Is the Normal Heart Rate Chaotic?
Data for study
In its June 2008 issue, the editors of Chaos announced a new feature, "Controversial Topics in Nonlinear Dynamics". The first controversial topic to be aired is "Is the Normal Heart Rate Chaotic?" (follow the link to an essay by Leon Glass summarizing the debate, and links to eight papers published in Chaos in its June 2009 issue, in response to the question).
Since major impediments to achieving consensus on the statistical properties of biologic time series have included the lack of open access time series, PhysioNet has provided (below) a set of 15 heart beat (RR-interval) time series in health (series n1rr, n2rr, n3rr, n4rr, and n5rr) and disease (congestive heart failure: c1rr, c2rr, c3rr, c4rr, and c5rr; and atrial fibrillation: a1rr, a2rr, a3rr, a4rr, and a5rr). Each time series is about 24 hours long (roughly 100,000 intervals), and is provided as a text file for analysis (for example, n1rr.txt) and as an image for visual review (for example, n1rr.pdf).
The time series belonging to the first two groups (healthy and congestive heart failure) are all in sinus rhythm. Those in the third group (a1rr, a2rr, a3rr, a4rr, and a5rr) are provided as examples of a cardiac rhythm that is not sinus rhythm; in that group, the rhythm is atrial fibrillation (AF), an atrial arrhythmia producing an erratic and typically rapid ventricular response. All of the time series were derived from continuous ambulatory (Holter) electrocardiograms (ECGs) that are available elsewhere on the PhysioNet web site; see the text file RECORDS (below) for additional information about the sources, including where to find the original ECGs and beat annotations from which these series were derived. For each of the 10 healthy and CHF time series, the RECORDS file also indicates the time of day corresponding to the beginning of the time series, and the gender and age of the subject. This information is not available for any of the 5 AF time series, nor are there annotations for any of the time series with respect to activity level and sleep. Sleeping hours in healthy subjects, however, reliably correspond to sustained periods during which the inter-beat intervals are consistently relatively long for that individual.
Each line in the *rr.txt files contains information about one RR interval, in three fields:
- the length of the RR interval, in seconds;
- a code indicating the type of heart beat that ends the RR interval (N is normal, and anything else is abnormal); and
- the elapsed time, in seconds, from the beginning of the time series to the end of the RR interval.
Since many methods for characterizing the dynamics of time series are extremely sensitive to outliers, and since outlier detection in these time series is non-trivial, we have also provided a set of "filtered" time series from which almost all of the outliers have been removed (using the nguess software available here as part of the WFDB software package). To the extent possible, these series contain only intervals between consecutive normal (N) heart beats, and they are therefore designated as the "nn" series. Series n1nn is the "filtered" version of series n1rr, etc. As for the "rr" series, the "nn" series are provided as text files (n1nn.txt, etc.) and as image files (n1nn.pdf, etc), in the same formats as for the "rr" series files.
The file named Make-Data is a shell script (batch file) that generated the .txt and .pdf files in this data set, using annotated ECGs and open-source software available from PhysioNet. The annotated ECGs come from among those in the MIT-BIH Normal Sinus Rhythm Database, the BIDMC Congestive Heart Failure Database, and the Long-Term Atrial Fibrillation Database; the specific ECGs used for each time series are shown in Make-Data and also in RECORDS. The open-source software used came from the WFDB and plt software packages.
By choosing to use the "nn" time series, you may be able to avoid having to deal with outliers in your analysis, but you may be able to get better results starting with the "rr" series, applying a more (or less) agressive outlier rejection strategy that is better matched to the characteristics of your analytic methods. In any case, it may be helpful to refer to both the "rr" and the "nn" series in order to assess how outliers influence your results.
We encourage participants in the Chaos Controversies issue to use the 15 RR interval time series provided here as a common focus of analysis. If you use other time series, we hope you will be willing to make them freely available at the PhysioNet website so that other participants can apply their analyses to them. Contributions of additional open-source implementations of algorithms related to this topic are also encouraged so that any differences in analyses and conclusions can be more readily understood. Credit will be given to the contributors. Please write to us if you wish to contribute data or software. Use of these data sets, or contributions of data or algorithms to PhysioNet, will not be criteria for acceptance of an article, however.
PhysioNet offers over 40 other collections of physiologic signals and time series, together with a large library of open-source software for exploring and analyzing them, and a set of tutorials and reference manuals that introduce and document this resource. We invite you to explore PhysioNet further!