Validation of the neuronal avalanche in in vitro and in vivo recording
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.