- Research article
- Open Access
Cingulate seizure-like activity reveals neuronal avalanche regulated by network excitability and thalamic inputs
© Wu et al.; licensee BioMed Central Ltd. 2014
Received: 1 November 2013
Accepted: 30 December 2013
Published: 3 January 2014
Cortical neurons display network-level dynamics with unique spatiotemporal patterns that construct the backbone of processing information signals and contribute to higher functions. Recent years have seen a wealth of research on the characteristics of neuronal networks that are sufficient conditions to activate or cease network functions. Local field potentials (LFPs) exhibit a scale-free and unique event size distribution (i.e., a neuronal avalanche) that has been proven in the cortex across species, including mice, rats, and humans, and may be used as an index of cortical excitability. In the present study, we induced seizure activity in the anterior cingulate cortex (ACC) with medial thalamic inputs and evaluated the impact of cortical excitability and thalamic inputs on network-level dynamics. We measured LFPs from multi-electrode recordings in mouse cortical slices and isoflurane-anesthetized rats.
The ACC activity exhibited a neuronal avalanche with regard to avalanche size distribution, and the slope of the power-law distribution of the neuronal avalanche reflected network excitability in vitro and in vivo. We found that the slope of the neuronal avalanche in seizure-like activity significantly correlated with cortical excitability induced by γ-aminobutyric acid system manipulation. The thalamic inputs desynchronized cingulate seizures and affected the level of cortical excitability, the modulation of which could be determined by the slope of the avalanche size.
We propose that the neuronal avalanche may be a tool for analyzing cortical activity through LFPs to determine alterations in network dynamics.
The brain is a complex system, in which neurons can integrate various inputs and process certain functions [1, 2]. Serious neuronal insult can break the excitation/inhibition (E/I) balance and cause severe dysfunctions [1–5]. Traditional clinical diagnoses focus on the electroencephalography (EEG) waveform and frequency. With the increase in computing power, the accurate and objective identification of collective cerebral activity transmission, including waves, oscillations, and synchrony, becomes more critical. The rules for signal-transferring processing generally include spatial and temporal correlations and coherence, and these rules are broadly used in the analysis of the EEG under spontaneous cortical activity in clinical examinations and animal studies. The spatial and temporal properties of these phenomena can be described by mathematical models, the neuronal avalanche, which was proposed by Plenz and Beggs, and could be a potential model to evaluate network dynamics . The neuronal avalanche is a cascade of bursts of activity in neuronal networks, whose size distribution can be approximated by a power law distribution. Recent studies indicated that the neuronal avalanche could be found in both in vitro and in vivo recording systems [7–10].
Several complex systems, such as earthquakes [11, 12] and forest fires [13–15], show similar activity transmission. A single unit with a specific threshold can dissipate activity back to the system as a processing cascade [15, 16]. This dynamic has been found in neuronal networks, known as a neuronal avalanche, whose distribution possibility in local field potentials (LFPs) can be an approximation to a power-law distribution [6–8]. The neuronal avalanche is a cascade of bursts of activity in neuronal networks whose size distribution could be approximated by a power law distribution. Previous studies have proven the universality of this phenomena, and network activity could be optimized for information processing in this dynamic range, the critical state [7–10, 17]. One of the main signatures in neuronal avalanche is the size distribution, which decays as a power-law with exponents, α, around −1.5 in local field potential and −2.1 in spikes. This slope, α value, may relate to the activities of the neuronal network. Recently studies indicated that the neuronal network behaved oscillation, which is proximal near the critical state. It is essential to maintain the E/I balance for homeostatic mechanism in the signal processing . Now it is an important tool to monitor information processing in higher cortical function with a scale-invariant dynamics .
Some pathological conditions, such as seizures, may alter the cortical network and show a prolonged period of hyperactivity and an aberrant avalanche [20–22]. Simulations have indicated that the dynamic range of inputs is optimized in the critical state [6, 7, 17, 23, 24]. These studies, however, are still controversial with regard to the correlation of some parameters of the neuronal avalanche, such as the slope of the power-law distribution and the status of network activity. Furthermore, the cortical network displays spontaneous activity that persists in the absence of sensory stimuli. This is a robust feature of cortical dynamics because it is only modulated to a small extent by stimulus presentation [6, 9, 25]. However, the correlation between the inputs and neuronal avalanche is still unclear. Our previous study characterized the cortical neuronal avalanche in response to nociceptive stimulation in vivo[10, 14]. The results implied that the slope of the power-law distribution in a network might be regulated by external inputs.
