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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; Friston, Karl J. (editor)

PLoS Computational Biology, 2008, Vol.4(10) [Tạp chí có phản biện]

ISSN: 1553-734X ; E-ISSN: 1553-7358 ; DOI: 10.1371/journal.pcbi.1000194 ; PMCID: 2561290 ; PMID: 18949023

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  • Nhan đề:
    The Inactivation Principle: Mathematical Solutions Minimizing the Absolute Work and Biological Implications for the Planning of Arm Movements
  • Tác giả: Berret, Bastien ; Darlot, Christian ; Jean, Frédéric ; Pozzo, Thierry ; Papaxanthis, Charalambos ; Gauthier, Jean Paul
  • Friston, Karl J. (editor)
  • Chủ đề: Research Article ; Computational Biology/Computational Neuroscience ; Computer Science/Systems And Control Theory ; Mathematics ; Neuroscience/Behavioral Neuroscience ; Neuroscience/Motor Systems ; Neuroscience/Theoretical Neuroscience
  • Là 1 phần của: PLoS Computational Biology, 2008, Vol.4(10)
  • Mô tả: 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.
  • Số nhận dạng: ISSN: 1553-734X ; E-ISSN: 1553-7358 ; DOI: 10.1371/journal.pcbi.1000194 ; PMCID: 2561290 ; PMID: 18949023

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