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

Abstract

Abstract 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 $$p = 2.8 \times 10^{-10}$$ p = 2.8 × 10 - 10 ; fit was $$54.5\% \pm 5.2$$ 54.5 % ± 5.2 % vs. $$50.2\% \pm 4.8$$ 50.2 % ± 4.8 %, $$p = 6.8 \times 10^{-10}$$ p = 6.8 × 10 - 10 . Conclusion Second-order models give significantly better goodness-of-fit than first-order 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.