Sports Engineering

, Volume 19, Issue 2, pp 117–127 | Cite as

Modeling and predicting heart rate dynamics across a broad range of transient exercise intensities during cycling

  • Michael J. Mazzoleni
  • Claudio L. Battaglini
  • Kerry J. Martin
  • Erin M. Coffman
  • Brian P. Mann
Original Article


Prior studies have investigated heart rate dynamics from a variety of perspectives, but are often inadequate for predicting heart rate responses across a broad range of transient exercise intensities. The aim of this study was to develop a nonlinear model to describe the heart rate response of an individual during cycling and to investigate whether heart rate is more accurately predicted by a combination of power output and cadence than by power output alone. The proposed model can account for the transient fluctuations of an individual’s heart rate while they participate in exercise that varies in intensity. The participants for this study each performed a fifty minute bout of cycling on an electric-braked cycle ergometer in the laboratory. The testing protocol for the cycling bout was designed to challenge the predictive capabilities of the model and the participants therefore abruptly changed their power outputs and cadences throughout the tests, which resulted in significant transient fluctuations in their heart rate responses. Due to the nonlinear nature of the proposed heart rate model, a heuristic algorithm was developed to perform the parameter estimation. The model predictions for heart rate matched very well with the experimental heart rate responses for each of the participants, especially when considering the challenges inherent to predicting abrupt transient behavior in the heart rate response. Model comparisons also indicated that heart rate is more accurately predicted by a combination of power output and cadence than by power output alone.


Heart rate Cycling Exercise intensity Dynamical systems Mathematical modeling 


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Copyright information

© International Sports Engineering Association 2016

Authors and Affiliations

  • Michael J. Mazzoleni
    • 1
  • Claudio L. Battaglini
    • 2
  • Kerry J. Martin
    • 2
  • Erin M. Coffman
    • 2
  • Brian P. Mann
    • 1
  1. 1.Department of Mechanical Engineering and Materials Science, Dynamical Systems Research LaboratoryDuke UniversityDurhamUSA
  2. 2.Department of Exercise and Sport Science, Exercise Oncology Research LaboratoryUniversity of North Carolina at Chapel HillChapel HillUSA

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