We previously demonstrated that seizure-like activity in the anterior cingulate cortex (ACC) could be induced by 4-aminopyridine (4AP) and bicuculline (Bic), antagonists of selected voltage-gated potassium channels and γ-aminobutyric acid-A (GABAA) receptors, respectively [11, 13, 26–28]. The ACC is mainly connected with thalamic nuclei whose inputs exert a desynchronous influence on epileptiform activity and inhibitory mechanism that further suppresses seizure augmentation . We hypothesize that network excitability and thalamic input regulation can be revealed and quantified by calculating the slope of the distribution. The present study examined 4AP- and Bic-induced seizures with and without remote thalamic inputs. We hypothesized that the neuronal avalanche can be a tool to determine alterations in network dynamics in vitro and in vivo.
Neuronal avalanche is evident in cortical seizure-like activity
Neuronal avalanche in an enhanced network activity
The power density in each frequency band was significantly decreased in the slow-wave (0–1.5 Hz), delta (1.5-4 Hz), theta (4–8 Hz), and alpha (8–13 Hz) frequency domains in the 50 μM Bic group (Figure 3H and I; n = 6, p < 0.001). The brain slice was oriented so that the cortical layers were aligned with the horizontal channel direction. We calculated the coherence between the recording channels in cortical columns in the vertical direction or layer II/III in the horizontal direction. The coherence of each rhythmic band calculated in the horizontal and vertical directions was compared between the low-concentration (black line) and high-concentration (red line) Bic groups (Figure 3J). A high concentration of Bic significantly increased coherence in the horizontal direction in the alpha band compared with the low concentration group (Student’s t-test, n = 6, p < 0.01). In the vertical direction, coherence in the alpha band was significant decreased by the application of the high concentration of Bic (Figure 3J; Student’s t-test, n = 6, p < 0.01). This effect indicated that the potentiation of network activity may influence the propagation efficiency in different directions and within specific frequency bands [3, 34, 35]. The distribution of the avalanche size and lifetime distribution of the two states of network activity are shown in Figure 3K and L, respectively. Both of the network activities showed a power-law distribution, indicating that the neuronal network with drug-induced seizure activity exhibited scale-invariant dynamics (i.e., a neuronal avalanche). The α value was increased with the higher concentration of Bic from −1.67 to −1.47 (Figure 3M). However, the lifetime of the α value was not affected by the higher concentration of Bic (Figure 3L).
Neuronal avalanche in a suppressed network
The coherence of each rhythmic band was calculated in the horizontal and vertical directions with the low Bic concentration (black line) and high Bic concentration (red line; Figure 4J). In the Oct group, coherence in the horizontal direction was significantly increased in the delta, theta, and alpha bands compared with the control group (Figure 4J, upper panel; Student’s t-test, n = 6, p < 0.01). In the vertical direction, coherence also increased in the same rhythm group (Figure 4J, lower panel; Student’s t-test, n = 6, p < 0.01). The distribution of the avalanche size and lifetime of two states of network activity are shown in Figure 4K, L, and M, respectively. The slope of the avalanche size was changed from −1.67 in the control group to −1.82 in the Oct group. No significant change in lifetime was observed. The α value of the avalanche size can be taken as an index of network dynamics. Based on the results presented in Figures 2 and 3, we found that the average discharge and α value of the avalanche size increased with enhanced network activity. The average discharges and α value were decreased in suppressed network activity.
