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A gain-field encoding of limb position and velocity in the internal model of arm dynamics.

Hwang EJ, Donchin O, Smith MA, Shadmehr R - PLoS Biol. (2003)

Bottom Line: The gain-field encoding makes the counterintuitive prediction of hypergeneralization: there should be growing extrapolation beyond the trained workspace.Furthermore, nonmonotonic force patterns should be more difficult to learn than monotonic ones.We confirmed these predictions experimentally.

View Article: PubMed Central - PubMed

Affiliation: Laboratory for Computational Motor Control, Department of Biomedical Engineering, Johns Hopkins School of Medicine, Baltimore, Maryland, USA. ehwang@bme.jhu.edu

ABSTRACT
Adaptability of reaching movements depends on a computation in the brain that transforms sensory cues, such as those that indicate the position and velocity of the arm, into motor commands. Theoretical consideration shows that the encoding properties of neural elements implementing this transformation dictate how errors should generalize from one limb position and velocity to another. To estimate how sensory cues are encoded by these neural elements, we designed experiments that quantified spatial generalization in environments where forces depended on both position and velocity of the limb. The patterns of error generalization suggest that the neural elements that compute the transformation encode limb position and velocity in intrinsic coordinates via a gain-field; i.e., the elements have directionally dependent tuning that is modulated monotonically with limb position. The gain-field encoding makes the counterintuitive prediction of hypergeneralization: there should be growing extrapolation beyond the trained workspace. Furthermore, nonmonotonic force patterns should be more difficult to learn than monotonic ones. We confirmed these predictions experimentally.

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Adaptation with Basis Elements That Encode Limb Position and Velocity as a Gain-Field(A) A polar plot of activation pattern for a typical basis function in the model. The polar plot at the center represents activation for an eight-direction center-out reaching task (targets at 10 cm). Starting point of each movement is the center of the polar plot. The shaded circle represents the activation during a center-hold period and the polygon represents average activation during the movement period. The eight polar plots on the periphery represent activation for eight different starting positions. Each starting position corresponds to the location of the center of each polar plot. The preferred positional gradient of this particular basis function has a rightward direction. The preferred velocity is an elbow flexion at 62°/s.(B) A state diagram of weights in a simple system with two basis functions. The trajectory from the origin to (½kd, −½kd) shows how weights converge to the final values trial-by-trial. Three dotted lines represent weights for no errors on the left, center, and right movements, respectively. Two vectors represent the direction of weight change after left and right movements each.(C) The bases were used in an adaptive controller to learn the task in Figure 1. Format is the same as Figure 2A; correlation coefficient of the simulated to subject data is 0.97.(D) Simulated movement errors in an experiment where spatial distance was the same as in Group 4 in Figure 2B; correlation coefficient is 0.86.(E) Learning index of the last target set against spatial distance. Dotted lines are from the simulation and thick solid lines are from subjects; correlation coefficient is 0.96. Note that thick solid lines are the same lines as in Figure 2C.(F) Generalization index in the last target set against spatial distance. Dotted lines are from the simulation and solid lines are from subjects; correlation coefficient is 0.99.
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pbio.0000025-g003: Adaptation with Basis Elements That Encode Limb Position and Velocity as a Gain-Field(A) A polar plot of activation pattern for a typical basis function in the model. The polar plot at the center represents activation for an eight-direction center-out reaching task (targets at 10 cm). Starting point of each movement is the center of the polar plot. The shaded circle represents the activation during a center-hold period and the polygon represents average activation during the movement period. The eight polar plots on the periphery represent activation for eight different starting positions. Each starting position corresponds to the location of the center of each polar plot. The preferred positional gradient of this particular basis function has a rightward direction. The preferred velocity is an elbow flexion at 62°/s.(B) A state diagram of weights in a simple system with two basis functions. The trajectory from the origin to (½kd, −½kd) shows how weights converge to the final values trial-by-trial. Three dotted lines represent weights for no errors on the left, center, and right movements, respectively. Two vectors represent the direction of weight change after left and right movements each.(C) The bases were used in an adaptive controller to learn the task in Figure 1. Format is the same as Figure 2A; correlation coefficient of the simulated to subject data is 0.97.(D) Simulated movement errors in an experiment where spatial distance was the same as in Group 4 in Figure 2B; correlation coefficient is 0.86.(E) Learning index of the last target set against spatial distance. Dotted lines are from the simulation and thick solid lines are from subjects; correlation coefficient is 0.96. Note that thick solid lines are the same lines as in Figure 2C.(F) Generalization index in the last target set against spatial distance. Dotted lines are from the simulation and solid lines are from subjects; correlation coefficient is 0.99.

Mentions: One way to represent limb position and velocity is with basis elements that encode each variable and then add them. However, additive encoding cannot adapt to fields that are nonlinear functions of position and velocity, e.g., f (x, ẋ) = (x / d)·Bẋ. This is the force field that describes the task we considered in the previous section. A theoretical study suggests that to adapt to such nonlinear fields, the basis functions of the combined space must be formed multiplicatively rather than additively (Pouget and Sejnowski 1997). We chose to use a multiplicative combination of position and velocity. Thus, we hypothesized that position and velocity encoding are combined via a gain-field mechanism; i.e., the bases have velocity-dependent receptive fields, and the discharges in these receptive fields are linearly modulated by arm position (Figure 3A).


