Autism spectrum disorder (ASD) is a lifelong neurodevelopmental disability affecting around 2.3% children aged 8 years. It involves difficulties in social interaction, communication and by repetitive behaviors or restricted interests[1]. Emerging evidence suggests that individuals with ASD often exhibit altered intrinsic brain activity and functional connectivity[2–4]. Studies have demonstrated that these alterations in brain activity and functional connectivity can be characterized by local overconnectivity and long-range underconnectivity, which may contribute to the corresponding behavioral impairments[5, 6].
The human brain is a sophisticated system distinguished by its dynamic neural communications within functionally specialized assemblies and extensive long-range mutual interactions across these assemblies[7, 8]. Focusing solely on abnormal local brain activity or changes in brain activity may be in sufficient given the current understanding of human brain. Neurophysiologic signals obtained from electroencephalography (EEG), magnetoencephalography (MEG) and functional magnetic resonance imaging (fMRI) exhibit complex temporal fluctuations that reflects the state of neural activity[9, 10]. Increasing studies reveals the atypical dynamic connectivity patterns in early autism brain and established some reliable findings[11–14]. For example, in compare with typical developed brain, autistic brain exhibits lower temporal variance in default mode network (DMN) and lower dynamic functional connectivity between precuneus and precentral gyrus[11]. While some studies showed higher temporal variability functional connectivity between precuneus/ post cingulate gyrus and temporal pole[14]. These studies also revealed that symptom severity is associated with the variance of dynamic functional connectivity. Although some fruitful results have been obtained, previous studies seem to have overlooked the complexity of brain activity.
The complexity of the human brain increases progressively throughout its developmental trajectory[15]. The autistic brain, however, shown abnormal early overgrowth occurs during the first 2 year of life. By age 2 to 4, the most pronounced overgrowth is observed in structures that underlie high-order cognitive, emotional, social, and language functions[16]. Such overgrowth may inevitably result in aberrations in brain activity, thereby compromising the complexity of brain signals. However, the findings regarding the complexity of brain signals during development stage exhibit inconsistencies across different studies. For example, Takahashi et al. explored MEG signal variability between ASD children and typical developed (TD) children. They found increased signal variability in ASD children[12]. On the contrary, Bosl et al. explored EEG signal variability between high-risk ASD infants (confirmed family history of ASD) and TD infants. They found decreased EEG signal variability in high-risk ASD infants[17]. While, fMRI studies reported inconsistence results as well. A study recruit resting-state fMRI signal complexity as features and using support-vector machine to distinguish ASD patients from TD individuals. It revealed lower signal complexity in ASD patients compare to TD individuals[18]. Another study examining the resting-state fMRI signal complexity in children with and without ASD and found both increase and decrease signal complexity in occurring specific brain regions[19]. These results appear to be incongruent with the theory “loss of brain complexity hypothesis”. The measure of complexity, as posited by this theory, encompasses not only the system’s randomness but also its quantity of transmitted information[20]. The existing studies on brain complexity in autism, however, appear to overlook the consideration of information transmission.
Entropy indicates system complexity. In the context of neurophysiological signals, by utilizing approximate entropy or sample entropy (SampEn), we can assess the regularity and predictability of fluctuations within a time series, by quantifying the probability that similar patterns of observations will not be succeeded by additional similar observations[21]. SampEn has been successfully applied to variety of mental conditions, including ASD[22–24]. On the other hand, by utilizing transfer entropy (TE), we can measure the amount of directed (time-asymmetric) information flow between two random processes, by quantifying the how much the state of one variable uniquely contributes to the future state of another variable, beyond what is already contained in the past of the affected variable[25]. It is worth noting that there are various entropy algorithms that can evaluate the complexity of neurophysiological signals. For example, the utilization of multiscale entropy, which developed based on SampEn, is prevalent in EEG researches, and the utilization of permutation entropy in MEG research[26, 27]. Multiscale entropy can be used to evaluate the complexity and dynamics of brain signals at multiple time scale. However, permutation entropy is particularly advantageous for real-time analysis and for cases where the data length is limited. Since our objective is to assess the flow of information among different brain regions, TE is a suitable option.
The TE is widely recognized for evaluating effective connectivity, distinguishing itself from dynamic causal modeling (DCM) by its ability to assess the directional influence between two brain regions, it determines whether a causal relationship exists[28, 29]. Signal transmission between brain regions exhibit linearity or nonlinearity[30]. In compared with Granger causality (GC), TE is more appropriate for analyzing nonlinear causality[31]. The purpose here does not aim to determine whether GC or TE is superior in terms of effective connectivity. A previous study employed both of the methods on the adult ASD patients, we observed that while GC exhibited strong performance in detecting linear causal connections, it demonstrated limited efficacy in detecting non-linear causal connections. In contrast, TE displayed a relatively balanced ability to detect both linear and non-linear causal connections compared to GC[32].
The symptoms of ASD typically manifest between the ages of 12 and 36 months. However, little is known about the changes of brain characteristics during this stage. That’s because it is extremely difficult to conduct fMRI studies in children at this developmental stage. In the early 2000s, “sleep fMRI” was initially employed to characterize brain functionality in typically developing infants and toddlers[33, 34]. The previous fMRI studies on autism research have mainly focused on high-functioning autistic subjects who are highly cooperative and older subjects, which may introduce bias due to the specific sample selection[35]. Although those bias can be eliminated by “sleep fMRI”, fMRI scanning in the natural sleep state is still very difficult and require adaptive training[36].
In this study, we investigated the differences in brain complexity between children with ASD and TD children in sleeping-state. We opted to investigate the fMRI of children with ASD during natural sleep due to emerging evidence suggesting intricate associations between sleep and ASD[37]. Moreover, the sleeping state may be the most sensitive time to detecting neurodevelopmental abnormalities in children, even before they are observable in behavior[38]. Therefore, we intended to investigate brain complexity in children with ASD during sleep, although this is a challenging study.