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Edited by: Luca Mesin, Politecnico di Torino, Italy

Reviewed by: Makoto Wada, National Rehabilitation Center for Persons With Disabilities, Japan; Andrej Kral, Hannover Medical School, Germany

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Brain connectivity is often altered in autism spectrum disorder (ASD). However, there is little consensus on the nature of these alterations, with studies pointing to either increased or decreased connectivity strength across the broad autism spectrum. An important confound in the interpretation of these contradictory results is the lack of information about the directionality of the tested connections. Here, we aimed at disambiguating these confounds by measuring differences in directed connectivity using EEG resting-state recordings in individuals with low and high autistic traits. Brain connectivity was estimated using temporal Granger Causality applied to cortical signals reconstructed from EEG. Between-group differences were summarized using centrality indices taken from graph theory (

Autism is a complex neurodevelopmental condition characterized by several behavioral peculiarities, involving avoidance of social interactions, reduced communication, and restricted interests [see the

Indeed, many recent studies have reported that individuals within the autism spectrum disorder (ASD) exhibit altered brain connectivity compared to typically developing individuals. However, literature reports are often inconsistent [see review papers by

Some of these differences, of course, can derive from methodological issues. Connectivity is an elusive concept that can be dramatically affected by the measurement technique adopted (for instance, fMRI vs. EEG/MEG), by the particular task involved (vs. resting state analysis), and perhaps more importantly, by the specific measure employed to estimate the connection strength (e.g., functional, effective or anatomical connectivity, directed or undirected measures, bivariate or multivariate). Indeed, most connectivity measures in literature are not-directional and hence are inadequate to discover differences in lateralization or in top-down vs. bottom-up information processing (

In particular, it is well-known that cognitive functions are characterized by a complex balance between integration, involving the coordination among several brain areas, and segregation, involving specialized computations in local areas. According to the predictive coding theory (

Recent hypotheses (

The aforementioned alterations in predictive coding may be caused by altered brain connectivity, especially concerning top-down vs. bottom-up circuitry (

Finally, increasing evidence both at the genetic and behavioral levels demonstrates that autism does not represent a dichotomy condition (i.e., one ON/OFF in type) but is best described as a spectrum of manifestations ranging from clinical forms to trait-like expressions within the general population (

Following these ideas, in a recent paper (

The present study aims to further extend the previous work on a larger cohort allowing for an improved connectivity analysis by implementing measures taken from the graph theory. In particular, new aspects of the present study concern: (i) the use of a larger data set; (ii) a preliminary analysis at the lobe level; (iii) the use of more sophisticated indices taken from the graph theory, such as hubness and authority; (iv) the use of a more sophisticate statistical analysis (i.e., the use of sparse connectivity matrices) to better point out differences in connectivity between the two groups.

Particularly, graph theory represents a powerful tool able to summarize complex networks consisting of hundreds of edges, using a few parameters with a clear geometrical meaning. Recently, this theory has been applied with increasing success as an integrative approach, able to evaluate the complex networks that mediate brain cognitive processes (

Forty participants (23 female; age range 21–30, mean age = 24.1, SD = 2.4), with no neurocognitive or psychiatric disorders, took part in the study. All participants signed a written informed consent before taking part in the study, conducted according to the Declaration of Helsinki and approved by the Bioethics Committee of the University of Bologna. All participants completed the Autism-Spectrum Quotient test (AQ) (

Participants comfortably sat in a room with dimmed lights. Electroencephalographic activity (EEG) was recorded at rest for 2 min while participants kept their eyes closed. A set of 64 electrodes was mounted according to the international 10–10 system. EEG was measured with respect to a vertex reference (Cz), and all impedances were kept below 10 kΩ. EEG signals were acquired at a rate of 1000 Hz. EEG was processed offline with custom MATLAB scripts (version R2020b) and the EEGLAB toolbox (

Since we were interested in connectivity analysis, cortical source activity was reconstructed from pre-processed EEG signals. To this aim, intracortical current densities were estimated using the Matlab toolbox Brainstorm (

sLORETA (standardized Low-Resolution Electromagnetic Tomography) algorithm was used for cortical sources estimation. sLORETA is a functional imaging technique belonging to the family of linear inverse solutions for 3D EEG distributed source modeling (

Then, the cortical vertices were grouped into cortical regions according to the Desikan–Killiany atlas (

The approximate mapping of the “Desikan-Killiany” ROIs to the lobes.

