Autism spectrum disorder (ASD) is a neurodevelopmental disorder characterized by an impairment in social communication, restricted interests and stereotypical behaviors (Rapin, 1997). The estimated prevalence of ASD in America is 1 in 68, reflecting a nearly 30% rate increase within the last 2 years (Deborah et al., 2015). The causes and pathologic mechanisms of autism are still unclear (Trottier et al., 1999). Genetic studies have revealed that several single-gene disorders and rare copy number variants appear to be strongly associated with ASD; however, genetic syndromes, mutations, and single-gene etiologies account for only 10 to 20% of ASD cases, and in many cases individuals with these genetic syndromes do not have an ASD diagnosis (Abrahams and Geschwind, 2008). Recently, neuroimaging tools have been applied for the evaluation or assistant diagnosis of ASD. For examples, functional magnetic resonance imaging (fMRI) have demonstrated functional under-connectivity in ASD (Just et al., 2007) and reported abnormalities in individuals with ASD when performing tasks that include working memory and face recognition (Pierce et al., 2001; Koshino et al., 2008).

Some studies have demonstrated the imbalances between excitation and inhibition in synaptic transmission and neural circuits in autism spectrum disorders (Dickinson et al., 2016; Lee et al., 2016). Pathophysiological alterations in the glutamate (Glu) andγ-aminobutyric acid (GABA) metabolism might lead to an excitatory-inhibitory imbalance. Glu is the most important excitatory and GABA the most important inhibitory neurotransmitter in brain. Some authors have proposed the idea that such genetic changes lead to an imbalance of excitation and inhibition in cortical regions, which might be a critical cause correlate of autistic symptoms (Rubenstein and Merzenich, 2003; Rubenstein, 2010). Recent anatomic studies have shown that autism is closely associated with abnormalities in cortical minicolumns. The latter are reduced in size and increased in number in ASD, especially within the dorsolateral prefrontal cortex (DLPFC) (Casanova, 2006). This may cause a bias in the ratio of cortical excitation to inhibition, which adversely affects the functional distinctiveness of minicolumnar activation.

Transcranial direct current stimulation (tDCS) and transcranial magnetic stimulation (TMS) are non-invasive brain stimulation techniques that have yielded promising and encouraging outcomes for the treatment of psychiatric disorders. A number of clinical studies have reported positive outcome measures when using TMS as a therapeutic intervention for ASD (Casanova et al., 2014; Panerai et al., 2014; Sokhadze et al., 2014), and TMS is considered safe if applied within safety guideline (Rossi et al., 2009). tDCS provides a weak constant current, ranging from 1 to 2 mA to the scalp through two electrodes: an anode and a cathode (Nitsche et al., 2008). It can modulate the spontaneous neuronal activity by inducing either positive (anodal) or negative (cathode) intracranial current flow in specific brain regions. Anodal stimulation increases cortical excitability, whereas cathode stimulation inhibits the same (Nitsche and Paulus, 2000; Terney et al., 2008). These currents modify the transmembrane neuronal potential and thus influence the level of excitability thus modulating the firing rate of neurons in response to additional inputs (Wagner et al., 2007). In addition, anodal stimulation can induce a significant increase in the regional cerebral blood flow (rCBF) combined with functional near-infrared spectroscopy (fNIRS), which offers a measure of regional blood oxygenation state in cortical tissue and cerebral blood flow that could reflect neuronal activity (Merzagora et al., 2010). The effects of tDCS are associated with a number of different mechanisms, including local changes in ionic concentrations (hydrogen, calcium) and levels of cyclic adenosine monophosphate (cAMP), alterations in protein synthesis, and modulation of N-methyl-D-aspartate (NMDA) receptor efficacy (Islam et al., 1995; Nitsche et al., 2004; Merzagora et al., 2010). Magnetic resonance spectroscopy (MRS) has shown that anodal stimulation reduces local concentrations of the inhibitory neurotransmitter GABA, whereas cathodal stimulation reduces excitatory glutamate levels (Stagg et al., 2009; Clark et al., 2011). In this study, we try to demonstrate the effects of the tDCS on the ASD. In our study the dorsolateral prefrontal cortex was selected due to its important role in cognition. In addition, some studies have incriminated functional abnormalities in this cortical region as a contributor to the pathogenesis of autism and there is a relationship between social disability and metabolic dysfunction in this region (Fujii et al., 2010).

