THE HEART RATE AND HEART RATE VARIABILITY AFTER COMMENCEMENT OF EXERCISE ARE FRACTALS

Abstract

It is already well known that exercise can result in acceleration of heart rate (HR) and progressive withdrawal of vagal activity. However, the ways in which HR and the heart rate variability (HRV) change progressively during the initial stage of exercise have not been fully investigated. The aim of this study is to find a suitable mathematical description for the temporal evolutions of HR and HRV after the initiation of exercise, and to search for possible relation between HR and HRV during exercise in normal subjects. The index of HRV used in this study was the standard deviation (SD) of the heart beat intervals (RRI) measured within sequential steps of predetermined sampling period, and the HR is the inverse of the mean (Mn) of the RRI. We found that both Mn and SD of the RRI decrease progressively with increasing exercise time after the initiation of exercise. The temporal evolutions of both Mn and SD during exercise can be better described by power-law scaling relations. When different sampling periods were used in the calculation of Mn and SD of the RRI, there is self-similarity in time in the distribution of Mn and SD . These findings demonstrated that both HR and HRV after the initiation of exercise are temporal fractals. Fractal dimensions Dm and Ds, defined from the scaling exponents of the power-law scaling relations for HR and HRV, determine the rate of increase in HR and the rate of decrease in HRV after the initiation of exercise, respectively. Because of the fractal nature of HR and HRV during the early phase of exercise, the relation between HR and HRV during exercise can also be described by power-law scaling relation. Consequently, the HRV during exercise is inversely related to HR.