ROI | Label | Lobe | ROI | Label | Lobe |

Banks of Sup. Temp. Sulcus | BK | Temporal | Parahippocampal | PH | Temporal |

Caudal anterior cingulate | cAC | Frontal | Pars opercularis | pOP | Frontal |

Caudal middle frontal | cMF | Frontal | Pars orbitalis | pOR | Frontal |

Cuneus | CU | Occipital | Pars triangularis | pTR | Frontal |

Entorhinal | EN | Temporal | Pericalcarine | PCL | Occipital |

Frontal pole | FP | Frontal | Postcentral | POC | Parietal |

Fusiform | FU | Temporal | Posterior cingulate | PCG | Parietal |

Inferior parietal | IP | Parietal | Precentral | PRC | Frontal |

Inferior temporal | IT | Temporal | Precuneus | PCU | Parietal |

Insula | IN | Parietal | Rostral anterior cingulate | rAC | Frontal |

Isthmus cingulate | IST | Parietal | Rostral middle frontal | rMF | Frontal |

Lateral occipital | LO | Occipital | Superior frontal | SF | Frontal |

Lateral orbitofrontal | lOF | Frontal | Superior parietal | SP | Parietal |

Lingual | LG | Occipital | Superior temporal | ST | Temporal |

Medial orbitofrontal | mOF | Frontal | Supramarginal | SMG | Parietal |

Middle temporal | MT | Temporal | Temporal pole | TP | Temporal |

Paracentral | PAC | Frontal | Transverse temporal | TT | Temporal |

The Desikan–Killiany atlas comprises 34 ROIs in each hemisphere. The mapping proposed by FreeSurfer (

Once the time waveform in each cortical ROI was estimated (as described above), for each participant

Let’s indicate with _{k,i}[_{k,j}[_{i} and _{j}) for participant _{i} to _{j} as the improvement in predictability of _{k,j}[_{k,j} and past values of _{k,i}, compared to a univariate AR representation, including only past values of _{k,j}. Mathematically, the following two equations hold for the univariate and bivariate AR model, respectively.

Index _{k,j} (at time sample _{k,i}. _{k,j}[_{k,j}[_{k,i} to _{k,j} is defined as the logarithm of the ratio between the variances of the two prediction errors, i.e.,

The measure in Eq. 3 is always positive: the larger its value, the larger the improvement in _{k,j}[_{k,i} together with the past of _{k,j}, and this is interpreted as a stronger causal influence from _{i} to _{j}. Similarly, Granger Causality from _{k,j} to _{k,i}, _{k,ROIj→ROIi}, is computed _{k,i}.

For each participant

As previously reported by other authors (

A graph is the mathematical abstraction of the relationships between some entities. The entities connected in a relationship are called “nodes” of the graph and are often represented graphically in the form of points. These nodes are connected by edges. While the simplest form of a graph is undirected (i.e., the edges do not have orientation), the graph we use to describe a brain network is a weighted directed graph (or digraph), i.e., it has oriented edges, each one with a weight representing the strength of the connection.

To obtain the graphs, for each participant the connectivity matrix was normalized so that its elements provided a sum of 100 (i.e., each connectivity value was divided by the total sum of connections and multiplied by 100). Furthermore, the normalized 68×68 matrices (which we will be calling “complete” matrices for clarity) were turned into 68×68 sparse matrices by removing (i.e., setting to zero) any connection that was not significantly different between the High and Low AQ score Groups. In particular, a two-tailed Monte-Carlo testing was applied (5,000 permutations) and, based on its results, not significant connections were defined as having an uncorrected p-value greater than 0.05.

Forty graphs (one per participant) were obtained both for the complete normalized and the sparse matrices. For each of these graphs, centrality indices were then computed. Although a preliminary investigation was performed on the complete matrices, our analysis is mainly focused on sparse matrices since by excluding “similar” connections we expect to better capture differences in the connectivity patterns and in graph indices between the two groups.

Graph theory defines a multitude of indices and coefficients that allow describing the topology of a network from different points of view. Centrality indices are part of these. They measure the importance of a particular node in the network. The four centrality indices considered in this study (

In the following, _{i,j} of the matrix will represent the weight of the edge connecting node

As a result of their direct dependence on the strength of input and output connections,

_{i}

_{i}

These indices were computed using the function provided by the Matlab’s libraries contained in the Category “Graph and network algorithms” (Matlab R2021a), particularly the command “digraph/centrality.” This function sets both α and β equal to 1 and calculates

Similar to

For each participant, starting from either the complete normalized or the sparse 68×68 matrix, the four centrality indices were computed at each of the 68 ROIs. Additionally, we computed the average complete and sparse connectivity matrix in the Low AQ score Group and in the High AQ score Group, and then their difference.

Initially, we performed an analysis at the level of macro regions (englobing several ROIs) rather than at single ROI level. To this aim, we considered 8 regions corresponding to brain lobes (frontal, parietal, temporal, and occipital lobes, both left and right). Specifically, for each participant, the 68×68 connectivity matrix was transformed into an 8×8 connectivity matrix; the elements of the 8×8 matrix were filled in with the sum of all the connections going from one lobe to another. The elements of the 8×8 matrices were subsequently tested for statistical significance across the two groups of participants, by applying a two-tailed

Then, a more detailed analysis was performed at the level of each ROI.

