. 21 For halothane, a value of 0.72 was used based on previous measurements. 20 
Tissue Uptake Measurements
Individual slices were weighed, removing excess fluid from the tissue surface using a Kimwipe (Kimberly-Clark Corp., Roswell, GA), and transferred to a brain slice recording chamber perfused with ACSF at 2.5 ml/min. Slices were exposed to drug-containing solutions at 22°C via  superfusion for 7.5, 15, 30, 60, 120, 240, or 480 min and then transferred by forceps into an equilibration vial partially filled with saline. F6 was allowed to equilibrate between the slice, aqueous, and gas phases by shaking for 1 h, and the headspace was then sampled for gas chromatographic analysis. Tissue concentrations were calculated based on the saline/gas and saline/tissue partition coefficients and the relative volumes of tissue, headspace, and solution in each vial according to the equation:MATH
For halothane, a value for λsaline/tissueof 0.125 was used based on previous measurements. 22 For F6, a value for λsaline/tissueof 0.0135 was determined based on the gas phase concentrations that resulted from the longest uptake times (8 h). Because of slow equilibration between tissue and saline, it is likely that incomplete recovery of F6 from the slice occurred during the 1-hour incubation period. Diffusion modeling (see Modeling Concentration–Depth–Time Profiles) indicated that this would result in errors in actual tissue concentration of up to 12% for the longest tissue uptake times. Therefore, corrections to the F6 slice concentrations were made to account for incomplete reequilibration in the vial.
Modeling Concentration–Depth–Time Profiles
Concentration–depth–time profiles for diffusion into a 500-μm tissue slab were calculated according to a general solution for one-dimensional transfer. 23 This model is based on the geometry of an infinite sheet with a finite thickness. Because the thickness of our tissue slices was small (500 μm) compared to cross-sectional dimension (approximately 1 cm × 1 cm), this model is appropriate. The solution is an infinite series, and the number of terms required to achieve a stable solution was found to depend on the steepness of the concentration gradient. Where the gradient was the greatest, i.e  ., at the earliest time points (<1 min) and near the surface of the tissue (<50 μm deep), up to 10 terms were required to yield stable solutions. Therefore, 10 terms were used for all further calculations.
To estimate the influence of incomplete equilibration on tissue concentration measurements, a finite difference algorithm based on Fick's second law of diffusion was used to model tissue concentrations during uptake and subsequent equilibration in a measurement vial. The concentration at time t (Ct) in a vertical section of depth z and thickness Δz was calculated as:MATH
Δz and Δt were varied to assure convergence of the solution, with final values of Δz = 20 μm and Δt = 2 s leading to stable solutions. Based on λsaline/tissue≪ 1, the aqueous drug concentration was assumed to be zero to model diffusion out of the tissue during reequilibration, and the initial concentration profile in the tissue was given by the modeled concentration profile in the slice at a given time. The concentration profile of drug remaining in the slice after the 60-min reequilibration interval was then determined, thus allowing us to calculate the original tissue content from the measured aqueous concentration.
Statistical Analysis
Results are presented as mean ± SD. Student t  test was used to compare mean values.
Results
We examined the effects of F6 and halothane on evoked population responses in the CA1 region of rat hippocampal brain slices. PS amplitudes and population EPSPs were measured before, during, and after 40-min applications of drugs in the ACSF superfusate (fig. 1). At an aqueous concentration of 24 μm (≈1.5 MACpredequivalent), F6 had no significant effect on PS amplitude (103 ± 4.6% control) or EPSP slope (96.2 ± 12% control). Subsequent application of halothane (270 μm ≈ 1 MAC equivalent) reduced PS amplitude (70.3 ± 5.9% control, mean ± SD) and EPSP slope (78.5 ± 7.6% control, P  < 0.01 for both). These changes were rapid (fig. 1, B  , τ= 7 min) and were readily reversible following washout of halothane.
Fig. 1. Effect of F6 and halothane on evoked responses in hippocampal slices. Extracellular field potentials were recorded from stratum pyramidale in response to electrical stimulation of stratum radiatum. (A  ) Representative recordings from an individual experiment. F6 (24 μm) did not alter the evoked response. Subsequent application of halothane (270 μm) reduced the amplitude of the population spike and the slope of the population excitatory postsynaptic potential. Responses were measured after 40 min of drug application. Calibration 1 mV, 10 ms. (B  ) Time series plot of population spike amplitude. Population spike amplitude (mean ± SD) is plotted for 11 experiments with F6. For six experiments, application of halothane followed a 40-min wash period. In each case, responses were normalized to the average population spike amplitude during the control period. (Insets  ) Onset and offset of halothane actions on the evoked population spike. Average amplitudes (from data described previously; error bars omitted) were fit by monoexponential functions (solid lines  ).
Fig. 1. Effect of F6 and halothane on evoked responses in hippocampal slices. Extracellular field potentials were recorded from stratum pyramidale in response to electrical stimulation of stratum radiatum. (A 
	) Representative recordings from an individual experiment. F6 (24 μm) did not alter the evoked response. Subsequent application of halothane (270 μm) reduced the amplitude of the population spike and the slope of the population excitatory postsynaptic potential. Responses were measured after 40 min of drug application. Calibration 1 mV, 10 ms. (B 
	) Time series plot of population spike amplitude. Population spike amplitude (mean ± SD) is plotted for 11 experiments with F6. For six experiments, application of halothane followed a 40-min wash period. In each case, responses were normalized to the average population spike amplitude during the control period. (Insets 
	) Onset and offset of halothane actions on the evoked population spike. Average amplitudes (from data described previously; error bars omitted) were fit by monoexponential functions (solid lines 
	).
Fig. 1. Effect of F6 and halothane on evoked responses in hippocampal slices. Extracellular field potentials were recorded from stratum pyramidale in response to electrical stimulation of stratum radiatum. (A  ) Representative recordings from an individual experiment. F6 (24 μm) did not alter the evoked response. Subsequent application of halothane (270 μm) reduced the amplitude of the population spike and the slope of the population excitatory postsynaptic potential. Responses were measured after 40 min of drug application. Calibration 1 mV, 10 ms. (B  ) Time series plot of population spike amplitude. Population spike amplitude (mean ± SD) is plotted for 11 experiments with F6. For six experiments, application of halothane followed a 40-min wash period. In each case, responses were normalized to the average population spike amplitude during the control period. (Insets  ) Onset and offset of halothane actions on the evoked population spike. Average amplitudes (from data described previously; error bars omitted) were fit by monoexponential functions (solid lines  ).
