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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) for comparing the Fourier and Legendre polynomial basis temporal synergies actuating the tethered mass system, tracing the benchmark trajectories [T1, … T4]. The synergy training is carried out using least-squares and full-dimensional inverse dynamics—The obtained weight matrices for the four trajectories are represented as Hinton diagrams (ellipse size is the magnitude, a dark region denotes positive weight and white region denotes a negative weight) for the (A) Fourier basis of size 2 × 9, and (B) Legendre polynomials of size 2 × 5. The corresponding cumulative normalized HSV magnitudes for (C) Fourier, and (D) Legendre polynomial basis synergies with the threshold tr = 0.975 represented in both cases by the solid black line. The DR was computed as fourier = [1, 3, 2, 3], and legendre = [1, 3, 3, 3]. The straight line trajectory has the minimum dimensionality for both of these synergy bases.
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Figure 4: Trajectory Specific Dimensionality Analysis (TSDA) for comparing the Fourier and Legendre polynomial basis temporal synergies actuating the tethered mass system, tracing the benchmark trajectories [T1, … T4]. The synergy training is carried out using least-squares and full-dimensional inverse dynamics—The obtained weight matrices for the four trajectories are represented as Hinton diagrams (ellipse size is the magnitude, a dark region denotes positive weight and white region denotes a negative weight) for the (A) Fourier basis of size 2 × 9, and (B) Legendre polynomials of size 2 × 5. The corresponding cumulative normalized HSV magnitudes for (C) Fourier, and (D) Legendre polynomial basis synergies with the threshold tr = 0.975 represented in both cases by the solid black line. The DR was computed as fourier = [1, 3, 2, 3], and legendre = [1, 3, 3, 3]. The straight line trajectory has the minimum dimensionality for both of these synergy bases.

Mentions: The result of the weight training can be seen in the Hinton diagrams of the weight matrices in Figures 4A,B. The weights, represented by the size of the shaded ellipses, clearly capture the temporal components of each of the trajectories. However, some trajectories are easier to interpret and understand for one kind of synergy alone. For instance, while the weights corresponding to trajectory T1 are identical in both rows, in the case of T3, mirroring of weights across the inputs is seen only for the Fourier basis synergy.


Do muscle synergies reduce the dimensionality of behavior?

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

Trajectory Specific Dimensionality Analysis (TSDA) for comparing the Fourier and Legendre polynomial basis temporal synergies actuating the tethered mass system, tracing the benchmark trajectories [T1, … T4]. The synergy training is carried out using least-squares and full-dimensional inverse dynamics—The obtained weight matrices for the four trajectories are represented as Hinton diagrams (ellipse size is the magnitude, a dark region denotes positive weight and white region denotes a negative weight) for the (A) Fourier basis of size 2 × 9, and (B) Legendre polynomials of size 2 × 5. The corresponding cumulative normalized HSV magnitudes for (C) Fourier, and (D) Legendre polynomial basis synergies with the threshold tr = 0.975 represented in both cases by the solid black line. The DR was computed as fourier = [1, 3, 2, 3], and legendre = [1, 3, 3, 3]. The straight line trajectory has the minimum dimensionality for both of these synergy bases.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: Trajectory Specific Dimensionality Analysis (TSDA) for comparing the Fourier and Legendre polynomial basis temporal synergies actuating the tethered mass system, tracing the benchmark trajectories [T1, … T4]. The synergy training is carried out using least-squares and full-dimensional inverse dynamics—The obtained weight matrices for the four trajectories are represented as Hinton diagrams (ellipse size is the magnitude, a dark region denotes positive weight and white region denotes a negative weight) for the (A) Fourier basis of size 2 × 9, and (B) Legendre polynomials of size 2 × 5. The corresponding cumulative normalized HSV magnitudes for (C) Fourier, and (D) Legendre polynomial basis synergies with the threshold tr = 0.975 represented in both cases by the solid black line. The DR was computed as fourier = [1, 3, 2, 3], and legendre = [1, 3, 3, 3]. The straight line trajectory has the minimum dimensionality for both of these synergy bases.
Mentions: The result of the weight training can be seen in the Hinton diagrams of the weight matrices in Figures 4A,B. The weights, represented by the size of the shaded ellipses, clearly capture the temporal components of each of the trajectories. However, some trajectories are easier to interpret and understand for one kind of synergy alone. For instance, while the weights corresponding to trajectory T1 are identical in both rows, in the case of T3, mirroring of weights across the inputs is seen only for the Fourier basis synergy.

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.