A joint-space numerical model of metabolic energy expenditure for human multibody dynamic system

Joo H. Kim, Dustyn Roberts

Research output: Contribution to journalArticlepeer-review


Metabolic energy expenditure (MEE) is a critical performance measure of human motion. In this study, a general joint-space numerical model of MEE is derived by integrating the laws of thermodynamics and principles of multibody system dynamics, which can evaluate MEE without the limitations inherent in experimental measurements (phase delays, steady state and task restrictions, and limited range of motion) or muscle-space models (complexities and indeterminacies from excessive DOFs, contacts and wrapping interactions, and reliance on in vitro parameters). Muscle energetic components are mapped to the joint space, in which the MEE model is formulated. A constrained multi-objective optimization algorithm is established to estimate the model parameters from experimental walking data also used for initial validation. The joint-space parameters estimated directly from active subjects provide reliable MEE estimates with a mean absolute error of 3.6±3.6% relative to validation values, which can be used to evaluate MEE for complex non-periodic tasks that may not be experimentally verifiable. This model also enables real-time calculations of instantaneous MEE rate as a function of time for transient evaluations. Although experimental measurements may not be completely replaced by model evaluations, predicted quantities can be used as strong complements to increase reliability of the results and yield unique insights for various applications.

Original languageEnglish (US)
Pages (from-to)e02721
JournalInternational Journal for Numerical Methods in Biomedical Engineering
Issue number9
StatePublished - Sep 1 2015


  • First law of thermodynamics
  • Generalized coordinates
  • Heat dissipation
  • Joint space
  • Mechanical work
  • Metabolic energy expenditure
  • Muscle activation

ASJC Scopus subject areas

  • Software
  • Biomedical Engineering
  • Modeling and Simulation
  • Molecular Biology
  • Computational Theory and Mathematics
  • Applied Mathematics


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