Identification of heart rate dynamics during treadmill exercise: comparison of first- and second-order models

Wang, Hanjie; Hunt, Kenneth James (2021). Identification of heart rate dynamics during treadmill exercise: comparison of first- and second-order models BioMedical Engineering OnLine, 20(1) BioMed Central 10.1186/s12938-021-00875-7

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Background: Characterisation of heart rate (HR) dynamics and their dependence on exercise intensity provides a basis for feedback design of automatic HR control systems. This work aimed to investigate whether the second-order models with separate Phase I and Phase II components of HR response can achieve better fitting performance compared to the first-order models that do not delineate the two phases. Methods: Eleven participants each performed two open-loop identification tests while running at moderate-to-vigorous intensity on a treadmill. Treadmill speed was changed as a pseudo-random binary sequence (PRBS) to excite both the Phase I and Phase II components. A counterbalanced cross-validation approach was implemented for model parameter estimation and validation. Results: Comparison of validation outcomes for 22 pairs of first- and second-order models showed that root-mean-square error (RMSE) was significantly lower and fit (normalised RMSE) significantly higher for the second-order models: RMSE was 2.07 bpm ± 0.36 bpm vs. 2.27 bpm ± 0.36 bpm (bpm = beats per min), second order vs. first order, with p = 2.8 × 10^{−10} ; fit was 54.5% ± 5.2 % vs. 50.2% ± 4.8 %, p = 6.8 × 10^{−10}. Conclusion: Second-order models give significantly better goodness-of-fit than firstorder models, likely due to the inclusion of both Phase I and Phase II components of heart rate response. Future work should investigate alternative parameterisations of the PRBS excitation, and whether feedback controllers calculated using second-order models give better performance than those based on first-order models.

Item Type:

Journal Article (Original Article)


School of Engineering and Computer Science > Institut für Rehabilitation und Leistungstechnologie IRPT
BFH Centres > BFH centre for Health technologies


Wang, Hanjie and
Hunt, Kenneth James


T Technology > TA Engineering (General). Civil engineering (General)




BioMed Central


Organisations 320030 not found.




Kenneth James Hunt

Date Deposited:

20 Dec 2021 14:59

Last Modified:

20 Dec 2021 14:59

Publisher DOI:





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