Biomechanics and Modeling in Mechanobiology

, Volume 18, Issue 6, pp 1837–1846 | Cite as

Assessment of the energy-related cost function over a range of walking speeds

  • Emiliano Pablo RaveraEmail author
  • Marcos José Crespo
  • Paola Andrea Catalfamo Formento
Original Paper


Cost funtions are needed for calculation of muscle forces in musculoskeletal models. The behavior of the energy-related cost function, proposed by Praagman et al. (J Biomech 39(4):758–765, 2006. (CFP), can be used as an optimization criteria in musculoskeletal models for studying gait. In particular, in this work, its performance is compared against two empirical phenomenological models at different walking speed conditions. Also, the sensitivity of the CFP function to model parameters, such as muscle mass, maximal isometric muscle force, optimal muscle fiber length and maximum muscle velocity of the contractile element, was analyzed. The obtained results showed that CFP presents different behavior (in terms of the normalized root-mean-squared deviation (NRMSD) and the coefficient of multiple correlation (CMC)) for different muscles. Also, it provided estimates with median of NRMSD between 0.176 and 0.299 and median of CMC between 0.703 and 0.865 both metrics for slow, free and fast walking speed, which could be considered as acceptable results. Furthermore, the results indicated that CFP is insensitive to changes in muscle mass and relatively sensitive to maximal isometric muscle force. However, CFP presented a noisy behavior on estimations of muscle energy rate for some muscle as compared to phenomenological models. Finally, estimations by CFP during gait are within the values obtained by the empirical phenomenological models.


Musculoskeletal model Optimization criteria Metabolic energy rate Walking speed conditions 



The authors thank the FLENI Institute for Neurological Research for providing data from healthy subjects.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Emiliano Pablo Ravera
    • 1
    • 2
    Email author
  • Marcos José Crespo
    • 3
  • Paola Andrea Catalfamo Formento
    • 1
    • 2
  1. 1.Group of Analysis, Modeling, Processing and Clinician Implementation of Biomechanical Signals and Systems, Bioengineering and Bioinformatics InstituteCONICET-UNEROro VerdeArgentina
  2. 2.Human Movement Research Laboratory (LIMH), School of EngineeringNational University of Entre Ríos (UNER)Oro VerdeArgentina
  3. 3.Laboratorio de análisis de marcha y movimientoLAMM y Tecnología en rehabilitación, Clínica de tecnología asistiva, TA. FLENIEscobarArgentina

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