A first analysis was performed on the complete normalized connectivity matrix to understand the Granger flow in some key regions. Normalization of the connectivity matrix was necessary to avoid the presence of a few individuals with higher connectivity strongly affects the final results.

In particular, we computed the authority and the hubness of each ROI in each individual subject, and evaluated the correlation between these centrality indices and the AQ score. In this way, we identified the ROIs which exhibit a significant correlation between the centrality indices (in particular authority and hubness) and the AQ score. The

In the case of the sparse matrix, for each centrality index, we identified the ROIs that exhibited a significant statistical difference between the two groups. ROI’s significance was defined as a Bonferroni-corrected

Then, both in case of the complete and sparse matrix, once the significant ROIs were identified for each index, the connectivity differences between the Low and High AQ Score Group were plotted for the significant ROIs only, separately for each index (in particular in case of the

Using the complete connectivity matrix, the connection difference between the two groups does not reach a significativity level. Hence the following results can only be considered just as a preliminary exploratory analysis, and connection differences can be only regarded as indicative of a main flow pattern in the two groups. The results are illustrated in

Patterns of the main connection differences linking the four lobes (Frontal left and right, Fl and Fr, Temporal left and right, Tl and Tr, Parietal left and right, Pl and Pr, Occipital left and right, Ol and Or). The left panel

For what concerns authority, seven regions (EN r, IST l, IST r, LO r, PH r, ST r, and SMG l) exhibited a significant correlation between the AQ score and authority (see

Correlation between the authority and the AQ score [upper panel

For what concerns hubness, only two regions (PCL l and ST r) exhibited a significant correlation between the AQ score and hubness; in both cases, the correlation was positive, signifying that hubness increased with the autistic traits (see

The left panel in

Patterns of the main connection difference which exit from the ROIs with a significant correlation between authority and the AQ score [left panel

The figure shows that the majority of connections entering the authority regions were stronger in the Low AQ score Group (as expected from the previous analysis), and these connections were mainly top-down in type (especially entering into the LO r) and left to right (especially entering into the EN r and the ST r). Conversely, the majority of connections exiting from the two hubs, PCL l and ST r, were stronger in the High AQ score Group (as expected from the previous analysis), with a bottom-up connectivity, especially emerging from the PCL l, and right-to left from ST r. These results are coherent with those at lobe level displayed in

The previous analysis, accomplished on the overall normalized connectivity matrix, pointed out the presence of some authority nodes especially involved in top-down and left-to-right connectivity for the low-autistic trait population, and some hubness nodes characterized by bottom-up and right-to-left connectivity for the high-autistic trait population. The difficulty in the use of a complete connectivity matrix, however, derives from the presence of many connections with no clear statistical difference between the two groups. This is reflected in the poor statistical significance of the connection difference and, for what concerns the correlation, in a

For this reason, in order to better unmask differences, in the following a different analysis is presented, by focusing attention only on the connections which exhibited a significant statistical difference in the two groups. Hence, as described in the Section “Materials and methods,” we consider sparse connectivity matrices. This kind of analysis has the benefit of revealing a greater number of regions with statistical differences in connection flow.

Bar plots representing the centrality indices [in degree: panel

In order to further investigate the results arising from the above histograms,

Representation of the connections linking the eight lobes of the brain, Frontal (F), Parietal (P), Temporal (T), and Occipital (O), considering separately the right (r) and left (l) hemispheres. Only the connections that exhibited a statistically significant difference between the two groups (

Positions of the ROIs which exhibited a significant difference in the

In order to gain a deeper understanding of the previous patterns (limited to

Representation of the connection differences

Positions of the ROIs which exhibited a significant difference in the

Representation of the connection differences

The results illustrated in

The present paper analyzes the differences in brain connectivity between two groups of non-clinical individuals who differ in the degree of autistic traits (low vs. high), as classified based on the Autistic Quotient (

A critical point may be the selection of the threshold used to discriminate between the two classes. Despite the inherent arbitrariness of the choice, we used as a discriminative threshold the average AQ score obtained in a nonclinical population from the large-sample work of

In the following, we will first analyze methodological issues, then the neurophysiological significance of the obtained results will be explored. Finally, limitations of the present study will be analyzed.

In this work, we have chosen temporal Granger causality as a tool to reconstruct brain connectivity from EEG data. This measure mathematically represents the impact that knowledge of an upstream signal can have on the prediction of a downstream temporal signal. Thus, it represents a causal directed index of connectivity. Indeed, Granger Causality is widely employed in neuroscience today (

The analysis was initially performed (see Section “Analysis of the complete connectivity matrix”) on the complete normalized connectivity matrix, to show the main characteristics of the Granger flow in the two groups. Then, to improve the significance of the results, we considered only connections which exhibited a significant statistical difference between the two populations, thus working with a sparse matrix (i.e., all connections which did not show statistically significant differences between the two groups were set at zero). In other terms, the graphs in Section “Analysis on the sparse connectivity matrix” do not represent the overall connectivity patterns, but rather highlight the differences between the two populations.

