A pairwise maximum entropy model accurately describes resting-state human brain networks

Watanabe, Takamitsu; Hirose, Satoshi; Wada, Hiroyuki; Imai, Yoshio; Machida, Tatsuya; Shirouzu, Ichiro; Konishi, Seiki; Miyashita, Yasushi; Masuda, Naoki

doi:10.1038/ncomms2388

Cited by 159 publications

(256 citation statements)

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“…If the system is not well described by this maximum entropy distribution then we know from the work of Jaynes [18] that other information beyond pairwise relationships would need to be taken into account. Similar analyses have since been applied in neuroscience [19][20][21] However, the data to accurately estimate the needed bivariate probability distributions may not be available. To get around this some researchers have used the first two moments of the variables as constraints instead of the full bivariate distributions [26,27] -effectively using the cross-correlations as their constraints.…”

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confidence: 99%

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“…They either coarse grain to binary variables where it is equivalent to conditioning on the distributions [19] -potentially losing important information -or use higher cardinality variables where it is only a linear approximation [26,27]. Our approach based on mutual information can be applied in these cases; the associated entropies can be estimated with as few as 2 H/2 data points [42] (H is measured in bits).…”

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“…Our method results inÊ[I m /I T ] 1 in both regimes, and across all discretizations and tuple sizes, while the cross-correlation only does so for binary variables. Resting-State Human Brain Networks: To illustrate the applicability of our methodology in real-world data situations, we apply it to neuroimaging data, in a similar context as in [19]. In particular, we want to assess to what extent the multivariate activity distribution is determined by purely bivariate dependence patterns.…”

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Pairwise network information and nonlinear correlations

2016

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Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the units can be considered pairwise and, thus, can be modeled as an interaction network with simple links corresponding to pairwise interactions. In principle this can be determined by comparing the maximum entropy given the bivariate probability distributions to the true joint entropy. In many practical cases this is not an option since the bivariate distributions needed may not be reliably estimated, or the optimization is too computationally expensive. Here we present an approach that allows one to use mutual informations as a proxy for the bivariate probability distributions. This has the advantage of being less computationally expensive and easier to estimate. We achieve this by introducing a novel entropy maximization scheme that is based on conditioning on entropies and mutual informations. This renders our approach typically superior to other methods based on linear approximations. The advantages of the proposed method are documented using oscillator networks and a resting-state human brain network as generic relevant examples. Pairwise measures of dependence such as crosscorrelations (as measured by the Pearson correlation coefficient or covariance matrix) and mutual information are widely used to characterize the interactions within complex systems. They are a key ingredient to techniques such as principal component analysis, empirical orthogonal functions, and functional networks (networks inferred from dynamical time series) [1][2][3]. These techniques are widespread since they provide greatly simplified descriptions of complex systems, and allow for the analysis of what might otherwise be intractable problems [4]. In particular, functional networks have been widely applied in fields such as neuroscience [4,5], genetics [6], and cell physiology [7], as well as in climate research [1,8].In this paper we study how faithfully these measures alone can represent a given system. With the increasing use of functional networks this topic has received much attention recently, and many technical concerns have been brought to light dealing with the inference of these networks. Previous studies have shown that the estimates of the functional networks can be negatively affected by properties of the time series [9][10][11], as well as properties of the measure of association, e.g. crosscorrelations [12][13][14][15]. In this work however, we address a more fundamental question: How well do pairwise measurements represent a system?In principle this can be evaluated using a maximum entropy approach. The corresponding framework was first laid out in [16] and later applied in [17], where they assessed the rationale of only looking at the pairwise correlations between neurons. They examined how well the maximum entropy distribution, consistent with all the pairwise correlations described...

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Pairwise network information and nonlinear correlations

2016

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“…Antomical ROIs representing the default mode network and frontoparietal attention network were selected based on the literature (Table 2). 10,23,45 The ROIs were then generated in MNI space using the closest parcellation to previous reported results (Fig. 1).…”

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Altered brain connectivity in sagittal craniosynostosis

