Cargando…

The Inactivation Principle: Mathematical Solutions Minimizing the Absolute Work and Biological Implications for the Planning of Arm Movements

An important question in the literature focusing on motor control is to determine which laws drive biological limb movements. This question has prompted numerous investigations analyzing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually...

Descripción completa

Detalles Bibliográficos
Autores principales: Berret, Bastien, Darlot, Christian, Jean, Frédéric, Pozzo, Thierry, Papaxanthis, Charalambos, Gauthier, Jean Paul
Formato: Texto
Lenguaje:English
Publicado: Public Library of Science 2008
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2561290/
https://www.ncbi.nlm.nih.gov/pubmed/18949023
http://dx.doi.org/10.1371/journal.pcbi.1000194
_version_ 1782159719371112448
author Berret, Bastien
Darlot, Christian
Jean, Frédéric
Pozzo, Thierry
Papaxanthis, Charalambos
Gauthier, Jean Paul
author_facet Berret, Bastien
Darlot, Christian
Jean, Frédéric
Pozzo, Thierry
Papaxanthis, Charalambos
Gauthier, Jean Paul
author_sort Berret, Bastien
collection PubMed
description An important question in the literature focusing on motor control is to determine which laws drive biological limb movements. This question has prompted numerous investigations analyzing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually performed satisfies an optimality criterion. In the framework of optimal control theory, a first approach is to choose a cost function and test whether the proposed model fits with experimental data. A second approach (generally considered as the more difficult) is to infer the cost function from behavioral data. The cost proposed here includes a term called the absolute work of forces, reflecting the mechanical energy expenditure. Contrary to most investigations studying optimality principles of arm movements, this model has the particularity of using a cost function that is not smooth. First, a mathematical theory related to both direct and inverse optimal control approaches is presented. The first theoretical result is the Inactivation Principle, according to which minimizing a term similar to the absolute work implies simultaneous inactivation of agonistic and antagonistic muscles acting on a single joint, near the time of peak velocity. The second theoretical result is that, conversely, the presence of non-smoothness in the cost function is a necessary condition for the existence of such inactivation. Second, during an experimental study, participants were asked to perform fast vertical arm movements with one, two, and three degrees of freedom. Observed trajectories, velocity profiles, and final postures were accurately simulated by the model. In accordance, electromyographic signals showed brief simultaneous inactivation of opposing muscles during movements. Thus, assuming that human movements are optimal with respect to a certain integral cost, the minimization of an absolute-work-like cost is supported by experimental observations. Such types of optimality criteria may be applied to a large range of biological movements.
format Text
id pubmed-2561290
institution National Center for Biotechnology Information
language English
publishDate 2008
publisher Public Library of Science
record_format MEDLINE/PubMed
spelling pubmed-25612902008-10-24 The Inactivation Principle: Mathematical Solutions Minimizing the Absolute Work and Biological Implications for the Planning of Arm Movements Berret, Bastien Darlot, Christian Jean, Frédéric Pozzo, Thierry Papaxanthis, Charalambos Gauthier, Jean Paul PLoS Comput Biol Research Article An important question in the literature focusing on motor control is to determine which laws drive biological limb movements. This question has prompted numerous investigations analyzing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually performed satisfies an optimality criterion. In the framework of optimal control theory, a first approach is to choose a cost function and test whether the proposed model fits with experimental data. A second approach (generally considered as the more difficult) is to infer the cost function from behavioral data. The cost proposed here includes a term called the absolute work of forces, reflecting the mechanical energy expenditure. Contrary to most investigations studying optimality principles of arm movements, this model has the particularity of using a cost function