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The authors have declared that no competing interests exist.

Conception and implementation of the biomarker as described in this paper: RFG. Conceived and designed the experiments: RFG JLPV LGD. Performed the experiments: JLPV. Analyzed the data: RFG LGD. Contributed reagents/materials/analysis tools: RFG LGD JLPV. Wrote the paper: RFG JLPV LGD.

We present an efficient approach to discriminate between typical and atypical brains from macroscopic neural dynamics recorded as magnetoencephalograms (MEG). Our approach is based on the fact that spontaneous brain activity can be accurately described with stochastic dynamics, as a multivariate Ornstein-Uhlenbeck process (mOUP). By fitting the data to a mOUP we obtain: 1) the functional connectivity matrix, corresponding to the drift operator, and 2) the traces of background stochastic activity (noise) driving the brain. We applied this method to investigate functional connectivity and background noise in juvenile patients (n = 9) with Asperger’s syndrome, a form of autism spectrum disorder (ASD), and compared them to age-matched juvenile control subjects (n = 10). Our analysis reveals significant alterations in both functional brain connectivity and background noise in ASD patients. The dominant connectivity change in ASD relative to control shows enhanced functional excitation from occipital to frontal areas along a parasagittal axis. Background noise in ASD patients is spatially correlated over wide areas, as opposed to control, where areas driven by correlated noise form smaller patches. An analysis of the spatial complexity reveals that it is significantly lower in ASD subjects. Although the detailed physiological mechanisms underlying these alterations cannot be determined from macroscopic brain recordings, we speculate that enhanced occipital-frontal excitation may result from changes in white matter density in ASD, as suggested in previous studies. We also venture that long-range spatial correlations in the background noise may result from less specificity (or more promiscuity) of thalamo-cortical projections. All the calculations involved in our analysis are highly efficient and outperform other algorithms to discriminate typical and atypical brains with a comparable level of accuracy. Altogether our results demonstrate a promising potential of our approach as an efficient biomarker for altered brain dynamics associated with a cognitive phenotype.

There is a current debate in the autism field related to the concept of “disconnection” in the autistic brain that became popular from psychological and neuroimaging evidence. Proposals of disruption of coordinated timing in neuronal activity in autism were advanced

Most of these studies have relied on metabolic measurements. A complementary approach is the analysis of electroencephalographic signals, which have greater time resolution thus allowing for the study of transient coordination patterns. Indeed, the crucial aspect of these patterns in normal cognition is their transience: widespread long-lasting synchrony is normally associated with unconsciousness or disease

While connectivity measures are providing important insight into brain function, an area that remains very much under-investigated relates to the detailed analysis of the background, resting nervous system activity. Examination of noise and fluctuations in neurophysiological signals rather than concentrating on averages and magnitudes as is customary, is crucial for a complete understanding of nervous system function and its relation to behavior

The outline of our results is as follows. We first investigate global differences between the connectivity matrices in the control and ASD groups. In particular, we show that the matrices of each group cluster in a high-dimensional space. We then investigate which specific features of the matrices account for this clustering. Specifically, we show that certain pair-wise interactions are significantly different. Finally, we demonstrate that in addition to having some different functional connections, the brains from control and ASD differ in the spatial distribution of background noise driving the network.

In the absence of stimulation, the non-linear dynamics of the brain reduces to noise-driven fluctuations around a state of equilibrium, which in realistic neural-mass models of brain dynamics corresponds to a hyperbolic fixed point _{ij}_{ij}_{ij}

_{ij}

_{ij}

After obtaining the connectivity matrices for the control subjects (n = 10) and the ASD subjects (n = 9), we investigated if these matrices where significantly different when considered as a whole. To this end, we first “reshaped” the matrices as column vector (

Percentage | p-value | |

84 | 0.0029 | |

80 | 0.0780 | |

88 | 0.0054 | |

84 | 0.0013 |

Having shown that the functional connectivity matrices for control and ASD subjects are different when considered as a whole, we proceeded to investigate if those differences resulted from difference in the global properties of the matrices. We first investigated the maximal real part of the eigenvalues, which corresponds to a linear stability analysis of system (1). In order for (1) to be a valid model of brain dynamics in the resting state, all eigenvalues must have a negative real part. Otherwise, the brain would be linearly unstable, i.e. epileptic. _{ij}_{ij}_{ij}_{ij}

