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Topological analysis of LFP data
{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\textquoterights 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.}
@misc{item_3134952, title = {{Topological analysis of LFP data}}, journal = {{BMC Neuroscience}}, 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\textquoterights 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.}}, volume = {20}, pages = {98}, publisher = {BioMed Central}, year = {2019}, slug = {item_3134952}, author = {Fedorov, L and Dijkstra, T and Murayama, Y and Bohle, C and Logothetis, NK} }