×
We considered two possible reasons why we observed no effects of F6 on the PS and EPSP. One explanation would be that unlike halothane, F6 does not have any significant effects on the underlying physiologic processes at the concentrations tested. 15 Alternatively, F6 may not have been present in the tissue at or near the intended concentration because of a slow rate of equilibration between superfusate and tissue. Such a condition might arise because of the physical properties of F6: like other halogenated hydrocarbons, this drug is highly lipid soluble, but unlike halothane and other volatile anesthetics, it is highly nonpolar and thus has very low aqueous solubility.
To determine the rate of equilibration of F6 between the aqueous superfusate and the brain slice tissue under our experimental conditions, we used gas chromatography to measure the amount of F6 contained in slices that had been exposed to F6-containing ACSF. For these experiments, brain slices were placed in a recording chamber to simulate the conditions of our electrophysiologic experiments and were exposed to F6-containing ACSF for durations ranging from 7.5 to 480 min. The total F6 content of a slice was then determined by removing the slice from the recording chamber; placing it into a Teflon-sealed glass vial containing saline and air; allowing the drug to equilibrate between tissue, saline, and air; and then measuring the concentration of F6 in the gas phase using gas chromatography. The concentration in the slice was then calculated, taking into account partition coefficients and the volumes of liquid, gas, and tissue in the equilibration vial. The results are shown in figure 2, A  . The increase in concentration was fit by a monoexponential function with a time constant τequil= 124 min.
Fig. 2. Uptake of F6 and halothane into brain slices. Tissue concentration, normalized to the final equilibrium value, is plotted as a function of the duration of exposure to F6 (A  ) or halothane (B  ) via  superfusion. Each data point represents the average tissue concentration obtained from an individual brain slice.
Fig. 2. Uptake of F6 and halothane into brain slices. Tissue concentration, normalized to the final equilibrium value, is plotted as a function of the duration of exposure to F6 (A 
	) or halothane (B 
	) via 
	superfusion. Each data point represents the average tissue concentration obtained from an individual brain slice.
Fig. 2. Uptake of F6 and halothane into brain slices. Tissue concentration, normalized to the final equilibrium value, is plotted as a function of the duration of exposure to F6 (A  ) or halothane (B  ) via  superfusion. Each data point represents the average tissue concentration obtained from an individual brain slice.
×
Thus, the rate of equilibration of F6 between saline and tissue was slow compared with the 40-min drug application that we used in our physiologic experiments. This finding seems to be consistent with the hypothesis that the lack of effect of F6 on population activity was due to inadequate drug delivery rather than lack of physiologic action. However, the concentration that we measured in these uptake experiments reflected the average tissue concentration in the whole slice. Because recording electrodes were typically positioned near the upper surface of the tissue (approximately 100–150 μm below the surface), we considered whether the drug concentration at relevant tissue sites might have increased more rapidly than the whole tissue uptake data indicated.
To test the correspondence between rate of tissue uptake and rate of physiologic action, we also measured the rate of uptake of halothane for comparison with the rate at which halothane altered population activity. Using an uptake measurement technique similar to that which we used for F6, we determined that halothane equilibrated with brain slices with τequil= 14.7 min (fig. 2, B  ). Although this is considerably faster than the equilibration rate of F6, it is still considerably slower than the time required for halothane to affect evoked population activity (fig. 1, B  , τ= 7 min). Thus, the increase rate of halothane at relevant tissue sites is indeed faster than the increase rate of its average tissue concentration, and this should apply to F6 as well.
Given the findings of (1) a slow rate of F6 equilibration between the ACSF and tissue but also (2) a more rapid onset of physiologic action for halothane than the equilibration rate would indicate, what was the concentration of F6 that was actually achieved at relevant tissue sites during the 40-min drug application that we used? To address this question, we used a one-dimensional diffusion model (fig. 3) to estimate the depth- and time-dependent increase in tissue concentration that would occur with drug delivery to one surface of a finite tissue slab in response to a step concentration increase in the ACSF superfusate. This model was chosen based on the geometry of our brain slices (approximately 1 cm × 1 cm × 0.5 mm thick, sitting on the glass recording chamber coverslip) and the rapid solution flow rate over the surface of the tissue (2.5 ml/min into a chamber of 1 ml volume) compared with the measured equilibration time (> 2 h).
Fig. 3. Model of drug diffusion into tissue used to calculate tissue concentration as a function of depth and time following a step increase in bath drug concentration at time t = 0. Equivalent models of diffusion into both surfaces (left  ) or top surface only (right  ) are based on the condition of no net flux across the midline when both surfaces are exposed. Dimensionless parameters of concentration (C  ), depth (X  ), and time (θ) are used to calculate concentrations for drugs of different diffusion coefficient (D  ).
Fig. 3. Model of drug diffusion into tissue used to calculate tissue concentration as a function of depth and time following a step increase in bath drug concentration at time t = 0. Equivalent models of diffusion into both surfaces (left 
	) or top surface only (right 
	) are based on the condition of no net flux across the midline when both surfaces are exposed. Dimensionless parameters of concentration (C 
	), depth (X 
	), and time (θ) are used to calculate concentrations for drugs of different diffusion coefficient (D 
	).
Fig. 3. Model of drug diffusion into tissue used to calculate tissue concentration as a function of depth and time following a step increase in bath drug concentration at time t = 0. Equivalent models of diffusion into both surfaces (left  ) or top surface only (right  ) are based on the condition of no net flux across the midline when both surfaces are exposed. Dimensionless parameters of concentration (C  ), depth (X  ), and time (θ) are used to calculate concentrations for drugs of different diffusion coefficient (D  ).
×
An example of the time- and depth-dependent tissue concentration profile that this model predicts, for a 500-μm-thick brain slice following a step increase in drug concentration in ACSF, is shown in figure 4. As expected, the concentration increases more rapidly near the exposed surface than at sites deeper within the tissue. This concentration profile was calculated using a diffusion coefficient of 0.1 × 10−6cm2/s, which we estimated to be the diffusion coefficient of F6 by the following method. First, we calculated the average whole slice concentration–time profile for a given diffusion coefficient by integrating the concentration over depth. We then repeated this calculation for different values of the diffusion coefficient, yielding a family of average tissue concentration profiles (fig. 5). Comparing the drug uptake data to these concentration–time profiles yielded a diffusion coefficient for F6 of approximately 0.1 × 10−6cm2/s (fig. 5, A  ). For halothane, a diffusion coefficient of 0.8 × 10−6cm2/s was obtained (fig. 5, B  ), consistent with the approximately eightfold faster rate that was measured by gas chromatography (fig. 2).