Since global properties could not account for the differences between connectivity matrices, we also investigated all pairwise interactions, _{ij}_{ij}_{ij}_{ij}

We then asked whether in addition to significant connectivity changes, the background noise driving the brain activity in the resting state could also be different in ASD compared to control. To test this, we obtained the traces of background noise _{ij}_{ij}

The matrices

Percentage | p-value | |

94 | 0.0002 | |

100 | 0.0044 | |

88 | 0.0174 | |

94 | 0.0002 |

The determination of the background noise traces allows us to investigate its spatial structure as well. Indeed, whereas the noise is not temporally correlated (white), it displays spatial correlations. The spatial patterns of the correlated noise are evident from a principal component analysis of the residuals (see _{ij}

The spatial complexity of the background noise in control is significantly higher than in ASD, as quantified in the inset (Wilcoxon ranksum text, p<<0.01). Numbers on top of the plots show the values of spatial complexity.

Our study has revealed alterations in brain connectivity and background noise in juvenile ASD patients, more specifically, signs of increased excitation were found from occipital to frontal areas. Perhaps even more interestingly, we found that background noise is spatially correlated over wide areas, that is, its spatial complexity is lower in ASD recordings. The analysis has been performed using a novel analytical method to investigate brain activity by determining two of its most fundamental aspects: the direction of functional connections and the temporal and spatial structure of the stochastic inputs driving cortical networks.

There is an increasing demand for adequate discrimination of patients in a variety of psychiatric syndromes using relatively safe and non-invasive methods such as EEG, MEG or neuroimaging recordings. The analytical techniques involved range from pattern recognition of neuroimaging data, as recently shown to classify patients with attention deficit hyperactivity disorder

The main connectivity change in ASD relative to control showing enhanced functional excitation from occipital to frontal areas is an indication of another general characteristic of aberrant brain function that is becoming apparent in current research: enhanced neural excitability seems to underlie neuropsychiatric disorders

The term “functional connectivity” has been ambiguously employed to date. In some studies functional connectivity is synonymous with covariance, in some others with synchrony or coherence, etc. We propose here a concept of functional connectivity that has three important advantages: 1) Contrary to previous approaches, we do not focus on the analysis of functional connectivity in the context of psycophysical experiments but rather on ongoing, resting-state activity. This facilitates the estimation of functional connections because the activity of the underlying neural networks does not saturate, so the neural interactions can be well resolved. 2) Our method detects the direction of functional connections, i.e. whether area A excites (or inhibits) area B more strongly or vice versa. Other methods have been previously proposed to detect directionality of network interactions: a) Granger causality, b) the imaginary component of the coherency, and c) the coupling function of phase oscillators. However, methods a) and c) are model-dependent, i.e. they make assumptions about the nature of the signals that oftentimes do not apply to EEG/EMG recordings; and method b) is defined in the frequency domain, so its value depends on the frequency components of the signals. This limits its applicability as a measure of connectivity, which one wants to define by means of a number rather than as a function. 3) To our knowledge, our method is the only one to date that allows one to infer the temporal and spatial structure of the stochastic inputs driving the cortical networks in the brain’s resting state. This is quite remarkable, as the classification of controls and ASD is even more accurate considering the spatial covariance of the noise,

MEG recordings have some limitations to keep in mind. The signals detected by MEG and the source estimates derived from these signals reflect population-scale levels of activity in large neuronal networks. Every individual neuronal component from which an MEG signal is comprised possesses complex non-linear relationships with its synaptically connected neighbors and surrounding glia. The complexity of these interactions cannot be accessed with precise detail from the level of the MEG signal because it provides measurements that are too coarse to reveal such dependencies. As a result, insights gained from the investigation of MEG data are limited to coarse relationships between large populations of cells rather than the detailed understanding of interactions between individual cells. Moreover, spontaneous activity at any given sensor may contain activity from multiple distributed sources, and conversely, the activity of a single signal source can introduce coordinated changes at multiple sensors (cross-talk), which could lead to spurious interactions among MEG sensors. With these caveats in mind, all of our analyses focused on changes in one group (ASD) relative to the other (control). For example, we do not make any conclusions from the absolute connectivity between areas A and B in the brain, but rather from the change in connectivity between A and B in ASD compared to control.

