Sports Engineering

, Volume 21, Issue 1, pp 31–41 | Cite as

A dynamical systems approach for the submaximal prediction of maximum heart rate and maximal oxygen uptake

  • Michael J. Mazzoleni
  • Claudio L. Battaglini
  • Kerry J. Martin
  • Erin M. Coffman
  • Jordan A. Ekaidat
  • William A. Wood
  • Brian P. Mann
Original Article
First Online:

Abstract

This study examines the viability of utilizing a dynamical system model and heuristic parameter estimation algorithm to make predictions for maximum heart rate (\(\mathrm {HR_{max}}\)) and maximal oxygen uptake (\(\dot{\mathrm {V}}{\mathrm {O_{2max}}}\)) using data collected from a submaximal testing protocol. \(\dot{\mathrm {V}}{\mathrm {O_{2max}}}\) is widely considered to be the best single measurement of overall fitness in humans. When a \(\dot{\mathrm {V}}{\mathrm {O_{2max}}}\) assessment is not available, \(\mathrm {HR_{max}}\) is often used to prescribe exercise intensities for training and rehabilitation. In the absence of maximal cardiopulmonary exercise testing (CPET), \(\mathrm {HR_{max}}\) and \(\dot{\mathrm {V}}{\mathrm {O_{2max}}}\) are typically estimated using traditional submaximal prediction methods with well-known limitations and inaccuracies. For this study, 12 regularly exercising healthy young adult males performed a bout of maximal CPET on a cycle ergometer to determine their true \(\mathrm {HR_{max}}\) and \(\dot{\mathrm {V}}{\mathrm {O_{2max}}}\). Participants also performed a submaximal bout of exercise at varied intensities. A dynamical system model and heuristic parameter estimation algorithm were applied to the submaximal data to estimate the participants’ \(\mathrm {HR_{max}}\) and \(\dot{\mathrm {V}}{\mathrm {O_{2max}}}\). The submaximal predictions were evaluated by computing the coefficient of determination \({R^2}\) and the standard error of the estimate (SEE) through comparisons with the true maximal values for \(\mathrm {HR_{max}}\) (\({R^2 = 0.96}\), SEE = 2.4 bpm) and \(\dot{\mathrm {V}}{\mathrm {O_{2max}}}\) (\({R^2 = 0.93}\), SEE = 2.1 mL kg\(^{-1}\) min\(^{-1}\)). The results from this study suggest that a dynamical system model and heuristic parameter estimation algorithm can provide accurate predictions for \(\mathrm {HR_{max}}\) and \(\dot{\mathrm {V}}{\mathrm {O_{2max}}}\) using data collected from a submaximal testing protocol.

Keywords

Dynamical systems Heuristic algorithms Maximal oxygen uptake Maximum heart rate Nonlinear dynamics Parameter estimation Submaximal predictions 
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Notes

Compliance with ethical standards

Conflict of interest

The authors have filed a U.S. provisional patent application (No. 62/271,411) and an international patent application (PCT/US2016/068814) related to the systems and methods for predicting \(\mathrm {HR_{max}}\) and \(\dot{\mathrm {V}}{\mathrm {O_{2max}}}\) discussed in this paper.

Ethical standard

All aspects of this study were approved by the institutional review board, and informed written consent was obtained from each participant.

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Copyright information

© International Sports Engineering Association 2017

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and Materials ScienceDuke UniversityDurhamUSA
  2. 2.Department of Exercise and Sport ScienceUniversity of North Carolina at Chapel HillChapel HillUSA
  3. 3.Department of KinesiologyUniversity of North Carolina at GreensboroGreensboroUSA
  4. 4.Lineberger Comprehensive Cancer CenterUniversity of North Carolina at Chapel HillChapel HillUSA

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