Fig. 4. Tissue concentration as a function of time and depth, for a drug with diffusion coefficient D = 0.1 × 10−6cm2/s. Near the exposed surface of the tissue (depth = 0) the drug concentration increases rapidly. However, at the bottom of the tissue (depth = 500 μm), the concentration has increased only slightly by the end of 40 min.
Fig. 4. Tissue concentration as a function of time and depth, for a drug with diffusion coefficient D = 0.1 × 10−6cm2/s. Near the exposed surface of the tissue (depth = 0) the drug concentration increases rapidly. However, at the bottom of the tissue (depth = 500 μm), the concentration has increased only slightly by the end of 40 min.
Fig. 4. Tissue concentration as a function of time and depth, for a drug with diffusion coefficient D = 0.1 × 10−6cm2/s. Near the exposed surface of the tissue (depth = 0) the drug concentration increases rapidly. However, at the bottom of the tissue (depth = 500 μm), the concentration has increased only slightly by the end of 40 min.
×
Fig. 5. Estimating the diffusion coefficients of F6 and halothane. Measurements of drug content in brain slices (from fig. 2) are superimposed on derived average concentration profiles for diffusion into a 500-μm-thick tissue slice, for diffusivities ranging from 0.05 to 3.2 × 10−6cm2/s. (A  ) The measured rate of F6 uptake (○ corresponds to a diffusion coefficient of approximately 0.1 × 10−6cm2/s. (B  ) The measured rate of halothane uptake (•) corresponds to a diffusion coefficient of approximately 0.8 × 10−6cm2/s. Data for F6 (○ are repeated from panel A  , on the expanded time scale.
Fig. 5. Estimating the diffusion coefficients of F6 and halothane. Measurements of drug content in brain slices (from fig. 2) are superimposed on derived average concentration profiles for diffusion into a 500-μm-thick tissue slice, for diffusivities ranging from 0.05 to 3.2 × 10−6cm2/s. (A 
	) The measured rate of F6 uptake (○ corresponds to a diffusion coefficient of approximately 0.1 × 10−6cm2/s. (B 
	) The measured rate of halothane uptake (•) corresponds to a diffusion coefficient of approximately 0.8 × 10−6cm2/s. Data for F6 (○ are repeated from panel A 
	, on the expanded time scale.
Fig. 5. Estimating the diffusion coefficients of F6 and halothane. Measurements of drug content in brain slices (from fig. 2) are superimposed on derived average concentration profiles for diffusion into a 500-μm-thick tissue slice, for diffusivities ranging from 0.05 to 3.2 × 10−6cm2/s. (A  ) The measured rate of F6 uptake (○ corresponds to a diffusion coefficient of approximately 0.1 × 10−6cm2/s. (B  ) The measured rate of halothane uptake (•) corresponds to a diffusion coefficient of approximately 0.8 × 10−6cm2/s. Data for F6 (○ are repeated from panel A  , on the expanded time scale.
×
Having thus estimated the diffusion coefficients for F6 and halothane, we were able to determine their expected concentrations in the tissue as functions of depth and time. For halothane, we noted previously that the onset of physiologic action (τ= 7 min) was more rapid than the average tissue uptake rate would indicate (τ= 14.7 min), and we postulated that this was due to a more rapid rate of drug accumulation near the top surface of the tissue where recording electrodes were positioned. For the estimated diffusion coefficient of halothane derived from uptake data (0.8 × 10−6cm2/s), the diffusion model predicted that concentration would increase with a time constant of 7 min at a depth of 125 μm (fig. 6), which corresponds well to a typical recording electrode depth. Because it is likely that the electrophysiologic signals we recorded were generated not at a single point source at this depth but rather came from tissue sites above and below this location, we also compared this value with the increase in average tissue concentration (integral) in the portion of tissue between a depth of 25 μm (above which cells are not generally viable) and various depths below the surface (fig. 6, A  ). In this case, the rate of increase was not a simple exponential function. However, the average concentration did increase to 63% of its final equilibrium value (i.e  ., equivalent to one time constant) over 7 min within the uppermost 250 μm of the slice (fig. 6, B  ). These results demonstrate that there is a good correspondence between the observed rate of onset of halothane actions and the predicted increase rate of drug concentration at relevant tissue sites based on estimates of diffusion rates. Using these values for diffusion coefficient of halothane and tissue depth of physiologic signals, the halothane concentration obtained after 40 min of drug application is calculated to be 93% of its final equilibrium concentration.
Fig. 6. Increase in tissue concentration in the superficial portions of the brain slice. (A  ) For a drug with diffusion coefficient = 0.8 × 10−6cm2/s (i.e  ., halothane), the diffusion model was used to generate the concentration profile (normalized to the final equilibrium value) for depths between 25 and 250 μm. From this profile, an average tissue concentration may be obtained by integration. (B  ) Average tissue concentrations for superficial portions of the brain slice between 25 μm and the depths indicated, derived from simulations such as that illustrated in panel A  . In addition, the concentration at a depth of 125 μm is shown (dashed line  ). Note that drug concentration at this depth, and average concentration in a slab centered around this depth, has reached 63% of its equilibrium value (i.e  ., one time constant) after 7 min. This depth corresponds to that which generates field potentials as measured in electrophysiologic experiments. Compare with figure 1, B  (inset  ).
Fig. 6. Increase in tissue concentration in the superficial portions of the brain slice. (A 
	) For a drug with diffusion coefficient = 0.8 × 10−6cm2/s (i.e 
	., halothane), the diffusion model was used to generate the concentration profile (normalized to the final equilibrium value) for depths between 25 and 250 μm. From this profile, an average tissue concentration may be obtained by integration. (B 
	) Average tissue concentrations for superficial portions of the brain slice between 25 μm and the depths indicated, derived from simulations such as that illustrated in panel A 
	. In addition, the concentration at a depth of 125 μm is shown (dashed line 
	). Note that drug concentration at this depth, and average concentration in a slab centered around this depth, has reached 63% of its equilibrium value (i.e 
	., one time constant) after 7 min. This depth corresponds to that which generates field potentials as measured in electrophysiologic experiments. Compare with figure 1, B 
	(inset 
	).
