Henriques Teresa S, Mariani Sara, Burykin Anton, Rodrigues Filipa, Silva Tiago F, Goldberger Ary L
Wyss Institute for Biologically Inspired Engineering at Harvard University, Boston, MA, USA.
Center for Anesthesia Research and Excellence (CARE), Beth Israel Deaconess Medical Center, Boston, MA, USA.
BMC Med Inform Decis Mak. 2016 Feb 9;16:17. doi: 10.1186/s12911-016-0252-0.
Poincaré delay maps are widely used in the analysis of cardiac interbeat interval (RR) dynamics. To facilitate visualization of the structure of these time series, we introduce multiscale Poincaré (MSP) plots.
Starting with the original RR time series, the method employs a coarse-graining procedure to create a family of time series, each of which represents the system's dynamics in a different time scale. Next, the Poincaré plots are constructed for the original and the coarse-grained time series. Finally, as an optional adjunct, color can be added to each point to represent its normalized frequency.
We illustrate the MSP method on simulated Gaussian white and 1/f noise time series. The MSP plots of 1/f noise time series reveal relative conservation of the phase space area over multiple time scales, while those of white noise show a marked reduction in area. We also show how MSP plots can be used to illustrate the loss of complexity when heartbeat time series from healthy subjects are compared with those from patients with chronic (congestive) heart failure syndrome or with atrial fibrillation.
This generalized multiscale approach to Poincaré plots may be useful in visualizing other types of time series.
庞加莱延迟映射广泛应用于心脏搏动间期（RR）动力学分析。为便于可视化这些时间序列的结构，我们引入了多尺度庞加莱（MSP）图。
该方法从原始RR时间序列开始，采用粗粒化程序创建一系列时间序列，每个序列代表系统在不同时间尺度下的动力学。接下来，为原始时间序列和粗粒化时间序列构建庞加莱图。最后，作为一种可选的辅助手段，可以为每个点添加颜色以表示其归一化频率。
我们在模拟的高斯白噪声和1/f噪声时间序列上展示了MSP方法。1/f噪声时间序列的MSP图显示相空间面积在多个时间尺度上相对守恒，而白噪声的MSP图显示面积显著减小。我们还展示了如何使用MSP图来说明健康受试者的心跳时间序列与慢性（充血性）心力衰竭综合征患者或心房颤动患者的心跳时间序列相比复杂性的丧失。
这种广义的庞加莱图多尺度方法可能有助于可视化其他类型的时间序列。
