Aguilar-Molina Ana María, Angulo-Brown Fernando, Muñoz-Diosdado Alejandro
Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edif. No.9 U.P. Zacatenco, Mexico City 07738, Mexico.
Unidad Profesional Interdisciplinaria de Biotecnología, Instituto Politécnico Nacional, Av. Acueducto s/n, Barrio la Laguna, Ticomán, Mexico City 07340, Mexico.
Entropy (Basel). 2019 Jun 11;21(6):581. doi: 10.3390/e21060581.
We calculate the multifractal spectra of heartbeat RR-interval time series (tachograms) of healthy subjects and patients with congestive heart failure (CHF). From these time series, we obtained new subseries of 6 h durations when healthy persons and patients were asleep and awake respectively. For each time series and subseries, we worked out the multifractal spectra with the Chhabra and Jensen method and found that their graphs have different shapes for CHF patients and healthy persons. We suggest to measure two parameters: the curvature around the maximum and the symmetry for all these multifractal spectra graphs, because these parameters were different for healthy and CHF subjects. Multifractal spectra of healthy subjects tend to be right skewed especially when the subjects are asleep and the curvature around the maximum is small compared with the curvature around the maximum of the CHF multifractal spectra; that is, the spectra of patients tend to be more pointed around the maximum. In CHF patients, we also have encountered differences in the curvature of the multifractal spectra depending on their respective New York Heart Association (NYHA) index.
我们计算了健康受试者和充血性心力衰竭（CHF）患者心跳RR间期时间序列（心动周期图）的多重分形谱。从这些时间序列中，我们分别获取了健康人和患者在睡眠和清醒状态下时长为6小时的新子序列。对于每个时间序列和子序列，我们用Chhabra和Jensen方法算出多重分形谱，发现CHF患者和健康人的多重分形谱图形状不同。我们建议测量所有这些多重分形谱图的两个参数：最大值处的曲率和对称性，因为健康受试者和CHF受试者的这些参数不同。健康受试者的多重分形谱往往向右偏斜，尤其是当受试者处于睡眠状态时，且最大值处的曲率与CHF多重分形谱最大值处的曲率相比很小；也就是说，患者的谱在最大值附近往往更尖锐。在CHF患者中，我们还发现多重分形谱的曲率因其各自的纽约心脏协会（NYHA）分级而有所不同。