Fig. 6. Increase in tissue concentration in the superficial portions of the brain slice. (A  ) For a drug with diffusion coefficient = 0.8 × 10−6cm2/s (i.e  ., halothane), the diffusion model was used to generate the concentration profile (normalized to the final equilibrium value) for depths between 25 and 250 μm. From this profile, an average tissue concentration may be obtained by integration. (B  ) Average tissue concentrations for superficial portions of the brain slice between 25 μm and the depths indicated, derived from simulations such as that illustrated in panel A  . In addition, the concentration at a depth of 125 μm is shown (dashed line  ). Note that drug concentration at this depth, and average concentration in a slab centered around this depth, has reached 63% of its equilibrium value (i.e  ., one time constant) after 7 min. This depth corresponds to that which generates field potentials as measured in electrophysiologic experiments. Compare with figure 1, B  (inset  ).
×
Applying the same methods to estimate the concentration of F6 at relevant tissue sites, we found that for a drug with diffusion coefficient of 0.1 × 10−6cm2/s, at the end of 40 min, the average tissue concentration between 25 and 200 μm below the surface would have increased to 58% of its final equilibrium value (fig. 7). Thus, taking into account the concentration of F6 in ACSF, the tissue/saline partition coefficient, the diffusion coefficient of F6 in brain tissue, and the application duration, we calculated that the F6 concentration that was achieved during our experiments at relevant tissue sites was approximately 14 μm (aqueous), which is 0.87 × MACpred.
Fig. 7. Model of the concentration profile of F6 in brain slice tissue during a physiologic experiment. (A  ) Using the diffusion model and an estimated diffusion coefficient of 0.1 × 10−6cm2/s (see fig. 5), the expected concentration profile of F6 in the top half of the tissue during a 40-min drug application was calculated. (B  ) At the depth at which field potentials are generated (i.e  ., 125 μm, or the average concentration between 25 and 200 μm), the concentration at 40 min has reached approximately 58% of its final equilibrium value.
Fig. 7. Model of the concentration profile of F6 in brain slice tissue during a physiologic experiment. (A 
	) Using the diffusion model and an estimated diffusion coefficient of 0.1 × 10−6cm2/s (see fig. 5), the expected concentration profile of F6 in the top half of the tissue during a 40-min drug application was calculated. (B 
	) At the depth at which field potentials are generated (i.e 
	., 125 μm, or the average concentration between 25 and 200 μm), the concentration at 40 min has reached approximately 58% of its final equilibrium value.
Fig. 7. Model of the concentration profile of F6 in brain slice tissue during a physiologic experiment. (A  ) Using the diffusion model and an estimated diffusion coefficient of 0.1 × 10−6cm2/s (see fig. 5), the expected concentration profile of F6 in the top half of the tissue during a 40-min drug application was calculated. (B  ) At the depth at which field potentials are generated (i.e  ., 125 μm, or the average concentration between 25 and 200 μm), the concentration at 40 min has reached approximately 58% of its final equilibrium value.
×
Discussion
We found that at a brain tissue concentration equivalent to 0.87 times MACpred, F6 did not alter either PS amplitude or EPSP slope. This finding stands in contrast with the effects of volatile anesthetics, which have clear effects at these concentrations. Given that concentrations lesser than those achieved in our electrophysiologic experiments are known to produce amnesia in vivo  , as assessed by effects on fear conditioning, 3 our results suggest that the mechanism by which F6 produces amnesia does not include changes in synaptic excitation or pyramidal cell spike generation by pyramidal neurons. If the mechanism by which F6 and halothane produce amnesia is the same, this implies that the depression of the EPSP and PS by halothane is also not instrumental in the amnestic action of this anesthetic.
Our electrophysiology results for F6 are in general agreement with those of Taylor et al  ., 15 who previously found this drug to have no significant effects on the PS and inconsistent effects on the EPSP. For their experiments, they prepared solutions by bubbling ACSF at 22°C with F6 at gas phase concentrations up to 0.096 atm; physiologic measurements were made after 20 min of drug application. Using our diffusion model and based on our estimates of the diffusion coefficient of F6, the tissue depth from which extracellular responses arise, and the solubility of F6 at 22°C, this translates to aqueous concentrations of 103 μm and final tissue concentrations of 46 μm, or approximately 2.9 × MACpred. Because F6 produces convulsions at concentrations only slightly greater than MACpred, it thus seems that the physiologic processes that contribute to evoked population responses in hippocampal slices are not instrumental in the induction of seizures by F6.
Population responses in the hippocampal slice preparation reflect the combined effects of several different physiologic processes. The lack of effect of F6 on the PS and EPSP implies that this drug does not alter excitatory transmitter release, activation of the postsynaptic α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid subtype of glutamate receptors, or the various voltage-dependent currents that influence action potential threshold in pyramidal neurons. This is consistent with the previously reported lack of effect on a number of potential anesthetic targets, including potassium-stimulated neurotransmitter release, 24 glutamate receptors, 25,26 γ-aminobutyric acid type A receptors, 27 voltage-gated neuronal sodium channels, 28 or tandem pore domain potassium channels. 29 
Our measurements of the rate of anesthetic uptake were limited in accuracy by the following factors. (1) Residual saline on the surface of brain slices being weighed would have caused systematic overestimation of their mass. Complete drying of the slices was not attempted as this could adversely affect the health of the tissue and thus possibly alter the kinetics of anesthetic uptake. Attempts were made to remove as much superficial saline as possible without disrupting the tissue surface and without exposing the tissue to air for more than 20 s. However, this error would be expected to have little impact on values for diffusion coefficients that were derived from uptake measurements. Because the volume of tissue in the measurement vials was small compared with the volume of air and λsaline/gasand λsaline/tissuewere of similar magnitude, this systematic error would have influenced the absolute tissue concentration that was calculated from gas phase measurements, but it would have caused little change in the shape of the equilibration profile from which the values for diffusion coefficients were derived. (2) Our estimates of the equilibrium concentration of volatile agents in the tissue and λsaline/tissuerelied on the assumption that these parameters remained constant throughout the uptake experiment, unaltered by changes in slice physiology. However, durations up to 8 h were required for some of the uptake experiments, and this was followed by gently shaking the tissue within a gas-tight glass vial to equilibrate drugs among the slice, saline, and air. Although this did not result in any gross alterations in the appearance of the tissue, it is possible that tissue characteristics changed to some extent, for example via  lipid peroxidation, protein degradation, or other means. This factor may account for the slight decrease in halothane concentration (∼13%, fig. 2, B  ) that occurred between 2 and 4 h. (3) We allowed only 1 h for drugs to diffuse out of the tissue during the equilibration phase of measurement. This would have led to a systematic underestimate of the concentration of drug in the tissue. We did use our tissue diffusion model to determine the impact that this would have on measured tissue concentrations for different uptake durations and found that the error would be slightly greater for longer uptake times (approximately 12%). Therefore, we corrected tissue concentrations for this error. However, we expect that this error did not substantially impact our estimates of diffusion coefficients or our conclusions, because even uncorrected concentrations yielded essentially identical results. (4) Our estimate of the concentration that was achieved at physiologically relevant tissue sites rests on the simplifying assumption that neuronal circuitry that underlies the observed population responses is contained within a slab of tissue parallel to the surface of the tissue. Although this is unlikely to be strictly true, tissue slices were cut at an angle approximately orthogonal to the long axis of the hippocampus, and the dendrites of pyramidal neurons in such slices extend in a plane approximately parallel to the surface of the tissue, suggesting that this simplification is reasonable.