Cortical network dynamics regulated by medial thalamic inputs
Neuronal avalanche regulated by thalamic inputs in vivo
Analytical values of the power distribution of the neuronal avalanche
−10.032 ± 0.379
22.8 ± 1.584
19.8 ± 5.954
1.317 ± 0.022
High bic (50 μM)
−8.6152 ± 0.837
44.2 ± 4.732*
34.5 ± 7.445*
1.322 ± 0.035
Oct (100 μM)
−9.710 ± 0.729
11.2 ± 1.018*
11.5 ± 2.339*
1.297 ± 0.041
−13.22 ± 0.053*
13.4 ± 0.456*
61.4 ± 5.341*
1.358 ± 0.020
−9.112 ± 0.512
21.9 ± 3.401
32.4 ± 1.147
1.221 ± 0.072
−10.015 ± 0.692
24.8 ± 2.921
32.7 ± 1.098
1.329 ± 0.061
−10.862 ± 0.462
26.3 ± 1.866
33 ± 0.912
1.365 ± 0.095
Neuronal avalanche size and lifetime distribution
Validation of the neuronal avalanche in in vitro and in vivorecording
The spontaneously activity of brain slices from adult mice did not exhibit a neuronal avalanche because they lacked synchronized activity. Excitatory neurotransmitters can induce more spontaneous activity and display a neuronal avalanche [7, 8]. We tested the neuronal avalanche in drug-induced seizures in vitro and in vivo, in which robust ongoing activity generalized to lighter anesthesia. Previous studies have demonstrated the neuronal avalanche in these recording systems [10, 17].
Network dynamics in spontaneous cortical activity and neuronal avalanches
Spontaneous neuronal oscillations in cortical circuits have been described with regard to several aspects, such as the phase of activity, frequency coherence, and propagation patterns [20, 22]. The distribution of the avalanche size with its probability could be roughly fitted by the power-law in a scale-free event size [6, 7, 17]. We found that the slope of the neuronal avalanche size was approximately −1.4 to −1.6 with in vitro and in vivo recording, which is within the range reported in previous studies [6, 9]. We found a significant correlation between excitability and the α value. The α value would change within a range with the alteration of network activity, showing an inverted-U dose-dependent dopamine-NMDA regulation relationship . Optimal stimulation and moderate activity might maximize the occurrence of oscillation and spatiotemporal correlations [26–28]. The inhibitory system, however, can shift network dynamics and impair the signal processing of epileptic activity, with the possible involvement of GABAA receptors [27, 29–32]. Previous studies found that disinhibition of GABAA receptors altered cortical oscillations. We found that the slope of the neuronal avalanche was positively correlated with cortical excitability within a network of increased under GABAA receptor blockade. The present results suggest that network modulation in an inhibitory system may be different from an excitatory system.
Neuronal avalanche in seizure activity
A cortical seizure could be induced by abnormal excessive or synchronous neuronal activity. The relationship between the neuronal avalanche and seizure-like activity has been reported in a previous study. An aberrant neuronal avalanche was reported for cortical tissue that was removed from a juvenile epilepsy patient . This indicates that neuronal avalanches are abnormally regulated in slices that are removed from epilepsy patients. This tissue exhibited prolonged periods of hyperactivity and an increase in the branching parameter. Our study experimentally demonstrated that the α value correlated with total activity in vitro and in vivo. To avoid pathological seizures, cortical networks maintain moderate average synchrony with maximally variable synchrony . These results suggest that the distinctions between health and disease are scale-dependent. What is abnormal and the definition of dysfunction are not the propagation itself but rather activities that are sufficiently large to interfere with the normal function of the cortical network . Our results indicate that the network excitability in certain seizure activities could be dramatically changed by the disinhibition of cortical activity and cause cortical dysfunction.
Our results strongly suggest that avalanche size is a more reliable indicator of network excitability than lifetime. We found that the lifetime remained unchanged in both enhanced and suppressed network activity. The correlation between size and lifetime showed a tendency toward an increase in slope in enhanced network activity, whereas the slope decreased in suppressed network activity. The change in slope could be explained by the decrease in the alpha value of size in enhanced network activity and increase in the alpha value of size in suppressed network activity. A previous study also reported that the scale-invariance in the avalanche size is accompanied by scale-invariance in the avalanche lifetime . Our data showed that the lifetime distribution was scale-invariant and varied greatly, even for avalanches of any size, in which the large avalanche size tended to have a longer lifetime under more excitable network conditions.
