Cross-approximate entropy of cortical local field potentials quantifies effects of anesthesia - a pilot study in rats
- Matthias Kreuzer†1,
- Harald Hentschke†2, 3Email author,
- Bernd Antkowiak2,
- Cornelius Schwarz3, 4,
- Eberhard F Kochs1 and
- Gerhard Schneider1
© Kreuzer et al; licensee BioMed Central Ltd. 2010
Received: 26 February 2010
Accepted: 23 September 2010
Published: 23 September 2010
Anesthetics dose-dependently shift electroencephalographic (EEG) activity towards high-amplitude, slow rhythms, indicative of a synchronization of neuronal activity in thalamocortical networks. Additionally, they uncouple brain areas in higher (gamma) frequency ranges possibly underlying conscious perception. It is currently thought that both effects may impair brain function by impeding proper information exchange between cortical areas. But what happens at the local network level? Local networks with strong excitatory interconnections may be more resilient towards global changes in brain rhythms, but depend heavily on locally projecting, inhibitory interneurons. As anesthetics bias cortical networks towards inhibition, we hypothesized that they may cause excessive synchrony and compromise information processing already on a small spatial scale. Using a recently introduced measure of signal independence, cross-approximate entropy (XApEn), we investigated to what degree anesthetics synchronized local cortical network activity. We recorded local field potentials (LFP) from the somatosensory cortex of three rats chronically implanted with multielectrode arrays and compared activity patterns under control (awake state) with those at increasing concentrations of isoflurane, enflurane and halothane.
Cortical LFP signals were more synchronous, as expressed by XApEn, in the presence of anesthetics. Specifically, XApEn was a monotonously declining function of anesthetic concentration. Isoflurane and enflurane were indistinguishable; at a concentration of 1 MAC (the minimum alveolar concentration required to suppress movement in response to noxious stimuli in 50% of subjects) both volatile agents reduced XApEn by about 70%, whereas halothane was less potent (50% reduction).
The results suggest that anesthetics strongly diminish the independence of operation of local cortical neuronal populations, and that the quantification of these effects in terms of XApEn has a similar discriminatory power as changes of spontaneous action potential rates. Thus, XApEn of field potentials recorded from local cortical networks provides valuable information on the anesthetic state of the brain.
It has long been known that anesthetics alter neuronal activity of the brain, yet it is still unclear which of the alterations of brain activity are instrumental in causing sedation, amnesia and unconsciousness. Anesthetics likely disrupt communication between cortical areas , and thus impair large-scale integration of information hypothesized to be a prerequisite to proper brain function, particularly conscious perception [2–5]. A number of experimental observations are in agreement with this concept. In rats stimulated with light flashes, volatile anesthetics disrupted anterior-posterior phase synchronization of field responses  and depressed long-latency spike responses in visual cortex, thought to arise from cortico-cortical interactions . In humans, during the transition from waking to loss of consciousness, various general anesthetics decoupled gamma rhythms between anterior and posterior cortical areas as well as between homologous areas in different hemispheres . Employing transcranial magnetic stimulation, Ferrarelli et al. recently demonstrated a breakdown of cortical effective connectivity upon loss of consciousness induced by midazolam .
A complementary insight into network effects of anesthetics was recently provided by Hudetz and colleagues, who demonstrated that in rats volatile anesthetics diminished the independence of spontaneous electroencephalographic (EEG) signals recorded from different hemispheres : isoflurane, and halothane above 0.4%, reduced cross-approximate entropy (XApEn), a nonlinear information statistical parameter which quantifies the independence (or dissimilarity) of signals. Fittingly, cholinergic stimulation reversed the isoflurane-induced decrease of XApEn . These findings suggest that anesthetics induce changes of thalamocortical networks and slow predominant frequencies. This impairs brain function by promoting uniformity of signals and impeding an exchange of independent information between cortical areas, as a contrast to the transient synchronization of fast oscillations which has been suggested as the mechanism underlying conscious perception .
It is less clear at present in which manner anesthetics impair information processing on a much smaller spatial scale. In local cortical networks, subnetworks defined by strong excitatory connections exist which may operate quite independently of each other [12, 13]. With anesthetics, their independence of operation may be compromised by a general decrease of cortical neuronal excitability [14–18]. Furthermore, inhibitory interneurons project locally and have a great potential to pace their postsynaptic targets [19, 20]. Under conditions of pharmacologically enhanced GABAergic transmission, they may coerce independent subnetworks into more synchronous, uniform activity patterns [21, 22].