Other experimental models incorporating multicellular layers have been developed to measure diffusion of other drugs. For example, because access of anticancer drugs to tumors can be limited by diffusion through tissue lacking microvasculature, diffusion coefficients have been measured for some of these agents. Values obtained were generally similar to that which we measured for halothane. For example, tirapazamine has a diffusion coefficient of 0.7 × 10−6cm2/s, 30 similar to the value of 0.8 × 10−6cm2/s that we obtained for halothane in brain tissue. The reason that F6 diffuses so slowly through brain tissue is not entirely clear. It has been noted that other highly lipid-soluble drugs such as diazepam and propofol also produce a slow onset of action in brain slice preparations. 18 Because there is no delay in onset of drug action when these agents are applied directly to the surfaces of cells, it is likely that the slow onset reflects the rate of access of the drugs to tissue sites of action. However, it would appear that the high lipid solubility of F6 is not the only factor that slows diffusion, because halothane, which has a higher lipid solubility than F6 (F6 λoil:gas= 43.5 vs  . halothane λoil:gas= 214), diffuses more rapidly into tissue. The extremely low aqueous solubility of F6 (F6 λsaline:gas= 0.026 vs  . halothane λsaline:gas= 0.72) may also contribute. If tissue structure is considered as a series of aqueous and lipid barriers, low aqueous solubility would limit the transfer of drug between successive lipid sites at which it accumulates. This situation may be analogous to the finding that a series of such barriers is effective at limiting transfer of water through tissue layers, 31 though in that case, relative solubilities in lipid versus  aqueous phases are reversed.
In addition to slow diffusion through brain tissue, other methodologic difficulties of working with F6 and other nonimmobilizers have been noted. A recent editorial highlighted the importance of measuring aqueous phase concentrations for these and other volatile agents, as losses are common and can lead to erroneous conclusions. 32 Also, reductions in aqueous oxygen concentration may occur if high concentrations are required because of low potency 15 or as these agents diffuse out of oxygenated saline into headspace gas. 33 A source of possible delay in tissue bath delivery that we did not appreciate until we measured aqueous concentrations for our experiments is the drip chamber in the perfusion line. These are often used to monitor and control solution flow rates and to provide electrical isolation of the bath to reduce 60-Hz noise from the environment. Because of the low aqueous solubility of F6, it can take considerable time for sufficient amounts of F6 to diffuse into the gas space of the drip chamber to achieve equilibration between gas and aqueous phases, thus delaying the increase in concentration in the recording chamber by tens of minutes, depending on the volume of the drip chamber and solution flow rate.
Our results can be used to estimate or predict the actual drug concentration as a function of time that would be present at the soma during single-cell recordings if the slice thickness, depth of the cell body, and drug diffusion coefficient are known (fig. 3). Also, our results suggest two practical measures that can be taken to hasten onset of drug action for drugs that diffuse slowly into tissue. (1) Use tissue slices that are as thin as possible, consistent with the requirements of the experiment. Depending on the brain region, slices as thin as 150 μm may remain healthy, though in our experience, hippocampal circuitry and cell health are compromised in such thin slices. (2) Deliver drugs to both surfaces of a slice, e.g  ., by suspending the tissue slice on mesh and allowing solution to flow below and above the tissue. This effectively reduces the thickness of the slice by one half (fig. 3). Because equilibration time is inversely related to the square of tissue thickness (dimensionless time τ in the model, fig. 3), these changes can have a large impact on drug delivery. These considerations apply to the optimal delivery other substances, not just volatile agents or nonimmobilizers.
The authors thank Donna Cole, B.S., and Mark Perkins, B.S. (Research Specialists, University of Wisconsin, Madison, Wisconsin), for expert technical assistance.
