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

摘要

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. 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. 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 $$p = 2.8 imes 10^{-10}$$ ; fit was $$54.5% pm 5.2$$ % vs. $$50.2% pm 4.8$$ %, $$p = 6.8 imes 10^{-10}$$ . 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.