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

Autor: Frédéric Jean, Bastien Berret, Thierry Pozzo, Jean-Paul Gauthier, Charalambos Papaxanthis, Christian Darlot
Přispěvatelé: Autard, Delphine, Motricité - Plasticité, Université de Bourgogne (UB)-Institut National de la Santé et de la Recherche Médicale (INSERM), Ecole Nationale Supérieure des Télécommunications (ENST), École Nationale Supérieure de Techniques Avancées (ENSTA Paris), Istituto Italiano di Tecnologia (IIT), Laboratoire des Sciences de l'Information et des Systèmes (LSIS), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Arts et Métiers Paristech ENSAM Aix-en-Provence-Centre National de la Recherche Scientifique (CNRS), This work is in part supported by the Centre National d'Etudes Spatiales and the Conseil Régional de Bourgogne, Centre National de la Recherche Scientifique (CNRS)-Arts et Métiers Paristech ENSAM Aix-en-Provence-Université de Toulon (UTLN)-Aix Marseille Université (AMU), Université de Bourgogne ( UB ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ), Ecole Nationale Supérieure des Télécommmunications [Paris] ( ENST Paris ), ENST Paris, École Nationale Supérieure de Techniques Avancées ( Univ. Paris-Saclay, ENSTA ParisTech ), Istituto Italiano di Tecnologia ( IIT ), Laboratoire des Sciences de l'Information et des Systèmes ( LSIS ), Aix Marseille Université ( AMU ) -Université de Toulon ( UTLN ) -Arts et Métiers Paristech ENSAM Aix-en-Provence-Centre National de la Recherche Scientifique ( CNRS )
Jazyk: angličtina
Rok vydání: 2008
Předmět:
Male
MESH: Range of Motion
Articular

MESH : Physical Exertion
MESH : Movement
Optimality criterion
[SDV.MHEP.PHY] Life Sciences [q-bio]/Human health and pathology/Tissues and Organs [q-bio.TO]
Computer science
MESH: Muscle Contraction
MESH: Gravitation
MESH : Models
Biological

MESH: Movement
Kinematics
MESH: Postural Balance
MESH : Gravitation
0302 clinical medicine
Neuroscience/Motor Systems
MESH : Feedback
MESH : Biomechanics
Range of Motion
Articular

MESH: Arm
MESH : Joints
lcsh:QH301-705.5
Postural Balance
MESH: Biomechanics
0303 health sciences
Neuroscience/Behavioral Neuroscience
Ecology
[ SDV.MHEP.PHY ] Life Sciences [q-bio]/Human health and pathology/Tissues and Organs [q-bio.TO]
MESH: Feedback
MESH : Adult
Biomechanical Phenomena
Mathematical theory
MESH: Joints
Computational Theory and Mathematics
Modeling and Simulation
Arm
Research Article
Gravitation
Muscle Contraction
Computer Science/Systems and Control Theory
Adult
MESH : Male
Movement
Physical Exertion
Computational Biology/Computational Neuroscience
MESH: Psychomotor Performance
Models
Biological

MESH : Arm
Feedback
MESH: Physical Exertion
03 medical and health sciences
Cellular and Molecular Neuroscience
MESH : Postural Balance
Control theory
[SDV.MHEP.PHY]Life Sciences [q-bio]/Human health and pathology/Tissues and Organs [q-bio.TO]
Genetics
Humans
Neuroscience/Theoretical Neuroscience
Molecular Biology
Ecology
Evolution
Behavior and Systematics

Simulation
030304 developmental biology
MESH: Humans
MESH : Humans
Work (physics)
MESH: Models
Biological

Motor control
MESH: Adult
MESH : Psychomotor Performance
Function (mathematics)
Optimal control
MESH: Male
Term (time)
MESH : Range of Motion
Articular

lcsh:Biology (General)
MESH : Muscle Contraction
Joints
030217 neurology & neurosurgery
Mathematics
Psychomotor Performance
Zdroj: PLoS Computational Biology
PLoS Computational Biology, 2008, 4 (10), pp.e1000194. ⟨10.1371/journal.pcbi.1000194⟩
PLoS Computational Biology, Public Library of Science, 2008, 4 (10), pp.e1000194. ⟨10.1371/journal.pcbi.1000194⟩
PLoS Computational Biology, Vol 4, Iss 10, p e1000194 (2008)
PLoS Computational Biology, Public Library of Science, 2008, 4 (10), pp.e1000194. 〈10.1371/journal.pcbi.1000194〉
ISSN: 1553-7358
1553-734X
DOI: 10.1371/journal.pcbi.1000194⟩
Popis: 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.
Author Summary When performing reaching and grasping movements, the brain has to choose one trajectory among an infinite set of possibilities. Nevertheless, because human and animal movements provide highly stereotyped features, motor strategies used by the brain were assumed to be optimal according to certain optimality criteria. In this study, we propose a theoretical model for motor planning of arm movements that minimizes a compromise between the absolute work exerted by the muscles and the integral of the squared acceleration. We demonstrate that under these assumptions agonistic and antagonistic muscles are inactivated during overlapping periods of time for quick enough movements. Moreover, it is shown that only this type of criterion can predict these inactivation periods. Finally, experimental evidence is in agreement with the predictions of the model. Indeed, we report the existence of simultaneous inactivation of opposing muscles during fast vertical arm movements. Therefore, this study suggests that biological movements partly optimize the energy expenditure, integrating both inertial and gravitational forces during the motor planning process.
Databáze: OpenAIRE