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Numerical instability of Hill-type muscle models

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posted on 2023-02-03, 10:50 authored by Sang-Hoon Yeo, Jasper Verheul, Walter Herzog, Shinjiro Sueda

 Hill-type muscle models are highly preferred as phenomenological modelsfor musculoskeletal simulation studies despite their introduction almost acentury ago. The use of simple Hill-type models in simulations, instead ofmore recent cross-bridge models, is well justified since computationally‘light-weight’—although less accurate—Hill-type models have great valuefor large-scale simulations. However, this article aims to invite discussionon numerical instability issues of Hill-type muscle models in simulationstudies, which can lead to computational failures and, therefore, cannotbe simply dismissed as an inevitable but acceptable consequence ofsimplification. We will first revisit the basic premises and assumptions onthe force–length and force–velocity relationships that Hill-type models arebased upon, and their often overlooked but major theoretical limitations.We will then use several simple conceptual simulation studies to discusshow these numerical instability issues can manifest as practical compu-tational problems. Lastly, we will review how such numerical instabilityissues are dealt with, mostly in an ad hoc fashion, in two main areas ofapplication: musculoskeletal biomechanics and computer animation.  Hill-type muscle models are highly preferred as phenomenological modelsfor musculoskeletal simulation studies despite their introduction almost acentury ago. The use of simple Hill-type models in simulations, instead ofmore recent cross-bridge models, is well justified since computationally‘light-weight’—although less accurate—Hill-type models have great valuefor large-scale simulations. However, this article aims to invite discussionon numerical instability issues of Hill-type muscle models in simulationstudies, which can lead to computational failures and, therefore, cannotbe simply dismissed as an inevitable but acceptable consequence ofsimplification. We will first revisit the basic premises and assumptions onthe force–length and force–velocity relationships that Hill-type models arebased upon, and their often overlooked but major theoretical limitations.We will then use several simple conceptual simulation studies to discusshow these numerical instability issues can manifest as practical compu-tational problems. Lastly, we will review how such numerical instabilityissues are dealt with, mostly in an ad hoc fashion, in two main areas ofapplication: musculoskeletal biomechanics and computer animation. 

History

Published in

Journal of the Royal Society. Interface

Publisher

The Royal Society

Version

  • VoR (Version of Record)

Citation

Yeo, S. H., Verheul, J., Herzog, W., & Sueda, S. (2023) 'Numerical instability of Hill-type muscle models', Journal of the Royal Society Interface, 20(199), 20220430.

Print ISSN

1742-5689

Electronic ISSN

1742-5662

Cardiff Met Affiliation

  • Cardiff School of Sport and Health Sciences

Cardiff Met Authors

Jasper Verheul

Cardiff Met Research Centre/Group

  • High Performance

Copyright Holder

  • © The Authors

Language

  • en

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