References
Franks NP, Lieb WR: Molecular and cellular mechanisms of general anaesthesia. Nature 1994; 367: 607–14Franks, NP Lieb, WR
Koblin DD, Chortkoff BS, Laster MJ, Eger EI II, Halsey MJ, Ionescu P: Polyhalogenated and perfluorinated compounds that disobey the Meyer-Overton hypothesis. Anesth Analg 1994; 79: 1043–8Koblin, DD Chortkoff, BS Laster, MJ Eger, EI Halsey, MJ Ionescu, P
Kandel L, Chortkoff BS, Sonner J, Laster MJ, Eger EIII: Nonanesthetics can suppress learning. Anesth Analg 1996; 82: 321–6Kandel, L Chortkoff, BS Sonner, J Laster, MJ Eger, EI
Sonner J, Li J, Eger EI: Desflurane and nitrous oxide, but not nonimmobilizers, affect nociceptive responses. Anesth Analg 1998; 86: 629–34Sonner, J Li, J Eger, EI
Steffey EP, Laster MJ, Ionescu P, Eger EI, Emerson N: Ventilatory effects of the nonimmobilizer 1,2-dichlorohexafluorocyclobutane (2N) in swine. Anesth Analg 1998; 86: 173–8Steffey, EP Laster, MJ Ionescu, P Eger, EI Emerson, N
Maurer AJ, Sessler DI, Eger EI, Sonner JM: The nonimmobilizer 1,2-dichlorohexafluorocyclobutane does not affect thermoregulation in the rat. Anesth Analg 2000; 91: 1013–6Maurer, AJ Sessler, DI Eger, EI Sonner, JM
Sonner JM, Li JA, Eger EI: Desflurane and the nonimmobilizer 1,2- dichlorohexafluorocyclobutane suppress learning by a mechanism independent of the level of unconditioned stimulation. Anesth Analg 1998; 87: 200–5Sonner, JM Li, JA Eger, EI
Eger EI, Koblin DD, Sonner J, Gong D, Laster MJ, Ionescu P, Halsey MJ, Hudlicky T: Nonimmobilizers and transitional compounds may produce convulsions by two mechanisms. Anesth Analg 1999; 88: 884–92Eger, EI Koblin, DD Sonner, J Gong, D Laster, MJ Ionescu, P Halsey, MJ Hudlicky, T
Perouansky M, Baranov D, Salman M, Yaari Y: Effects of halothane on glutamate receptor-mediated excitatory postsynaptic currents: A patch-clamp study in adult mouse hippocampal slices. A nesthesiology 1995; 83: 109–19Perouansky, M Baranov, D Salman, M Yaari, Y
MacIver MB, Mikulec AA, Amagasu SM, Monroe FA: Volatile anesthetics depress glutamate transmission via  presynaptic actions. A nesthesiology 1996; 85: 823–34MacIver, MB Mikulec, AA Amagasu, SM Monroe, FA
Tanelian DL, Kosek P, Mody I, MacIver MB: The role of the GABAAreceptor/chloride channel complex in anesthesia. A nesthesiology 1993; 78: 757–76Tanelian, DL Kosek, P Mody, I MacIver, MB
Pearce RA: Volatile anesthetic enhancement of paired-pulse depression investigated in the rat hippocampus in vitro. J Physiol (Lond) 1996; 492: 823–40Pearce, RA
MacIver MB, Roth SH: Inhalation anaesthetics exhibit pathway-specific and differential actions on hippocampal synaptic responses in vitro. Br J Anaesth 1988; 60: 680–91MacIver, MB Roth, SH
Lingamaneni R, Krasowski MD, Jenkins A, Truong T, Giunta AL, Blackbeer J, MacIver MB, Harrison NL, Hemmings HC: Anesthetic properties of 4-iodopropofol: Implications for mechanisms of anesthesia. A nesthesiology 2001; 94: 1050–7Lingamaneni, R Krasowski, MD Jenkins, A Truong, T Giunta, AL Blackbeer, J MacIver, MB Harrison, NL Hemmings, HC
Taylor DM, Eger EI II, Bickler PE: Halothane, but not the nonimmobilizers perfluoropentane and 1,2-dichlorohexafluorocyclobutane, depresses synaptic transmission in hippocampal CA1 neurons in rats. Anesth Analg 1999; 89: 1040–5Taylor, DM Eger, EI Bickler, PE
Hagan CE, Pearce RA, Trudell JR, MacIver MB: Concentration measures of volatile anesthetics in the aqueous phase using calcium sensitive electrodes. J Neurosci Methods 1998; 81: 177–84Hagan, CE Pearce, RA Trudell, JR MacIver, MB
Banks MI, Pearce RA: Dual actions of volatile anesthetics on GABA(A) IPSCs: Dissociation of blocking and prolonging effects. A nesthesiology 1999; 90: 120–34Banks, MI Pearce, RA
Thomson AM, Bannister AP, Hughes DI, Pawelzik H: Differential sensitivity to Zolpidem of IPSPs activated by morphologically identified CA1 interneurons in slices of rat hippocampus. Eur J Neurosci 2000; 12: 425–36Thomson, AM Bannister, AP Hughes, DI Pawelzik, H
MacIver MB, Turnquist PA, Bieda M, Pittson S: Slow diffusion into brain slices decreases the apparent potency of an anesthetic (abstract). A nesthesiology 2002; 96: A790MacIver, MB Turnquist, PA Bieda, M Pittson, S
Franks NP, Lieb WR: Selective actions of volatile general anaesthetics at molecular and cellular levels. Br J Anaesth 1993; 71: 65–76Franks, NP Lieb, WR
Raines DE: Anesthetic and nonanesthetic halogenated volatile compounds have dissimilar activities on nicotinic acetylcholine receptor desensitization kinetics. A nesthesiology 1996; 84: 663–71Raines, DE
Eger EI: Anesthetic Uptake and Action. Baltimore, Williams & Wilkins, 1974
Bennett CO, Myers JE: Momentum, Heat, and Mass Transfer, 3rd edition. New York, McGraw-Hill, 1982
Eilers H, Kindler CH, Bickler PE: Different effects of volatile anesthetics and polyhalogenated alkanes on depolarization-evoked glutamate release in rat cortical brain slices. Anesth Analg 1999; 88: 1168–74Eilers, H Kindler, CH Bickler, PE
Minami K, Wick MJ, Stern-Bach Y, Dildy-Mayfield JE, Brozowski SJ, Gonzales EL, Trudell JR, Harris RA: Sites of volatile anesthetic action on kainate (glutamate receptor 6) receptors. J Biol Chem 1998; 273: 8248–55Minami, K Wick, MJ Stern-Bach, Y Dildy-Mayfield, JE Brozowski, SJ Gonzales, EL Trudell, JR Harris, RA
Dildy-Mayfield JE, Eger EI II, Harris RA: Anesthetics produce subunit-selective actions on glutamate receptors. J Pharmacol Exp Ther 1996; 276: 1058–65Dildy-Mayfield, JE Eger, EI Harris, RA
Mihic SJ, McQuilkin SJ, Eger EI II, Ionescu P, Harris RA: Potentiation of gamma-aminobutyric acid type a receptor-mediated chloride currents by novel halogenated compounds correlates with their abilities to induce general anesthesia. Mol Pharmacol 1994; 46: 851–7Mihic, SJ McQuilkin, SJ Eger, EI Ionescu, P Harris, RA
Ratnakumari L, Vysotskaya TN, Duch DS, Hemmings HC Jr: Differential effects of anesthetic and nonanesthetic cyclobutanes on neuronal voltage-gated sodium channels. A nesthesiology 2000; 92: 529–41Ratnakumari, L Vysotskaya, TN Duch, DS Hemmings, HC
Gray AT, Winegar BD, Leonoudakis DJ, Forsayeth JR, Yost CS: Tok1 is a volatile anesthetic stimulated K+channel. A nesthesiology 1998; 88: 1076–84Gray, AT Winegar, BD Leonoudakis, DJ Forsayeth, JR Yost, CS
Kyle AH, Minchinton AI: Measurement of delivery and metabolism of tirapazamine to tumour tissue using the multilayered cell culture model. Cancer Chemother Pharmacol 1999; 43: 213–20Kyle, AH Minchinton, AI
Franks NP, Lieb WR: Rapid movement of molecules across membranes: Measurement of the permeability coefficient of water using neutron diffraction. J Mol Biol 1980; 141: 43–61Franks, NP Lieb, WR
Borghese CM, Harris RA: Anesthetic-induced immobility: neuronal nicotinic acetylcholine receptors are no longer in the picture. Anesth Analg 2002; 95: 509–11Borghese, CM Harris, RA
Kendig JJ, Kodde A, Gibbs LM, Ionescu P, Eger EIII: Correlates of anesthetic properties in isolated spinal cord: Cyclobutanes. Eur J Pharmacol 1994; 264: 427–36Kendig, JJ Kodde, A Gibbs, LM Ionescu, P Eger, EI
Fig. 1. Effect of F6 and halothane on evoked responses in hippocampal slices. Extracellular field potentials were recorded from stratum pyramidale in response to electrical stimulation of stratum radiatum. (A  ) Representative recordings from an individual experiment. F6 (24 μm) did not alter the evoked response. Subsequent application of halothane (270 μm) reduced the amplitude of the population spike and the slope of the population excitatory postsynaptic potential. Responses were measured after 40 min of drug application. Calibration 1 mV, 10 ms. (B  ) Time series plot of population spike amplitude. Population spike amplitude (mean ± SD) is plotted for 11 experiments with F6. For six experiments, application of halothane followed a 40-min wash period. In each case, responses were normalized to the average population spike amplitude during the control period. (Insets  ) Onset and offset of halothane actions on the evoked population spike. Average amplitudes (from data described previously; error bars omitted) were fit by monoexponential functions (solid lines  ).