The seizures are defined as an underlying transient abnormality of cortical neuronal activity in the clinical manifestation . The phenotypic expression in seizure activities could be determined and characterized by its origin and the spreading in the spatial dimension, and the subsequent development and kindling progression in the temporal dimension . In the spatial dimension, we demonstrate the neuronal avalanche could be detected and in limited cortical area, ACC, and it might be applied in the different and larger cortical area by the scale free manner . In the temporal dimension, the seizure events usually consisted of ital., tonic and clonic phases and the underlying mechanisms of each individual stage are different [38, 39]. In the present study, the neuronal avalanche describes the properties of the network activity of the whole series of seizure event instead of the individual stages of the events. In considering to calculate the avalanche of individual seizure stages, the duration of each individual seizure stage is significant shorter and cause the limitation to analysis the difference between the ictal, tonic and clonic state in the seizure activities. To collect sufficient data which covering the series of events from short duration to long duration, it will require the increase of the sampling time and sampling space. In the increase of the sampling space, it means that the number of electrodes in a multi- electrode array must be increased to record sufficient amount of the data. The electrode array we used in the present study only has 60 recording points and thus it is limited in sampling sufficient data for further analysis of the avalanche of individual seizure stage. Recently, a high-density multi-electrode array, CMOS-MEA, has been applied in neuronal recording . Thus it is anticipated that the avalanche property of individual seizure stage could be resolved by using such high-density electrode array to gain the sufficient cortical seizure events in the limited temporal duration.
Neuronal avalanche and EEG
Several aspects of the parameters analyzed in the present study deserve particular attention. In traditional EEG, the traces patterns, frequency distributions, and correlations between remote regions are important indices for evaluating cortical conditions [34, 35]. The recurrence rate and 2D-CSD can measure the cortical neuronal state, which may represent an index of physiological homeostasis. However, the present results revealed some discrepancies, in which these parameters may not faithfully represent network excitability. For example, the amplitude and duration of typical activity and alterations in the 2D-CSD areas were not correlated with the excitability of network activity. Previous studies indicated that the neuronal avalanche could exhibited in cortical networks and might be potential candidates to measure brain activity in the processing of different tasks [10, 19, 28]. In the present study, we found that the slope of the power-law distribution could be a sufficient signature of cortical network excitability and contribute to the formation of criticality in the cortical network. Multi-level criticality may contribute to the subsequent class of dynamic systems, and each of them allows criticality to jointly emerge at multiple levels separated by a characteristic scale, which is traditionally considered contradictory in systems with self-organized criticality . Scale-free dynamics of oscillatory neuronal networks would provide important insights into clinical diagnosis.
Local cortical activity could be modulated by thalamic inputs
In this study, remote thalamic inputs could modulate cortical signal processing as a negative input to 4AP- and Bic-induced cortical seizures, and this modulation could be determined by the α value of the avalanche size in vitro and in vivo. Thalamic relay neurons synapse onto both excitatory and inhibitory neurons in cortical regions. The synapses between the thalamus and inhibitory interneurons are much stronger than those between the thalamus and excitatory pyramidal neurons . Thus, the thalamic inputs could restrain the firing of pyramidal neurons by disynaptic feedforward inhibition. We found that lesions of the thalamus enhanced cortical seizures, indicating that thalamic inputs might influence seizures through feedforward inhibition. Previous in vivo studies also showed that thalamic inputs might be involved in the termination of seizures . The basal ganglia may act as an online control system to desynchronize thalamocortical activity and contribute to seizure termination . On the other hand, previous studies indicated that medial thalamic inputs can regulate nociceptive processing in the cingulate cortex [1, 2, 15]. Peripheral noxious inputs may alter network activity in which the neuronal avalanche can reflect alterations in excitability. Medial thalamic inputs might also play a modulatory role in drug-induced cingulate cortical seizures, and the removal of this input may represent enhanced network dynamics [1, 2, 4, 5, 13]. In the present study, we demonstrated that epilepsy could be modulated by external inputs and alter network activity with the confinement of spatiotemporal scales of these power-law phenomena. Some studies indicated that epilepsy results from a failure of modulation, possibly located in part of the cortex itself or in deep brain nuclei [12, 43]. Furthermore, some studies indicated that network stability can be maintained and well-tuned by homeostatic plasticity via remote inputs, which might be crucial in critical-state organization and cortical function [8, 14, 18, 44].
