Over the last ten years, numerous research works have evidenced the existence of scale invariance (or scaling) phenomena (mostly, power law autocorrelation functions at large lags, or, equivalently, 1/f power spectral density in the limit of the fine frequencies) in human brain activity from resting state data recorded using various neuroimaging modalities (electro- and magneto-encephalography or functional Magnetic Resonance Imaging). Such scaling have also been observed in evoked activity during activation paradigms indicating therefore that ongoing and evoked activity are not necessarily independent one of the other, as usually assumed in most of classical neuroimaging methods. However, the functional and biological meanings (attention or perception levels, …) of such scaling phenomena in human brain activity have not been clearly understood neither from the measurements themselves nor from any reconstructed neuronal activity, even with highly resolved data both in space and time on the cortical surface. Nonetheless, the evidence of scaling in animals from electrophysiology recordings and its modulation by external stimuli or under the influence of drugs or biological substance simulating neuronal diseases relates scale invariance to brain dynamics complexity. This has been emphasized for instance by low scaling characteristics in immature brain.
The research goals developed in the current proposal are manyfolds and pluridisciplinary. It aims first at associating a biological content to the scaling phenomena observed on MEG/EEG/fMRI data, at acquiring long duration data, both under rest and brain activation protocols. Also, we will investigate the relations and transfers of these scaling properties across the various types of brain activity (hemodynanic, electromagnetic). We will go beyond the direct analyses of empirical data and will address generative model data multimodal fusion, as proposed in Thomas Vincent’s PhD thesis. This should enable us to reconstruct neuronal source activities over the cortical surface with high and joint time and space resolution. On the methodology side, this proposal aims at extending so far univariate fractal and multifractal analysis procedures to multivariate data. This has barely been done so far and implies addressing severe conceptual difficulties for multifractal analysis. Such procedures will then be applied to data or sources, making use of local regularization techniques aiming at accounting for the space correlation necessarily implied by brain anatomy. Further, another goal is to devise rigourous statistical tests whose goal is to decide whether the observed scaling phenomena only result from rest brain activity or also reflect exogenous variable effects, such as attention or cencentration levels, performance level of the task to perform. Finally, the ultimate goal lies in developing original methods aiming at exploring the level of functional connectivity. First, they will be based on the sole long memory (or Hurst) parameter, hence on the second statistical order (covariance or spectrum) only. Then, extension to multifractal parameters (i.e., to higher and lower statistical order) will be considered. The objective underlying such analyses is the identification of specific funtional networks, such as those reflecting rest spontaneous activity. To this end, three categories of approaches are considered : The first is based on source separation techniques, applied not the signals themselves but instead to their wavelet decompositions, so as to better identify network based on their scaling properties. The second relies on non supervised clustering with an automated estimation of the number of clusters and where clusters are constructed from scaling parameters. The third relies on the analyses of data component intercorrelation matrices, comparing them to the prediction of the so-called « fractal connectivity » model, that mostly states that scaling observed on inter-spectra are straightforwardly deduced from those seen on auto-spectra. The final goal is to investigate the extent to which the discovery that a sole scaling phenomenon is shared by a set of voxels enables to evidence the existence of a network. Further, we will entend such an approach to analyses based on the multifractal paradigm, seeking at defining the notion of « multifractal connectivity ». Eventually, we will investigate the ability of these connectivy indices to provide practitioners with relevant predictors for the reinforcement (or the inhibition) of such networks induced by some given experimental task. This constitutes a necessary step towards evaluating their in fine potential ability to serve as bio-marker for certain disorders, such as dyslexia for children, or neural pathologies, such as epsilepsy or Alzheimer’s disease for adults.