In the present pilot study, we investigated to what degree anesthetics alter signal independence in the somatosensory ('barrel') cortex of the rat. We recorded spontaneous local field potential (LFP) activity from multiple, closely spaced electrodes, which sample from a much smaller subset of neurons than EEG electrodes [23, 24]. The effects of the volatile anesthetics isoflurane, enflurane and halothane were evaluated in three animals. Our results show that the independence of activity patterns across recording sites as quantified by XApEn is a monotonously declining function of anesthetic concentration, suggesting that volatile anesthetics strongly promote uniform activity already on the level of local neocortical circuits.
At all concentrations applied, isoflurane greatly enhanced the amplitude of low-frequency signal components (up to ~20 Hz) and reduced high frequency components (above 100 Hz, Figure 1B, C). At the highest concentration (1.45%), high-amplitude LFP 'spikes' occurred, and in one animal burst suppression patterns appeared. Enflurane and halothane led to signal changes which were similar at low concentrations, but at concentrations close to 1 MAC the anesthetics clearly differed in their tendency to produce high-amplitude LFP spikes and burst suppression patterns (enflurane > isoflurane > halothane). Both the shifts in the spectral composition of neural activity common to all three anesthetics and the agent-specific differences are in agreement with electroencephalographic observations in rats [10, 11, 18, 27–29].
XApEn calculated from the LFP of closely spaced intracortical sites showed significant changes with anesthetic concentrations. This finding demonstrates that volatile anesthetics coerce small cortical sub-networks, here represented by rat barrel cortex, into uniform, synchronized activity patterns.
Barrel cortex forms a large part of rodent somatosensory cortex, characterized by a one-to-one correspondence between the sensory organs (follicles at the base of the large facial whiskers) and cytoarchitectonically segregated structures in layer 4 termed 'barrels' [35–37]. This columnar, somatotopic organization results in an orderly bottom-up spread of sensory-evoked activity which, in the initial stage of processing, is spatially restricted to the discrete termination zones of the major thalamic afferents [38–40]. Yet, barrel cortex is also characterized by a large degree of synaptic divergence and interconnectivity, characteristic of neocortex in general . Axons of pyramidal neurons may span several barrels, especially in layers 2/3 [40, 42], and other cortical areas including contralateral barrel cortex form reciprocal, spatially dispersed connections [37, 43]. Probably owing to this high degree of cortical interconnectivity, the permanent, ongoing activity therein, unrelated to sensory input, has a spatiotemporal profile which is largely independent of the barrel architecture [44, 45]. In the present study, we recorded and analyzed this activity. Signal characteristics showed a dramatic and fundamental change during administration of volatile anesthetics.
The decrease of XApEn with all three volatile anesthetics suggests that these agents transform the diversity of synaptic inputs impinging on closely spaced pyramidal cells into a more uniform, synchronous pattern. These patterns may arise from an enhancement of GABAergic currents and a weakening of glutamatergic currents , which bias synaptic communication towards inhibition. Specifically, GABAergic interneurons likely gain in influence on cortical activity patterns by entraining local networks to common rhythms. Both the relative insensitivity of some interneuron classes to GABAergic inhibition  and the finding that inhibitory inputs in neighboring pyramidal neurons are more synchronous than excitatory inputs  are consistent with this idea. Furthermore, input via long-range connections from other cortical areas is impaired under anesthesia [9, 48, 49]. Experimental findings on figure-ground separation in monkey visual cortex could also be interpreted along the lines of a functional disconnection of cortical areas with anesthetics . Therefore, it seems likely that the long-range excitatory synaptic inputs emanating from various cortical areas have an overall desynchronizing influence on local network activity in barrel cortex, and, by extension, that the impairment of this input by volatile anesthetics contributes to more local synchrony and thus a decrease of XApEn as observed.
Given that intracortical connections outnumber subcortical afferents  and that volatile anesthetics alter network activity in isolated cortical networks in vitro [16, 51] we argue that the decline of XApEn was to a substantial part due to intracortical effects of the anesthetics. In addition, decreases in XApEn probably also reflect the anesthetic-induced transformation of activity in subcortical areas projecting to cortex. In particular thalamus, with its intricate reciprocal connections to cortex [36, 37], must be considered . Shown to be sensitive to volatile anesthetics and prone to bursting behavior, it may imprint its activity patterns on cortex [53–55]. Other likely candidates include the basal forebrain, which modulates cortical activity via cholinergic, GABAergic and glutamatergic afferents [56–58] as well as hypothalamic sleep pathways .