The connectivity matrices so obtained were then used to compute some indices taken from Graph Theory.

Several studies using Graph Theory in ASD have appeared in recent years: most of them suggest that ASD individuals exhibit alterations in modularity (i.e., densely connected modules that are more segregated), in global efficiency (i.e., average path length required to go from one node to another), in betweenness (the capacity of a node to connect to other nodes) or in connection density (

Accordingly, an essential novelty of the present study concerns the use of some specific centrality indices (

The connectivity analysis was performed at two levels. First, we concentrated on the connectivity among macro-regions (lobes) of the cortex, the frontal, parietal, temporal, and occipital zones, to discover the main traits of connectivity differences.

This analysis confirms the result of a previous preliminary study (

The same patterns were confirmed by computing (from the sparse matrices) the connectivity among the macro-regions and plotting only those which exhibited a significant statistical difference. As shown in

Besides connectivity analysis at lobe level, we performed connectivity analysis at single ROI level. To this aim,

An important result of our study is that hubness and authority provided more significant differences compared with in degree and out degree, respectively; hence we suggest that these indices should be used to characterize the flow in a network of multiple ROIs. In particular, by comparing in degree vs. authority in

To understand why authority and hubness are more powerful compared with in degree and out degree, we remind that authority does not only take into account the number and strength of the connections entering a node but also weights these connections by the

Using these indices, we then mapped the stronger connections that exited from ROIs with higher

We remind, however, that these connectivity patterns reflect

In general, the present results support the findings obtained in our previous study on a smaller population (

These results support the idea that the brain network in individuals with higher autistic traits vs. individuals with lower autistic traits is not characterized by a general reduction in connectivity (as hypothesized in some theorizations) but rather that mixed patterns of under- and over-connectivity can be appreciated. Over-connectivity is evident in the fronto-posterior axis, involving bottom-up influences, whereas hypoconnectivity involves many tempo-parietal regions, especially in the left hemisphere.

Several hypotheses on brain connectivity in ASD have been formulated in past years, with apparently contradictory outcomes: while some authors hypothesized more robust connectivity in ASD, others reported reduced connectivity (see Section “Introduction”). These contradictions, however, can be reconciled by thinking that differences between control and individuals within the autistic spectrum can especially reflect a directionality in the connections rather than the number and total strength of edges in the overall network. Furthermore, a mixed pattern of increased connectivity among some regions and decreased among others probably characterizes the autistic brain. Directionality in the connectivity patterns, in turn, may reflect a hierarchical organization of the processing stream, with bottom-up connections (especially from the occipital towards the frontal lobes) involved in sensory processing and top-down connections reflecting context modulation, and prior knowledge, planning, and attention. This connectivity organization agrees with the so-called predictive coding theory, which assumes that environmental and internal signals are joined together to form a unified model of reality. In particular, the predictive coding theory of ASD (

A limitation of the present study may be the limited sample size (19 vs. 21 participants). Actually, this number is in line with (and in many cases higher than) the sample employed in published works that use similar experimental procedures and investigate similar phenomena [see

In this study, we did not include participants with a diagnosis of ASD, hence we cannot be confident that the present results would stand up also in a clinical population. However, the results obtained go exactly in the direction hypothesized by theoretical and empirical work on connectivity features in clinical ASD. Moreover, substantial behavioral (

An interesting point concerns the relationship between the Granger connectivity, evaluated in this study, and the structural connectivity (i.e., the physical traits that connect brain regions, generally estimated by diffusion-weighted imaging). Some studies (e.g.,

Finally, in the present study we have observed differences in bottom-up and top-down connectivity in the two groups. Works in the literature emphasize that these connections can be implicated in sensory processing, especially in multisensory conditions (

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

This study was conducted according to the guidelines of the Declaration of Helsinki and approved by the Bioethics Committee of the University of Bologna (protocol code 201723, approved on August 26, 2021). Informed consent was obtained from all participants involved in the study. The patients/participants provided their written informed consent to participate in this study.

MU, VR, and LT contributed to the conception and design of the study. LT and VR collected the data. MS, GR, and EM developed the software for the analysis, collected the results, and prepared figures. MU wrote the first draft of the manuscript. MS wrote sections of the manuscript. EM reviewed all the manuscript. All authors contributed to the results interpretation, manuscript editing, and read and approved the submitted version.

We thank Maria Eugenia Martelli for the data collection.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.