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Quantification of the heartbeat rhythm using characteristic equation of autoregressive model of R-R intervals in ECG

The heartbeat rhythm is affected by various factors such as respiration, blood pressure, body temperature regulation, and arrhythmia. Other external factors also affect the variation of the heart-rate with various frequency components. The heart-rate variability (HRV) has been used as an index for the heartbeat variation, but it represents the variation caused by a large number of factors through a single measure, since it is determined from the overall time-series of heartbeats. Consequently, it does not have a clear interpretation and can represent only macroscopic information. If an arbitrary frequency component can be extracted from the heartbeat rhythm and HRV derived based on that component, a detailed and clear information will be obtained. 
 
 
 
This paper proposes a method to extract a fluctuation component for an arbitrary frequency. The autoregressive (AR) model is applied to the time-series of heartbeats, and the power spectrum density function is decomposed based on the characteristic equation of the AR model. HRV for arbitrary frequency component is examined. The time-series of heartbeat is decomposed into frequency components. A time-series is generated by simulation with the same statistical property as the decomposed component, and is analyzed to verify the effectiveness. The method is applied to the exercise ECG for analysis. As a result, the usefulness of the method was demonstrated by indicating that the information which cannot be obtained from the overall time-series can be obtained from the generated series having only a decomposed component.