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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.