Address correspondence to Dr. Roger D. Traub, Department of Physical Sciences, IBM T.J. Watson Research Center, Yorktown Heights, New York, NY 10598, U.S.A. E-mail: firstname.lastname@example.org
Purpose: We describe a form of very fast oscillation (VFO) in patient electrocorticography (ECoG) recordings, that can occur prior to ictal events, in which the frequency increases steadily from ∼30–40 to >120 Hz, over a period of seconds. We dub these events “glissandi” and describe a possible model for them.
Methods: Four patients with epilepsy had presurgical evaluations (with ECoG obtained in two of them), and excised tissue was studied in vitro, from three of the patients. Glissandi were seen spontaneously in vitro, associated with ictal events—using acute slices of rat neocortex—and they were simulated using a network model of 15,000 detailed layer V pyramidal neurons, coupled by gap junctions.
Key findings: Glissandi were observed to arise from human temporal neocortex. In vitro, they lasted 0.2–4.1 s, prior to ictal onset. Similar events were observed in the rat in vitro in layer V of frontal neocortex when alkaline solution was pressure-ejected; glissandi persisted when γ-aminobutyric acid A (GABAA), GABAB, and N-methyl-d-aspartate (NMDA), and alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors were blocked. Nonalkaline conditions prevented glissando generation. In network simulations it was found that steadily increasing gap junction conductance would lead to the observed steady increase in VFO field frequency. This occurred because increasing gap junction conductance shortened the time required for an action potential to cross from cell to cell.
Significance: The in vitro and modeling data are consistent with the hypothesis that glissandi arise when pyramidal cell gap junction conductances rise over time, possibly as a result of an alkaline fluctuation in brain pH.
In this article we use the term “glissando,” a musical term referring to a sequence of notes—such as would be produced by running the fingers across the strings of a harp— notes that are of steadily rising pitch. VFO “glissandi” occur in electrocorticography (ECoG) recordings in at least some epilepsy patients, just prior to seizures, with frequencies starting in beta/gamma range (tens of Hertz), and rising gradually to >100 Hz. Glissandi can also be observed in experimental in vitro conditions, with human or rodent neocortical tissue, under baseline conditions, but especially when the extracellular medium is made alkaline; chemical synaptic transmission is not necessary. Using simulations, we show that the axonal crossing time (the time it takes for a spike in one axon to evoke a spike in an electrically coupled axon) is expected to change with gap junction conductance: a parameter that is pH sensitive. As a result, in simulations as in in vitro experiments and in patients, a characteristic VFO of increasing frequency can be generated, from a few tens of Hertz to well over 100 Hz. Because of the sensitivity of gap junction conductances (Spray et al., 1981), and of VFO itself (Draguhn et al., 1998), to pH, our data suggest that increasing brain pH may be a factor in the initiation of epileptic seizures. This is consistent with other recent in vivo and clinical observations (Schuchmann et al., 2006; Helmy et al., 2011; Schuchmann et al., 2011; Tolner et al., 2011).
Data from slice studies were derived from three additional patients with medically intractable temporal lobe epilepsy undergoing elective neurosurgical tissue resection. All patients gave their informed consent, before surgery, for the use of the resected brain tissue. This study was approved by the County Durham & Tees Valley 1 Local Research Ethics Committee (06/Q1003/51) (date of review 03/07/06), and had clinical governance approved by the Newcastle Upon Tyne Hospitals NHS Trust (CM/PB/3707). Details on these three patients are as follows:
Patient 1 was a 56-year-old man with a history of epilepsy from the age of 10 years. His epilepsy took the form of complex partial seizures with automatisms (5–10 per month), drop attacks (3–4 per annum), and secondary generalization (<1 per annum). The patient’s medication consisted of levetiracetam, carbamazepine, phenytoin, pregabalin, and lamotrigine. Electroencephalography (EEG) recordings revealed an active left temporal lobe focus, with magnetic resonance imaging (MRI) investigations demonstrating a cavernoma posterior and inferior to the motor strip. Following surgery to remove the cavernoma, the patient has been seizure free. In vitro recordings were conducted in slices of inferior temporal gyrus.
