The DOI matches its Crossref record; 35 of the 35 references it cites were found in a registry or an index.
Physiological time-series analysis: what does regularity quantify?
Abstract
Approximate entropy (ApEn) is a recently developed statistic quantifying regularity and complexity that appears to have potential application to a wide variety of physiological and clinical time-series data. The focus here is to provide a better understanding of ApEn to facilitate its proper utilization, application, and interpretation. After giving the formal mathematical description of ApEn, we provide a multistep description of the algorithm as applied to two contrasting clinical heart rate data sets. We discuss algorithm implementation and interpretation and introduce a general mathematical hypothesis of the dynamics of a wide class of diseases, indicating the utility of ApEn to test this hypothesis. We indicate the relationship of ApEn to variability measures, the Fourier spectrum, and algorithms motivated by study of chaotic dynamics. We discuss further mathematical properties of ApEn, including the choice of input parameters, statistical issues, and modeling considerations, and we conclude with a section on caveats to ensure correct ApEn utilization.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Determining Lyapunov exponents from a time series
Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(85)90011-9 · Cited by 9,499
Approximate entropy as a measure of system complexity.
Pincus, S. M. (1991) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.88.6.2297 · Cited by 5,811
Self-citationMeasuring the strangeness of strange attractors
Grassberger, P., & Procaccia, I. (1983) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(83)90298-1 · Cited by 5,650
Ergodic theory of chaos and strange attractors
Eckmann, J. P., & Ruelle, D. (1985) · Reviews of Modern Physics · doi:10.1103/revmodphys.57.617 · Cited by 4,941
Independent coordinates for strange attractors from mutual information
Fraser, A. M., & Swinney, H. L. (1986) · Physical Review A · doi:10.1103/physreva.33.1134 · Cited by 4,606
Kleiger, R. E., Miller, J. P., Bigger, J. T., & Moss, A. J. (1987) · The American Journal of Cardiology · doi:10.1016/0002-9149(87)90795-8 · Cited by 3,995
Extracting qualitative dynamics from experimental data
Broomhead, D. S., & King, G. P. (1986) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(86)90031-x · Cited by 2,278
Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series
Sugihara, G., & May, R. M. (1990) · Nature · doi:10.1038/344734a0 · Cited by 1,932
Predicting chaotic time series
Farmer, J. D., & Sidorowich, J. J. (1987) · Physical Review Letters · doi:10.1103/physrevlett.59.845 · Cited by 1,929
Estimation of the Kolmogorov entropy from a chaotic signal
Grassberger, P., & Procaccia, I. (1983) · Physical Review A · doi:10.1103/physreva.28.2591 · Cited by 1,440
Cited by
Physiological time-series analysis using approximate entropy and sample entropy
Richman, J. S., & Moorman, J. R. (2000) · American Journal of Physiology-Heart and Circulatory Physiology · doi:10.1152/ajpheart.2000.278.6.h2039 · Cited by 7,880
Heart rate variability: A review
Rajendra Acharya, U., Paul Joseph, K., Kannathal, N., Lim, C. M., & Suri, J. S. (2006) · Medical & Biological Engineering & Computing · doi:10.1007/s11517-006-0119-0 · Cited by 2,820
Heart Rate Variability ? A Historical Perspective
Billman, G. E. (2011) · Frontiers in Physiology · doi:10.3389/fphys.2011.00086 · Cited by 786
“There are several other non-linear methods that have been used to evaluate HRV (Denton et al., 1990; Goldberger, 1990; Skinner et al., 1993; Pincus and Goldberger, 1994; Iyengar et al., 1996; Ho et al., 1997; Voss et al., 1998; Mäkikallio et al., 2001a,b; Perkiömäki et al., 2001a,b,c; Jokinen et…”
MethodSassi, R., Cerutti, S., Lombardi, F., Malik, M., Huikuri, H. V., Peng, C.-K., Schmidt, G., Yamamoto, Y., Reviewers:, D., Gorenek, B., et al. (2015) · Europace · doi:10.1093/europace/euv015 · Cited by 727
Dynamics of stability: the physiologic basis of functional health and frailty
Lipsitz, L. A. (2002) · The Journals of Gerontology Series A: Biological Sciences and Medical Sciences · doi:10.1093/gerona/57.3.b115 · Cited by 646
Metadata
- Authors
- Pincus, S. M., & Goldberger, A. L.
- Venue
- American Journal of Physiology-Heart and Circulatory Physiology
- Publisher
- American Physiological Society
- Published
- 1994-04-01
- Volume
- 266
- Issue
- 4
- Pages
- H1643-H1656
- ISSN
- 0363-6135 (ISSN-L)
- 1522-1539
- OpenAlex
- W1776514298
- Cited by
- 1,315
- References
- 35
- FWCI
- 7.19
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Physiological time-series analysis: what does regularity quantify? https://app.cochat.ai/papers/10.1152/ajpheart.1994.266.4.h1643
- The paper
- Pincus, S. M., & Goldberger, A. L. (1994). Physiological time-series analysis: what does regularity quantify? American Journal of Physiology-Heart and Circulatory Physiology. https://doi.org/10.1152/ajpheart.1994.266.4.h1643
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.