Non-sinusoidal waveform is emerging as an important feature of neuronal oscillations. However, the role of single cycle shape dynamics in rapidly unfolding brain activity remains unclear. Here, we develop an analytical framework that isolates oscillatory signals from time-series using masked Empirical Mode Decomposition to quantify dynamical changes in the shape of individual cycles (along with amplitude, frequency and phase) using instantaneous frequency. We show how phase-alignment, a process of projecting cycles into a regularly sampled phase-grid space, makes it possible to compare cycles of different durations and shapes. 'Normalised shapes' can then be constructed with high temporal detail whilst accounting for differences in both duration and amplitude. We find that the instantaneous frequency tracks non-sinusoidal shapes in both simulated and real data. Notably, in local field potential recordings of mouse hippocampal CA1, we find that theta oscillations have a stereotyped slow-descending slope in the cycle-wise average, yet exhibiting high variability on a cycle-by-cycle basis. We show how Principal Components Analysis allows identification of motifs of theta cycle waveform that have distinct associations to cycle amplitude, cycle duration and animal movement speed. By allowing investigation into oscillation shape at high temporal resolution, this analytical framework will open new lines of enquiry into how neuronal oscillations support moment-by-moment information processing and integration in brain networks.

中文翻译：

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周期内瞬时频率曲线报告振荡波形动态

非正弦波形正在成为神经元振荡的一个重要特征。然而，单周期形状动力学在快速展开的大脑活动中的作用仍不清楚。在这里，我们开发了一个分析框架，使用掩蔽经验模式分解将振荡信号与时间序列隔离，以使用瞬时频率量化各个周期形状（以及幅度、频率和相位）的动态变化。我们展示了相位对齐（将周期投影到定期采样的相位网格空间中的过程）如何使比较不同持续时间和形状的周期成为可能。然后可以用高时间细节构建“标准化形状”，同时考虑持续时间和幅度的差异。我们发现瞬时频率在模拟数据和实际数据中都遵循非正弦形状。值得注意的是，在小鼠海马 CA1 的局部场电位记录中，我们发现 θ 振荡在周期平均值中具有刻板的缓慢下降斜率，但在逐周期基础上表现出较高的变异性。我们展示了主成分分析如何识别与周期幅度、周期持续时间和动物运动速度具有明显关联的 θ 周期波形的基序。通过允许以高时间分辨率研究振荡形状，该分析框架将为神经元振荡如何支持大脑网络中的即时信息处理和整合开辟新的研究方向。