We found that the three volatile anesthetics differed in their potency to alter cortical activity patterns as quantified by XApEn. While isoflurane and enflurane were indistinguishable, halothane had significantly weaker effects. This finding fits the profile of this anesthetic, which has previously been found to exert weaker effects than isoflurane on XApEn computed from interhemispheric EEG  and on spontaneous action potential activity in neocortex in vitro and in vivo [16, 51]. In rat visual cortex, Imas et al. found an enhancement of event-related gamma oscillations at intermediate concentrations of halothane , a finding which underlines the particular characteristic of this anesthetic. A potential limitation of our results is the fact that body temperature of the animals was not controlled, possibly leading to hypothermia during anesthesia. To minimize the influence of this phenomenon, the animals were placed into a plastic housing which provided some thermal insulation, and therefore at least it seems unlikely that they experienced severe hypothermia.
It is surprising that isoflurane- and halothane-induced changes of XApEn computed from interhemispheric EEG and LFP match qualitatively so well (Hudetz et al. used a different set of filter frequencies and computational parameters, so that a quantitative comparison of values may not lead to valid results [10, 11]). First, although the basal mechanisms underlying EEG and LFP signals are identical - synaptic population currents in pyramidal cells giving rise to extracellular potential gradients - the populations of cells sampled from are not. EEG electrodes record potentials from a much larger population than intracortical electrodes. Furthermore, EEG signals are dominated by the largest dipole-generating contributors, pyramidal cells of layer 5, which extend their dendrites to layer 1. Intracortical signals, by contrast, are sampled from a restricted spatial volume  and are thus lamina-dependent [25, 26]. Second, cortical sites separated by less than 1-2 mm as in our experiments receive a great deal of common synaptic input [20, 61], and consequently exhibit more synchronous activity than cortical networks in different hemispheres. Thus, the qualitatively similar depression of XApEn values reported by Hudetz et al. and here show that anesthetics unfold synchronizing effects on widely different spatial scales.
Anesthetics affect intracortical connections as well as corticocortical connections and inputs from subcortical areas. A disconnection or suppression of communication between different cortical areas is hypothesized to be a key player in the process of unconsciousness [1, 62]. Buzsáki  suggested that local computations register in large parts of the cortex through long range-connections, and that this local-global wiring is necessary for subjective experiences. Our results suggest that local intracortical communication suffers from the uniformity of signals induced by volatile anesthetics, in parallel to a suppression or disconnection of long-range interareal connections as evident in EEG studies. Thus, our results underline the usefulness of multisite electrophysiological recordings - be it LFP in experimental animals or EEG in humans - in combination with XApEn and related parameters [29, 63] for the quantification of anesthetic effects. By the same token, such approaches may serve to probe specific hypotheses on the neurophysiological correlate of consciousness, particularly those postulating a precisely timed convergence of synaptic inputs in neocortex , and possibly also to detect pathological connectivity between brain areas.
In vivo surgery & recording
All procedures described were in accordance with the policy on the use of animals in neuroscience research of the Society for Neuroscience and approved by the Ethical Committee on Animal Care and Use of the Government of Baden Württemberg, Germany. The experimental procedures were identical to those described in Hentschke et al  and the field potential data analyzed here were won from three of the four animals in the same study. Briefly, male or female Sprague-Dawley rats aged 12-16 weeks were anesthetized with ketamine/xylazine (100 mg/kg and 15 mg/kg, respectively). A craniectomy over the right hemisphere was performed, the dura was removed and a steel ring (O.D. 5 mm) placed on the pial surface. 4-16 custom-made etched tungsten microelectrodes (impedance 1-5 MΩ, tip separation ~180 μm) arranged as single or double linear arrays (one animal, 1 × 4; two animals, 2 × 8) were implanted through the steel ring into the neocortical somatosensory representation of the mystacial vibrissae ('barrel cortex'). Stereotactical target coordinates were Bregma -3.2 mm and lateral 4 mm. The array was oriented at an angle of 30-40° relative to the cortical surface such that the medial electrode row touched the cortical surface first and was thus located in a deeper cortical lamina than the lateral electrode row; the latter was aimed at the border of layers 4 and 5 (depth of penetration for this row from the point of contact with the pia was ~1100 um). Proper location of the electrodes within barrel cortex was verified by mapping of neuronal responses elicited by manual deflection of individual vibrissae. The electrode array and a head post were then fixed with dental cement and via 7-9 stainless steel screws driven into the skull. Recordings commenced after a recovery period of 2-4 d. The animals were head-restrained, sitting in a plastic housing, and placed in a sealable plexiglass box into which vaporizers (Drägerwerke, Lübeck, Germany) driven by air pumps delivered the anesthetics. For any given concentration, animals were exposed for periods of 27-39 min to the anesthetic. After discontinuation of the anesthetic, the animals were exposed to air for 40-60 min. A maximum of one recording session was performed per day.
