Altered default mode network causal connectivity patterns in autism spectrum disorder revealed by Liang information flow analysis

Abstract

Autism spectrum disorder (ASD) is a pervasive developmental disorder with severe cognitive impairment in social communication and interaction. Previous studies have reported that abnormal functional connectivity patterns within the default mode network (DMN) were associated with social dysfunction in ASD. However, how the altered causal connectivity pattern within the DMN affects the social functioning in ASD remains largely unclear. Here, we introduced the Liang information flow method, widely applied to climate science and quantum mechanics, to uncover the brain causal network patterns in ASD. Compared with the healthy controls (HC), we observed that the interactions among the dorsal medial prefrontal cortex (dMPFC), ventral medial prefrontal cortex (vMPFC), hippocampal formation, and temporo‐parietal junction showed more inter‐regional causal connectivity differences in ASD. For the topological property analysis, we also found the clustering coefficient of DMN and the In‐Out degree of anterior medial prefrontal cortex were significantly decreased in ASD. Furthermore, we found that the causal connectivity from dMPFC to vMPFC was correlated with the clinical symptoms of ASD. These altered causal connectivity patterns indicated that the DMN inter‐regions information processing was perturbed in ASD. In particular, we found that the dMPFC acts as a causal source in the DMN in HC, whereas it plays a causal target in ASD. Overall, our findings indicated that the Liang information flow method could serve as an important way to explore the DMN causal connectivity patterns, and it also can provide novel insights into the nueromechanisms underlying DMN dysfunction in ASD.

Liang information flow method was used to construct the causal connectivity network. The dorsal medial prefrontal cortex (MPFC) and ventral MPFC are important causal sources in the default mode network (DMN) in ASD. The altered causal connectivity in the DMN is correlated with the clinical symptoms of ASD. The causal connectivity difference of DMN shows a hierarchical regulation model.

1. INTRODUCTION

Autism spectrum disorder (ASD) is a pervasive neurodevelopmental disorder worldwide, with point prevalence exceeding ~1% (Rolls et al., 2020). Individuals with ASD mainly exhibit severe difficulties in social interaction and communication, as well as restricted and repetitive stereotyped behaviors (American Psychiatric Association, 2013). Yet, the pathophysiology of ASD remains unknown. Most previous studies have reported that the abnormal functional connectivity patterns within and between the default mode network (DMN) are highly related to the clinical symptoms of ASD (Assaf et al., 2010; Feng et al., 2022; Lombardo et al., 2019). However, the causal connectivity pattern within the DMN in ASD, which is believed to provide an important clue to understanding the underlying neuro‐mechanism of ASD, remains largely unclear.

The DMN is a large‐scale brain network that shows reduced activity when the participants perform a task and becomes more active when they are at rest (Bathelt & Geurts, 2021; Raichle et al., 2001). It consists of a set of brain regions, including posterior cingulate cortex (PCC), medial prefrontal cortex (MPFC), precuneus, and the medial, lateral, and inferior parietal regions (Andrews‐Hanna et al., 2010; Chen et al., 2021), responsible for self‐reference processing (Broyd et al., 2009; D'Argembeau et al., 2005; Gusnard et al., 2001), autobiographical memory (Nielsen et al., 2014), social cognition (Mars et al., 2012; Schilbach et al., 2008), emotional processing (Broyd et al., 2009), theory of mind (ToM) (Chen et al., 2021; Saxe & Kanwisher, 2003), and so on. Numerous neuroimaging studies have demonstrated abnormal DMN structure and function in ASD (Lynch et al., 2013; Monk et al., 2009; Padmanabhan et al., 2017). For instance, Lynch et al. (2013) found that the over‐connectivity of the PCC and precuneus within DMN is related to the social severity of ASD. Padmanabhan et al. (2017) showed that PCC, dorsal and ventral MPFC, and temporal–parietal junction (TPJ) play distinct interacting roles in monitoring the mental state of the self and the evaluation of others. Monk et al. (2009) found that the functional connectivity (FC) between the PCC and superior frontal gyrus was decreased, while the FC between the PCC and the right temporal lobe and right parahippocampal gyrus were increased in ASD by comparing with the control group. In our previous study, we also found that low intra‐DMN FC variability was associated with social deficits in ASD (Feng et al., 2022). However, these studies are mainly based on FC analysis, which cannot capture the direction of information interaction.

FC refers to the spatial–temporal correlation between brain regions without the flow of information (Biswal et al., 1995), while effective connectivity (EC) refers to the causal influence exerted by one brain region on another (Kamiński et al., 2001). Recently, many studies have demonstrated that causal connections in brain networks can better reflect the interactions between brain regions (Rolls et al., 2020; Talebi et al., 2019). Compared with FC analysis, EC or causal connectivity analysis can not only evaluate the interaction strength between brain regions, but also capture the flow of information. Several common methods are widely used in constructing causal connectivity networks, such as Granger causality analysis (GCA) and transfer entropy (TE). GCA uses a data‐driven method to infer the causal relationship between multivariate time series based on multivariate autoregressive (MVAR) (Venkatesh & Grover, 2015). Sridharan et al. (2008) found that the right anterior insula plays an important causal role in switching the DMN and executive‐control network (ECN) during cognitive information processing using the GCA. Wang et al. (2020) found that the MPFC showed significant causal influences on the PCC within the DMN in healthy subjects using the GCA. Transfer entropy (TE) is an extension of the concept of mutual information, which is based entropy to infer quantified information transfer (Schreiber, 2000). For example, Zhao et al. (2021) found the decreased causal connectivity from right ventral posterior cingulate cortex to right ventral anterior cingulate cortex and increased causal connectivity from right dorsal frontal cortex to left piriform cortex within the DMN in ASD using entropy connectivity. Dejman et al. (2017) also found a significant difference in average degree between HC and ASD groups during a passive face processing task by integrating transfer entropy and graph theory.

Although traditional causal analysis methods provide new perspectives for causal network construction, they have shortcomings in their application. For example, GCA makes assumptions in the calculation process (Harmah et al., 2020), and it requires stationarity of the time series analyzed in the GCA calculation. Furthermore, GCA measures causal relation in a statistical sense, and a larger GCA value does not necessarily mean a higher true causal relation (Harmah et al., 2020). TE requires long time series, and the computation is complex (Hlaváčková‐Schindler et al., 2007). Recently, Liang proposed a novel method to calculate the causal relation, namely Liang information flow (Liang, 2008; Liang, 2014; Liang, 2016b; Liang & Kleeman, 2005). Liang (2014) defined the calculation method of Liang information flow through a rigorously derived formalism and gave a specific calculation expression. The Liang information flow method have been shown to be effective in capturing the causal relation between time series (Liang, 2021; Zhang et al., 2021), and has been widely applied to a variety of fields in different disciplines, such as quantum mechanics (Yi & Bose, 2022), climate science (Cheng & Redfern, 2022; Docquier et al., 2022; Liang et al., 2021), brain electroencephalography (EEG) network (Hristopulos et al., 2019). Its advantages include its very effective performance in computing, as well as its accuracy, and, most of all, its universal applicability because of its firm physical ground, and hence many intrinsic properties that make accurate causal discovery possible. Thus, the Liang information flow method can provide a new effective way to capture the causal connectivity within the DMN.