Fig. 1. Effect of F6 and halothane on evoked responses in hippocampal slices. Extracellular field potentials were recorded from stratum pyramidale in response to electrical stimulation of stratum radiatum. (A 
	) Representative recordings from an individual experiment. F6 (24 μm) did not alter the evoked response. Subsequent application of halothane (270 μm) reduced the amplitude of the population spike and the slope of the population excitatory postsynaptic potential. Responses were measured after 40 min of drug application. Calibration 1 mV, 10 ms. (B 
	) Time series plot of population spike amplitude. Population spike amplitude (mean ± SD) is plotted for 11 experiments with F6. For six experiments, application of halothane followed a 40-min wash period. In each case, responses were normalized to the average population spike amplitude during the control period. (Insets 
	) Onset and offset of halothane actions on the evoked population spike. Average amplitudes (from data described previously; error bars omitted) were fit by monoexponential functions (solid lines 
	).
Fig. 1. Effect of F6 and halothane on evoked responses in hippocampal slices. Extracellular field potentials were recorded from stratum pyramidale in response to electrical stimulation of stratum radiatum. (A  ) Representative recordings from an individual experiment. F6 (24 μm) did not alter the evoked response. Subsequent application of halothane (270 μm) reduced the amplitude of the population spike and the slope of the population excitatory postsynaptic potential. Responses were measured after 40 min of drug application. Calibration 1 mV, 10 ms. (B  ) Time series plot of population spike amplitude. Population spike amplitude (mean ± SD) is plotted for 11 experiments with F6. For six experiments, application of halothane followed a 40-min wash period. In each case, responses were normalized to the average population spike amplitude during the control period. (Insets  ) Onset and offset of halothane actions on the evoked population spike. Average amplitudes (from data described previously; error bars omitted) were fit by monoexponential functions (solid lines  ).
×
Fig. 2. Uptake of F6 and halothane into brain slices. Tissue concentration, normalized to the final equilibrium value, is plotted as a function of the duration of exposure to F6 (A  ) or halothane (B  ) via  superfusion. Each data point represents the average tissue concentration obtained from an individual brain slice.
Fig. 2. Uptake of F6 and halothane into brain slices. Tissue concentration, normalized to the final equilibrium value, is plotted as a function of the duration of exposure to F6 (A 
	) or halothane (B 
	) via 
	superfusion. Each data point represents the average tissue concentration obtained from an individual brain slice.
Fig. 2. Uptake of F6 and halothane into brain slices. Tissue concentration, normalized to the final equilibrium value, is plotted as a function of the duration of exposure to F6 (A  ) or halothane (B  ) via  superfusion. Each data point represents the average tissue concentration obtained from an individual brain slice.
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Fig. 3. Model of drug diffusion into tissue used to calculate tissue concentration as a function of depth and time following a step increase in bath drug concentration at time t = 0. Equivalent models of diffusion into both surfaces (left  ) or top surface only (right  ) are based on the condition of no net flux across the midline when both surfaces are exposed. Dimensionless parameters of concentration (C  ), depth (X  ), and time (θ) are used to calculate concentrations for drugs of different diffusion coefficient (D  ).
Fig. 3. Model of drug diffusion into tissue used to calculate tissue concentration as a function of depth and time following a step increase in bath drug concentration at time t = 0. Equivalent models of diffusion into both surfaces (left 
	) or top surface only (right 
	) are based on the condition of no net flux across the midline when both surfaces are exposed. Dimensionless parameters of concentration (C 
	), depth (X 
	), and time (θ) are used to calculate concentrations for drugs of different diffusion coefficient (D 
	).
Fig. 3. Model of drug diffusion into tissue used to calculate tissue concentration as a function of depth and time following a step increase in bath drug concentration at time t = 0. Equivalent models of diffusion into both surfaces (left  ) or top surface only (right  ) are based on the condition of no net flux across the midline when both surfaces are exposed. Dimensionless parameters of concentration (C  ), depth (X  ), and time (θ) are used to calculate concentrations for drugs of different diffusion coefficient (D  ).
×
Fig. 4. Tissue concentration as a function of time and depth, for a drug with diffusion coefficient D = 0.1 × 10−6cm2/s. Near the exposed surface of the tissue (depth = 0) the drug concentration increases rapidly. However, at the bottom of the tissue (depth = 500 μm), the concentration has increased only slightly by the end of 40 min.
Fig. 4. Tissue concentration as a function of time and depth, for a drug with diffusion coefficient D = 0.1 × 10−6cm2/s. Near the exposed surface of the tissue (depth = 0) the drug concentration increases rapidly. However, at the bottom of the tissue (depth = 500 μm), the concentration has increased only slightly by the end of 40 min.