Network dynamics and excitation/inhibition balance
The traditional evaluation of cortical seizures is based on analyzing the spatiotemporal distributions of EEG signals under physiological and pathological conditions. Previous studies indicated that self-organized criticality that occurs over a limited range of E/I conditions contributes to neuronal avalanches and peak information capacity and emerges together with balanced E/I [10, 16, 27, 45, 46]. In this study, we used Oct, which is known to act on T-type calcium channels to suppress network activity . However, previous studies showed that T-type calcium subunit (α1G−/−) knockout mice exhibited normal susceptibility to 4-AP-induced tonic-clonic seizures , suggesting that T-type calcium channels are not involved in the pathogenesis of 4-AP-induced seizures. The convulsant we used in this experiment was 4-AP, which is a potassium channel blocker that affects A-type and D-type K+ currents [49, 50]. The epileptogenetic mechanism of 4-AP administration might be attributable to the enhancement of both excitatory and inhibitory transmission  and depolarization of the membrane potential. Several studies showed that the application of ethosuximide, a T-type channel blocker, did not suppress 4-AP-induced seizure activity in vivo or in vitro[52, 53]. Therefore, we concluded that the major effect of Oct in suppressing 4-AP-induced seizure occurred through the regulation of gap junctions.
The neuronal avalanche reveals the constitution of scale-invariant cortical synchronization in three principle dimensions: temporal sequence, spatial distribution, and clustered neuronal activity [6, 9]. These principle properties may represent network dynamics to calculate synchrony and dispersion, which are manipulated by the network E/I balance. These mechanisms are dysfunctional in several type of seizure disorders and cause changes in the E/I balance of cortical networks [4, 7–10]. Furthermore, the tuning of the activities in brain networks is essential for the criticality on multiple levels of neuronal organization, in which the power-law scaling can emerge on multiple temporal scales in constitutive oscillating networks . The slope of the distribution in the lifetime of the neuronal avalanche is not significantly changed and represents the general properties of cortical networks. Thus, the slope of the avalanche size might provide a range of tuning of network activity. The increase of the alpha value could represent the more excitable status of the neuronal network activities in the physiological and pathological condition and vice versa.
Functional application of the neuronal avalanche
Several studies that applied the neuronal avalanche using EEG have found that avalanche dynamics are related to long-range temporal correlations [21, 54–56]. The repertoire of neural activity patterns may constrain and maximize the ability of the network to transfer and process information [23, 24, 26, 27]. The present results may provide insights into the evaluation of information processing and dynamic alterations between physiological and pathological conditions [25, 46, 57–59]. Future investigations of physiological functions and pathological conditions in macroscopic scale networks should be conducted.
In the present study, we emphasized the slope of the neuronal avalanche and comparisons with traditional aspects of LFP analysis. Power-law behaviors in cortical activity were associated with oscillations and could potentially be reflected in excitability and relayed inputs. Anterior cingulate cortex activity exhibited a neuronal avalanche. The slope of the avalanche size was sensitive to the change in network excitability and may reveal insights into higher functions in the cortex. Thus, the slope of the avalanche size could be a useful index to indicate network dynamics.
In brain slice recordings, we used 4- to 6-week-old mice (25–35 g body weight, C57Bl/6 J) that were housed in groups of five per cage with a 12 h/12 h light/dark cycle at 22°C. To maintain a similar recording site and avoid serious damage in cortical areas caused by the four shanks of the Michigan probe, male Sprague–Dawley rats (300–400 g) were used for the in vivo experiments. The mice and rats were housed in an air-conditioned room with free access to food and water. All of the experiments were performed in accordance with the guidelines established by the Academia Sinica Institutional Animal Care and Utilization Committee. Efforts were made to minimize animal suffering and reduce the number of animals used.
Acute slice preparation
The mouse brains were removed from halothane-anesthetized animals and cooled for 3 min in chilled, oxygenated artificial cerebrospinal fluid (aCSF; 124 mM NaCl, 4.4 mM KCl, 1 mM NaH2PO4, 2 mM MgSO4, 2 mM CaCl2, 25 mM NaHCO3, and 10 mM D-glucose, bubbled with 95% O2 and 5% CO2). Brain slices were prepared according to a previously published procedure [15, 60]. Briefly, the thalamocingulate block was hand-cut with two sagittal cuts and two angled cuts that were ventral and parallel to the pathway. The brain block was attached to an angular plate with cyanoacrylate adhesive, and a cut was made just above the turning point of the pathway. The stage was unfolded, flattened, and glued onto the chamber stage of a Vibratome (Series 1000, Vibratome, St. Louis, MO, USA). The brain slices were cut in ice-cold oxygenated aCSF with a 400–600 μm thickness. The slices were incubated in oxygenated aCSF at room temperature for at least 1 h before recording. Brain slices prepared using this procedure can preserve the connectivity between the MT and ACC. The oblique section angle was aligned with the trajectory of the thalamic inputs, which could maintain the intactness of the columnar structure of the cingulate cortex.
