Changes of Entropy Connectivity of the Default Mode and Central Executive Networks in ASD

Background: Autism spectrum disorder (ASD) is a heterogeneous disorder characterized by different levels of repetitive and stereotypic behavior as well as cognitive decit. Brain structural and functional changes of individuals with ASD have been reported in previous investigations. To provide more implications for clinical diagnosis and treatment of ASD, it is necessary to further explore the changes of cerebral neural activities in ASD. Method: We reinvestigate the brain functional networks (viz. the default mode network (DMN) and central executive network (CEN)) of ASD utilizing entropy connectivity (a kind of causal connectivity) method and nodal degree (a topological property in graph theoretical analysis). Eighty-nine patients with ASD and 94 age-matched typical developing (TD) teenagers participated in this study. Result: Two-sample t tests revealed weakened entropy connectivity in the right dorsolateral prefrontal cortex and the left supramarginal gyrus in the CEN, as well as reduced entropy connectivity in the ventral posterior cingulate cortex and the retrosplenial cingulate cortex but enhanced asynchronous output entropy connectivity from the right dorsal frontal cortex to the left piriform cortex in the DMN in patients with ASD. In addition, we also noted signicantly decreased nodal degrees in the right somatosensory association cortex and the supramarginal gyrus in individuals with ASD. Limitation: The differences of data from different sites in MRI acquisition settings, such as keep eye open or close, decline the credibility of the results. And further discussion is blocked for BAs template, the lack of ADOS data in ABIDE I and regardless of the effect of sensorimotor related cortex. Conclusion: These ndings indicate that overconnecitivity and underconnecitivity in the CEN and DMN might be an important factor that contributes to executive and cognitive disorders of individuals with ASD. present study investigated changes of entropy connectivity (a kind of causal connectivity) in the brain of ASD using resting-state functional magnetic resonance imaging (fMRI). The main ndings of this study are described as follows: Compared with TD, ASD presented weakened entropy connectivity in the CEN and the DMN. These ndings provide some implications for clinical diagnosis and treatment of ASD. present study, we investigated the changes of entropy connectivity in the DMN and CEN. Our ndings indicate that overconnecitivity and underconnecitivity in the CEN and DMN might be an important factor that contributes to executive and cognitive disorders of individuals with ASD.


Background
Autism spectrum disorder (ASD) is an abnormal neurodevelopmental disorder. According to the latest CDC (Centers for Disease Control and Prevention) statistics (2020), one out of every 54 children is diagnosed with ASD. The main symptoms of ASD are de cits in social interaction, abnormal nonverbal behavior, and stereotypical or repetitive behavior [1]. Magnetic resonance imaging has been used to study ASDs and Researchers have obtained some signi cant discovers. Kohli et al. found that ASDs presented larger Local Gyri cation Index (LGI) in left parietal, right frontal, and temporal regions in the early stages of life, as compared with typically developing (TD) controls. However, LGI rapidly decreased with age, but more steeply in ASD in left precentral, right lateral occipital, and middle frontal clusters [2]. Similar study also revealed thinner temporal and parietal cortices during adolescence and young adulthood for individuals with ASD in comparison with TD controls [3]. Some longitudinal investigations found difference developmental changes in cortical volume [4], cortical thickness [5,6], and cortical surface area [7] across both ASD and TD control groups. In addition, the study based on diffusion weighted imaging showed that adolescents with ASD presented decreased fractional anisotropy in the inferior fronto-occipital and longitudinal fasciculi compared with agematched TD controls [8].
To explore whether the brain structural changes lead to functional abnormalities, many researchers studied this issue and reported changes of brain functional connectivity(FC) in ASDs. Granger causality analysis revealed weaker causal connectivity from ventral attention network to salience-executive network in adolescent with high-functioning autism [9]. Bi et al. studied resting-state brain functional networks using linear independent component analysis method and found that individuals with ASD presented enhanced FC in auditory network (AN) and somato-motor network (SMN) but weaker FC in dorsal attention network (DAN) compared with TD controls [10]. Decreased FC between the precuneus and medial prefrontal cortex/anterior cingulate cortex, and other default mode sub-networks areas [11]. A longitudinal study revealed localized age-dependency of functional connectivity alterations in ASDs during adolescence [12]. Altered intra-and interhemispheric dynamic functional connectivity density was also found in the medial prefrontal cortex and the inferior temporal gyrus in children with ASD compared with TD controls [13].
The default mode network (DMN) is a critical network causing social dysfunction in ASD [14], and children and adults with autism presented increased or decreased neural activity and FC [15] .The central executive network (CEN) is responsible for higher-order cognitive activities. ASD displayed reduced activation and underconnectivity in the CEN as performancing complex executive tasks, for example, visuospatial attention[16], colour matching (CMT) [17], and sentence comprehension tasks [18]. These atypical functional changes of this two networks in patients with ASD might contribute to broken internal and external information processing and abnormal network resource allocation and further lead to executive disorders, such as self-representation, the theory of mind, autobiographical memory, and restricted and repetitive behaviors [19][20][21] [22,23].
Although a lot of investigating results have been reported on the brain structure and function of ASD, it is necessary to further explore the changes of cerebral neural activities in ASD. To provide more implications for clinical diagnosis and treatment of ASD, in this study, we reinvestigate the brain functional network of ASD utilizing entropy connectivity (a kind of causal connectivity) method [24]. Our study focuses on exploring changes in the CEN and DMN.

