Phase reorganization leads to transient β-LFP spatial wave patterns in motor cortex

The final paper from my thesis is, at long last, published [get PDF]. 

We studied traveling waves observed in electrical Local Field Potential (LFP) signals in primate motor cortex. We found that the structure of traveling waves in beta LFP oscillations was more complex than previously appreciated. 

Previous theoretical work noted that traveling waves in the brain do not always reflect "true" traveling waves, like the ripples from throwing a stone into water: They can also arise from common inputs arriving at different times, or from transient spatial reorganization of coupled oscillators.

We sought to clarify which of these scenarios is consistent with beta-LFP traveling waves in motor cortex. Our previous work looking at the role of single neurons suggested that the waves may be phase waves in coupled oscillators, rather than traveling pulses from a defined source.

This study supports the phase wave scenario. We also discovered a rich variety of spatial structures not previously reported, such as spiral and radiating waves and more complex structures. 

Many thanks to Carlos Vargas-Irwin, John P. Donoghue, and Wilson Truccolo. This work can be cited as

Rule, M.E., Vargas-Irwin, C., Donoghue, J.P. and Truccolo, W., 2018. Phase reorganization leads to transient β-LFP spatial wave patterns in motor cortex during steady-state movement preparation. Journal of neurophysiology, 119(6), pp.2212-2228. 

Figure 3, surveying the variety of patterns:

Fig. 3. Transient beta-local field potential (β-LFP) oscillations exhibit a rich variety of spatiotemporal wave patterns. In addition to traveling plane waves, beta spatiotemporal dynamics showed synchronous states, radiating and rotating waves, and other more complex wave patterns. Each example was taken from the 4×4-mm² area sampled by the 10×10 multielectrode array in ventral premotor cortex area of subject S. Missing electrodes were interpolated from nearest neighbors. Average phase-delay maps were computed by wrapping Hilbert phases at the median frequency of the wave event before computing the average analytic signal. The mean analytic signal was smoothed at a 2-mm scale to generate the phase-delay maps pictured. The smoothed Hilbert phase (φ) was differentiated to extract critical points from the wave dynamics, shown as a blue dot for a radiating wave and red dots for rotating waves. Spatially synchronized states were detected as patterns where the angular distribution of analytic signals was concentrated as shown by the first (top to bottom) example. Plane-wave states were detected as spatial patterns where the angular distribution of the phase gradient (∇φ) direction was concentrated, as shown by the second example.

A video of the LFP waves that we analyzed: 

The video shows the LFP (≤250 Hz) oscillation on all channels from a triple multi-electrode array implant, during one trial of the Cued Grasp with Instruct Delay task (see also Vargas-Irwin et al. 2015). Beta frequency (10-45 Hz) waves dominate, and occur in transients. The video is slowed down by a factor of 12.5. [get original original .avi video from Github]

Wave events in the phase plane

Each point represents the amplitude and phase of beta-LFP oscillations on a single electrode in polar (r,θ) coordinates. Recordings are from primary motor cortex (M1; red), ventral premotor cortex (PMv; green), and dorsal premotor cortex (PMd; blue). Beta-LFP wave events correlate with transient synchronization of ~0.4 mm scale populations. [get original avi video from Github]

Some animated GIFs of β-LFP events:

Animated GIFs of some β-LFP events, showing filtered beta-LFP on each channel (left), enoised beta-LFP (middle), and extracted oscillation phase (right).