To investigate the cross-talk between sensors we plotted the covariance between two channels as a function of their relative distance in

Potential limitations in the design of the experiments cannot account for the differences between groups uncovered with our method either. To facilitate the participation of the children in the experiments and minimize distraction, they were asked to press a button at will with their right hand a few times during the recording session (30 s for each subject). Button pressing was not significantly different between both groups, as shown in

As in any population study, one must take into consideration the possibility of finite size effects. In statistical terms, the fact that we can establish significant differences in functional connectivity and background noise in relatively small populations suggests that those features are robust. Usually large sample sizes are required to establish the level of significance and accuracy that we obtained in our studies for a smaller sample size. We also note that all the participating children from the ASD group had been clinically diagnosed with Asperger’s syndrome. They clearly had behavioral and cognitive differences with respect to children in the control group. ASD certainly develops over time, but once it is diagnosed based on cognitive parameters it should be possible to observe differences in terms of neural dynamics as well. And that is what we have addressed in this study.

There are two natural extensions of our work for future studies. The first extension is to investigate the applicability of our approach to other cognitive phenotypes to identify alterations in functional brain connectivity and background noise activity. The second extension is methodological and consists in considering nonlinearities in the stochastic model so that it can be applied beyond the resting state to investigate how functional connectivity is modulated by sensory stimulation, attention and other cognitive tasks.

Data were drawn from a larger sample of children enrolled in a previous study

Magnetoencephalographic (MEG) recordings were acquired at 625 Hz sampling rate, DC-100 Hz bandpass, third-order spatial gradient noise cancellation using a CTF Omega 151 channel whole head system (CTF Systems Inc., Port Coquitlam, Canada). Out of the 151 sensors, we discarded 10 that were not comparable across all patients due to artifacts or a very low signal-to-noise ratio. Our analysis thus focused on the recordings from the remaining 141 sensors in all patients. Subjects were tested supine inside the magnetically shielded room. Head movement was tracked by measuring the position of three head coils every 30 ms, located at the nasion, left and right ear, and movements less than 5 mm were considered acceptable. Children were instructed to remain at rest during the recording session that lasted between 30 and 60 s per child. To facilitate the involvement of the children in the experiment and minimize distraction, they were asked to press a button at will with their right hand a few times during the recording session. For each child, an epoch of 30 s was taken off for analysis of functional brain connectivity. All children were awake and had their eyes open during the experiment.

Eye-blinking and muscular artifacts were present in most recordings. These artifacts appeared across many channels with high amplitude relative to baseline fluctuations and thus dominated the first few principal components of the data. Removal of 1 to 6 principal components efficiently eliminated the artifacts without affecting the actual baseline fluctuations.

Rewriting system (1) in vector notation one has

For a multivariate Ornstein-Uhlenbeck process like system (2) the time-lagged covariance,

Finally, we note that if the zero-lag covariance matrix of the data,

For a multivariate Ornstein-Uhlenbeck process like (2), the covariance matrix of the residuals,

The fact that

The vectors representing reshaped connectivity matrices (see

Group separability was addressed by comparing the performance of the support vector classifier with a linear kernel on the original groups to the performance of the same type of classifier on randomized groups (obtained by randomly permuting the group labels)

To determine if a given element of the connectivity matrix,

We note that the distribution of the difference of the means for the surrogate data converges fairly quickly to a Gaussian as the number of surrogate samples increases. This allows us to easily compute the z-score of the change in connectivity as the actual difference of the means divided by the standard deviation of this distribution.

Spatial complexity was calculated using a similar algorithm to that already described in

Quantification of cross-talk between sensors.

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Experimental paradigm and data preprocessing cannot account for differences between groups.

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Random permutation tests were performed in parallel on the High Performance Computing Cluster at Case Western Reserve University.