Electroencephalography (EEG) provides a precise millisecond-timescale temporal dynamics to measure the postsynaptic activity in the neocortex and is a powerful tool to study the complex neuropsychiatric disorders. Previous studies showed EEG changes in some brain regions of the children with autism. Some EEG analysis methods have been used to reveal these EEG changes in ASD during resting state or performing some specific tasks. Resting-state EEG studies of ASD suggest a U-shaped profile of electrophysiological power alterations, with excessive power in low-frequency and high-frequency bands (Wang et al., 2013). The EEG recordings have also been used for assessing functional connectivity between different brain regions and calculating the spectral power changes of ASD (Murias et al., 2007; Wang et al., 2013; Righi et al., 2014). In the context of entropy, a high entropy value implies the ability to store more information within a neural network. The recent nonlinear approaches characterizing complex temporal dynamics have provided new insights into EEG dynamic complexity in mental disorders including ASD. The multiscale entropy approach was used to measure the changes in EEG complexity for ASD after electroconvulsive therapy (Takahashi, 2013). Combining discrete wavelet transform (DWT), entropy (En) and artificial neural network (ANN) methods were used for assisting autism diagnosis (Djemal et al., 2017). Transfer entropy methods could reconstruct connectivity of simulated neuronal networks of both excitatory and inhibitory neurons (Orlandi et al., 2014). Maximum entropy ratio (MER) is a new symbolic analysis approach for the detection of recurrence domains of complex dynamical systems from time series (Graben and Hutt, 2013; Beim Graben and Hutt, 2015). The method has been successfully adapted to investigate the high-dimensional electrocorticogram (ECoG) data for epilepsy patients (Yan et al., 2016). In this paper, this method will be used to measure the changes of EEG of patients with ASD. Previous studies have shown that such an imbalance could cause low entropy neural network dynamics (Catarino et al., 2011; Okazaki et al., 2015), suggesting that the mechanism which causes low entropy in autistic brain circuits may be an imbalance of cortical excitation and inhibition. We aimed to investigate the EEG changes induced by anodal tDCS over the DLPFC during the resting state of ASD children and if it was effective to alter the excitatory and inhibitory imbalance. In this paper, a MER is applied for calculating and comparing pre- to post-tDCS changes of EEG data from a group of children with ASD who received 10 times anodal tDCS modulation over the left dorsolateral prefrontal cortex (F3 in the 10/20 international electrode placement system) and EEG data changes of non-modulation from another group of autistic children matched by gender and age who were waiting for the next experiments.

We aimed to investigate whether tDCS had some effects on the EEG complexity of autistic children using the MER method. The results showed that the MER value was higher when comparing post-tDCS to pre-tDCS for experimental group and almost remained unchanged for controls, which means that the EEG complexity increased after one session of tDCS stimulation.

In this study 100 EEG epochs (50 from pre-tDCS and 50 from post-tDCS) from 13 ASD children were used for analysis. Each epoch's length is 5 s. The sample rate is 250 Hz. Figure 2B is the recurrence plot of the EEG data in Figure 2A, with ε = 13.2. We also calculate the entropy H(ε) and Cardinality M(ε) with the change of ε (Figures 2C,D) shows the symbolic recurrence plot using the MER algorithm, while Figure 2E shows the maximum entropy MER changing with ε, with a peak value of 0.0403 (correspondingly normalized maximum entropy NMER is 0.1100), and the optimal encoding ε^* is 13.2. The MER analysis result shown in Figure 3 is for a 5 s post-tDCS EEG. We calculated MER value based on the average of 19 channels which were chose for a more accurate result including Fp1, Fp2, F3, F4, C3, C4, P3, P4, O1, O2, F7, F8, T7, T8, P7, P8, Fz, Cz, and Pz. Every channel was given a value after calculation and we obtained the average result which showed the brain condition for autisitic children and the controls. The maximum entropy MER value is 0.0833, normalized maximum entropy NMER is 0.2275, and the optimal encoding ε^* is 10.88. The results showed that the normalized maximum entropy NMER value is 0.1100 before tDCS, and increased to 0.2275 after one session tDCS treatment and t test statistical method was used (p = 0.0259 < 0.05). The statistical results are listed in Table 1. MER was significant lower at the pre-tDCS state. On the other hand, the optimal encoding ε^* was within a lower range at the post-tDCS state.

