1287_ch12.pdf

Cortical Control of

Motor Learning

Camillo Padoa-Schioppa, Emilio Bizzi,

and Ferdinando A. Mussa-Ivaldi

CONTENTS

Abstract

12.1Dynamics

12.2Internal Models

12.3Evidence for Inverse Internal Models

12.4Neuronal Activity Recorded during Adaptation: Learning a New

Dynamics

12.5Motor Performance and Motor Learning in the Primary Motor Cortex

12.6Neuronal Plasticity in Other Motor Areas

12.7Review of Studies on Cortical Plasticity

12.8Conclusions and Future Directions on Motor Learning

References

ABSTRACT

The execution of the simplest gestures requires the accurate coordination of several

muscles. In robotic systems, engineers coordinate the action of multiple motors by

writing computer code that speciﬁes how the motors must be activated for achieving

the desired robot motion and for compensating for unexpected disturbance. Humans

and animals follow another path. Something akin to programming is achieved in

nature by the biological mechanisms of synaptic plasticity; that is, by the variation

in efﬁcacy of neural transmission brought about by past history of pre- and post-

synaptic signals. However, robots and animals differ in another important way.

Robots (at least those of the current generations) have ﬁxed mechanical structure

and dimensions. In contrast, the mechanics of muscles, bones, and ligaments change

over time: the length of our limbs varies as we grow into adulthood; some part of

our body may lose its functionality following a lesion or a degenerative process;

muscle mechanics may vary over just a few minutes of intense activity. Because of

these changes, the central nervous system must continuously adapt motor commands

to the mechanics of the body. Adaptation — the ability to carry previously learned

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motor skills into new mechanical contexts — is a form of motor learning. In this

chapter, we present a view of motor learning that starts from the analysis of the

computational problems associated with the execution of the simplest gestures. We

discuss the theoretical idea of internal models and present some evidence and

theoretical considerations suggesting that internal models of limb dynamics may be

obtained by the combination of simple modules or “motor primitives.” Then, we

review some experimental results on the activity of neurons in the cortex during a

learning task. These ﬁndings suggest that the motor cortical areas include neurons

that process well-acquired movements as well as neurons that change their behavior

during and after being exposed to a new task.

12.1 DYNAMICS

According to the laws of Newtonian mechanics, in order to impress a motion upon

an object one must apply a force directly proportional to the desired acceleration.

This is Newton’s equation

A desired motion of an object is a sequence of positions

= m

x(t)

that one wishes

. Such a sequence is called a

trajectory and is mathematically represented as a function,

. To use Newton’s

equation for deriving the needed time-sequence of forces, one must calculate the

ﬁrst temporal derivative of the trajectory, the velocity, and then the second temporal

derivative, the acceleration. Finally, one obtains the desired force from this acceler-

ation. This is an example of inverse dynamic computation. The problem of direct

dynamics is to compute the trajectory resulting from the application of a force.

One of the central questions in motor control is how the central nervous system

solves the inverse dynamics problem and generates the motor commands that guide

our limbs.

x = x(t)

A system of second-order nonlinear differential equations is generally

considered to be an adequate representation for the passive dynamics of a limb. A

compact expression for such a system is as follows:

D qqq

(, ˙ , ˙˙ )

=τ

( )

(12.1)

where represent the limb conﬁguration vector — for example the vector

of joint angles — and its ﬁrst and second time derivatives. The term

qq q

()

is a vector

of joint torques at time

— it plays the role of

in Newton’s equation. In practice,

— may have a few terms for a

two-joint planar arm ( Figure 12.1 ) or it may take several pages for more realistic

models of the arm’s multiple-joint geometry. The inverse dynamics approach to the

control of multiple-joint limbs consists in solving explicitly for a torque trajectory

— which corresponds to m

(

) given a desired trajectory of the limb

D ()

. This is done by replacing

D ()

the variable

on the left side of Equation 12.1:

() ( (), ˙ (), ˙˙ ())

Dqt qtqt

(12.2)

the limb to occupy at subsequent instants of time

, d

the expression for

for

0.8

0.6

0.4

0.2

q 2

q 1

–0.6

–0.4

–0.2

0.2

0.4

0.6

D 1 = (I 1 + I 2 + m 2 l 1 l 2 cos (q 2 ) +

m 1 l 1 2 + m 2 l 2 2

+ m 2 l 1 2 ) ¨ 1 +

+ (I 2 + cos (q 2 ) +

m 2 l 1 l 2

m 2 l 2 2

) ¨ 2 –

m 2 l 1 l 2

sin (q 2 )q ˙ 2 2 +

– m 2 l 1 l 2 sin(q 2 )q ˙ 1 q ˙ 2 + b 1 (q 1 ,q 2 ,q ˙ 1 ,q ˙ 2 )

D 2 = (I 2 + cos (q 2 ) +

m 2 l 1 l 2

m 2 l 2 2

) ¨ 1 + (I 2 +

m 2 l 2 2

) ¨ 2 +

m 2 l 1 l 2

–

sin(q ˙ 2 )q ˙ 1 2 + b 2 (q 1 ,q 2 ,q ˙ 1 ,q ˙ 2 )

