Power and phase properties of oscillatory neural responses in the presence of background activity

Abstract

Natural sensory inputs, such as speech and music, are often rhythmic. Recent studies have consistently demonstrated that these rhythmic stimuli cause the phase of oscillatory, i.e. rhythmic, neural activity, recorded as local field potential (LFP), electroencephalography (EEG) or magnetoencephalography (MEG), to synchronize with the stimulus. This phase synchronization, when not accompanied by any increase of response power, has been hypothesized to be the result of phase resetting of ongoing, spontaneous, neural oscillations measurable by LFP, EEG, or MEG. In this article, however, we argue that this same phenomenon can be easily explained without any phase resetting, and where the stimulus-synchronized activity is generated independently of background neural oscillations. It is demonstrated with a simple (but general) stochastic model that, purely due to statistical properties, phase synchronization, as measured by 'inter-trial phase coherence', is much more sensitive to stimulus-synchronized neural activity than is power. These results question the usefulness of analyzing the power and phase of stimulus-synchronized activity as separate and complementary measures; particularly in the case of attempting to demonstrate whether stimulus-synchronized neural activity is generated by phase resetting of ongoing neural oscillations.

Figure 1

The probability density function of the phase of neural measurements when stimulus-synchronized activity is generated independently of background activity. The probability distribution is distinct from the uniform distribution (solid gray line), as long as stimulus-synchronized activity has non-zero amplitude.

Figure 2

(a) The statistical power of four significance tests as a function of SNR when background activity is subject to the Gaussian distribution. Each point in the figure is a Monte Carlo numerical result; the theoretical statistical power, when available, is plotted as a solid gray line. Test statistics whose curves lie more to the left possess greater statistical power at the same SNR than those to the right. Similarly, to achieve 80% statistical power, each test requires a different minimum SNR, where smaller SNR values demonstrate greater overall statistical power. (b) The SNR required for 80% statistical power, for background activity subject to the generalized Gaussian distribution (smaller SNR values demonstrate a more effective significance test). Phase coherence is much more effective than response power when testing the significance of a neural response.

Figure 3

The number of trials needed to achieve 80% statistical power at different SNR values, for background activity subject to a Gaussian (c = 2) or Laplacian (c = 1) distribution. Each point in the figure is a Monte Carlo numerical result. Theoretical values, when known, are plotted as solid gray lines. Test statistics whose curves lie more to the left possess greater statistical power at the same SNR than those to the right. To achieve similar statistical power, the response power test needs dramatically more measurement trials compared with other statistical tests.