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Do muscle synergies reduce the dimensionality of behavior?

Kuppuswamy N, Harris CM - Front Comput Neurosci (2014)

Bottom Line: Dimensionality of various reaching trajectories is compared when using idealized temporal synergies.The results indicate that a trajectory and synergy basis specific DR of behavior results from muscle synergy control.The implications of these results for the synergy hypothesis, optimal motor control, motor development, and robotics are discussed.

View Article: PubMed Central - PubMed

Affiliation: Artificial Intelligence Laboratory, Department of Informatics, University of Zürich Zürich, Switzerland.

ABSTRACT
The muscle synergy hypothesis is an archetype of the notion of Dimensionality Reduction (DR) occurring in the central nervous system due to modular organization. Toward validating this hypothesis, it is important to understand if muscle synergies can reduce the state-space dimensionality while maintaining task control. In this paper we present a scheme for investigating this reduction utilizing the temporal muscle synergy formulation. Our approach is based on the observation that constraining the control input to a weighted combination of temporal muscle synergies also constrains the dynamic behavior of a system in a trajectory-specific manner. We compute this constrained reformulation of system dynamics and then use the method of system balancing for quantifying the DR; we term this approach as Trajectory Specific Dimensionality Analysis (TSDA). We then investigate the consequence of minimization of the dimensionality for a given task. These methods are tested in simulations on a linear (tethered mass) and a non-linear (compliant kinematic chain) system. Dimensionality of various reaching trajectories is compared when using idealized temporal synergies. We show that as a consequence of this Minimum Dimensional Control (MDC) model, smooth straight-line Cartesian trajectories with bell-shaped velocity profiles emerged as the optima for the reaching task. We also investigated the effect on dimensionality due to adding via-points to a trajectory. The results indicate that a trajectory and synergy basis specific DR of behavior results from muscle synergy control. The implications of these results for the synergy hypothesis, optimal motor control, motor development, and robotics are discussed.

No MeSH data available.


Trajectory Specific Dimensionality Analysis (TSDA) used to compare four benchmark trajectories. (A) The task is to reach position (0.5, 0.5) in 3 s tracing each of the four trajectories [T1, … T4]. Two kinds of temporal synergies are tested: (B) Fourier basis (order 4), and (C) Legendre polynomial basis (order 4) actuating the tethered mass system.
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Figure 3: Trajectory Specific Dimensionality Analysis (TSDA) used to compare four benchmark trajectories. (A) The task is to reach position (0.5, 0.5) in 3 s tracing each of the four trajectories [T1, … T4]. Two kinds of temporal synergies are tested: (B) Fourier basis (order 4), and (C) Legendre polynomial basis (order 4) actuating the tethered mass system.

Mentions: A set of four benchmark trajectories, denoted by Ti = ϕi(t), were compared using TSDA for the tethered mass system. Each trajectory described a motion from the origin to a target output position of [0.5, 0.5], each thus representing a solution to the reaching task. The trajectories, seen in Figure 3A, were specified by via-points in Cartesian space and cubic-spline fit was computed with smoothness conditions enforced at the boundaries (2nd order boundary conditions set to 0). The weight matrix Ŵi for the control of each of the trajectories were computed using a least-squares fit of the corresponding inverse dynamic control signals udi(t). Two kinds of synergies were compared: Fourier and Legendre polynomial bases of order 4 each as seen in Figures 3B,C. In the case of the Fourier basis temporal synergy 9 components are necessary corresponding to the sinusoidal and co-sinusoidal parts of the Fourier basis as seen in Figure 3B.


Do muscle synergies reduce the dimensionality of behavior?

Kuppuswamy N, Harris CM - Front Comput Neurosci (2014)

Trajectory Specific Dimensionality Analysis (TSDA) used to compare four benchmark trajectories. (A) The task is to reach position (0.5, 0.5) in 3 s tracing each of the four trajectories [T1, … T4]. Two kinds of temporal synergies are tested: (B) Fourier basis (order 4), and (C) Legendre polynomial basis (order 4) actuating the tethered mass system.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4066703&req=5

Figure 3: Trajectory Specific Dimensionality Analysis (TSDA) used to compare four benchmark trajectories. (A) The task is to reach position (0.5, 0.5) in 3 s tracing each of the four trajectories [T1, … T4]. Two kinds of temporal synergies are tested: (B) Fourier basis (order 4), and (C) Legendre polynomial basis (order 4) actuating the tethered mass system.
Mentions: A set of four benchmark trajectories, denoted by Ti = ϕi(t), were compared using TSDA for the tethered mass system. Each trajectory described a motion from the origin to a target output position of [0.5, 0.5], each thus representing a solution to the reaching task. The trajectories, seen in Figure 3A, were specified by via-points in Cartesian space and cubic-spline fit was computed with smoothness conditions enforced at the boundaries (2nd order boundary conditions set to 0). The weight matrix Ŵi for the control of each of the trajectories were computed using a least-squares fit of the corresponding inverse dynamic control signals udi(t). Two kinds of synergies were compared: Fourier and Legendre polynomial bases of order 4 each as seen in Figures 3B,C. In the case of the Fourier basis temporal synergy 9 components are necessary corresponding to the sinusoidal and co-sinusoidal parts of the Fourier basis as seen in Figure 3B.

Bottom Line: Dimensionality of various reaching trajectories is compared when using idealized temporal synergies.The results indicate that a trajectory and synergy basis specific DR of behavior results from muscle synergy control.The implications of these results for the synergy hypothesis, optimal motor control, motor development, and robotics are discussed.

View Article: PubMed Central - PubMed

Affiliation: Artificial Intelligence Laboratory, Department of Informatics, University of Zürich Zürich, Switzerland.

ABSTRACT
The muscle synergy hypothesis is an archetype of the notion of Dimensionality Reduction (DR) occurring in the central nervous system due to modular organization. Toward validating this hypothesis, it is important to understand if muscle synergies can reduce the state-space dimensionality while maintaining task control. In this paper we present a scheme for investigating this reduction utilizing the temporal muscle synergy formulation. Our approach is based on the observation that constraining the control input to a weighted combination of temporal muscle synergies also constrains the dynamic behavior of a system in a trajectory-specific manner. We compute this constrained reformulation of system dynamics and then use the method of system balancing for quantifying the DR; we term this approach as Trajectory Specific Dimensionality Analysis (TSDA). We then investigate the consequence of minimization of the dimensionality for a given task. These methods are tested in simulations on a linear (tethered mass) and a non-linear (compliant kinematic chain) system. Dimensionality of various reaching trajectories is compared when using idealized temporal synergies. We show that as a consequence of this Minimum Dimensional Control (MDC) model, smooth straight-line Cartesian trajectories with bell-shaped velocity profiles emerged as the optima for the reaching task. We also investigated the effect on dimensionality due to adding via-points to a trajectory. The results indicate that a trajectory and synergy basis specific DR of behavior results from muscle synergy control. The implications of these results for the synergy hypothesis, optimal motor control, motor development, and robotics are discussed.

No MeSH data available.