The same calculating method was used to measure the changes of MER values for the controls and the results were shown in Figures 4, 5. The results showed that the normalized maximum entropy NMER value is 0.1164 for the first EEG data and it is 0.1171 (p = 0.6223>0.05) for the second data after 3 weeks, which showed a tiny change. The statistical results are listed in Table 2.

This paper is the first one describing tDCS-induced changes of EEG complexity in children with ASD. Specifically, the MER algorithm was used and the results showed an obvious increase when the ASD children received 10 tDCS interventions.

As presented in the introduction, several authors have proposed the idea that the neuronal network excitation and inhibition imbalance might be the critical component in the pathogenesis of ASD and severe behavioral deficits in autism have been found arising from elevation in the cellular balance of excitation and inhibition within the neural microcircuitry (Gogolla et al., 2009; Yizhar et al., 2011). For autism, repetitive/restricted behavior is expected to be generated by repetitive/restricted neural network dynamics, which have low entropy than typical development children. Previous research has shown that EEG complexity, as an index for neural information processing and neural connectivity (Sakkalis et al., 2008) is reduced in ASD patients. The presence of reduced EEG complexity was demonstrated in adults with a diagnosis of ASD, supporting the hypothesis that EEG complexity is a sensitive marker for the presence or predisposition of an autistic condition (Catarino et al., 2011).

TDCS research will produce acceptable, non-invasive, safe, quick-acting, and long-lasting treatments. It also can target specific tissues and neural networks with minimal or no deleterious side effects for neurocognitive and behavioral functions. The depolarizing effects of anodal tDCS on neuronal resting membrane potentials and its demonstrated influence on LTP in neuronal circuits provide some account for the observed excitatory effects of anodal stimulation on behavior (Meinzer et al., 2015).

In this study, The MER changed significantly from 13 autism children who received 10 times tDCS modulation. Compared with another waiting group, there was almost no change. Thus, the results helped to reinforce the idea that tDCS applied over the left DLPFC preferentially affects the brain complexity, which can be measured by the alteration of entropy. This change in EEG complexity is specific to the site of stimulation and could be used to target activity as an outcome measure in clinical trials. In fact, tDCS can modulate brain activity in ways that benefit aspects of cognition that are directly related to learning, acquisition, and performance (Coffman et al., 2014). Anodal tDCS intervention over DLPFC could increases the cortical excitability for ASD children and balances the excitation and inhibition of neurons. Previous studies have reported that a single stimulation of anodal tDCS over the left DLPFC resulted in a significantly greater increase in peak alpha frequency measured from the F3 electrode (Amatachaya et al., 2015).

There are some limitations in this study. First, resting-state EEG of ASD children can be influenced by many factors, including EOG and other movements. Second, the stimulation region of DLPFC was not confirmed by neuroimaging but rather by using a slightly less accurate F3 placement of the standard international system. Additionally, sham stimulation was not obtained in the experiment. Despite these limitations, our study demonstrated that anodal tDCS over DLPFC increases EEG complexity. Up to date, there are only symptomatic treatments for autism children may of which suffer from serious side effects. tDCS may be an alternative for ASD patients who are not interested in or decline psychopharmacological treatment. Further research is needed to examine the potential of brain stimulation treatments for ASD and to interpret the mechanisms of these treatments using neuroimaging techniques.

JK: Writing and data analysis; EC, JH, and ZT: Data recording; XinL: Data analysis; ES and MC: revise; GO: computational analysis; XiaL: Design and revise.