Patient 2 was a 29-year-old woman with congenital right hemiparesis who has had a history of seizures from the age of 3 years. The patient experiences two to three seizures per day and these are associated with foul taste in the mouth, oral automatisms, coughing, and belching. The patient has also experienced one episode of status epilepticus at the age of 10 years. The patient’s medication consisted of valproate, carbamazepine, topiramate, pregabalin, and clonazepam. EEG recordings revealed a left temporal slow wave discharge and MRI investigations showed left hippocampal sclerosis with porencephaly in the left parietal region. Her single photon emission computed tomography study was significantly abnormal, showing hypoperfusion in the left temporoparietal region. A selective amygdalohippocampectomy was carried out and the patient was then seizure free for 3 years; however, seizures have recurred with the semiology as described above. In vitro recordings were conducted in slices of inferior temporal gyrus.
Patient 3 was a 49-year-old woman with a history of seizures from the age of 31 years. These events, approximately one per month, are associated with epigastric sensations, agitation, and loss of consciousness. The patient’s medication consisted of valproate, carbamazepine, and lamotrigine. EEG recordings revealed sharp waves in the right temporal lobe, and MRI investigations demonstrated a right temporal pole lesion. A right anterior temporal lobectomy was conducted, and subsequent histologic analysis demonstrated that the lesion was a grade II astrocytoma. ECoG was obtained perioperatively. The patient has had three seizures per month postoperatively. In vitro recordings were conducted in slices of posterior superior temporal gyrus.
In vitro human neocortex recordings
Human slices were derived from material removed as part of surgical treatment of medically intractable cortical epilepsy from the left and right temporal regions with written informed consent of the patients. Anesthesia was induced with intravenous remifentanil with/without alfentanil (0.2–0.4 μg/kg, 1 mg/kg, respectively). At induction, a bolus dose of propofol (1–2 mg/kg) was administered intravenously. The patient also received the muscle relaxant vecuronium (0.1 mg/kg). Anesthesia was maintained with remifentanil, oxygen, and desflurane at minimum alveolar concentration volume of 0.5–1. Resected tissue was immediately transferred to sucrose-containing artificial cerebrospinal fluid (sACSF) containing (mm): 252 sucrose, 3 KCl, 1.25 NaH2PO4, 2 MgSO4, 2 CaCl2, 24 NaHCO3, and 10 glucose. Neocortical slices containing all layers were cut at 450 μm (Microm HM 650 V), incubated at room temperature for 20–30 min, and then transferred to a standard interface recording chamber at 34–36°C perfused with oxygenated ACSF containing (mm): 126 NaCl, 3 KCl, 1.25 NaH2PO4, 1 MgSO4, 1.2 CaCl2, 24 NaHCO3 and 10 glucose. The time between resection and slice preparation was <1 min. Extracellular recordings (DC–500 Hz) were conducted with ACSF-filled glass microelectrodes (2 MΩ) connected to an extracellular amplifier (EXT-10-2F; Npi electronic GmbH, Tamm, Germany).
In vitro rat neocortex recordings
Horizontal slices of 450-μm thickness were prepared from adult male Wistar rats (150–250 g). Neocortical slices containing frontal and/or temporal association areas were maintained at 34°C at the interface between warm wetted 95% O2/5% CO2 and ACSF containing (in mm): 3 KCL, 1.25 NaH2PO4, 1 MgSO4, 1.2 CaCl2, 24 NaHCO3, 10 glucose, and 126 NaCl. Extracellular recordings from layer V were obtained using glass micropipettes containing the above ACSF (resistance <0.5 MΩ). Signals were analog filtered at 1–2 kHz and digitized at 10 kHz. Epileptiform events were evoked by pressure ejection of 30–70 nL ACSF containing 100–200 mm NaOH (pH 8.2–8.9) onto layer 5. Droplets were placed in layer V, approximately 100–300 μm from the recording site (also in layer V). (Application directly onto the recording site did not generate glissandi, perhaps because of a lack of time dependence of local pH changes.) The main chemical synaptic pathways were blocked by bath application of 2,3-dihydroxy-6-nitro-7-sulfamoyl-benzo[f]quinoxaline-2,3-dione (NBQX) (20 μm), D-(2R)-amino-5-phosphonopentanoate (D-AP5) (50 μm), gabazine (1 μm), and (2S)-3-[[(1S)-1-(3,4-dichlorophenyl)ethyl] amino-2-hydroxypropyl](phenylmethyl) phosphinic acid (CGP55845) (10 μm) (respectively, blocking alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA), N-methyl-d-aspartate [NMDA], γ-aminobutyric acid (GABA)A, and GABAB receptors), all obtained from Tocris (Bristol, United Kingdom). For control experiments, BAPTA (1,2-bis(o-aminophenoxy)ethane-N,N,N′,N′-tetraacetic acid) was purchased from Sigma (Gillingham, United Kingdom).