Entropy connectivity (a kind of causal connectivity)
Entropy connectivity is a kind of causal connectivity and has been introduced in the previously published study [24]. If the changes of the BOLD (blood oxygen level dependent) signals in two brain regions are strong correlation, furthermore, the current state change of the BOLD signal in one brain region presents synchoronous or asynchronous coupling with the future state change of the other, then there exist an entropy connectivity (causal connectivity) between the two brain regions (i.e., one brain area is the response system and the other is the drive system). Entropy connectivity that is away from a brain area is de ned as the output entropy connectivity of the brain area. In contrast, entropy connectivity that pointes toward a brain area is regarded as the input entropy connectivity of the brain area. Enhanced output entropy connectivity between two brain regions implies that the increased in uence of one brain region on the other. On the contrast, Weakened output entropy connectivity between two brain regions indicates that the decreased in uence of one brain region on the other.
We selected all BAs as seeds of entropy connectivity and investigate the cross-group differences of entropy connectivity. Multiple comparison correction was used to correct the results of entropy connectivity. Correction parameters are described as follows. Seventy samples were selected randomly in each group, p<0.05, positive reproducible test (PRT) corrected, reproducible rate= 0.85, repeated number of PRT= 1000.

Result
Demographic and behavioral data test A chi-squared test revealed no signi cant difference in gender between both ASD and TD groups. Two-sample-test was performed to examine whether there is signi cant difference in age across the two groups, and no signi cant difference was found ( Table 2). Table 2 Demographic characteristics of participants . We studied the changes of entropy connectivity in CEN. Compared with TD, ASD represented weakened synchronous output entropy connectivity for BA 46R with BA 7R (Fig.1 D); BA 40 L with BA 46 R (Fig.1 E). Weakened synchronous input entropy connectivity for BA 9L with BA 21L (Fig.1 A). Weakened asynchronous output for BA 46R with BA 39L (Fig.1 C); BA 9R with BA 2L (Fig.1 B).

Changes of nodal degrees
We studied the changes of nodal degrees in the DMN and CEN. As shown in Figure 7, two-sample t tests revealed a signi cantly decreased synchronous input nodal degree for the right somatosensory association cortex (BA 7R) and a signi cantly decreased asynchronous output nodal degree for the supramarginal gyrus (BA 40L) in ASD. However, no signi cant changes of nodal degrees were observed in the DMN. Table 3 Indexes and corresponding brain regions

Discussion
The present study investigated changes of entropy connectivity (a kind of causal connectivity) in the brain of ASD using resting-state functional magnetic resonance imaging (fMRI). The main ndings of this study are described as follows: Compared with TD, ASD presented weakened entropy connectivity in the CEN and the DMN. These ndings provide some implications for clinical diagnosis and treatment of ASD.