In this study, we combined the Liang causal information flow method and graph theory to investigate the resting‐state DMN causal connectivity patterns in ASD and HC. We first construct the DMN causal connectivity networks for the two groups using the Liang information flow. We then compared the differences in causal network connectivity patterns between the two groups. Finally, we also correlated the causal connectivity patterns to the ASD symptom severity scores to better understand the underlying neural mechanism of ASD. In addition, using the causal connectivity patterns as features, we construct a classification model for identifying ASD. Our results provide a novel perspective for understanding the DMN causal connectivity pattern in ASD.

2. MATERIALS AND METHOD

2.1. Participants

The study includes 79 patients with ASD and 105 healthy controls (HCs). All subjects are recruited from the public site at NYU Langone Medical Center in ABIDE (http://fcon_1000.projects.nitrc.org/indi/abide/) (Di Martino et al., 2014). The criteria for the inclusion of the subjects were as follows: (1) age between 6 and 18 years old; (2) head motion not exceeding 2 mm translation or 2° rotation in any direction; (3) subjects with mean framewise displacement (FD) (Power et al., 2012) below mean + 2 × SD; (4) subjects with complete scanned images. Finally, 48 ASD patients (42 boys, six girls; age: 6–18 years) and 48 HC subjects (39 boys, nine girls; age: 6–18 years) were selected for our study. The Autism Diagnostic Observation Schedule (ADOS) (Lord et al., 2000) and Autism Diagnostic Interview‐Revised (ADI‐R) (Lord et al., 1994) were used as clinical symptoms assessment for further analysis. The detailed demographic information for the included participants is listed in Table 1.

TABLE 1.

The demographics of the participants

	ASD (n = 48)	HC (n = 48)	p‐value
Age (year)	11.73 ± 2.56 (6–18)	11.71 ± 2.95 (6–18)	.9734 a
Gender	42/6 (M/F)	39/9 (M/F)	.3991 b
Mean FD	0.16 ± 0.07	0.12 ± 0.04	.0028 a
FIQ	106.83 ± 17.79	113.81 ± 13.32	.0323 a
PIQ	109.48 ± 19.29	110.38 ± 14.59	.7980 a
VIQ	103.40 ± 15.50	113.94 ± 12.13	.0004 a
ADI‐R
Social score	20.09 ± 5.11 (n = 45)	—	—
Communication score	15.76 ± 4.01 (n = 46)	—	—
RRB score	6.02 ± 2.65 (n = 46)	—	—
ADOS
Social score	8.06 ± 9.96	—	—
Communication score	3.46 ± 1.65	—	—
Total score	11.52 ± 4.24	—	—
RRB score	2.73 ± 1.54	—	—

Note: Values shown are: mean ± SD.

Abbreviations: ADI‐R, Autism Diagnostic Interview‐Revised; ADOS, Autism Diagnostic Observation Schedule; FD, framewise displacement; FIQ, Full‐Scale Intelligence Quotient; PIQ, Performance Intelligence Quotient; RRB score, Restricted, Repetitive and Stereotyped Behaviors; VIQ, Verbal Intelligence Quotient.

^a p value was obtained by two‐sample t‐test, two‐tailed.

^b p value was obtained by chi‐square test, two‐tailed.

2.2. Resting‐state fMRI data acquisition

All original resting‐state images of participants were scanned by 3 Tesla Siemens Allegra scanner using an echo‐planar imaging (EPI) sequence with whole‐brain coverage. During the resting‐state fMRI scan, most participants were instructed to open their eyes and relax while projecting a white crosshair on a screen against a black background. The acquisition parameters of the resting state fMRI images are: repetition time (TR) = 2000 ms, echo time (TE) = 15 ms, slice number = 33, slice thickness = 4.0 mm, flip angle (FA) = 90°, field of view = 240 mm, voxel size = 3.0 × 3.0 × 4.0 mm³. For each subject, a 6‐min scanning was performed, resulting in 180 volumes.

2.3. fMRI data preprocessing

All original resting‐state fMRI data were preprocessed using the Data Procession Assistant for Resting‐State fMRI toolbox (Yan & Zang, 2010) (DPARSF, http://rfmri.org/DPARSF), which is based on the Statistical Parametric Mapping 12 toolbox (SPM12, https://www.fil.ion.ucl.ac.uk/spm/) on the MATLAB 2018a platform. The first 10 volumes were removed to ensure the magnetic field was stable, leaving 170 volumes. All the blood‐oxygen‐level‐dependent (BOLD) time series were corrected for temporal differences in slice timing. Then, head movement correction was performed. All images were normalized to the standard Montreal Neurological Institute (MNI) space, and the voxel size after normalization was 3 × 3 × 3 mm³. All normalized images were smoothed with a Gaussian kernel (full width at half maximum = 6 mm) and then linearly detrended. The signals from the white matter, cerebrospinal fluid, 24 rigid body motion parameters, and head motion scrubbing regressors were regressed from the data. The head motion scrubbing regressors were applied with an FD threshold above 0.5 as well as two back and one forward neighbor. Global signal regression (GSR) is still controversial in resting‐state research. Several studies show that using GSR may produce anti‐correlation (Murphy et al., 2009; Murphy & Fox, 2017). We thus did not perform GSR in the current study. Finally, bandpass filtering (0.01–0.08 Hz) was performed to reduce the influence of high‐frequency noise (He et al., 2020).

2.4. Analysis procedure

Figure 1 shows the data analysis process. We first extracted the time series of the regions of interest (ROIs) within the DMN. Then, using the Liang information flow method, we constructed the DMN causal connectivity networks for ASDs and HCs. To better understand the causal connectivity pattern of DMN, we further calculated the network topology properties for the two groups. After that, we compared the causal connectivity differences between the two groups and revealed the relationships between the connectivity with significant differences and clinical symptoms of ASD. Finally, the obtained causal connectivity and network properties were used to construct a classification model to classify the two groups. The details of these steps are described in the following sections.