Detailed multicompartment neuronal models
The methods used are similar to those described in Traub et al. (2010), with some variations described below. Briefly, we used a model of a layer V tufted pyramidal cell similar to the 61-compartment one described in Traub et al. (2005). The major difference was that the transient (“A”) K+ current was increased in the axon, approximately following data of Shu et al. (2007). (The current described by Shu et al. (2007) is slowly inactivating, whereas the current we used inactivated rapidly; this, however, was not important for our purposes.) For the sake of simplicity, we blocked high-threshold calcium conductance (gCa) and slow afterhyperpolarization currents, suppressing the tendency of the cells to generate intrinsic bursts.
We ran simulations of single neurons and of large populations. Single-neuron simulations were used to study the effect of gap junction conductance on the transmission of a spike from one axon to another. This was done by injecting current into the distal axon, as would occur if a spike in a coupled axon was occurring and was coupled to the simulated cell through a conductance; this latter conductance was then varied as a parameter. For network simulations, we used 15,000 model neurons, electrically coupled through gap junctions between distal axonal compartments, in a random network topology. Based on analysis of the behavior of simplified network models (Vladimirov et al., 2011), we believe that the details of the topology are not critical for the results reported here. There was an average of 3.333 gap junctions on each axon. In the network simulations, there were two parameters studied, the gap junction conductance, assumed to be equal at all gap junctions in the network; and the density of the “M” type of K+ conductance, a noninactivating type of K+ conductance that is activated by depolarization, that relaxes with a time constant in the tens of milliseconds at potentials near the resting potential, and that is present in the axon as well as soma and dendrites (Pan et al., 2006). We varied gK(M) in a systematic way, as follows: we started with a baseline density of the conductance in different compartments (30 mS/cm2 on the axon, 11.9 mS/cm2 on the soma, 19.0 mS/cm2 on the apical shaft, oblique and basilar dendrites, and 5.6 mS/cm2 in the tuft), a distribution arrived at by multiple trial-and-error simulations, and not assumed to be uniquely capable of replicating experimental traces. We then used a “scaling parameter,” from 0 to 3.5, that multiplied the baseline conductance density in each compartment. We also systematically varied gap junction conductances. Chemical synapses were not simulated.
Simulations of the 15,000 cell network were run on 40 processors of an IBM (Armonk, NY, U.S.A.) e1350 Linux cluster and on 20 processors of an IBM 7040-681 AIX parallel computer. Code for the models is available from email@example.com.
A random network topology was used in the detailed simulations for the following reason. In order to demonstrate best the effects of localized network connectivity, very large networks are required, with hundreds of thousands of cells (Traub et al., 2010); it was not considered practical to simulate such large networks using detailed model neurons. Networks of 15,000 “realistic” neurons are large enough to study frequency effects of parameter variations, but not spatial properties. The physical point that this article seeks to demonstrate—that there is a basic time scale determined by gap junction conductance—should hold true in any network topology, however.
Glissandi can occur in electrocorticography recordings from human epileptic brain in situ, prior to a seizure
An example of a preictal glissando, in a human ECoG recording, is shown in Fig. 1. As seen in Fig. 1A, there are large, slow, baseline fluctuations (marked by the horizontal bar) before the electrographic seizure. A glissando discharge is unmasked by removal of the slow baseline fluctuation with a higher pass band filter (lower trace). As seen in Fig. 1B, using a sliding window spectrogram, the glissando lasts about 4 s, and runs from ∼30 Hz to ∼125 Hz. An additional spontaneous glissando, similar to that shown in Fig. 1, was also observed in the 9 h of overnight ECoG recording analyzed.
