International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Tokyo 113-0033, Japan.
J Neurosci Methods. 2022 May 15;374:109578. doi: 10.1016/j.jneumeth.2022.109578. Epub 2022 Mar 23.
Phase-amplitude coupling (PAC) is a key neuronal mechanism. Here, a novel method for quantifying PAC via the Wasserstein distance is presented.
The Wasserstein distance is an optimization algorithm for minimizing transportation cost and distance. For the first time, the author has applied this distance function to quantify PAC and named the Wasserstein Modulation Index (wMI). As the wMI accommodates the product of the amplitude value in each phase position and the coupling phase position, it allows for extraction of more detailed PAC features from the data.
The validity of the wMI calculations was examined using various simulation data, including sinusoidal and non-sinusoidal waves and empirical data sets. The current findings showed that the wMI is a more robust and stable index for quantifying PAC under various measuring conditions. Specifically, it can better reflect the timing of coupling and distinguish the shape of the coupling distribution than other measurements, both of which are the most significant parameters related to the functionality of PAC. Furthermore, the wMI is also suitable for many applications, such as more data-driven approaches and direct comparisons.
COMPARISON WITH EXISTING METHOD(S): Compared with Euler-based PAC methods and the Modulation Index (MI), the wMI is not easily affected by the non-sinusoidal nature of neural oscillation and the short data length and enables better reflection of the natures of PAC, such as the timing of coupling and the amplitude distribution in the phase plane, than the MI.
The wMI is expected to extract more detailed PAC characteristics, which could considerably contribute to the neuroscience field.
相位-幅度耦合（PAC）是一种关键的神经元机制。本文提出了一种通过 Wasserstein 距离量化 PAC 的新方法。
Wasserstein 距离是一种优化算法，用于最小化运输成本和距离。作者首次将该距离函数应用于量化 PAC，并将其命名为 Wasserstein 调制指数（wMI）。由于 wMI 容纳了每个相位位置的幅度值与耦合相位位置的乘积，因此它允许从数据中提取更详细的 PAC 特征。
使用各种模拟数据（包括正弦波和非正弦波以及经验数据集）检验了 wMI 计算的有效性。目前的研究结果表明，wMI 是一种在各种测量条件下量化 PAC 的更稳健和稳定的指标。具体来说，它可以更好地反映耦合的时间，并比其他测量方法更好地区分耦合分布的形状，这两者都是与 PAC 功能最相关的重要参数。此外，wMI 还适用于许多应用，如更多的数据驱动方法和直接比较。
与基于 Euler 的 PAC 方法和调制指数（MI）相比，wMI不易受到神经振荡的非正弦性质和数据长度较短的影响，并且比 MI 更好地反映了 PAC 的性质，例如耦合的时间和相位平面中的幅度分布。
wMI 有望提取更详细的 PAC 特征，这将对神经科学领域做出重要贡献。