FIGURE 1.

The analysis procedure.

2.5. Regions of interest

Inspired by previous studies (Andrews‐Hanna et al., 2010; Bathelt & Geurts, 2021; Du et al., 2016), 11 ROIs were selected, which are crucial regions of the DMN. The DMN can be mainly divided into three parts, namely, the midline core including the PCC and aMPFC, the dMPFC subsystem, including the dMPFC, TPJ, LTC, and TempP, and the MTL subsystem, including the vMPFC, pIPL, Rsp, PHC, and HF. According to previous studies (Andrews‐Hanna et al., 2010; Du et al., 2016), only the left and middle areas were used in our study to prevent a strong correlation between mirror structures. The ROIs were defined as a sphere with a radius of 6 mm centered on the corresponding MNI coordinate. The MNI coordinates for these 11 ROIs are listed in Table 2. After that, we extracted the averaged time series signals for each ROI across subjects. These time series were used for calculating the causal connectivity network.

TABLE 2.

Montreal Neurological Institute (MNI) coordinates of 11 ROIs within DMN

Brain regions	MNI coordinates
	x	y	z
Posterior cingulate cortex (PCC)	−8	−56	26
Anterior medial prefrontal cortex (aMPFC)	−6	52	−2
Dorsal medial prefrontal cortex (dMPFC)	0	52	26
Temporo‐parietal junction (TPJ)	−54	−54	28
Lateral temporal cortex (LTC)	−60	−24	−18
Temporal pole (TempP)	−50	14	−40
Ventral medial prefrontal cortex (vMPFC)	0	26	−18
Posterior inferior parietal lobule (pIPL)	−44	−74	32
Retrosplenial cortex (Rsp)	−14	−52	8
Parahippocampal cortex (PHC)	−28	−40	−12
Hippocampal formation (HF)	−22	−20	−26

2.6. Construction of the causal network of the DMN

This study used the unnormalized multivariate Liang information flow analysis proposed by Liang et al. (2021) to construct the causal connectivity network of the DMN. For each subject, we obtained an 11 × 11 directed causal connectivity matrix. For these directed causal connectivity matrices, we first used the built‐in test method in the Liang information flow to test the statistical significance of the causal matrix, and the details are listed in Section Liang information flow analysis. We set the confidence level at 90% and considered the causal connectivity that failed the significance test to be spurious causal relation, which we hereafter set to zero. After that, we performed the z‐score on the causal connectivity matrices to remove the physical units (Abdi, 2007). Subsequently, we regressed the mean FD (Chen et al., 2016) across subjects to further reduce the impact of head motion. The new sparse causality connectivity matrices were used for the following analysis. Finally, we calculated the group‐averaged causal connectivity matrix for the ASDs and HCs. We also calculated the distance of the mean causal matrix between ASD and HC using Pearson's correlation (Benesty et al., 2009) to assess the similarity of the causal network architecture. The Liang information flow method will be further introduced below.

2.7. Liang information flow analysis

Information flow is a real concept in general physics and system dynamics, it is only vaguely studied in a loose sense without a formal expression (Liang & Kleeman, 2005). Motivated by a finding by Liang and Kleeman (2005), Liang (2016b) was able to put information flow on a rigorous footing and establish the whole formalism from the first principles. A particular feature is the natural embedding of causality within formalism, thanks to a proven theorem on causality. This is in contrast to the previous studies where “information flow” and causality are irrelated because of the inappropriate ways to define information flow (Lizier & Prokopenko, 2010).

Recently, Liang conducted a maximum likelihood estimation (MLE) for the result in Liang (2016b), providing a very concise formula for quantitative causal discovery, which can effectively capture the causal relation among time series (Liang, 2014, 2021). This explicitly obtained expression is very concise, involving only sample covariance (Liang, 2014, 2021). In the following, we only list the final result; for a brief description of the theory, please refer to Liang et al. (2021), section 2.

For a vector of state variables $\mathbf{X}=\left(X_1,\dots X_d\right)$, consider a d‐dimensional continuous‐time stochastic system

$$d\mathbf{X}=\mathbf{F}\left(\mathbf{X},t\right)\mathit{dt}+\mathbf{B}\left(\mathbf{X},t\right)d\mathbf{W},$$ (1)

where $\mathbf{F}=\left(F_1,F_2,\dots F_d\right)$ may be arbitrary nonlinear differentiable functions of $\mathbf{X}$ and $t$, $\mathbf{W}$ is a vector of standard Wiener processes, and $\mathbf{B}={\left(b_{\mathit{ij}}\right)}_{d\times m}$ is the matrix of perturbation amplitudes which may also be any differentiable functions of $\mathbf{X}$ and $t$. Liang (2016b) established that the rate of information flowing from $X_j$ to $X_i$ is (in nats per unit time) is:

$$T_{j\to i}=-E\left(\frac{1}{{\rho }_i}{\int }_{{\mathrm{ℝ}}^{d-2}}\frac{\partial F_i{\rho }_{\bcancel{j}}}{\partial x_i}{\mathit{dx}}_{\bcancel{\mathit{ij}}}\right)+\frac{1}{2}E\left(\frac{1}{{\rho }_i}{\int }_{{\mathrm{ℝ}}^{d-2}}\frac{{\partial }^2\left(g_{\mathit{ii}}{\rho }_{\bcancel{j}}\right)}{\partial x_i^2}{\mathit{dx}}_{\bcancel{\mathit{ij}}}\right),$$ (2)

where ${\mathit{dx}}_{\bcancel{\mathit{ij}}}$ signifies ${\mathit{dx}}_1\dots {\mathit{dx}}_{i-1}{\mathit{dx}}_{i+1}\dots {\mathit{dx}}_{j-1}{\mathit{dx}}_{j+1}\dots {\mathit{dx}}_d$, E stands for mathematical expectation, $g_{\mathit{ii}}={\sum }_{k=1}^2{b}_{\mathit{ik}}{b}_{\mathit{ik}},$ ${\rho }_i={\rho }_i\left(x_i\right)$ is the marginal pdf of $X_i$, and ${\rho }_{\bcancel{j}}={\int }_{\mathrm{ℝ}}\rho \left(x\right){\mathit{dx}}_{\bcancel{j}}$ Theoretically, if $T_{j\to i}$ is not zero, then $X_j$ is cause to $X_i$, and its magnitude measures the size of the causality; otherwise, it is not causal. Of course, in real applications, a significance test must be performed.

