We modeled the multifractal heart rate variability (HRV) in health and other physiological conditions, including autonomic blockades and congestive heart failure, by using multiplicative random cascade. A method is proposed to extract the cascade model parameters from experimental data. The results provide the basis for simulating the pathological conditions. Our main conclusion is that the approach from multifractal to monofractal HRV, a property commonly seen in the transition from cardiovascular health to heart disease, can be made by turning off the small scale fluctuation. As a result, the generating mechanism in the small scale becomes additive, rather than multiplicative. In contrast, the multifractal HRV appears robust against variation in the large scale. In particular, by turning off the large scale fluctuation, multifractality is preserved, a situation comparable to the condition of sympathetic blockade. We also showed the similar effect by disrupting the structure of the branching process. Based on the numerical simulation, we discuss the possible “design principle” leading to multifractal HRV in healthy state.
We used the so-called bounded cascade to generate artificial time series which is able to mimic some of the known phenomenology of heart rate variability (HRV) in healthy humans: (a) multifractal spectrum including 1/f power law, (b) the transition from stretch-exponential to gaussian probability density function in the inter-beat interval (RRi) increment data and (c) the Poisson excursion law in small RRi increment. The cascade consists of a discrete fragmentation process and assigning random weights to the cascade components of the fragmented time intervals. The artificial time series is finally constructed by multiplying the cascade components in each level.
We also compared additive versus multiplicative mechanism in the generation of the artificial data. We found that the probability laws of the cascade components and the underlying fragmentation process are more essential to the generation of HRV phenomenology than the additive/multiplicative mechanisms involved in the cascade process. After showing the numerical results, we will turn to experimental RRi and discuss its mathematical structure as well as some of the limitations of using cascade to simulate such a structure. Finally, we present some preliminary results on using a hybrid additive and multiplicative construct in generating the artificial HRV.
Supported by the National Institute of Biomedical Imaging and Bioengineering (NIBIB) under NIH grant number R01EB030362.