Glissandi occur in excised human epileptic neocortex, as spontaneous events in vitro
Field potential glissandi (Fig. 2) were observed to arise from human epileptic temporal neocortex in vitro (n = 3 patients; n = 70 events), lasting 0.2–4.1 s, with a duration of (mean ± standard error of the mean [SEM]) 0.8 ± 0.1 s, and with an average amplitude of 1.7 ± 0.1 mV. The mean initiation frequency of the glissandi was 37.9 ± 1.4 Hz and the glissando had a mean termination frequency of 121.5 ± 3.6 Hz.
Glissandi can be evoked in “normal” rat neocortical slices in alkaline conditions, and also when AMPA, NMDA, and GABA receptors are blocked
Transient, spatially localized alkalinization of layer V in adult rat neocortex generated ictal events lasting >30 s (Fig. 3A). The initial field potential event in each case was a low-amplitude (64 ± 12 μV) run of fast oscillations beginning 0.7 ± 0.3 s post application of alkaline solution. The initial peak frequency of this activity was 32 ± 7 Hz. The maximum frequency shifted to 180 ± 30 Hz over 0.5–2.2 s until onset of large amplitude ictaform events (Fig. 3B, p < 0.05, n = 5). Bathing slices in ACSF containing drugs to block AMPA, NMDA, and GABAA & B receptors abolished the ictal response to alkalinization in all cases; however, the initial, low amplitude fast oscillation persisted, lasting 0.6 ± 0.2 s with frequency increasing from 44 ± 8 to 220 ± 30 Hz (Fig. 3B), and latency from droplet application of 0.5 ± 0.2 s (n = 5). These initial fast oscillations resembled the glissando discharges seen in human cortex in vivo and in vitro suggesting that nonchemical intercellular transmission may play a role, and that chemical synapses are not required.
The production of a proepileptogenic low calcium environment (Haas & Jefferys, 1984) through alkalinization and subsequent precipitation of calcium ions out of the ACSF solution may, in principle, be a factor in the production of the glissandi. In order to address this issue, the fast calcium buffer, BAPTA (1 mm) was pressure ejected in the presence of the cocktail of chemical synaptic antagonists (for AMPA, NMDA, GABAA, and GABAB receptors). Following the brief application of BAPTA, no glissandi were observed (n = 3, data not shown).
The latency for a spike to cross from axon to axon is expected to depend on gap junction conductance
Furshpan and Potter (1959) showed, by direct dual recording from coupled axons, that a spike could cross from one axon to the electrically coupled other axon in <0.5 msec; this was in an invertebrate preparation (the isolated crayfish nerve cord) at room temperature. MacVicar and Dudek (1982) provided indirect evidence that spikes might cross from one hippocampal mossy fiber to another in about 0.2 msec (the reasoning behind this interpretation of their data is in Traub et al. (1999)). Mercer et al. (2006) recorded simultaneously from two CA1 pyramidal cell somata, and demonstrated that a spike in one cell could induce a spikelet in the other cell with latency about 0.5 msec; if the coupling is mediated between axons (which was not proven in the paper), then—allowing for conduction times—the axonal crossing time must be <0.5 msec. Dhillon and Jones (2000) demonstrated a similar phenomenon in entorhinal cortex. Wang et al. (2010) recorded simultaneously from two layer V pyramidal neurons, and reported spike/spikelet latencies of 0.18–1.8 msec. We are not aware of experimental data examining spike latencies that are modified by manipulations of gap junction conductance, and therefore examined this question with simulations (Fig. 4).
To construct Fig. 4, we first determined the waveform, V(t), of a simulated axonal action potential, over a time interval of 1.0 msec. We then simulated a current-induced spike, and injected, starting at time 10 msec (arrow in Fig. 4), the current g × V(t) into the distal axonal compartment, where g represents the putative gap junction conductance. We repeated this procedure for g=1, 2, 3,....,10 nS. The resulting axonal responses are shown, superimposed, in Fig. 4, and are taken to represent the properties of axon-axon spike transmission as a function of gap junction conductance. (The data in Fig. 4 do not, however, capture the effects of shunting when multiple nearby gap junctions are present on an axon.) Fig. 4 shows clearly that, as expected, once a threshold conductance is reached, the latency for spike transfer diminishes as the coupling conductance increases—with “diminishing returns,” however, at larger conductances. The difference in latency to the peak of the spike, from g =3–4 nS, is 0.08 msec; the difference in latency from g =3–10 nS, is 0.18 msec.
