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Topological analysis of multi-site LFP data

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Fedorov,  LA
Max Planck Institute for Biological Cybernetics, Max Planck Society;
Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Fedorov, L. (2019). Topological analysis of multi-site LFP data. Poster presented at Ninth International Workshop Statistical Analysis of Neuronal Data (SAND9), Pittsburgh, PA, USA.


Cite as: http://hdl.handle.net/21.11116/0000-0003-A5A4-9
Abstract
The Local Field Potential (LFP) summarizes synaptic and somato-dendritic currents in a bounded ball around the electrode and is dependent on the spatial distribution of neurons. Both fine-grained properties and the temporal distribution of typical waveforms in spontaneous LFP have been used to identify global brain states (see e.g. [1] for P-waves in stages of sleep). While some LFP signatures have been studied in detail (in addition to Pons, see e.g. sleep spindles in the Thalamus and areas of the cortex [2], sharp-wave-ripples [3] in the Hippocampus and k-complexes [4]), it stands to understand the relationship between simultaneous signaling in cortical and subcortical areas. To characterize the mesoscale spontaneous activity, we quantify data-driven properties of LFP and use them to describe different brain states. Inspired by [5], we treat frequency-localized temporary increases in LFP power simultaneously recorded from Cortex, Hippocampus, Pons and LGN as neural events that carry information about the brain state. Here, we give a characterization of neural events in the 0-60Hz frequency range using tools from topological data analysis. In detail, we look at collections of barcodes computed using persistence homology [6] in two different ways. First, we look at the sublevel set filtration of a neural event to describe its critical points. Second, we use Vietoris-Rips filtration of the point-cloud of the delay embedding [7,8] of a neural event to describe periodicity. Both collections of barcodes are mapped to their persistence landscape spaces [9,10] for statistical description of the neural events. Both neural events representations are stable with respect to noise. They can be used for comparison of sustained low-frequency activity between different brain sites, as well as local spatial variability of the electrode position.