Functional holography of recorded neuronal networks activity.

We present a new approach for analyzing multi-channel recordings, such as ECoG (electrocorticograph) recordings of cortical brain activity and of individual neuron dynamics, in cultured networks. The latter are used here to illustrate the method and its ability to discover hidden functional connectivity motifs in the recorded activity. The cultured networks are formed from dissociated mixtures of cortical neurons and glia-cells that are homogeneously spread over multi-electrode array for recording of the neuronal activity. Rich, spontaneous dynamical behavior is detected, marked by the formation of temporal sequences of synchronized bursting events (SBEs), partitioned into statistically distinguishable subgroups, each with its own characteristic spatio-temporal pattern of activity.In analogy with coherence connectivity networks for multi-location cortical recordings, we evaluated the inter-neuron correlation-matrix for each subgroup. Ordinarily such matrices are mapped onto a connectivity network between neuron positions in real space. In our functional holography, the correlations are normalized by the correlation distances Euclidian distances between the matrix columns. Then, we project the N-dimensional (for N channels) space spanned by the matrix of the normalized correlations, or correlation affinities, onto a corresponding 3D manifold (3D Cartesian space constructed by the three leading principal vectors of the principal component algorithm). The neurons are located by their principal eigenvalues and linked by their original (not normalized) correlations. By looking at these holograms, hidden causal motifs are revealed: each SBEs subgroup generates its characteristic connectivity diagram (network) in the 3D manifold, where the neuron locations and their links form simple structures. Moreover, the computed temporal ordering of neuron activity, when projected onto the connectivity diagrams, also exhibits simple patterns of causal propagation. We show that the method can expose functional connectivity motifs like the co-existence of subneuronal functional networks in the space of affinities. The method can be directly utilized to construct similar causal holograms for recorded brain activity. We expect that by doing so, hidden functional connectivity motifs with relevance to the understanding of brain activity might be discovered.