# A Neural Network Model for Estimating the Heart Rate Response to Constant Intensity Exercises
###### 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.  
c 2021  
exercise [9, 10]. Several methods may be found in the literature for the estimation of the parameters involved in the HR variability signals [11, 12, 13]. A review of the most popular techniques for the time-frequency representation of the HR variability signals is presented in [11], whereas [PERSON] et al. [12] compare the performance of five kernel-based time-frequency distributions in terms of their ability to estimate the instantaneous frequency of HR signals.  
Estimating the HR response to any exercise intensity and any cardiovascular condition is an open problem and a challenging task. Thus, we believe that the implementation of neural networks (NNs) is an attractive alternative for the problem of HR estimation. It may be worth testing the performance of NN models to such problems, since NNs have proven to be very efficient in various medical applications. The implementation of NNs may be very effective as regards dynamic, real-time prediction of the HR, which is of utter importance, not only for the general public, but especially for population groups for which direct HR recordings at intense exercise are not possible or not allowed, such as elderly people and pregnant women.  
Pertinent studies include, among others, the identification of the connection between exercise intensity and HR values [14], the estimation of the oxygen uptake from the HR values [15] and the prediction of the digoxin concentration for specific cardio-activities [16]. Furthermore, a feedforward NN has been proposed to reflect the effects of physical activity on the HR [17] and various NN models have been developed to monitor the HR and its variabilities from PPG signals [3, 8].  
Our study implements suitable Multilayer Perceptron (MLP) NNs to estimate the HR response to constant intensity exercise. The NNs are trained using beat-to-beat time intervals recorded during exercises of constant intensity. After describing the data collection process, as well as the basic steps of the NN modeling, we examine the performance of our proposed NN when compared to raw HR data of constant exercise intensity. We also provide a comparison between the estimated HR values provided by our NN model and the simulated values provided by a dynamical systems model [9, 10].