The Dependence of Spike Field Coherence on Expected Intensity

Abstract

The coherence between neural spike trains and local-field potential recordings, called spike-field coherence, is of key importance in many neuroscience studies. In this work, aside from questions of estimator performance, we demonstrate that theoretical spike-field coherence for a broad class of spiking models depends on the expected rate of spiking. This rate dependence confounds the phase locking of spike events to field-potential oscillations with overall neuron activity and is demonstrated analytically, for a large class of stochastic models, and in simulation. Finally, the relationship between the spike-field coherence and the intensity field coherence is detailed analytically. This latter quantity is independent of neuron firing rate and, under commonly found conditions, is proportional to the probability that a neuron spikes at a specific phase of field oscillation. Hence, intensity field coherence is a rate-independent measure and a candidate on which to base the appropriate statistical inference of spike field synchrony.

Primary motor and sensory cortical areas communicate via spatiotemporally coordinated networks at multiple frequencies

“…2A) These measures of coherence are presumed to represent the correlation of the outputs from both areas (MS) and the correlation of the outputs from one area with the inputs in the other (MSf and SMf). For each of the 5 sampled training days, D1-D5, we estimated coherence by using a 0.5-s sliding window with 0.01-s steps to show a time-resolved coherence profile in the theta (2-6 Hz), alpha (6-13 Hz), beta (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30), and gamma (30-50 Hz) bands. Coherence in these frequency bands is believed to play a role in attention, memory, motor control, and plasticity (16,(18)(19)(20).…”

“…S12; McNemar test, P < 0.01; Kruskal-Wallis, peak by Spike-field networks also exhibited preferred frequency bands; MSf coherence was stronger than SMf in theta, whereas SMf coherence was stronger than MSf in gamma [Kruskal-Wallis, peak by networks, theta: x 2 ð3,46590Þ = 3491, P = 0; gamma: x 2 ð3,6170Þ = 70, P = 5e-15; post hoc, P < 0.001]. Theoretic work has suggested that higher firing rates are correlated with stronger spike-field coherence (23). However, differences in firing rates of neurons cannot account for these results as no linear relations were found between firing rates of MIo or SIo neurons and the MSf/SMf coherence in either theta or gamma bands (Fig.…”

Population interactions between parietal and primary motor cortices during reach

“…As stated in RESULTS, spike-field coherence tends to overstate the population statistics for finite sample sizes. In our case low-firing rate neuronal spike trains have fewer spikes/samples than higher-firing rate spike trains, and thus because of bias effects these low-firing neurons may be selected on the earliest iterations (we also note, however, that the interaction of firing rates and spike-field coherence is more complex-in addition to bias, firing rates can contribute true effects in the spike-field coherence; e.g., Lepage et al 2011). Because of this potential bias, we needed to employ a second approach to superimposing the spike times of ensembles of neurons-selecting neurons with either similar or opposite directional bias to the M1 LFP-to test whether PSFC strength depends on movement direction.…”

Rate-adjusted spike–LFP coherence comparisons from spike-train statistics

“…Spike-field coherence is a particularly important metric of coordinated neuronal activity, since it indicates the degree to which individual neurons are rhythmically synchronized with bulk network activity, represented by the LFP. However, spike-field coherence is a function of the mean spike rate of the analyzed neuron (Lepage et al, 2011). …”

“…The spike auto-spectrum is given by (Bartlett, 1963; Lepage et al, 2011) $$\begin{array}{c}left{S}_{\mathrm{italicnn}}(f)=\mathrm{\Delta }{\displaystyle \sum _{\tau =-\infty }^{\infty }{r}_{\mathrm{italicnn}}(\tau )e^{-i2\pi f\tau \mathrm{\Delta }}}\\ =\mathrm{\Delta }{\displaystyle \sum _{\tau =-\infty }^{\infty }(\mu \mathrm{\Delta }{\delta }_{0,\tau }+{\mathrm{normal\Delta }}^2{r}_{\mathrm{\lambda }\mathrm{\lambda }}(\tau ))e^{-i2\pi f\tau \mathrm{\Delta }}}\\ \approx {\mathrm{normal\Delta }}^2(\mu +S_{\mathrm{\lambda }\mathrm{\lambda }}(f)).\end{array}$$the spike-field cross spectrum is similarly defined as $$S_{\mathit{ny}}false(ffalse)\equiv \mathrm{normal\Delta }true\sum _{\tau =-\infty }^{\infty }{r}_{\mathit{ny}}false(\tau false)e^{-i2\pi f\tau \mathrm{normal\Delta }},$$where $$r_{\mathit{ny}}false(\tau false)\equiv \mathrm{normalE}false[\mathrm{italicdn}false(tfalse)yfalse(t+\tau false)false]$$is the cross-correlation between dn ( t ) and y ( t ).…”