Heart Rate Modeling and Prediction Using Autoregressive Models and Deep Learning

Abstract

Physiological time series are affected by many factors, making them highly nonlinear and nonstationary. As a consequence, heart rate time series are often considered difficult to predict and handle. However, heart rate behavior can indicate underlying cardiovascular and respiratory diseases as well as mood disorders. Given the importance of accurate modeling and reliable predictions of heart rate fluctuations for the prevention and control of certain diseases, it is paramount to identify models with the best performance in such tasks. The objectives of this study were to compare the results of three different forecasting models (Autoregressive Model, Long Short-Term Memory Network, and Convolutional Long Short-Term Memory Network) trained and tested on heart rate beats per minute data obtained from twelve heterogeneous participants and to identify the architecture with the best performance in terms of modeling and forecasting heart rate behavior. Heart rate beats per minute data were collected using a wearable device over a period of 10 days from twelve different participants who were heterogeneous in age, sex, medical history, and lifestyle behaviors. The goodness of the results produced by the models was measured using both the mean absolute error and the root mean square error as error metrics. Despite the three models showing similar performance, the Autoregressive Model gave the best results in all settings examined. For example, considering one of the participants, the Autoregressive Model gave a mean absolute error of 2.069 (compared to 2.173 of the Long Short-Term Memory Network and 2.138 of the Convolutional Long Short-Term Memory Network), achieving an improvement of 5.027% and 3.335%, respectively. Similar results can be observed for the other participants. The findings of the study suggest that regardless of an individual's age, sex, and lifestyle behaviors, their heart rate largely depends on the pattern observed in the previous few minutes, suggesting that heart rate can be reasonably regarded as an autoregressive process. The findings also suggest that minute-by-minute heart rate prediction can be accurately performed using a linear model, at least in individuals without pathologies that cause heartbeat irregularities. The findings also suggest many possible applications for the Autoregressive Model, in principle in any context where minute-by-minute heart rate prediction is required (arrhythmia detection and analysis of the response to training, among others).

Keywords: autoregressive model; deep learning; forecasting; heart rate; modeling; prediction; time series analysis.

Figure 1

Forecast results for Participant 1. (Top) Results obtained from the AR(3) model. (Center) Results obtained from the Stacked LSTM architecture. (Bottom) Results obtained from the ConvLSTM architecture. AR(3): Autoregressive Model of order 3; LSTM: Long Short-Term Memory Network; ConvLSTM: Convolutional Long Short-Term Memory Network.

Figure 2

Autocorrelation function (ACF; top) and partial autocorrelation function (PACF; bottom) plots for Participant 1.