We repeated the simulations of Fig. 4, injecting currents in progressively more proximal axonal compartments, rather than the most distal one (not shown). Using the penultimate axomal compartment produced results similar to Fig. 4; however, with the next, more proximal, compartment, the spread in latencies became larger, almost 1 msec. This might suggest a larger spread in glissando frequencies, but see further on.
The functional significance of these latency differences, for network behavior, can be estimated as follows: in a VFO network modeled as a random graph, oscillation periods are expected to follow the mean path length, being of order twice this quantity (Traub et al., 1999). The “mean path length,” for a connected subregion of a graph, is the average number of steps it takes to traverse a shortest path from node 1 to node 2, where both nodes are chosen randomly. In a random graph with sufficiently high connectivity, there is a single connected subregion that is much larger than all the others, called the “large cluster.” Comments below refer to the large cluster. In a random graph, the statistical structure is determined entirely by the connectivity parameter c (equal to ½ the mean number of edges, or links, emanating from a node – the “mean index”); c in turn determines the relative size of the large cluster in the graph, G(c), a number lying between 0 and 1 (Erdös & Rényi, 1960). In our case, where the mean index of the 15,000 cell random graph is 3.333, c is equal to half of this, or about 1.667, and G(c) = 0.96. That is, the large cluster is 96% of the whole network. Following Newman et al. (2001), we may estimate the mean path length as
where N is the graph size, or 15,000. This quantity is about 8.0. Therefore, a difference in latency of 0.18 msec for a spike to cross from axon to axon (see above) is expected to translate into differences in VFO periods of the order of 2 × 8 × 0.18 msec–2.9 msec. That number is sufficient to make a major difference in network frequency. Therefore, if the fastest VFO frequency in the network were, say, 160 Hz, corresponding to a period of 6.25 msec, then the network might be capable of slowing down to a period of 6.25 + 2.9 = 9.15 msec, or a frequency of 109 Hz. Simulations (see below) and experiments (see above) indicate that networks can oscillate at even lower frequencies than this. Because the above analysis does not take into account the effects of shunting caused by multiple gap junctions, and by multiple axonal K+ conductances, we cannot expect it to account for the extremes of the network frequency range.
Glissandi are predicted to occur, in a detailed network model, as gap junction conductance increases, provided gK(M) is sufficiently large
To study the effects of gap junction conductance on VFO frequency in detailed network simulations (see Methods), we performed a large number of 1-s simulations as this parameter was varied, along with a parameter scaling gK(M), the density of the M-type of K+ conductance (Fig. 5A). Chemical synaptic conductances were not simulated. We found that VFO frequency would indeed steadily rise as gap junction conductance increased—predicting the existence of a glissando—provided that gK(M) was large enough. In Fig. 5A, the scaling parameter for gK(M) needed to be ∼1.5 or larger for a glissando to be expected.
Fig. 5B provides a more detailed view of network behavior, at a fixed gK(M) value (scaling factor 2.7, see Fig. 5A) for two specific values of gap junction conductance. The model predicts that spikelet frequency (in intracellular recordings) should increase as network frequency increases (compare Fig. 10.7 of Traub & Whittington, 2010).
Another parameter that influences network frequency under the conditions of Fig. 5 is axonal gK(A). Reductions of the density of this transient K+ conductance, approximately fourfold compared to Fig. 5, could lead to network frequencies approaching 300 Hz (not shown).
The network model replicates full glissandi, when gap junction conductance is increased over time, and over an appropriate range
In the simulation of Fig. 6, the gK(M) scaling factor was also 2.7 (c.f. Fig. 5), and gap junction conductance was increased from 2.0 to 12.0 nS, over a period of 2 s. Chemical synaptic conductances were not included in the simulation. The glissando thereby produced was strikingly similar to the examples recorded from patients and in in vitro slices in “nonsynaptic” conditions. We repeated this simulation (not shown) with gap junctions located in more proximal compartments, rather than the most distal axon. Use of the penultimate axon compartment led to a glissando similar to that shown in Fig. 6. Moving the gap junctions one more compartment proximally, however, and leaving all other parameters unchanged, led to a simulated field without oscillations. This can be attributed to failures of spike transmission across gap junctions, due to the impedance load of the soma and dendrites.
