Abstract
Estimating the heart rate (HR) response to exercises of a given intensity without the need of direct measurement is an open problem of great interest. We propose here a model that can estimate the heart rate response to exercise of constant intensity and its subsequent recovery, based on soft computing techniques. Multilayer perceptron artificial neural networks (NN) are implemented and trained using raw HR time series data. Our model’s input and output are the beat-to-beat time intervals and the HR values, respectively. The numerical results are very encouraging, as they indicate a mean relative square error of the estimated HR values of the order of 10−4 and an absolute error as low as 1.19 beats per minute, on average. Our model has also been proven to be superior when compared with existing mathematical models that predict HR values by numerical simulation. Our study concludes that our NN model can efficiently predict the HR response to any constant exercise intensity, a fact that can have many important applications, not only in the area of medicine and cardio-vascular health, but also in the areas of rehabilitation, general fitness, and competitive sport.
Highlights
We provide a comparison between the estimated heart rate (HR) values provided by our neural networks (NN) model and the simulated values provided by a dynamical systems model [9,10]
The testing procedure is performed with an independent dataset, which is kept unseen from the NNs during training
The latter indicates that the RMSEte may vary between 10−3 and 10−5, while the MAEte for all sets is 1.19 bpm on average; this is a satisfactory outcome, since results reported by other researchers, that employ techniques based on PPG signals to estimate HR, refer to average absolute errors of the order of 1.06 [4], 1.37 [5], 1.17 [6], 1 [7], and 1.03 [3] bpm
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The heart rate (HR), i.e., the number of heart beats per minute, is probably the most informative cardiovascular variable. The analysis of the HR response to physical activities may provide valuable information regarding cardiovascular health, as it can detect hidden physiological responses or abnormalities. HR estimation is of great interest in pre-diagnostics, rehabilitation, recuperation as well as prevention of cardiovascular diseases [1]
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