Recording in vitro
After 1 h preincubation in oxygenated aCSF at room temperature, each slice was transferred to a 60 channels MEA probe (Multi Channel Systems, Reutlingen, Germany). To cover the ACC, an 8 × 8 MEA with 100 μm electrode spacing was used in the experiment. The slice was positioned above the recording area on the MEA probe, and the upper region was aligned with one site of the ACC. A silver weight was placed on a net above the slice to provide mechanical stabilization. The chamber was kept at 30°C under continuous perfusion (2 ml/min) of oxygenated aCSF. Local field potentials were simultaneously recorded from 60 electrodes with high spatial and temporal resolution (inter-recording leads, 200 μm; total covered area, ∼1400 μm × 1400 μm). Local field potentials at each electrode were recorded against the bath electrode. 4AP (250 μM final concentration) and Bic (5 and 50 μM final concentrations) in aCSF were applied in the perfusion system to induce seizure activity. A 60-channel amplifier was used with a band-pass filter set between 1 Hz and 3 kHz (MEA-1060-BC, Multi Channel Systems, Reutlingen, Germany). The data were acquired using MC Rack software (Multi Channel Systems, Reutlingen, Germany) with continuous recording at a sampling rate of 10 kHz.
Recording in vivo
Anesthesia was induced with 4% isoflurane in pure O2 in a semitransparent acrylic box. The animal’s head was fixed in a small-animal stereotaxic instrument (David Kopf Instruments, Tujunga, CA, USA) and maintained under anesthesia with 2% isoflurane during surgery. The Michigan probe (NeuroNexus, Michigan, USA) with 32 contact points (150 μm lead interval, eight leads on one shank, and four parallel shanks), was used to record extracellular field potentials in the right ACC. The DiI (Invitrogen Molecular Probes, Oregon, USA) was dissolved in isopropanol at a saturated concentration and coated on the Michigan probe three times to ensure successful coating. The animals were subsequently maintained under anesthesia with 1.25% isoflurane during the experimental session. The depth of anesthesia was continuously monitored using an anesthesia monitor (Capnomac Ultima, General Electric Company, Fairfield, CT, USA). 4AP (30 μM final concentration) and Bic (2 μM final concentration) were added to the aCSF (50 μl) and then directly applied on the surface of the ACC for seizure induction. A tungsten electrode was inserted into the MT (−3.2 mm from bregma; lateral, 0.8 mm; depth, 5.0 mm) to make an electrolytic lesion, which was performed with a 100 μA direct current for 100 s by a constant current pulse generator (Model 2100, A-M Systems, Carlsborg, WA, USA) to deactivate the MT. After the lesion, the animals were transcardially perfused with normal saline followed by 4% paraformaldehyde. The entire brain was gently removed, post-fixed in 4% paraformaldehyde for 24 h, immersed in 30% sucrose, and cryosectioned at a thickness of 50 μm. The brain sections were processed for Nissl staining to histologically confirm the recording and lesion sites.
Data processing in vitro and in vivo
The recording data in vitro and in vivo were directly digitized at 20 kHz without filtering. The data were acquired and transformed using MC Rack and MC Data Tool software (Multi Channel Systems, Reutlingen, Germany). The data were analyzed using a custom MATLAB program (MathWorks, Natick, MA, USA). Briefly, event activity was first evaluated and filtered with a 200 Hz high-cut. To detect oscillatory events, we set two to four standard deviations (SDs) of the noise level as the threshold which is according to each background noise. The amplitudes of the peaks during an oscillation event and the seizure activities that surpassed this threshold were automatically detected by MC RACK software.
