Rationale:
Rhythms are common in healthy and pathological brain activity. Across different types of rhythms, the phase has been proposed to have functional consequences and relevance for therapeutic interventions, thus requiring its accurate specification from noisy data. For example, stimulating on specific phases of seizure waves in rats was critical for terminating a seizure.
1 Phase is usually specified using techniques that presume a near-sinusoidal rhythm. However, observed brain rhythms are non-sinusoidal and transient (e.g., appearing in bursts), such that phase estimates vary between analysis approaches. Moreover, most analyses do not consider confidence in the phase estimate, potentially obfuscating results including estimates with low certainty. We propose using multiple approaches or including confidence in phase estimation to mitigate this problem.
Methods:
We consider three common phase estimation methods: a finite impulse response (FIR) filter and Hilbert transform, a state space model of rhythms, and a Poincaré section. We discuss how each method introduces different underlying assumptions to estimate the phase of a brain rhythm. For the FIR-Hilbert and state space approaches we also estimate measures of confidence in the phase estimates. We apply these methods to estimate phase in simulated and
in vivo brain data. For simulated data, we compare the phase estimates across methods and across a range of filtering choices and use the circular standard deviation to capture the variability in phase differences between methods. For the
in vivo data, we consider how the different phase estimation methods impact the coherence (consistency in phase) in the delta band (0.25 – 1.5 Hz) from two frontal electrodes in an anaesthetized macaque monkey.
Results:
We found an inconsistency in phase estimates (median difference = 64 degrees) across different methods (Figure 1b,c,e). The difference in phase estimates due to different filtering approaches was much smaller (median difference less than 20 degrees in 15 out of 16 cases) than between phase estimation methods. However, intervals of signal exist with increased agreement (median difference = 39 degrees, Figure 1d) between all three methods; these intervals correspond to times when phase estimates have high confidence. For the analysis of delta coherence, we found that coherence increased from 0.3 to 0.7 (FIR-Hilbert), 0.3 to 0.75 (state space model) and 0.15 to 0.58 (Poincaré section) for high confidence phase intervals.
Conclusions:
Observed brain rhythms often do not contain the properties required to easily define phase and therefore depend on the estimation method. Estimates of phase can include measures of confidence, allowing results targeted to intervals when confidence in the phase estimates is high. Targeting high confidence intervals reduces inaccurate, noisy measures of phase when analyzing brain rhythms.
1 Takeuchi, Y., Harangozó, M., Pedraza, L., Földi, T., Kozák, G., Li, Q., & Berényi, A. (2021). Closed-loop stimulation of the medial septum terminates epileptic seizures. Brain, 144(3), 885-908.
Funding:
AW, MAK, FAM, and UTE were partially supported by NIH R01 NS110669 and R01EB026938.