The above formula is exact. It is, however, impossible to calculate the expectations if the joint probability distribution is not known. Liang et al. (2021) later on made a maximum likelihood estimation and found that the rate of Liang information flowing from X ₂ to X ₁ can be estimated as follows: (in nats per unit time) is

$${\widehat{T}}_{2\to 1}=\frac{1}{\det C}\cdot \sum _{j=1}^d{\Delta }_{2j}{C}_{j,d1}\cdot \frac{C_{12}}{C_{11}},$$ (3)

where C _ij denotes the sample covariance between X _i and X _j , C _j,d1 is the sample covariance between X _j and the derived series ${\stackrel{.}{X}}_1$, ${\stackrel{.}{X}}_1=\left\{{\stackrel{.}{X}}_{i,n}\right\}$ is the Euler forward differencing approximation of $\frac{{\mathit{dX}}_i}{\mathit{dt}}:{\stackrel{.}{X}}_{i,n}=\frac{X_{i,n+k}-X_{i,n}}{\mathit{k\Delta t}},$ $\mathit{k\Delta t}$ is the time interval between $X_{i,n+k}$ and $X_{i,n}$. To ensure accuracy, usually $k=1$. ${\mathrm{\Delta }}_{\mathit{ij}}$ represents the cofactors of the matrix $\mathbf{C}=\left(C_{\mathit{ij}}\right)$.

The T value obtained must be tested for significance. We can use the Fisher information matrix to simplify the problem. According to the property of maximum likelihood estimation, ${\widehat{T}}_{2\to 1}$ was approximately normally distributed near its true value with a variance ${\left(\frac{C_{12}}{C_{11}}\right)}^2{\widehat{\sigma }}_{a_{12}}^2$. Here ${\widehat{\sigma }}_{a_{12}}^2$ is the variance of ${\widehat{a}}_{12}$, which is estimated as follows. Denote $\theta =\left(f_1,a_{11},a_{12},\dots a_{1d},b_1\right)$, the Fisher information matrix can be calculated $\mathbf{I}=\left(I_{\mathit{ij}}\right)$,

$$I_{\mathit{ij}}=-\frac{1}{N}\sum _{n=1}^N\frac{{\partial }^2\log \rho \left(\left.{\mathbf{X}}_{n+1}\right|{\mathbf{X}}_n;\widehat{\theta }\right)}{\partial {\theta }_i\partial {\theta }_j}.$$ (4)

The inverse ${\left(N\mathbf{I}\right)}^{-1}$ is the covariance matrix of $\widehat{\theta }$, from which can be found ${\widehat{a}}_{12}$. Given a significance level the confidence interval can be easily found.

2.8. Granger causality analysis

In 1969, Granger introduced the concept of GCA, that is, if X ₂ is known to help predict the future of X ₁, then X ₂ “causes” X ₁ (Granger, 1969). In this article, we used the conditional Granger causality connectivity to calculate the causal connectivity through the “Granger causal connectivity analysis” (GCCA) toolbox (Seth, 2010).

To illustrate conditional Granger causality analysis, consider time series X _t , Y _t , and Z _t . First, let the joint autoregressive representation of X _t and Z _t be (Ding et al., 2006)

$$\begin{array}{l}{X}_t=\sum _{j=1}^{\infty }{a}_{1j}{X}_{t-j}+\sum _{j=1}^{\infty }{b}_{1j}{Z}_{t-j}+{\epsilon }_{1t},\\ Z_t=\sum _{j=1}^{\infty }{c}_{1j}{X}_{t-j}+\sum _{j=1}^{\infty }{d}_{1j}{Z}_{t-j}+{\gamma }_{1t},\end{array}$$ (5)

where the covariance matrix of the noise terms is as follows:

$${\sum }_1=\left(\begin{array}{cc}{\mathrm{\Lambda }}_1& {\mathrm{{\rm T}}}_1\\ {\mathrm{{\rm T}}}_1& {\mathrm{\Gamma }}_1\end{array}\right).$$ (6)

Then consider the joint autoregressive representation of all three processes X _t , Y _t , and Z _t

$$\begin{array}{l}{X}_t=\sum _{j=1}^{\infty }{a}_{2j}{X}_{t-j}+\sum _{j=1}^{\infty }{b}_{2j}{Y}_{t-j}+\sum _{j=1}^{\infty }{c}_{2j}{Z}_{t-j}+{\epsilon }_{2t},\\ Y_t=\sum _{j=1}^{\infty }{d}_{2j}{X}_{t-j}+\sum _{j=1}^{\infty }{e}_{2j}{Y}_{t-j}+\sum _{j=1}^{\infty }{f}_{2j}{Z}_{t-j}+{\eta }_{2t},\\ Z_t=\sum _{j=1}^{\infty }{u}_{2j}{X}_{t-j}+\sum _{j=1}^{\infty }{v}_{2j}{Y}_{t-j}+\sum _{j=1}^{\infty }{w}_{2j}{Z}_{t-j}+{\gamma }_{2t},\end{array}$$ (7)

where the covariance matrix of the noise terms is

$${\sum }_4=\left(\begin{array}{ccc}{\mathrm{\Gamma }}_{\mathit{XX}}& {\mathrm{\Gamma }}_{\mathit{XY}}& {\mathrm{\Gamma }}_{\mathit{XZ}}\\ {\mathrm{\Gamma }}_{\mathit{YX}}& {\mathrm{\Gamma }}_{\mathit{YY}}& {\mathrm{\Gamma }}_{\mathit{YZ}}\\ {\mathrm{\Gamma }}_{\mathit{ZX}}& {\mathrm{\Gamma }}_{\mathit{ZY}}& {\mathrm{\Gamma }}_{\mathit{ZZ}}\end{array}\right).$$ (8)

So the Granger causality from Y _t to X _t conditional on Z _t can be defined as

$$F_{Y\to X\left|Z\right.}=\ln \frac{{\mathrm{\Lambda }}_1}{{\mathrm{\Gamma }}_{\mathit{XX}}}$$ (9)

Therefore, $F_{Y\to X\left|Z\right.}=0$ meaning that no further improvement in the prediction of X _t can be expected by including past measurements of Y _t (Ding et al., 2006). And when there is still a direct component from Y _t to X _t , the inclusion of past measurements of Y _t in addition to that of X _t and Z _t results in better predictions of X _t , which may lead to ${\mathrm{\Gamma }}_{\mathit{XX}}<{\mathrm{\Lambda }}_1$, and $F_{Y\to X\left|Z\right.}>0$ (Ding et al., 2006).