Fig. 4. Tissue concentration as a function of time and depth, for a drug with diffusion coefficient D = 0.1 × 10−6cm2/s. Near the exposed surface of the tissue (depth = 0) the drug concentration increases rapidly. However, at the bottom of the tissue (depth = 500 μm), the concentration has increased only slightly by the end of 40 min.
×
Fig. 5. Estimating the diffusion coefficients of F6 and halothane. Measurements of drug content in brain slices (from fig. 2) are superimposed on derived average concentration profiles for diffusion into a 500-μm-thick tissue slice, for diffusivities ranging from 0.05 to 3.2 × 10−6cm2/s. (A  ) The measured rate of F6 uptake (○ corresponds to a diffusion coefficient of approximately 0.1 × 10−6cm2/s. (B  ) The measured rate of halothane uptake (•) corresponds to a diffusion coefficient of approximately 0.8 × 10−6cm2/s. Data for F6 (○ are repeated from panel A  , on the expanded time scale.
Fig. 5. Estimating the diffusion coefficients of F6 and halothane. Measurements of drug content in brain slices (from fig. 2) are superimposed on derived average concentration profiles for diffusion into a 500-μm-thick tissue slice, for diffusivities ranging from 0.05 to 3.2 × 10−6cm2/s. (A 
	) The measured rate of F6 uptake (○ corresponds to a diffusion coefficient of approximately 0.1 × 10−6cm2/s. (B 
	) The measured rate of halothane uptake (•) corresponds to a diffusion coefficient of approximately 0.8 × 10−6cm2/s. Data for F6 (○ are repeated from panel A 
	, on the expanded time scale.
Fig. 5. Estimating the diffusion coefficients of F6 and halothane. Measurements of drug content in brain slices (from fig. 2) are superimposed on derived average concentration profiles for diffusion into a 500-μm-thick tissue slice, for diffusivities ranging from 0.05 to 3.2 × 10−6cm2/s. (A  ) The measured rate of F6 uptake (○ corresponds to a diffusion coefficient of approximately 0.1 × 10−6cm2/s. (B  ) The measured rate of halothane uptake (•) corresponds to a diffusion coefficient of approximately 0.8 × 10−6cm2/s. Data for F6 (○ are repeated from panel A  , on the expanded time scale.
×
Fig. 6. Increase in tissue concentration in the superficial portions of the brain slice. (A  ) For a drug with diffusion coefficient = 0.8 × 10−6cm2/s (i.e  ., halothane), the diffusion model was used to generate the concentration profile (normalized to the final equilibrium value) for depths between 25 and 250 μm. From this profile, an average tissue concentration may be obtained by integration. (B  ) Average tissue concentrations for superficial portions of the brain slice between 25 μm and the depths indicated, derived from simulations such as that illustrated in panel A  . In addition, the concentration at a depth of 125 μm is shown (dashed line  ). Note that drug concentration at this depth, and average concentration in a slab centered around this depth, has reached 63% of its equilibrium value (i.e  ., one time constant) after 7 min. This depth corresponds to that which generates field potentials as measured in electrophysiologic experiments. Compare with figure 1, B  (inset  ).
Fig. 6. Increase in tissue concentration in the superficial portions of the brain slice. (A 
	) For a drug with diffusion coefficient = 0.8 × 10−6cm2/s (i.e 
	., halothane), the diffusion model was used to generate the concentration profile (normalized to the final equilibrium value) for depths between 25 and 250 μm. From this profile, an average tissue concentration may be obtained by integration. (B 
	) Average tissue concentrations for superficial portions of the brain slice between 25 μm and the depths indicated, derived from simulations such as that illustrated in panel A 
	. In addition, the concentration at a depth of 125 μm is shown (dashed line 
	). Note that drug concentration at this depth, and average concentration in a slab centered around this depth, has reached 63% of its equilibrium value (i.e 
	., one time constant) after 7 min. This depth corresponds to that which generates field potentials as measured in electrophysiologic experiments. Compare with figure 1, B 
	(inset 
	).
Fig. 6. Increase in tissue concentration in the superficial portions of the brain slice. (A  ) For a drug with diffusion coefficient = 0.8 × 10−6cm2/s (i.e  ., halothane), the diffusion model was used to generate the concentration profile (normalized to the final equilibrium value) for depths between 25 and 250 μm. From this profile, an average tissue concentration may be obtained by integration. (B  ) Average tissue concentrations for superficial portions of the brain slice between 25 μm and the depths indicated, derived from simulations such as that illustrated in panel A  . In addition, the concentration at a depth of 125 μm is shown (dashed line  ). Note that drug concentration at this depth, and average concentration in a slab centered around this depth, has reached 63% of its equilibrium value (i.e  ., one time constant) after 7 min. This depth corresponds to that which generates field potentials as measured in electrophysiologic experiments. Compare with figure 1, B  (inset  ).
×
Fig. 7. Model of the concentration profile of F6 in brain slice tissue during a physiologic experiment. (A  ) Using the diffusion model and an estimated diffusion coefficient of 0.1 × 10−6cm2/s (see fig. 5), the expected concentration profile of F6 in the top half of the tissue during a 40-min drug application was calculated. (B  ) At the depth at which field potentials are generated (i.e  ., 125 μm, or the average concentration between 25 and 200 μm), the concentration at 40 min has reached approximately 58% of its final equilibrium value.
Fig. 7. Model of the concentration profile of F6 in brain slice tissue during a physiologic experiment. (A 
	) Using the diffusion model and an estimated diffusion coefficient of 0.1 × 10−6cm2/s (see fig. 5), the expected concentration profile of F6 in the top half of the tissue during a 40-min drug application was calculated. (B 
	) At the depth at which field potentials are generated (i.e 
	., 125 μm, or the average concentration between 25 and 200 μm), the concentration at 40 min has reached approximately 58% of its final equilibrium value.
Fig. 7. Model of the concentration profile of F6 in brain slice tissue during a physiologic experiment. (A  ) Using the diffusion model and an estimated diffusion coefficient of 0.1 × 10−6cm2/s (see fig. 5), the expected concentration profile of F6 in the top half of the tissue during a 40-min drug application was calculated. (B  ) At the depth at which field potentials are generated (i.e  ., 125 μm, or the average concentration between 25 and 200 μm), the concentration at 40 min has reached approximately 58% of its final equilibrium value.
×