Voltage traces recorded from the electrodes were referenced to the steel ring (rat1 and rat2) or to one of the electrodes (rat3), amplified and passed through a bandpass filter (-3 dB passband 0.5-200 Hz), digitized at 20 kHz and stored with a multichannel extracellular recording system (MultiChannelSystems, Reutlingen, Germany). Deteriorated, low-impedance electrodes with a small signal amplitude were excluded from analysis. The number of useable electrodes were 3 (rat3), 6 (rat2) and 12 (rat1). Anesthetic concentration is expressed in volume-% or as MAC (minimum alveolar concentration) as given in : isoflurane 1.46%, enflurane 2.21%, halothane 1.03%.
Selection of data segments
Under control conditions, the field potential data contained episodes of oscillatory activity with a dominant peak at 8-9 Hz (theta component) and an additional (non-harmonic) peak at 13-16 Hz (beta component; an example is given in Figure 3). The nature of these oscillations, also called 'high voltage rhythmic spikes' (HVRS), is a matter of debate. They appear in resting animals, often in conjunction with low-amplitude whisker movements  (whisker 'twitching') and may reflect a specific kind of idling, responsive state of the whisker sensory system [67–69]. Others consider HVRS manifestations of absence epilepsies [70–72]. We observed that at subanesthetic to hypnotic concentrations (isoflurane, 0.3-0.75%; enflurane, 0.5-1.2%; halothane, 0.65-1.05%) characteristics of the oscillations changed in several ways. Most notably, they were less coherent across channels and lasted for shorter periods. Furthermore, the dominant frequency was between 13 and 16 Hz. At the highest concentrations, which were equal to or above MAC (isoflurane, 1.45%; enflurane, 2.4%; halothane, 1.6%) the oscillations subsided and low frequency components and/or burst suppression patterns dominated.
We decided to exclude data with HVRS from analysis due to the unresolved nature of this activity and because the computational load of our analysis restricted the amount of data that could be analyzed in reasonable time to about 10 seconds per recording. To this end, the data acquired under control conditions were divided into segments of 2048 points overlapping by 730 points. From these, the spectral power of the signals in the range 7-9 Hz was computed for all channels. Of the resulting segment-wise power values, the 75th and 90th percentile were determined for each channel. We rejected segments with a power greater than the 90th percentile on any of the recorded channels and/or with a power larger than the 75th percentile on 50% or more of all recorded channels. The procedure was repeated for recordings with anesthetics, but with power determined in the range 10-16 Hz. Finally, within each recording, groups of four consecutive (overlapping) intervals which satisfied the criteria above were combined to yield segments of 6002 points length, corresponding to ~3 s. Three of such segments per recording, picked randomly from the beginning, middle and end of each recording were subjected to the subsequent analysis.
Data analysis: Pearson's correlation and cross-approximate entropy
Φ m (r)(x || y)is the average of . is the number of times which a sequence of defined length m in signal x starting at data point i has a similar counterpart anywhere in signal y, divided by N-m+1 (the number of comparisons possible). Two sequences are defined as similar if none of their scalar component differences (x i - y i ) exceeds tolerance r (see Figure 2 for a detailed illustration of the computations). For analysis of the presented data, length m was set to 1 and tolerance r was 20% of the standard deviation of the signal in the channel combination with the lower channel number, i.e. if the channel combination was [1, 4], SD was calculated for the signal recorded from channel 1. These settings are in accordance with the settings recommended by Pincus . XApEn calculation was performed with MATLAB 6.5.
where and are the mean of the intervals x = [x1, ..., x n ] and y = [y1, ..., y n ], was calculated using LabView 6i (National Instruments, Austin, Tx, USA). R http://www.r-project.org/ was used for generating Figure 2.
This work was supported by the German Ministry for Education and Research (BMBF 0311858). Further support was provided by the Hertie Foundation and the Hermann and Lilly Schilling Foundation. The authors thank Kuno Kirschfeld for generous support of this study, and Susanne Kramer for excellent technical support.
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