Beckett

Brooks

Lacadie

et al. 2014

PED

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Object Sagittal nonsyndromic craniosynostosis (sNSC) is the most common form of NSC. The condition is associated with a high prevalence (> 50%) of deficits in executive function. The authors employed diffusion tensor imaging (DTI) and functional MRI to evaluate whether hypothesized structural and functional connectivity differences underlie the observed neurocognitive morbidity of sNSC. Methods Using a 3-T Siemens Trio MRI system, the authors collected DTI and resting-state functional connectivity MRI data in 8 adolescent patients (mean age 12.3 years) with sNSC that had been previously corrected via total vault cranioplasty and 8 control children (mean age 12.3 years) without craniosynostosis. Data were analyzed using the FMRIB Software Library and BioImageSuite. Results Analyses of the DTI data revealed white matter alterations approaching statistical significance in all supratentorial lobes. Statistically significant group differences (sNSC < control group) in mean diffusivity were localized to the right supramarginal gyrus. Analysis of the resting-state seed in relation to whole-brain data revealed significant increases in negative connectivity (anticorrelations) of Brodmann area 8 to the prefrontal cortex (Montreal Neurological Institute [MNI] center of mass coordinates [x, y, z]: −6, 53, 6) and anterior cingulate cortex (MNI coordinates 6, 43, 14) in the sNSC group relative to controls. Furthermore, in the sNSC patients versus controls, the Brodmann area 7, 39, and 40 seed had decreased connectivity to left angular gyrus (MNI coordinates −31, −61, 34), posterior cingulate cortex (MNI coordinates 13, −52, 18), precuneus (MNI coordinates 10, −55, 54), left and right parahippocampus (MNI coordinates −13, −52, 2 and MNI coordinates 11, −50, 2, respectively), lingual (MNI coordinates −11, −86, −10), and fusiform gyri (MNI coordinates −30, −79, −18). Intrinsic connectivity analysis also revealed altered connectivity between central nodes in the default mode network in sNSC relative to controls; the left and right posterior cingulate cortices (MNI coordinates −5, −35, 34 and MNI coordinates 6, −42, 39, respectively) were negatively correlated to right hemisphere precuneus (MNI coordinates 6, −71, 46), while the left ventromedial prefrontal cortex (MNI coordinates 6, 34, −8) was negatively correlated to right middle frontal gyrus (MNI coordinates 40, 4, 33). All group comparisons (sNSC vs controls) were conducted at a whole brain–corrected threshold of p < 0.05. Conclusions This study demonstrates altered neocortical structural and functional connectivity in sNSC that may, in part or substantially, underlie the neuropsychological deficits commonly reported in this population. Future studies combining analysis of multimodal MRI and clinical characterization data in larger samples of participants are warranted.

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Impairment of functional integration of the default mode network correlates with cognitive outcome at three months after stroke

Dacosta-Aguayo

Graña

Iturria-Medina

et al. 2014

Human Brain Mapping

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Resting-state studies conducted with stroke patients are scarce. The study of brain activity and connectivity at rest provides a unique opportunity for the investigation of brain rewiring after stroke and plasticity changes. This study sought to identify dynamic changes in the functional organization of the default mode network (DMN) of stroke patients at three months after stroke. Eleven patients (eight male and three female; age range: 48–72) with right cortical and subcortical ischemic infarctions and 17 controls (eleven males and six females; age range: 57–69) were assessed by neurological and neuropsychological examinations and scanned with resting-state functional magnetic ressonance imaging. First, we explored group differences in functional activity within the DMN by means of probabilistic independent component analysis followed by a dual regression approach. Second, we estimated functional connectivity between 11 DMN nodes both locally by means of seed-based connectivity analysis, as well as globally by means of graph-computation analysis. We found that patients had greater DMN activity in the left precuneus and the left anterior cingulate gyrus when compared with healthy controls (P < 0.05 family-wise error corrected). Seed-based connectivity analysis showed that stroke patients had significant impairment (P = 0.014; threshold = 2.00) in the connectivity between the following five DMN nodes: left superior frontal gyrus (lSFG) and posterior cingulate cortex (t = 2.01); left parahippocampal gyrus and right superior frontal gyrus (t = 2.11); left parahippocampal gyrus and lSFG (t = 2.39); right parietal and lSFG (t = 2.29). Finally, mean path length obtained from graph-computation analysis showed positive correlations with semantic fluency test (rs = 0.454; P = 0.023), phonetic fluency test (rs = 0.523; P = 0.007) and the mini mental state examination (rs = 0.528; P = 0.007). In conclusion, the ability to regulate activity of the DMN appears to be a central part of normal brain function in stroke patients. Our study expands the understanding of the changes occurring in the brain after stroke providing a new avenue for investigating lesion-induced network plasticity. Hum Brain Mapp 36:577–590, 2015. © 2014 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

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A pairwise maximum entropy model accurately describes resting-state human brain networks

Cited by 159 publications

References 60 publications

Pairwise network information and nonlinear correlations

Pairwise network information and nonlinear correlations

Altered brain connectivity in sagittal craniosynostosis

Impairment of functional integration of the default mode network correlates with cognitive outcome at three months after stroke

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