# A Neural Network Model for Estimating the Heart Rate Response to Constant Intensity Exercises
## 4 Conclusions  
Soft computing techniques, when used with raw HR time series data can be successfully used to predict the HR values during exercise of constant intensity and its subsequent recovery. In the present study, HR time series have been estimated by implementing and training MLP-NNs, using the beat-to-beat time intervals as input to the model. The quality of the estimation scheme has been assessed by calculating the \(MAE_{te}\) and the \(RMSE_{te}\) between the predicted and the testing HR samples. Our results demonstrated that the \(MAE_{te}\) does not exceed 1.2 beats per minute, on average, and the \(RMSE_{te}\) may vary between \(10^{-3}\) and \(10^{-5}\), albeit the performance of the model is generally better during the exercise than the recovery periods. Moreover, comparisons between the results of the proposed NN model and an existing mathematical model that simulates the HR values have shown that the former produces results closer to the measured values of the HR than the latter, especially during the recovery period. The superiority of our proposed NN model over the dynamical systems model is reflected in its applicability to the problem of predicting the HR values, without the need of numerically solving differential equations (as it is the case with the simulated values that the mathematical model provides). Its efficiency to provide accurate estimations of the HR time series proves our model to be of great value, in the fields of cardiovascular health, diagnosis, recuperation and recuperation, in the areas of competitive sport as well as general fitness, as well as in cases where direct HR measurements cannot be performed, and so HR predictions are indispensable. Our future work includes the application of the proposed NN model to HR data corresponding not only to a larger variety of cardiovascular stress, but also to a variety of physical condition levels. Conceptualization, M.S.Z., T.N.K. and I.O.V. ; methodology, M.S.Z., T.N.K. and I.O.V. ; software, T.N.K. and A.L. ; validation, T.N.K., M.P.I. and I.O.V. ; formal analysis, M.S.Z. and I.O.V. ; measurements, M.S.Z. ; investigation, T.N.K., A.L. and I.O.V. ; resources, T.N.K. and I.O.V. ; data curation, M.S.Z., A.L. and T.N.K. ; writing--original draft preparation, T.N.K., M.P.I. and I.O.V. ; writing--review and editing, M.S.Z., M.P.I. and I.O.V. ; visualization, A.L. and T.N.K. ; supervision, I.O.V. ; project administration, I.O.V. ; funding acquisition, M.P.I. and I.O.V. All authors have read and agreed to the published version of the manuscript. This research received no external funding. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Set** & \(\mathbf{MRAE^{pr}\) **(\%)** & \(\mathbf{MRAE^{me}\) **(\%)** & \(\mathbf{MRAE^{pr-si}\) **(\%)** \\ \hline (I)ex & 0.48 & 1.77 & 1.7 \\ (I)rec & 2.45 & 5.87 & 5.75 \\ (II)ex & 0.59 & 1.17 & 1.07 \\ (II)rec & 1.77 & 3.74 & 3.47 \\ (III)ex & 0.56 & 1.13 & 1.15 \\ (III)rec & 2.02 & 4.98 & 4.21 \\ (IV)ex & 0.56 & 0.98 & 0.83 \\ (IV)rec & 2.15 & 3.70 & 3.26 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison between the proposed NN model and the corresponding mathematical model [9,10], regarding the mean relative absolute error (%) for each exercise set. **Institutional Review Board Statement:** The present research meets the highest ethical standards and was carried out following the rules of the Declaration of Helsinki of 1975, as revised in 2013 [19]. The protocol had been approved by the local ethics committee of the RyC program in the Autonomous University of Barcelona (UAB), Spain (project identification code: 08104993432, 2006) [18]. **Informed Consent Statement:** Before data collection the participant gave his informed consent for inclusion before he participated in the study and he was fully informed that his anonymity was assured, why the research was being conducted, that there were no risks associated and how his data would be used [18]. **Data Availability Statement:** The data presented in this study are available on request from the corresponding author.