2.9. Network topology properties

To further explore the DMN causal network patterns, we calculated five common directed network topology properties, including characteristic path length (CPL), clustering coefficient (CC), global efficiency (GE), local efficiency (LE), and In–Out degree (D _in–out). The Brain Connectivity Toolbox (Bullmore & Sporns, 2009; Rubinov & Sporns, 2010) (https://www.nitrc.org/projects/bct/) was used to calculate the network properties for each subject. During the calculation, the causality matrices were first changed into their absolute values. Then, a weighted and directed matrix (causal matrix) was applied to calculate the topological network properties for each subject. These topological network properties can be defined as,

$${\mathrm{CPL}}^{\to }=\frac{1}{n}\sum _{i\in N}\frac{\sum _{j\in N,j\ne i}{d}_{\mathit{ij}}^{\to }}{n-1}$$ (10)

$${\mathrm{CC}}^{\to }=\frac{1}{n}\sum _{i\in N}\frac{\frac{1}{2}{\sum }_{j,h\in N}\left(a_{\mathit{ij}}+a_{\mathit{ji}}\right)\left(a_{\mathit{ih}}+a_{\mathit{hi}}\right)\left(a_{\mathit{jh}}+a_{\mathit{jh}}\right)}{\left(k_i^{\mathit{\text{out}}}+k_i^{\mathit{\text{in}}}\right)\left(k_i^{\mathit{\text{out}}}+k_i^{\mathit{\text{in}}}-1\right)-2\sum _{j\in N}{a}_{\mathit{ij}}{a}_{\mathit{ji}}}$$ (11)

$${\mathrm{GE}}^{\to }=\frac{1}{n}\sum _{i\in N}\frac{\sum _{j\in N,j\ne i}{\left(d_{\mathit{ij}}^{\to }\right)}^{-1}}{n-1}$$ (12)

$${\mathrm{LE}}^{\to }=\frac{1}{2n}\sum _{i\in N}\frac{\sum _{j,h\in N,j\ne i}\left(a_{\mathit{ij}}+a_{\mathit{ji}}\right)\left(a_{\mathit{ih}}+a_{\mathit{hi}}\right)\left({\left[d_{\mathit{jh}}^{\to }\left(N_i\right)\right]}^{-1}+{\left[d_{\mathit{hj}}^{\to }\left(N_i\right)\right]}^{-1}\right)}{\left(k_i^{\mathit{\text{out}}}+k_i^{\mathit{\text{in}}}\right)\left(k_i^{\mathit{\text{out}}}+k_i^{\mathit{\text{in}}}-1\right)-2\sum _{j\in N}{a}_{\mathit{ij}}{a}_{\mathit{ji}}}$$ (13)

$$D_{\text{in}‐\text{out}}=k_i^{\text{in}}-k_i^{\text{out}}$$ (14)

where $a_{\mathit{ij}}$ is the connection strength from nodes i to j, $d_{\mathit{ij}}^{\to }$ is the shortest directed path length from nodes i to j, $d_{\mathit{ij}}^{\to }={\sum }_{a_{\mathit{ij}}\in g_{i\to j}}{a}_{\mathit{ij}}$， where $g_{i\to j}$ is the directed shortest path from node i to j. $k_i^{\text{out}}$ is the out degree of node i, $k_i^{\text{out}}={\sum }_{j\in N}{a}_{\mathit{ij}}$, $k_i^{\mathit{\text{in}}}$ is the in‐degree of node i, $k_i^{\text{in}}={\sum }_{j\in N}{a}_{\mathit{ji}}$, n is the total node number of the current network. N is the number of the set of network nodes.

In addition, the In–Out degrees of the nodes were calculated to evaluate the causal source and target (Gao et al., 2011; Jiao et al., 2011). Nodes with positive In–Out degrees are considered causal targets, and the nodes with negative In–Out degrees are considered causal sources.

2.10. Identification of the ASD patients based on DMN causal connectivity patterns

Based on the casual connectivity and network properties, we attempted to identify ASD patients from the HCs. We first extracted causal connectivity and network topology properties indexes as features for each subject. Then, a 121‐dimensional causal connectivity and a 15‐dimensional network property features were obtained and used for classification. These features are normalized to −1 and 1. Given that several features are uninformative or redundant for classification, reducing the number of features can improve performance (Dosenbach et al., 2010). F score method (Liu et al., 2015; Zhang et al., 2019) was used to select features to improve the classification performance. In this study, support vector machine (SVM) classifier with linear kernel was used (Chang & Lin, 2011). To evaluate the performance of classifier, a leave‐one‐out cross‐validation (LOOCV) strategy was performed. In the linear kernel SVM, only parameter C (penalty coefficient) takes the default value (i.e., C = 1).

2.11. Statistical analysis

We used two‐sample t‐tests (two‐tailed) to compare the causal connectivity and network properties differences in DMN for two groups. For the causal connectivity difference, the significant difference level was set at p < .05 (pFDR corrected [Storey, 2002]). For the network property difference, the significant difference level was set at p < .05. Pearson's correlation coefficient (Benesty et al., 2009) was used to assess the relationships between causality relations and the clinical symptom of ASD (i.e., ADOS and ADI scores), where the correlation was considered significant when p < .05.

3. RESULTS

3.1. Between‐group DMN causal connectivity difference

GCA and Liang information flow are both popular causal analysis methods. Currently, the GCA is widely used in brain science, while Liang information flow method is commonly used in atmospheric science. In our study, we compared the causal connectivity patterns of DMN for ASD patients and HC using the Liang information flow (Figure 2a–d) and GCA (Figure 2e–h), respectively. For the GCA, we used the Akaike Information Criterion (AIC) and the Bayesian information criterion (BIC) to identify the AR order, the AR order was 10. Figure 2a,b,e,f show the group‐averaged causal connectivity of DMN using the Liang information flow and GCA in ASD and HC, respectively. We found the causal network architecture of the DMN is different between the two groups, where the correlation is 0.4239 and 0.3565 for Liang information flow and GCA.

FIGURE 2.

The mean causal connectivity patterns of DMN for ASD and HC groups were constructed by Liang information flow (a and b) and GCA (e and f), respectively. (c) The causal connectivity differences between the HC group and the ASD group (pFDR p < .05) were obtained using Liang information flow. (d) Causal connectivity differences t‐values map. (g) The causal connectivity differences between the HC group and the ASD group (pFDR p < .05) were obtained using GCA. (h) Causal connectivity differences t‐values map. The blue edges represent decreased causal connectivity. The red edges represent increased causal connectivity. The area marked with a star indicates a significant causal connectivity difference.

