An equivalent circuit model for onset and offset exercise response

Yi Zhang, Azzam Haddad, Steven W Su, Branko G Celler, Aaron J Coutts, Rob Duffield, Cheyne Donges, Hung T Ngyuyen

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)
6 Downloads (Pure)


Background: The switching exercise (e.g., Interval Training) has been a commonly used exercise protocol nowadays for the enhancement of exerciser’s cardiovascular fitness. The current difficulty for simulating human onset and offset exercise responses regarding the switching exercise is to ensure the continuity of the outputs during onset-offset switching, as well as to accommodate the exercise intensities at both onset and offset of exercise.
Methods: Twenty-one untrained healthy subjects performed treadmill trials following both single switching exercise (e.g., single-cycle square wave protocol) and repetitive switching exercise (e.g., interval training protocol). During exercise, heart rate (HR) and oxygen uptake (VO 2) were monitored and recorded by a portable gas analyzer (K4b 2, Cosmed). An equivalent single-supply switching resistance-capacitor (RC) circuit model was proposed to accommodate the observed variations of the onset and offset dynamics. The single-cycle square wave protocol was utilized to investigate the respective dynamics at onset and offset of exercise with the aerobic zone of approximate 70% - 77% of HR max , and verify the adaption feature for the accommodation of different exercise strengths. The design of the interval training protocol was to verify the transient properties during onset-offset switching. A verification method including Root-mean-square-error (RMSE) and correlation coefficient, was introduced for comparisons between the measured data and model outputs.
Results: The experimental results from single-cycle square wave exercises clearly confirm that the onset and offset characteristics for both HR and VO 2 are distinctly different. Based on the experimental data for both single and repetitive square wave exercise protocols, the proposed model was then presented to simulate the onset and offset exercise responses, which were well correlated indicating good agreement with observations.
Conclusions: Compared with existing works, this model can accommodate the different exercise strengths at both onset and offset of exercise, while also depicting human onset and offset exercise responses, and guarantee the continuity of outputs during onset-offset switching. A unique adaption feature by allowing the time constant and steady state gain to re-shift back to their original states, more closely mimics the different exercise strengths during normal daily exercise activities.
Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalBioMedical Engineering OnLine
Publication statusPublished - Oct 2014


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