that is not smooth. First, a mathematical theory related to both direct and inverse optimal control approaches is presented. The first theoretical result is the Inactivation Principle, according to which minimizing a term similar to the absolute work implies simultaneous inactivation of agonistic and antagonistic muscles acting on a single joint, near the time of peak velocity. The second theoretical result is that, conversely, the presence of non-smoothness in the cost function is a necessary condition for the existence of such inactivation. Second, during an experimental study, participants were asked to perform fast vertical arm movements with one, two, and three degrees of freedom. Observed trajectories, velocity profiles, and final postures were accurately simulated by the model. In accordance, electromyographic signals showed brief simultaneous inactivation of opposing muscles during movements. Thus, assuming that human movements are optimal with respect to a certain integral cost, the minimization of an absolute-work-like cost is supported by experimental observations. Such types of optimality criteria may be applied to a large range of biological movements. Public Library of Science 2008-10-24 /pmc/articles/PMC2561290/ /pubmed/18949023 http://dx.doi.org/10.1371/journal.pcbi.1000194 Text en Berret et al. http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
spellingShingle Research Article
Berret, Bastien
Darlot, Christian
Jean, Frédéric
Pozzo, Thierry
Papaxanthis, Charalambos
Gauthier, Jean Paul
The Inactivation Principle: Mathematical Solutions Minimizing the Absolute Work and Biological Implications for the Planning of Arm Movements
title The Inactivation Principle: Mathematical Solutions Minimizing the Absolute Work and Biological Implications for the Planning of Arm Movements
title_full The Inactivation Principle: Mathematical Solutions Minimizing the Absolute Work and Biological Implications for the Planning of Arm Movements
title_fullStr The Inactivation Principle: Mathematical Solutions Minimizing the Absolute Work and Biological Implications for the Planning of Arm Movements
title_full_unstemmed The Inactivation Principle: Mathematical Solutions Minimizing the Absolute Work and Biological Implications for the Planning of Arm Movements
title_short The Inactivation Principle: Mathematical Solutions Minimizing the Absolute Work and Biological Implications for the Planning of Arm Movements
title_sort inactivation principle: mathematical solutions minimizing the absolute work and biological implications for the planning of arm movements
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2561290/
https://www.ncbi.nlm.nih.gov/pubmed/18949023
http://dx.doi.org/10.1371/journal.pcbi.1000194
work_keys_str_mv AT berretbastien theinactivationprinciplemathematicalsolutionsminimizingtheabsoluteworkandbiologicalimplicationsfortheplanningofarmmovements
AT darlotchristian theinactivationprinciplemathematicalsolutionsminimizingtheabsoluteworkandbiologicalimplicationsfortheplanningofarmmovements
AT jeanfrederic theinactivationprinciplemathematicalsolutionsminimizingtheabsoluteworkandbiologicalimplicationsfortheplanningofarmmovements
AT pozzothierry theinactivationprinciplemathematicalsolutionsminimizingtheabsoluteworkandbiologicalimplicationsfortheplanningofarmmovements
AT papaxanthischaralambos theinactivationprinciplemathematicalsolutionsminimizingtheabsoluteworkandbiologicalimplicationsfortheplanningofarmmovements
AT gauthierjeanpaul theinactivationprinciplemathematicalsolutionsminimizingtheabsoluteworkandbiologicalimplicationsfortheplanningofarmmovements
AT berretbastien inactivationprinciplemathematicalsolutionsminimizingtheabsoluteworkandbiologicalimplicationsfortheplanningofarmmovements
AT darlotchristian inactivationprinciplemathematicalsolutionsminimizingtheabsoluteworkandbiologicalimplicationsfortheplanningofarmmovements
AT jeanfrederic inactivationprinciplemathematicalsolutionsminimizingtheabsoluteworkandbiologicalimplicationsfortheplanningofarmmovements
AT pozzothierry inactivationprinciplemathematicalsolutionsminimizingtheabsoluteworkandbiologicalimplicationsfortheplanningofarmmovements
AT papaxanthischaralambos inactivationprinciplemathematicalsolutionsminimizingtheabsoluteworkandbiologicalimplicationsfortheplanningofarmmovements
AT gauthierjeanpaul inactivationprinciplemathematicalsolutionsminimizingtheabsoluteworkandbiologicalimplicationsfortheplanningofarmmovements