For the Liang information flow, to compare the causal connectivity difference of the DMN between ASD and HC, we performed a two‐sample t‐test (pFDR, p < .05) on individual DMN causal connectivity matrices. Figure 2c,d display the causal connectivity differences of DMN between the two groups. Compared with the HC group, we found the causal connections in PCC → TempP, PCC → HF, aMPFC → dMPFC, dMPFC → vMPFC, dMPFC → PHC, and dMPFC → HF were significantly decreased in the ASD group. In contrast, the causal connections in the TPJ → TempP, TPJ → vMPFC, TPJ → HF, LTC → Rsp, TempP → vMPFC, and PHC → PCC were significantly increased in ASD. We also found that the PCC, dMPFC, TPJ, vMPFC, TempP, and HF produce more causal connectivity differences.

For the GCA, we also performed a two‐sample t‐test (pFDR, p < 0.05) on individual DMN causal connectivity matrices for the two groups. Figure 2g,h show the causal connectivity difference of DMN between ASD and HC. Compared with the HC group, we found the causal connections in dMPFC → PCC, TempP → PCC, TPJ → LTC, LTC → TPJ, pIPL → LTC, vMPFC → HF, pIPL → TempP, and pIPL → Rsp were significantly decreased in ASD, while the causal connections in aMPFC → Rsp, dMPFC → TPJ, dMPFC → Rsp, TPJ → TempP, PHC → Rsp, and HF → PCC were significantly increased in ASD. In addition, we found the dMPFC, PCC, TPJ, Rsp, and pIPL produce more causal connectivity differences.

The DMN causal connectivity differences based on both methods involve the dMPFC and MTL subsystems. The main difference between the two approaches is that the causal connectivity across vMPFC obtained by Liang information flow shows more difference, while GCA has no significant causal difference. In addition, compared with the GCA, we found that the causal connectivity difference shows a hierarchical regulation model using Liang information flow, which could provide a novel perspective for understanding the DMN causal connectivity pattern in ASD.

3.2. Between‐group DMN network topological properties difference

To better investigate the causal connectivity network patterns, we calculated the network properties for each subject and compared network properties differences between ASD and HC. Figure 3a shows the between‐group DMN network properties difference. We found significant differences in the clustering coefficient, while there were no significant differences in the characteristic path length, global efficiency, and local efficiency. We also found that the node aMPFC has significant differences (p = .0159) in In‐Out degree between ASD and HC.

FIGURE 3.

(a) The differences in four network properties between the two groups. The star represents the significant differences, where p < .05. (b) The mean In–Out degrees of the nodes in the ASD and HC group. The negative values represent the node as the causal source, and positive values represent the node as the causal target.

The mean In–Out degree of the nodes in the DMN is listed in Figure 3b. For the two groups, we consistently found that the In–Out degree of the TPJ, TempP, vMPFC, Rsp, and HF was >0 and they act as a causal target, while the In–Out degree of the PCC, aMPFC, pIPL, and PHC were <0 and they act as a causal source. In particular, we found that the causal directions of the dMPFC and LTC were opposite between ASD and HC.

3.3. Relationships between DMN causal network patterns and ASD symptoms

Figure 4 shows the correlations between the DMN causal network patterns and the clinical symptoms of ASD. For the causal connectivity, we found that the causal connectivity from dMPFC to vMPFC within DMN was negatively correlated with the ADOS social score (r = −.375, p = .0087), ADOS communication score (r = −.404, p = .0044), and ADOS total score (r = −.418, p = .0031). The causal connectivity from dMPFC to PHC was positively correlated with the ADOS communication score (r = .371, p = .0095), the causal connectivity from dMPFC to HF was negatively correlated with the ADOS communication score (r = −.287, p = .0480). For the network properties, we found that the clustering coefficient of the DMN was negatively correlated with the ADI‐R communication scores (r = −.413, p = .0043).

FIGURE 4.

The correlation between the difference in causal relations and the behavioral scales of the ASD group.

3.4. Classification of the two groups

We used the causal connectivity and network properties of the DMN as features to construct a classification model. Table 3 shows the classification results of SVM using the F‐score method in the different feature selection conditions. The highest classification accuracy (78.12%) was obtained based on the combination of causal connectivity and network properties.

TABLE 3.

Classification results of the SVM using F score based on the DMN causal patterns

	Causal relations differences	Network properties	Network properties and causal relations differences
Accuracy	77.08%	68.75%	78.12%
Sensitivity	73.91%	69.57%	80.43%
Specificity	84.00%	68.00%	80.00%

4. DISCUSSION

To the best of our knowledge, this is the first study to apply the Liang causal information flow method to fMRI data to explore the resting DMN inter‐regional causal connectivity patterns in ASD. Based on the seed method, we constructed the DMN causal connectivity network and calculated the network topology properties. Compared with HC, we observed that the interactions among the PCC, dMPFC, TPJ, TempP, vMPFC, and HF showed more inter‐regional causal connectivity differences in ASD. The network clustering coefficient and the In–Out degrees of aMPFC were significantly decreased in ASD. Moreover, these DMN causal connectivity network patterns, especially the causal connections from dMPFC to vMPFC, PHC, and HF, were correlated with the clinical symptoms (i.e., ADOS social, ADOS total, and ADOS communication) of ASD and can be important features to identify ASD. Our findings highlight the utility of the Liang information flow method in brain causal network analysis and verify that altered inter‐DMN causal connectivity patterns are associated with social deficits in ASD.

4.1. Methodological considerations

In terms of methodology, GCA and Liang information flow are both commonly used time series causality analysis tools (McCracken, 2016). GCA is a method that relies on models of the time series data for causal inference, that is, multivariate autoregressive (MVAR). However, several previous studies have indicated that the MVAR‐based causal model only considered the lag relation between time series, whereas the instantaneous effect is ignored (Faes et al., 2013; Salehi et al., 2022). In addition, Granger himself also pointed out that GCA may not necessarily a true causal relation (Granger, 1963). Compared with GCA, since the Liang information flow method is rigorously established from first principles, it does not require assumptions and may be able to capture the real causality of brain networks. For this reason, it has been widely used to quantify causal relations in classical systems (Liang, 2016b) and network theory (Li & Liu, 2019). It has been widely used in finance (Liang, 2016a), climate (Liang et al., 2021), quantum mechanics (Yi & Bose, 2022), and neuroscience (Hristopulos et al., 2019). Particularly, Hristopulos et al. (2019) applied this causal connectivity approach to the EEG time series to study the information flow disruption in a concussed brain, showing that it could effectively construct causal networks for different cognitive activities. Following this, we utilized the Liang information flow method to construct the causal connectivity network from resting‐state fMRI, which entailed some interesting results. Furthermore, we also compared the results of the two methods (see Appendix S1). Below we only discuss the results of Liang information flow.