Weakened entropy connectivity in the CEN
Previous studies reported abnormal functional connections of CEN in ASD, such as over-connectivity [27] or under-connectivity [32]. The term 'underconnectivity' theory was rstly proposed by Just et al. in a sentence comprehension task to explain the under-functioning of integrative circuitry and emergent cognitive, perceptual, and motor abilities in autism [18]. Under-connectivity of the cerebral cortex refers to weakened functional connectivity (FC) between brain regions, which leads to abnormal information integrative processing within brain and a lack of integrated information at cognitive levels. It's similar to the theory of weak central coherence [33] The under-connectivity theory has been supported by subsequent studies. These investigations nd that the weakened functional connection between the medial prefrontal cortex (mPFC) and posterior cingulate cortex (PCC) results in a decrease in the level of social cognition [22,34] and the lack of functional connections between the frontal and posterior cortex (i.e., the parietal, occipital, and temporal lobes) in individuals with ASD contributes to poor performance for complex cognitive tasks such as language comprehension, social interaction, and working memory [35][36][37]. In addition, under-connectivity of the brain structural network such as abnormalities of white matter tracts (corpus callosum, arcuate fasciculus, inferior frontal-occipital fasciculus, etc.) also lead to de cits of information transmission between brain regions [38][39][40]. Consistent with previous studies, in this current study, we found that ASD represented weakened entropy connectivity in the dorsolateral prefrontal cortex (BAs 46R, 9L and 9R), which is linked to regionally speci c cognitive function [41], such as working memory [42]. Additionally, ASD also presented weakened synchronous output entropy connectivity and decreased nodal degree in the left supramarginal gyrus (BA 40L), which involves in visual word recognition [43] and weakened synchronous input entropy connectivity and decreased nodal degree in the right superior parietal lobule (BA 7R) responsible for processing visual spatial information [44]. Moreover, there exists also a weakened entropy connectivity between posterior parietal cortex (contains BA 7 and BA 40) and dorsolateral prefrontal cortex. Therefore, these results indicates that under-connectivity in the CEN might lead to the enhanced functional separation and declined coordination in some brain regions, and further affect optimal allocation of network resources and lead to atypical cognitive activities [38].

