The inactivation principle: mathematical solutions minimizing the absolute work and biological implications for the planning of arm movements.

PLoS Computational Biology. 2008;4(10):e1000194 DOI 10.1371/journal.pcbi.1000194

 

Journal Homepage

Journal Title: PLoS Computational Biology

ISSN: 1553-734X (Print); 1553-7358 (Online)

Publisher: Public Library of Science (PLoS)

LCC Subject Category: Science: Biology (General)

Country of publisher: United States

Language of fulltext: English

Full-text formats available: PDF, HTML, XML

 

AUTHORS


Bastien Berret

Christian Darlot

Frédéric Jean

Thierry Pozzo

Charalambos Papaxanthis

Jean Paul Gauthier

EDITORIAL INFORMATION

Peer review

Editorial Board

Instructions for authors

Time From Submission to Publication: 32 weeks

 

Abstract | Full Text

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.