A computationally efficient algorithm to obtain an accurate and interpretable model of the effect of circadian rhythm on resting heart rate

OBJECTIVE Wrist-worn wearable devices equipped with heart rate sensors have become increasingly popular. The ability to correctly interpret the collected data is fundamental to analyse users well-being and perform early detection of abnormal physiological data. Circadian rhythm is a strong factor of variability in heart rate, yet few models attempt to accurately model its effect on heart rate. Approach: In this paper we present a mathematical derivation of the single-component cosinor model with multiple components that fits user data to a predetermined arbitrary function (the expected shape of the circadian effect on resting heart rate), thus permitting us to predict the user's circadian rhythm component (i.e., MESOR, Acrophase and Amplitude). Main results: We show that our model improves the accuracy of HR prediction compared to the single component cosinor model (10% lower RMSE), while retaining the readability of the fitted model of the single component cosinor. We also show that the model parameters can be used to detect sleep disruption in a qualitative experiment. The model is computationally cheap, depending linearly on the size of the data. The computation of the model does not need the full dataset, but only two surrogates, where the data is accumulated. This implies that the model can be implemented in a streaming approach, with important consequences for security and privacy of the data, that never leaves the user devices. Significance: The multiple component model provided in this paper can be used to approximate a user's resting heart rate with higher accuracy than single component model, providing traditional parameters easy to interpret (i.e., the same produced by the single component cosinor model). The model we developed goes beyond fitting circadian activity on resting heart rate, and it can be used to fit arbitrary periodic real valued time series, vectorial data, or complex data. .

[1]  Yan Li,et al.  Resting heart rate in the supine and sitting positions as predictors of mortality in an elderly Chinese population. , 2019, Journal of hypertension.

[2]  Shlomo Havlin,et al.  Neuronal noise as an origin of sleep arousals and its role in sudden infant death syndrome , 2018, Science Advances.

[3]  J. Taylor,et al.  Some tests of the Vaníček Method of spectral analysis , 1972 .

[4]  Davide Morelli,et al.  Profiling the propagation of error from PPG to HRV features in a wearable physiological-monitoring device , 2017, Healthcare technology letters.

[5]  José R. Fernández,et al.  Methods for Comparison of Parameters from Longitudinal Rhythmometric Models with Multiple Components , 2003, Chronobiology international.

[6]  J. Vanderplas Understanding the Lomb–Scargle Periodogram , 2017, 1703.09824.

[7]  Germaine Cornelissen,et al.  Cosinor-based rhythmometry , 2014, Theoretical Biology and Medical Modelling.

[8]  Maia Angelova,et al.  Multiscale adaptive analysis of circadian rhythms and intradaily variability: Application to actigraphy time series in acute insomnia subjects , 2017, PloS one.

[9]  Michael Fu,et al.  Association of heart rate with mortality in sinus rhythm and atrial fibrillation in heart failure with preserved ejection fraction , 2019, European journal of heart failure.

[10]  T. Saikawa,et al.  Circadian rhythm of the signal averaged electrocardiogram and its relation to heart rate variability in healthy subjects , 1998, Heart.

[11]  Robert B. Sothern,et al.  Introducing Biological Rhythms: A Primer on the Temporal Organization of Life, with Implications for Health, Society, Reproduction, and the Natural Environment , 2006 .

[12]  M Malik,et al.  Circadian rhythm of heart rate variability after acute myocardial infarction and its influence on the prognostic value of heart rate variability. , 1990, The American journal of cardiology.

[13]  F. Halberg,et al.  Plexo-serial linear-nonlinear rhythmometry of blood pressure, pulse and motor activity by a couple in their sixties. , 1981, Chronobiologia.

[14]  A. Edelman,et al.  Polynomial roots from companion matrix eigenvalues , 1995 .

[15]  E Kristal-Boneh,et al.  The association of resting heart rate with cardiovascular, cancer and all-cause mortality. Eight year follow-up of 3527 male Israeli employees (the CORDIS Study) , 2000, European heart journal.

[16]  Rossana Castaldo,et al.  Acute mental stress assessment via short term HRV analysis in healthy adults: A systematic review with meta-analysis , 2015, Biomed. Signal Process. Control..

[17]  Jean-Claude Tardif,et al.  Resting heart rate in cardiovascular disease. , 2007, Journal of the American College of Cardiology.

[18]  C W Whitney,et al.  Sleep-disordered breathing and cardiovascular disease: cross-sectional results of the Sleep Heart Health Study. , 2001, American journal of respiratory and critical care medicine.

[19]  F. Shaffer,et al.  An Overview of Heart Rate Variability Metrics and Norms , 2017, Front. Public Health.

[20]  Michael Goldsmith,et al.  Unwinding Ariadne's Identity Thread: Privacy Risks with Fitness Trackers and Online Social Networks , 2017, MPS@CCS.

[21]  I E Faria,et al.  Circadian changes in resting heart rate and body temperature, maximal oxygen consumption and perceived exertion. , 1982, Ergonomics.

[22]  Ignacio Refoyo,et al.  A Model of Heart Rate Kinetics in Response to Exercise , 2008 .

[23]  Tanya L Leise,et al.  Analysis of Nonstationary Time Series for Biological Rhythms Research , 2017, Journal of biological rhythms.

[24]  A. Cabrera de León,et al.  [Resting heart rate and cardiovascular disease]. , 2014, Medicina clinica.

[25]  Ana Leonor Rivera,et al.  A physicist’s view of homeostasis: how time series of continuous monitoring reflect the function of physiological variables in regulatory mechanisms , 2018, Physiological measurement.

[26]  Mauro Conti,et al.  Fitness Trackers: Fit for Health but Unfit for Security and Privacy , 2017, 2017 IEEE/ACM International Conference on Connected Health: Applications, Systems and Engineering Technologies (CHASE).

[27]  Mary E Harrington,et al.  Wavelet-Based Time Series Analysis of Circadian Rhythms , 2011, Journal of biological rhythms.