Fast Optimal Transport Averaging of Neuroimaging Data

Knowing how the Human brain is anatomically and functionally organized at the level of a group of healthy individuals or patients is the primary goal of neuroimaging research. Yet computing an average of brain imaging data defined over a voxel grid or a triangulation remains a challenge. Data are large, the geometry of the brain is complex and the between subjects variability leads to spatially or temporally non-overlapping effects of interest. To address the problem of variability, data are commonly smoothed before performing a linear group averaging. In this work we build on ideas originally introduced by Kantorovich to propose a new algorithm that can average efficiently non-normalized data defined over arbitrary discrete domains using transportation metrics. We show how Kantorovich means can be linked to Wasserstein barycenters in order to take advantage of the entropic smoothing approach used by. It leads to a smooth convex optimization problem and an algorithm with strong convergence guarantees. We illustrate the versatility of this tool and its empirical behavior on functional neuroimaging data, functional MRI and magnetoencephalography (MEG) source estimates, defined on voxel grids and triangulations of the folded cortical surface.

Single-trial decoding of auditory novelty responses facilitates the detection of residual consciousness

Detecting residual consciousness in unresponsive patients is a major clinical concern and a challenge for theoretical neuroscience. To tackle this issue, we recently designed a paradigm that dissociates two electro-encephalographic (EEG) responses to auditory novelty. Whereas a local change in pitch automatically elicits a mismatch negativity (MMN), a change in global sound sequence leads to a late P300b response. The latter component is thought to be present only when subjects consciously perceive the global novelty. Unfortunately, it can be difficult to detect because individual variability is high, especially in clinical recordings. Here, we show that multivariate pattern classifiers can extract subject-specific EEG patterns and predict single-trial local or global novelty responses. We first validate our method with 38 high-density EEG, MEG and intracranial EEG recordings. We empirically demonstrate that our approach circumvents the issues associated with multiple comparisons and individual variability while improving the statistics. Moreover, we confirm in control subjects that local responses are robust to distraction whereas global responses depend on attention. We then investigate 104 vegetative state (VS), minimally conscious state (MCS) and conscious state (CS) patients recorded with high-density EEG. For the local response, the proportion of significant decoding scores (M=60%) does not vary with the state of consciousness. By contrast, for the global response, only 14% of the VS patients' EEG recordings presented a significant effect, compared to 31% in MCS patients' and 52% in CS patients'. In conclusion, single-trial multivariate decoding of novelty responses provides valuable information in non-communicating patients and paves the way towards real-time monitoring of the state of consciousness.

Time-frequency mixed-norm estimates: sparse M/EEG imaging with non-stationary source activations

Magnetoencephalography (MEG) and electroencephalography (EEG) allow functional brain imaging with high temporal resolution. While solving the inverse problem independently at every time point can give an image of the active brain at every millisecond, such a procedure does not capitalize on the temporal dynamics of the signal. Linear inverse methods (minimum-norm, dSPM, sLORETA, beamformers) typically assume that the signal is stationary: regularization parameter and data covariance are independent of time and the time varying signal-to-noise ratio (SNR). Other recently proposed non-linear inverse solvers promoting focal activations estimate the sources in both space and time while also assuming stationary sources during a time interval. However such a hypothesis holds only for short time intervals. To overcome this limitation, we propose time-frequency mixed-norm estimates (TF-MxNE), which use time-frequency analysis to regularize the ill-posed inverse problem. This method makes use of structured sparse priors defined in the time-frequency domain, offering more accurate estimates by capturing the non-stationary and transient nature of brain signals. State-of-the-art convex optimization procedures based on proximal operators are employed, allowing the derivation of a fast estimation algorithm. The accuracy of the TF-MxNE is compared with recently proposed inverse solvers with help of simulations and by analyzing publicly available MEG datasets.

Markov models for fMRI correlation structure: Is brain functional connectivity small world, or decomposable into networks?

Correlations in the signal observed via functional Magnetic Resonance Imaging (fMRI), are expected to reveal the interactions in the underlying neural populations through hemodynamic response. In particular, they highlight distributed set of mutually correlated regions that correspond to brain networks related to different cognitive functions. Yet graph-theoretical studies of neural connections give a different picture: that of a highly integrated system with small-world properties: local clustering but with short pathways across the complete structure. We examine the conditional independence properties of the fMRI signal, i.e. its Markov structure, to find realistic assumptions on the connectivity structure that are required to explain the observed functional connectivity. In particular we seek a decomposition of the Markov structure into segregated functional networks using decomposable graphs: a set of strongly-connected and partially overlapping cliques. We introduce a new method to efficiently extract such cliques on a large, strongly-connected graph. We compare methods learning different graph structures from functional connectivity by testing the goodness of fit of the model they learn on new data. We find that summarizing the structure as strongly-connected networks can give a good description only for very large and overlapping networks. These results highlight that Markov models are good tools to identify the structure of brain connectivity from fMRI signals, but for this purpose they must reflect the small-world properties of the underlying neural systems.