General analysis of seizure activities
The analysis of the occurrence of seizure onset confirmed our earlier observations. Seizure-like activity induced by 4-AP and Bic were divided into ictal onset, a tonic phase, and a clonic phase based on frequency evolution shown by wavelets transformed from field potential recordings . The frequency of oscillation was 6.5-10 Hz in the tonic phase and 2.5-4 Hz in the clonic phase. The duration of an oscillation event was measured by subtracting the time-point between the first and last peaks that surpassed the threshold. Epileptiform activity appeared in 10 ~ 15 minute after drug application. Our previous time control experiment indicated that the maximal and stable responses appeared between 2 to 3 hour in vitro and 1 to 2 hour in vivo after drug application . Seizure-like activity was significantly reduced 4 hour in vitro and 3 hour in vivo after drug application. Thus we carefully design the experiment in vitro and in vivo during this period to exclude the concerning of the drug concentration changing and the immediately lesion effect in temporal scale. The color maps of the isopotential and 2D-CSD were calculated and constructed from the ictal peaks of field potential profiles [11, 13]. Blue represents current sinks, and red represents current sources in 2D-CSD color map profiles. The boundary site data were obtained by extrapolation. Correlation coefficients have been used to measure the degree of synchronization of two coupled neurons [6, 63]. The correlation coefficient is a free and scale-invariant parameter for measuring the degree of synchronization quantitatively. The correlation coefficient is a free and scale-invariant parameter for measuring the degree of synchronization quantitatively. The correlation coefficient is a free and scale-invariant parameter for quantitatively measuring the degree of synchronization. Briefly, one specific channel where the first ictal event of each epileptic oscillation was initiated in layer II/III of the ACC was selected as the calculation reference. The correlation coefficient color map was constructed from this selected channel and the remainder of the channels . The coherence coefficients by the same reference channel was calculated from the cross-spectral density [64, 65]. The power spectrum of the frequency distribution was collected from a typical response and calculated by Fast-Fourier Transformation (FFT). The intensities in power were normalized to values between 0 and 1. The coherence analysis was calculated from collected LFPs from the electrodes along the horizontal and vertical direction aligned with layer II/III and the cortical column, respectively, and analyzed using custom MATLAB programs.
Neuronal avalanche analysis
The nLFPs of seizure-like activity were used to calculate the distribution of the avalanche size and its lifetime. The time-point in nLFPs of each channel was detected from filtered data that reached 2 SDs for the in vitro recording and 4 SDs for the in vivo recording. This time-point was marked as the digital unit for further neuronal avalanche calculation. The processed data thus contained a serial time-point of nLFPs and could be framed by selected time bins. The 4 ms time bin was the optimal selection for assessing the neuronal avalanche when considering the speed of the spread of neuronal activity and distance of the nearest electrodes (200 μm). We calculated the average inter-event interval, which is defined as the interval between LFPs that occurred at all electrodes, to ensure that each of the counted events were successive from other electrodes. The LFP data were binned at finer temporal resolution, making it clear that LFPs did not appear at all electrodes at exactly the same time. Each avalanche size is defined as the summation of the number of digitized units in a single avalanche event. The framed numbers of various neuronal avalanche sizes were counted for the avalanche lifetime distribution. The avalanche size and lifetime distribution were calculated using custom MATLAB software and plotted using SigmaPlot software (Systat Software, Chicago, IL, USA). The slope of the power-law distribution was calculated by fitting the front of the power-law distribution (α value) and cut-off tail (β value) using the MATLAB program. The cut-off point and sudden bump point before the cut-off were collected and calculated. These recording data were further shuffled to disturb the spatial and temporal dependence to verify the spatiotemporal dependency of the neuronal avalanche in the power-law distribution. The exponential fitting was also performed, and only R square values > 0.9 were included in the subsequent analysis.
Branching parameter analysis
The branching parameter σ was given by 1 in the case of only one ancestor, in which d is the number of the descendants, p(d) is the probability of the activated descendants, and n max is the maximal number of active electrodes in each event.
The statistical analyses were performed using SPSS software (SPSS, Chicago, IL, U.S.A.). The data are expressed as mean ± standard error, and n indicates the number of slices or animals studied. The ANOVA and Tukey’s post hoc test were used to analyze group differences in the correlation of the avalanche size and lifetime. Student’s t-test was used to analyze the effects of network excitability and the medial thalamic inputs in general and perform the avalanche analysis. The results were considered significant at p ≤ 0.05.
We thank Dr. C. K. Chen, Institute of Physics, Academia Sinica, for valuable suggestions and comments during the experiment. This study was supported by grants from National Science Council grants (NSC 99-2320-B-001-016-MY3, NSC 100-2311-B-001-003-MY3, and NSC 102-2320-B-001-026-MY3). This work was undertaken at the Institute of Biomedical Sciences, which received funding from Academia Sinica.
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