Simpliﬁed model of planar limb dynamics. The mechanics of the arm are

approximated by a two-joint mechanism with angles

(with respect to the torso) and

(with respect to the forearm, respectively (

top

). The dynamics are described by two nonlinear

) to

the angular position velocity and acceleration of both joints. The parameters that appear in

these expressions are the lengths of the two segments (

bottom

) that relate the joint torques at the shoulder (

) and at the elbow (

and

); their masses (

and

);

). The numerical values used in the simulations are the

same as those listed in Table 1 of Shadmehr and Mussa-Ivaldi

and

and correspond to values

describe the viscoelastic behavior

of the resting arm. They are simulated here by linear stiffness and viscosity matrices. (From

Reference 4, with permission.)

and

12.2 INTERNAL MODELS

suggested that the nervous system may store speciﬁc

solutions of Equation 12.2 corresponding to the desired motions of the body. How-

ever, simple considerations about the geometrical space of meaningful behaviors are

sufﬁcient to establish that this approach would be inadequate.

2,3

An alternative

FIGURE 12.1

equations (

their moments of inertia (

estimated from an experimental subject. The terms

Early models of motor control

who studied the task of balancing

an inverted pendulum with a robotic arm. They found that robots can be trained to

carry out this task successfully when they can build an internal model of the dynamics

associated with the balancing act. Such a model may be constructed using data

derived from the observation of humans engaging competently in the same task.

The term

refers either to (1) the transformation from a motor

command to the consequent behavior, or to (2) the transformation from a desired

behavior to the corresponding motor command.

A model of the ﬁrst kind is called

a forward model. Forward models provide the control system with the means to

predict the outcome of a command, and to estimate the current state in the presence

of feedback delay. A representation of the mapping from planned actions to motor

commands is called an inverse model. Strong experimental evidence for the existence

of internal models has been offered by studies of the adaptation of arm movements

to perturbing force ﬁelds.

7–12

12.3 EVIDENCE FOR INVERSE INTERNAL MODELS

They asked

subjects to make reaching movements in the presence of externally imposed forces.

These forces were produced by a robot whose free endpoint was held as a pointer

by the subjects ( Figure 12.2A ). The subjects were asked to execute reaching move-

ments toward a number of visual targets. Since the force ﬁeld produced by the robot

(Figure 12.2B) signiﬁcantly changed the dynamics of the reaching movements, the

subjects’ movements initially were grossly distorted (Figure 12.2D) when compared

to the undisturbed movements (Figure 12.2C). However, with practice, the subjects’

hand trajectories in the force ﬁeld converged to a path similar to that produced in

absence of any perturbing force ( Figure 12.3 ).

Subjects’ recovery of performance is due to learning. After the training had been

established, the force ﬁeld was unexpectedly removed for the duration of a single

hand movement. The resulting trajectories ( Figure 12.4 ) , named after-effects, were

approximate mirror images of those that the same subjects produced when they had

initially been exposed to the force ﬁeld. The emergence of after-effects indicates

that the central nervous system had composed an internal model of the external ﬁeld.

The internal model was generating patterns of force that effectively anticipated the

disturbing forces that the moving hand was encountering. The fact that these learned

forces compensated for the disturbances applied by the robotic arm during the

subjects’ reaching movements indicates that the central nervous system programs

these forces in advance. The after-effects demonstrate that these forces are not the

products of some reﬂex compensation of the disturbing ﬁeld.

approach postulates that the motor system solves the problems of dynamics by

constructing internal representations of the way in which limbs respond to applied

forces. These representations would allow us to generate new behaviors and to handle

situations that we have not yet encountered. A vivid illustration of how explicit

representations of dynamics, also called internal models, may facilitate motor learn-

ing is offered by the work of Schaal and Atkeson,

internal model

One way to test for the existence of inverse internal models is by changing the

dynamics that the central nervous system must control in order to execute a desired

movement. This approach was adopted by Shadmehr and Mussa-Ivaldi.

0.5

–0.5

–1

10 cm

–1

–0.5

0.5

Hand x-velocity (m/s)

150

100

–50

–100

–150

–100 –50 0

Displacement

50 100 150

–150

–100

–50 0 50 100 150

Displacement

Adaptation to external force ﬁelds. (A) Experimental apparatus. Subjects

executed planar arm movements while holding the handle of the manipulandum. A monitor

(not shown) placed in front of the subjects and above the manipulandum displayed the location

of the handle as well as targets of reaching movements. (B) Velocity-dependent force ﬁeld

generated by the manipulandum corresponding to the expression

with

B =

−

10 1

−

11 2

Newton sec/m.

−

11 2

11 1

]. (C) Unperturbed

reaching trajectories executed by a subject when the manipulandum was not producing

disturbing forces. (D) Initial responses observed when the force ﬁeld shown in (B) was applied

unexpectedly. The circles indicate the target locations. (Modiﬁed from Reference 7.)

was linearly related to the velocity of the hand,

= [v

, v

were designed to test the generalization of motor adaptation to regions

where training had not occurred. In these experiments, subjects were asked to execute

point-to-point planar movements between targets placed in one section of the work-

space. Their hand grasped the handle of the robot, which was used to record and

perturb their trajectories. Again, as in the experiments of Shadmehr and Mussa-Ivaldi,

FIGURE 12.2

The force

It is of interest to ask what the properties of the internal model are, and in

particular whether the model could generalize to regions of the state space where

the disturbing forces were not experienced. Recent experiments by Gandolfo and

coworkers

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