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  Topological analysis of LFP data

Fedorov, L., Dijkstra, T., Murayama, Y., Bohle, C., & Logothetis, N. (2019). Topological analysis of LFP data. Poster presented at 28th Annual Computational Neuroscience Meeting (CNS*2019), Barcelona, Spain. doi:10.1186/s12868-019-0538-0.

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Fedorov, L1, 2, Author           
Dijkstra, T, Author
Murayama, Y2, 3, Author           
Bohle, C, Author
Logothetis, NK2, 3, Author           
Affiliations:
1Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497797              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497794              
3Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497798              

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 Abstract: The Local Field Potential (LFP) summarizes synaptic and somatodendritic
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 fine-grained characterization
of events in the 0-60Hz frequency range that differentiates the onset
and offset intervals from the ongoing short-term oscillation within the
event’s duration. For example, a fixed-amplitude oscillatory interval
can be conceptually thought of as a temporally resolved sample from
a circle, whereas the onset and offset can be regarded as samples from
spirals. Thus, the change within an event corresponds to a topological
change of the trajectory in phase space. We use topological data analysis
to detect this change in topology. In detail, we look at barcodes
computed using persistence homology [6] of the delay embedding [7,
8] of consecutive windows within a neural event. A persistence barcode
can be seen as a topological signature [9] of the reconstructed
trajectory. We rely on the difference between a circle and a spiral in
homology when this qualitative change is inferred from looking at
consecutive barcodes. This feature (Fig. 1) describes the onset-duration-
offset intervals for each oscillation, yet is agnostic to event type, recording site or brain state.

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 Dates: 2019-072019-11
 Publication Status: Published in print
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 Identifiers: DOI: 10.1186/s12868-019-0538-0
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Title: 28th Annual Computational Neuroscience Meeting (CNS*2019)
Place of Event: Barcelona, Spain
Start-/End Date: 2019-07-13 - 2019-07-17

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Title: BMC Neuroscience
Source Genre: Journal
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Publ. Info: BioMed Central
Pages: - Volume / Issue: 20 (Supplement 1) Sequence Number: P179 Start / End Page: 98 Identifier: ISSN: 1471-2202
CoNE: https://pure.mpg.de/cone/journals/resource/111000136905018