Fractal character of the electrocardiogram: distinguishing heart-failure and normal patients
Related Experiment Videos
1Columbia University, Department of Electrical Engineering, New York, NY, USA.
Insights
Statistical analysis of heartbeats reveals significant differences between healthy and heart failure patients. The Allan factor, a quantitative index, effectively distinguishes between these groups, aiding in heart failure detection.
Area of Science:
- Cardiology
- Statistical Analysis
- Dynamical Systems
Background:
- Heartbeat sequence analysis offers insights into cardiac health.
- Various statistical measures can characterize the human heartbeat's point process.
Purpose of the Study:
- To identify statistical measures that differentiate between normal and heart failure patient heartbeat data.
- To develop a quantitative index for heart failure detection based on heartbeat time series analysis.
Main Methods:
- Applied interevent interval and count-based statistical measures (e.g., Allan Factor, Fano Factor).
- Utilized phase-space reconstruction and surrogate data analysis.
- Modeled heartbeat sequences using a stochastic integrate-and-fire model with fractal-Gaussian noise.
Main Results:
- Statistically significant differences observed in heartbeat statistics between normal and heart failure groups.
- Identified 1/f-type fluctuations (long-duration power-law correlations) in heartbeat data.
- The Allan Factor proved effective in distinguishing between patient groups and is sensitive to both short-term and long-term heartbeat characteristics.
Conclusions:
- Heartbeat sequence analysis using statistical measures can reliably differentiate between healthy and heart failure states.
- The Allan Factor is a promising, easily calculable index for heart failure diagnosis.
- A stochastic model based on fractional Brownian motion accurately represents human electrocardiogram statistical behavior across time scales.
Abstract:
Statistical analysis of the sequence of heartbeats can provide information about the state of health of the heart. We used a variety of statistical measures to identify the form of the point process that describes the human heartbeat. These measures are based on both interevent intervals and counts, and include the interevent-interval histogram, interval-based periodogram, rescaled range analysis, the event-number histogram, Fano-factor, Allan Factor, and generalized-rate-based periodogram. All of these measures have been applied to data from both normal and heart-failure patients, and various surrogate versions thereof. The results show that almost all of the interevent-interval and the long-term counting statistics differ in statistically significant ways for the two classes of data. Several measures reveal 1/f-type fluctuations (long-duration power-law correlation). The analysis that we have conducted suggests the use of a conveniently calculated, quantitative index, based on the Allan factor, that indicates whether a particular patient does or does not suffer from heart failure. The Allan factor turns out to be particularly useful because it is easily calculated and is jointly responsive to both short-term and long-term characteristics of the heartbeat time series. A phase-space reconstruction based on the generalized heart rate is used to obtain a putative attractor's capacity dimension. Though the dependence of this dimension on the embedding dimension is consistent with that of a low-dimensional dynamical system (with a larger apparent dimension for normal subjects), surrogate-data analysis shows that identical behavior emerges from temporal correlation in a stochastic process. We present simulated results for a purely stochastic integrate-and-fire model, comprising a fractal-Gaussian-noise kernel, in which the sequence of heartbeats is determined by level crossings of fractional Brownian motion. This model characterizes the statistical behavior of the human electrocardiogram remarkably well, properly accounting for the behavior of all of the measures studied, over all time scales.