4.2. Altered causal network architecture of DMN in ASD

The DMN is a higher‐order cognitive network that shows substantial overlap with the “social brain” network (Blakemore, 2008). Many studies have reported that abnormal functional network patterns within‐ and between‐DMN were closely associated with social deficits in ASD (Feng et al., 2022; Lynch et al., 2013; Padmanabhan et al., 2017). The FC alteration in DMN could be a potential endophenotype for social deficits in ASD (Feng et al., 2022) because the DMN architecture has an important impact on the information integration of the brain during rest and task performance (Smallwood et al., 2021). Thirty years of brain imaging research have converged to uncover that the DMN is a heterogeneous brain system network that can be further fractionated into multiple dissociated “subsystems” and/or “subnetworks” (Andrews‐Hanna et al., 2010). In a previous study conducted by Andrews‐Hanna et al. (2010), it was found that the DMN comprises of three dissociated components, including a midline core, a dMPFC subsystem, and a Medial Temporal Lobe (MTL) subsystem.

In addition, our results revealed that, in terms of causal connectivity, ASD patients exhibit significantly reduced strengths from core to another two subsystems (i.e., PCC → TempP, PCC → HF, and aMPFC → dMPFC) and from dMPFC to MTL subsystem (i.e., dMPFC → vMPFC, dMPFC → PHC, and dMPFC → HF), as well as significantly increased strengths from TPJ to MTL subsystem (i.e., TPJ → vMPFC and TPJ → HF) compared with HC. Furthermore, the excitation–inhibition imbalance of DMN may lead to social impairment (Padmanabhan et al., 2017; Paine et al., 2017; Trakoshis et al., 2020). This finding indicated that the core (PCC and aMPFC) regions exerted less influence on other subsystems. The dMPFC and TPJ are two major regions in the dMPFC subsystem and the vMPFC and HF are two key regions in the MTL subsystem. The causal interaction difference among these four regions indicated that the dMPFC subsystem may act as a mentor to influence on the MTL subsystem, indicating the influence exerted by the dMPFC subsystem on the MTL subsystem may modulate the social function of the DMN. We also found that the DMN causal connectivity network architecture is relatively dissimilar (r = .4239) between ASD and HC compared with previous reported resting‐state functional connectivity network (Cole et al., 2014; Schultz & Cole, 2016; Zhang et al., 2019). This finding implied that the resting DMN inter‐regional information coupling does not have an “intrinsic” pattern between ASD and HC, whereas exhibiting a disease‐related excitation–inhibition imbalance causal network pattern. Thus, we suggested that the Liang information flow causal connectivity analysis could deepen our knowledge of the DMN network architecture and provide a new perspective to enrich our understanding of ASD.

4.3. Reduced causal connectivity aMPFC → dMPFC and dMPFC → vMPFC

The existing studies have shown that the MPFC is recognized as the key component of the neurocircuitry related to various social cognition (Smallwood et al., 2021). Damage to MPFC impairs the ability to process social information related to oneself (present and future self) in ASD (Guise & Shapiro, 2017; Maggi & Humphries, 2022; Padmanabhan et al., 2017). The MPFC often comprises three functionally dissociable and hierarchically organized subregions: vMPFC, aMPFC, and dMPFC(Gusnard et al., 2001). These three subregions are located in the different subsystems of the DMN, respectively, yet they are functionally inter‐connected with each other and play distinct roles in social cognition (Padmanabhan et al., 2017). In our study, we found that the causal connectivity aMPFC → dMPFC and dMPFC → vMPFC were significantly reduced in ASD compared with HC. Previously, Kim (2020) suggested that the distinctive subregions in the MPFC exhibited a hierarchical allostatic regulation model that integrates a wide range of MPFC functions. Such causal connectivity differences may provide new support for the hierarchical connectivity model of MPFC. Using the degree analysis, we also found that the dMPFC acts as a causal information target in ASD, but a causal information source in HC. Compared with HC, ASD patients showed significantly reduced In–Out degree in the aMPFC. The In–Out degree of a node can measure the relative contribution of a node to causality (Jiao et al., 2011). For the causal (effective) connectivity, the decreased causal connectivity may represent a reduction in the influence (inhibits/facilitates) of one region on another, while increased causal connections may represent an increase in the intervention (disruption or promotion) of one region on another (Jiao et al., 2011). These findings may imply that the aMPFC and dMPFC within DMN may be impaired in ASD, indicating weaker influence (directed interaction) of aMPFC on dMPFC and dMPFC on vMPFC.

Furthermore, we found that the causal connectivity dMPFC → vMPFC was significantly negatively correlated with the neuropsychological score (ADOS total, ADOS social, and ADOS communication) of ASD. The higher the ADOS and ADI‐R scores, the more severe the ASD symptoms (Lefort‐Besnard et al., 2020). This result indicated that the aberrant afferent connection of vMPFC from dMPFC inhibits social behavior in ASD. The dMPFC is a key region of the dMPFC subsystem of the DMN and is involved in self‐reference guidelines or introspective mental activity‐related spontaneity, while the vMPFC is a key region of the MTL subsystem of the DMN and is considered for the integration of cognitive and emotional processing (Gusnard & Raichle, 2001). In a previous study conducted by Inagaki and Meyer (2020), they suggested that the greater dMPFC subsystem connectivity at rest was associated with greater social support. Based on the transcranial magnetic stimulation (TMS) study, Ferrari et al. (2016) found that the dMPFC played a causal role in integrating social behaviors. Martin et al. (2017) using focal high‐definition transcranial direct current stimulation (HD‐tDCS), they demonstrated that the dMPFC played a causal role in integrating higher‐order information from others/external sources into that of the self across cognitive domains. In addition, Salehinejad et al. (2021) found that by using anodal tDCS to increase the activation of the vMPFC, the ASD symptoms were significantly reduced. Thus, we suspect that more suppressed from dMPFC to vMPFC may disrupt the social task performance by issuing signals to interfere with the control set maintained by vMPFC.