We have shown that “glissandi”—field oscillations of steadily increasing frequency, from tens of Hz evolving to over 100 Hz—occur spontaneously in human epileptic neocortical tissue. Experimentally, glissandi are favored by blockade of chemical synapses and by alkalinization of the tissue; however, blockade of chemical synapses does not appear to be essential (Fig. 3).
Glissandi can plausibly be explained by progressively opening gap junctions between principal neurons (Fig. 6). The essential physical idea is that altering gap junction conductance should modify the propagation time for a spike to pass from cell to cell, independent of the details of membrane kinetics. Other factors, however, that could increase VFO frequency cannot yet be definitively ruled out. Examples of such other factors would include increasing axonal excitability and increased rates of spontaneous firing in the axonal plexus (Traub et al., 1999; Lewis & Rinzel, 2000; Traub et al., 2010).
The occurrence of glissandi prior to seizures, as a proposed consequence of opening gap junctions, is consistent with suggestions that brain alkalinization, perhaps induced by hyperventilation, contributes to seizure initiation in certain clinical and experimental contexts (Schuchmann et al., 2006, 2011); and alkalinization could explain why acetazolamide is effective in at least some epilepsy patients. We would like to suggest that (possibly localized) brain alkalinization could contribute to the initiation of focal seizures (Fig. 3, and Traub et al., 2010), and that alkalinization is effective—at least in part—because of its effects on gap junctions between principal neurons. How might such proposals be tested?
First of all, it may be possible to measure brain pH in experimental animals that experience spontaneous seizures (Javaheri et al., 1981). Such studies could, at least in principle, establish a temporal correlation between tissue alkalinization and seizure initiation. That alkalinization occurs in epileptic temporal lobe has been previously suggested (Laxer et al., 1992), although the detailed time relations between pH changes and seizures was not determined. Even if an appropriate temporal correlation does exist, however, how can one be sure that the relevant physiologic effect is an opening of putative axonal gap junctions, and not a change in one or more other biologic parameters? This is a particularly troubling question given that (1) some axonal gap junctions (in hippocampal mossy fibers) appear to contain connexin36 (Hamzei-Sichani et al., 2007); (2) VFO in nonsynaptic conditions is enhanced by alkalinization (Draguhn et al., 1998); but (3) connexin36-containing gap junction channels appear to be closed—not opened—by alkalinization (Gonzáles-Nieto et al., 2008). In addition, low-calcium induced VFO in hippocampal slices appears identical in control mice as compared to connexin36 knockout mice (Hormuzdi et al., 2001). One must not assume, then, that putative axonal gap junctions contain connexin36 as their sole or major component. We would hypothesize that the putative axonal connexin, whatever it turns out to be, is opened by alkalinization.
We suggest that molecular techniques are required to unravel these questions. First, it is essential to identify which protein (or proteins) are the most important ones in putative gap junctions between principal neurons. (For example, connexin57 has been shown to mediate axoaxonal coupling in retina; Janssen-Bienhold et al., 2009). Second, it might be possible to genetically engineer this protein so as to render it more, or less, susceptible to conductance changes induced by pH alterations. Third, animals with the suitably engineered gap junction protein may be more, or less, susceptible to epileptogenesis in experimental protocols. Finally, identification of the critical protein should allow preparation of a specific antibody, which in turn would allow analyses of protein expression in epileptic versus nonepileptic human tissue.
Supported by NIH/NINDS (RO1NS044133 to RDT), IBM (RDT), the Alexander von Humboldt Stiftung (RDT), the Einstein Stiftung Berlin (RDT), the MRC Milstein Fund (United Kingdom), The Wolfson Foundation, The Royal Society, and the Newcastle upon Tyne Healthcare Charities Trust. MC is funded by the Dr Hadwen Trust and did not participate in experiments involving animals or cells or tissues from animals or from human embryos. The content is solely the responsibility of the authors and does not necessarily reflect the official views of the National Institutes of Health or the National Institute of Neurological Disorders and Stroke. We thank Drs. Yuhai Tu, Nikita Vladimirov, Erin Munro, Mark Kramer, and Geoffrey Grinstein for helpful discussions.
The authors have no conflicts of interest to report.
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