Abnormal entropy connectivity in the DMN
Abnormal functional connectivity in the DMN have been reported in autism-related studies [34,45], and weaker intrinsic connectivity in the DMN is associated with poorer social skills of ASD [14,23].The present study also observed weakened entropy connectivity between VPCC (BA 23) and VACC (BA 24) in the DMN of ASD. This under-connectivity might induce abnormal emotional processing and self-awareness disorders of patients with ASD. Hence, our report further highlights the association between attenuate ACC cooperation with PCC and abnormal emotional processing of ASD.
Previous study reported increased resting-state functional connectivity (FC) of the inferior frontal gyrus with PCC, as well as PCC with visual regions in ASD.
Especially, increased FC between PCC and visual regions was associated with poorer language processing performance in the ASD group [46]. However, this current study found weakened asynchronous output entropy connectivity from language and visual regions to PCC. These reduced inhibitions should be consistent with enhanced FC between these regions. Weakened asynchronous output of a brain region indicates the decline of some functions related to the brain region. Furthermore, the weakened node of asynchronous output entropy connectivity in Broca's area (BA 44L) implied the dysfunction of semantic encoding and retrieval, and further damages the capacity of social communication [47]. Thus, those reduced entropy connectivity of PCC with Broca's area and associative visual cortex might be one critical factor that causes the di culties of language processing and social-communicative development in ASD [48].
The retrosplenial cortex (RSC) composed of granular cortex (BA 29) and dysgranular cortex (BA 30) involves in multiple cognitive activities, including scene perception, spatial navigation and memory, episodic and contextual memory, and emotional processing, etc. [49][50][51][52] .The perirhinal cortex (PRC), a part of the medial temporal lobe (MTL) , is involved in visual perception and memory [53,54], visual discrimination [55], object recognition memory [56], and association processes of declarative memory [57] , etc. We also noted weakened synchronous entropy connectivity between PRC and RSC in ASD. This reduced cooperative relationship between PRC and RSC expresses bandwidth limitation between the anterior temporal and posterior medial systems. So it might link with dissociation between episodic and semantic autobiographical memory in ASD [58]. Furthermore, because weakened synchronous output entropy connectivity of a brain region might mean the disorder of some functions associated with this region but weakened synchronous input entropy connectivity of a brain region imply that some functions associated with the brain region will be enhanced due to decreased resource occupation [24] this may indicate that enhanced functions of PRC and weakened functions associated with RSC are consistent with abnormal episodic recollection and contextual retrieval, while familiarity and semantic memory are relatively normal in patients with ASD [58,59].
It is well known that the piriform cortex is the main primary olfactory cortex associated with odor perception and the integration of odor information. Previous studies displayed that odor perception experiment revealed decreased activations of piriform cortex in patients with ASD [60,61]. Therefore, in the present study, the enhanced asynchronous connectivity between the DMN and the piriform cortex might indicate de cits of olfactory perception in patients with ASD. Notably, previous researches generally con rm that the piriform cortex is a crucial region enabling trigger epilepsy [62,63] and because it has widely information transmission with limbic system and orbitofrontal cortex [62,64], these high connections can contribute to the proliferation of epilepsy [65].
Similarly, enhanced inhibition of the function of the piriform cortex from the DMN might result in the interference in mnemonic and emotional information ow related to olfaction between piriform cortex and other brain regions, further contributes to the changes of emotion and memory of ASD patients.

Limitations
(1) The standard MNI brain template described by Brodmann areas (BAs) was used in this study but this template cannot show abnormal changes of entropy connectivity related to subcortical structure. (2) We did not investigate the relationship between the changes of entropy connectivity in DMN, CEN and ADOS Score due to the lack of ADOS data of normal people in ABIDE I. (3) The recent study adopted data from various sites and preparations for the MRI Scan existed differences. (4) It is regrettable that our study did not discuss the speci c mechanism how the alteration of entropy connectivity between cognitive related network (DMN, CEN) and sensorimotor related cortex affect social cognitive features in detail, and we will explore them in the future.

Conclusions
In the present study, we investigated the changes of entropy connectivity in the DMN and CEN. Our ndings indicate that overconnecitivity and underconnecitivity in the CEN and DMN might be an important factor that contributes to executive and cognitive disorders of individuals with ASD. Availability of data and materials: The datasets used and analyzed during the current study are available from the corresponding author on reasonable request. marked sphere through red font in each sub gure indicates the seed brain region of entropy connectivity. The number next to the sphere is the index of BA (see Table 3 for details). The blue bars denote weakened interregional connections. Bar-widths represent T-values. The direction of the arrow indicates the direction of causal connectivity.

Figure 2
Changes of entropy connectivity in the DMN. A and D denotes synchronous entropy connectivity. B, C, and E denote asynchronous entropy connectivity. The marked sphere through red font in each sub gure indicates the seed brain region of entropy connectivity. The number next to the sphere is the index of BA (see Table 2 for details). The blue bars denote weakened interregional connections, and the red bars denote enhanced interregional connections. Bar-widths represent T-values. The direction of the arrow indicates the direction of causal connectivity.

Figure 3
Bar graphs of nodal degree changes. A denotes changes of synchronous input nodal degree of BA 7R in ASD. B denotes changes of asynchronous output nodal degree of BA 40L in ASD. Each signi cant difference (p<0.05, Bonferroni corrected) in any pair of two groups is indicated by the p values. Error bars: +/SDs (standard deviations).