4.4. Increased causal connectivity from TPJ to MTL subsystem

TPJ is another hub region in the dMPFC subsystem of DMN. Previous studies have shown that the TPJ plays a crucial role in mediating social cognition (Igelström et al., 2015; Igelström et al., 2017; Kelly et al., 2014) and ToM theory (Chen et al., 2021). It contributes to multisensory integration, a sense of agency, and stimulus‐driven attention functions (Eddy, 2016). Several studies also have shown that the lesions of the TPJ may cause ASD (Nobusako et al., 2017). We found that the causal connections from TPJ to MTL subsystem (TPJ → vMPFC, TPJ → HF) were significantly increased, indicating the TPJ exerted more influence on the MTL system. Andrews‐Hanna et al. (2010) demonstrated that the dMPFC subsystem is mainly involved in social processing, while the MTL subsystem is mainly involved in memory retrieval. Previous studies have also shown that TPJ is overactivated. For example, Chien et al. (2015) found that the posterior right TPJ was hyperconnected to the right ventral occipito‐temporal in ASD boys, and this abnormal hyperconnectivity was related to social behavior. Schulte‐Rüther et al. (2011) found increased activation of the right TPJ during self‐task in ASD patients. Furthermore, Hadjikhani et al. (2014) found increased activations in the TPJ of ASD during cognitive reappraisal compared with HC. Iidaka et al. (2019) found that the left TPJ was hyperconnected to the bilateral PCC using a large dataset from multiple sites in the ABIDEII. In addition, Eack et al. (2017) found that ASD had significantly enhanced connectivity between left TPJ and the left orbitofrontal cortex and bilateral medial prefrontal cortices compared with HC in the direct comparisons of connectivity strength. This abnormal hyperconnectivity was associated with the pathophysiology of ASD. These findings suggested that the enhanced causal connectivity observed in ASD may imply TPJ dysfunction. Combined with the discussion above, our results indicated that the excitation–inhibition imbalance (TPJ and dMPFC) within the dMPFC subsystem might lead to disorganized information processing in regional circuitry and potentially reduced sociability.

4.5. Global causal network topological properties within DMN

In addition to identifying the causal connectivity differences, we also assessed the causal network topographic properties for each subject. The brain network is a usually small‐world network that exhibits a large clustering coefficient and a small shortest path length (Bassett & Bullmore, 2006). We found that the global clustering coefficient was significantly lower in ASD compared with HC. However, no significant difference was apparent in characteristic path length, global efficiency, and local efficiency between the two groups. Our finding is in line with previous reports. For example, Rudie et al. (2013) found that the default and higher‐order visual regions displayed reduced functional segregation (lower clustering coefficient) in ASD. Based on the EEG network, Barttfeld et al. (2011) also found that the brain network topology of ASD patients departs from small‐world behavior, which has less clustering coefficient. The global clustering coefficient is a major measurement of the functional segregation of the whole network (Bullmore & Sporns, 2009; Rubinov & Sporns, 2010). In Yerys's report, they found that the DMN shows a pattern of poor functional segregation in ASD (Yerys et al., 2015). Thus, we suggested that the lower clustering coefficient could cause the loss of small‐world of DMN in ASD, affecting the efficiency of information transmission and storage within DMN. Furthermore, we found that higher scores accompanied lower global clustering coefficients. This topological alteration indicated an overall reduced causal segregation (i.e., excitation/inhibition imbalance) of the DMN with increasing ASD severity.

4.6. Identification of ASD using causal networks

In clinical diagnosis, a challenging problem is the accurate identification of ASD, and there is an urgent need to provide an effective method. Thus, in this study, we used the causal connectivity obtained by Liang information flow to classify ASD from HC. We found that the DMN causal connectivity pattern could be an important feature in identifying ASD (see Table 3), and the combination of features (causal connectivity and network properties) produced a higher classification accuracy than a single feature, achieving a 78.12% accuracy with a linear SVM classifier. Meanwhile, the traditional approach to distinguishing ASD from HC is based on functional connectivity (Hull et al., 2017; Santana et al., 2022). However, cognitive activity or connectivity of the brain is largely determined by the causal influences between brain regions. Figures 2 and 3 show that the changes in causal connectivity and network properties are important for ASD. Therefore, the Liang information flow method could offer a new strategy for the clinical diagnosis of ASD.

5. LIMITATIONS

There are some limitations in the current study. First, our sample size is relatively small since we only use the data from the NYU site in ABIDE. In addition, although previous studies have shown that the prevalence of ASD in males is ~3 to 4 times higher than in females (Lawrence et al., 2020), the gap between males and females was even greater in our study. Future studies should use multisite data and larger samples to overcome the gender mismatch problem, replication and further exploration. Second, we identified alterations in causal connectivity within the DMN and obtained the brain regions associated with social behaviors, but our study was based on resting‐state fMRI data and may not be able to capture real socially relevant processes. Future work should further explore the alteration of network causal connectivity during social tasks. In addition, we should combine TMS/tDCS to verify the causal connectivity results we obtained using the Liang information flow method in future studies.

6. CONCLUSION

To conclude, we used the Liang causal information flow method to explore the causal interactions within the DMN involving ASD patients. Our findings showed a specific disruption of causal connectivity among the core subsystem, dMPFC subsystem, and MTL subsystem of the DMN in ASD patients. Compared with the HC group, we found that the causal connectivity from the core subsystem to the dMPFC and MTL subsystem (PCC → TempP, PCC → HF, and aMPFC → dMPFC) was significantly decreased in the ASD group. We also found the imbalance inhibits/facilitates interactions from the dMPFC subsystem to the MTL subsystem, such as significantly increased causal connectivity in dMPFC → vMPFC, dMPFC → PHC, and dMPFC → HF, and significantly decreased causal connectivity in TPJ → TempP, TPJ → vMPFC, TPJ → HF, TempP → vMPFC, and PHC → PCC. For the topological property analysis, we also found the clustering coefficient of DMN and the In–Out degrees of aMPFC were significantly decreased in ASD. Moreover, these DMN causal connectivity network patterns, especially the causal connections from dMPFC to vMPFC, PHC, and HF, were correlated with the clinical symptoms of ASD and can be important features in identifying ASD. These differences in causal connectivity patterns indicated that the DMN inter‐regions information processing or signal issuing was perturbed in ASD, which might contribute to the deficits of social cognition.

CONFLICT OF INTEREST

The authors declare no conflict of interest.

Supporting information

Appendix S1. Supporting Information.

Cong, J. , Zhuang, W. , Liu, Y. , Yin, S. , Jia, H. , Yi, C. , Chen, K. , Xue, K. , Li, F. , Yao, D. , Xu, P. , & Zhang, T. (2023). Altered default mode network causal connectivity patterns in autism spectrum disorder revealed by Liang information flow analysis. Human Brain Mapping, 44(6), 2279–2293. 10.1002/hbm.26209

DATA AVAILABILITY STATEMENT

Original rs‐fMRI data and phenotypes were downloaded from the ABIDE repository (ABIDEs I, http://fcon_1000.projects.nitrc.org/indi/abide/).