A computationally efficient algorithm to obtain an accurate and interpretable model of the effect of circadian rhythm...

Wrist-worn wearable devices equipped with heart rate (HR) sensors have become increasingly popular. The ability to correctly interpret the collected data is fundamental to analyse user's well-being and perform early detection of abnormal physiological data. Circadian rhythm is a strong factor of variability in HR, yet few models attempt to accurately model its effect on HR.

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 HR (RHR)), thus permitting us to predict the user's circadian rhythm component (i.e. MESOR, Acrophase and Amplitude) with a high accuracy.

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.

The multiple component model provided in this paper can be used to approximate a user's RHR 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 RHR, and it can be used to fit arbitrary periodic real valued time series, vectorial data, or complex data.