A gain-field encoding of limb position and velocity in the internal model of arm dynamics.

Hwang EJ, Donchin O, Smith MA, Shadmehr R - PLoS Biol. (2003)

Adaptation with Basis Elements That Encode Limb Position and Velocity as a Gain-Field(A) A polar plot of activation pattern for a typical basis function in the model. The polar plot at the center represents activation for an eight-direction center-out reaching task (targets at 10 cm). Starting point of each movement is the center of the polar plot. The shaded circle represents the activation during a center-hold period and the polygon represents average activation during the movement period. The eight polar plots on the periphery represent activation for eight different starting positions. Each starting position corresponds to the location of the center of each polar plot. The preferred positional gradient of this particular basis function has a rightward direction. The preferred velocity is an elbow flexion at 62°/s.(B) A state diagram of weights in a simple system with two basis functions. The trajectory from the origin to (½kd, −½kd) shows how weights converge to the final values trial-by-trial. Three dotted lines represent weights for no errors on the left, center, and right movements, respectively. Two vectors represent the direction of weight change after left and right movements each.(C) The bases were used in an adaptive controller to learn the task in Figure 1. Format is the same as Figure 2A; correlation coefficient of the simulated to subject data is 0.97.(D) Simulated movement errors in an experiment where spatial distance was the same as in Group 4 in Figure 2B; correlation coefficient is 0.86.(E) Learning index of the last target set against spatial distance. Dotted lines are from the simulation and thick solid lines are from subjects; correlation coefficient is 0.96. Note that thick solid lines are the same lines as in Figure 2C.(F) Generalization index in the last target set against spatial distance. Dotted lines are from the simulation and solid lines are from subjects; correlation coefficient is 0.99.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC261873&req=5

pbio.0000025-g003: Adaptation with Basis Elements That Encode Limb Position and Velocity as a Gain-Field(A) A polar plot of activation pattern for a typical basis function in the model. The polar plot at the center represents activation for an eight-direction center-out reaching task (targets at 10 cm). Starting point of each movement is the center of the polar plot. The shaded circle represents the activation during a center-hold period and the polygon represents average activation during the movement period. The eight polar plots on the periphery represent activation for eight different starting positions. Each starting position corresponds to the location of the center of each polar plot. The preferred positional gradient of this particular basis function has a rightward direction. The preferred velocity is an elbow flexion at 62°/s.(B) A state diagram of weights in a simple system with two basis functions. The trajectory from the origin to (½kd, −½kd) shows how weights converge to the final values trial-by-trial. Three dotted lines represent weights for no errors on the left, center, and right movements, respectively. Two vectors represent the direction of weight change after left and right movements each.(C) The bases were used in an adaptive controller to learn the task in Figure 1. Format is the same as Figure 2A; correlation coefficient of the simulated to subject data is 0.97.(D) Simulated movement errors in an experiment where spatial distance was the same as in Group 4 in Figure 2B; correlation coefficient is 0.86.(E) Learning index of the last target set against spatial distance. Dotted lines are from the simulation and thick solid lines are from subjects; correlation coefficient is 0.96. Note that thick solid lines are the same lines as in Figure 2C.(F) Generalization index in the last target set against spatial distance. Dotted lines are from the simulation and solid lines are from subjects; correlation coefficient is 0.99.
Mentions: One way to represent limb position and velocity is with basis elements that encode each variable and then add them. However, additive encoding cannot adapt to fields that are nonlinear functions of position and velocity, e.g., f (x, ẋ) = (x / d)·Bẋ. This is the force field that describes the task we considered in the previous section. A theoretical study suggests that to adapt to such nonlinear fields, the basis functions of the combined space must be formed multiplicatively rather than additively (Pouget and Sejnowski 1997). We chose to use a multiplicative combination of position and velocity. Thus, we hypothesized that position and velocity encoding are combined via a gain-field mechanism; i.e., the bases have velocity-dependent receptive fields, and the discharges in these receptive fields are linearly modulated by arm position (Figure 3A).

Bottom Line: The gain-field encoding makes the counterintuitive prediction of hypergeneralization: there should be growing extrapolation beyond the trained workspace.Furthermore, nonmonotonic force patterns should be more difficult to learn than monotonic ones.We confirmed these predictions experimentally.

View Article: PubMed Central - PubMed

Affiliation: Laboratory for Computational Motor Control, Department of Biomedical Engineering, Johns Hopkins School of Medicine, Baltimore, Maryland, USA. ehwang@bme.jhu.edu

ABSTRACT
Adaptability of reaching movements depends on a computation in the brain that transforms sensory cues, such as those that indicate the position and velocity of the arm, into motor commands. Theoretical consideration shows that the encoding properties of neural elements implementing this transformation dictate how errors should generalize from one limb position and velocity to another. To estimate how sensory cues are encoded by these neural elements, we designed experiments that quantified spatial generalization in environments where forces depended on both position and velocity of the limb. The patterns of error generalization suggest that the neural elements that compute the transformation encode limb position and velocity in intrinsic coordinates via a gain-field; i.e., the elements have directionally dependent tuning that is modulated monotonically with limb position. The gain-field encoding makes the counterintuitive prediction of hypergeneralization: there should be growing extrapolation beyond the trained workspace. Furthermore, nonmonotonic force patterns should be more difficult to learn than monotonic ones. We confirmed these predictions experimentally.

Show MeSH
Related in: MedlinePlus