The Organization and Planning of Movement
Motor Commands Arise Through Sensorimotor Transformations
The Central Nervous System Forms Internal Models of Sensorimotor Transformations
Movement Inaccuracies Arise from Errors and Variability in the Transformations
Different Coordinate Systems May Be Employed at Different Stages of Sensorimotor Transformations
Motor Signals Are Subject to Feedforward and Feedback Control
Motor Systems Must Adapt to Development and Experience
Motor Learning Involves Adapting Internal Models for Novel Kinematic and Dynamic Conditions
Kinematic and Dynamic Motor Learning Rely on Different Sensory Modalities
IN THE PRECEDING PART OF THIS BOOK we considered how the brain constructs internal representations of the world around us. These internal representations have no intrinsic value and are behaviorally meaningful only when used to guide movement, whether foraging for food or attracting a waiter’s attention. Thus the ultimate function of the sensory representations is to shape the actions of the motor systems. Sensory representations are the framework in which the motor systems plan, coordinate, and execute the motor programs responsible for purposeful movement.
In this part of the book we describe the principles of motor control that allow the brain and spinal cord to maintain balance and posture; to move our body, limbs, and eyes; and to communicate through speech and gesture.
Although movements are often classified according to function—eye movements, prehension (reach and grasp), posture, locomotion, breathing, and speech—many of these functions are subserved by overlapping groups of muscles. In addition, the same groups of muscles can be controlled voluntarily, rhythmically, or reflexively. For example, the muscles that control respiration can be used to take a deep breath voluntarily before diving under water, to breathe automatically and rhythmically in a regular cycle of inspiration and expiration, or to act reflexively in response to a noxious stimulus in the throat, producing a cough.
Voluntary movements are those that are under conscious control by the brain. Rhythmic movements can also be controlled voluntarily, but many such movements differ from voluntary movements in that their timing and spatial organization is to a large extent controlled autonomously by spinal or brain stem circuitry. Reflexes are stereotyped responses to specific stimuli that are generated by simple neural circuits in the spinal cord or brain stem. Although reflexes are highly adaptable to changes in behavioral goals, mainly because several different circuits exist to connect sensory and motor neurons, they cannot be directly controlled voluntarily.
In this chapter we focus on voluntary movements, using arm and hand movements to illustrate principles of sensorimotor control. Reflexes and rhythmic movements are discussed in detail in Chapters 35 and 36.
Conscious processes are not necessary for moment-to-moment control of movement. Although we may be aware of the intent to perform a task or of planning certain sequences of actions and at times are aware of deciding to move at a particular moment, movements generally seem to occur automatically. We carry out the most complicated movements without a thought to the actual joint motions or muscle contractions required. The tennis player does not consciously decide which muscles to use to return a serve with a backhand or which body parts must be moved to intercept the ball. In fact, thinking about each body movement before it takes place can disrupt the player’s performance.
In this chapter we review the principles that govern the neural control of movement using concepts derived from behavioral studies and from computational models that are used both to understand the brain and to control the movements of robots. First, we look at how the brain transforms sensory inputs into motor outputs through a cascade of sensorimotor transformations. Second, we examine how sensory feedback can be used to correct errors that arise during movement. Finally, we see how motor learning allows us to improve our performance; to adapt to new mechanical conditions, as when using a tool; or to adapt to novel correspondences between sensory and motor events, for example when learning to use a computer mouse to control a cursor.
Motor Commands Arise Through Sensorimotor Transformations
Motor outputs are neural commands that act on the muscles, causing them to contract and generate movement. These outputs are derived from sensory inputs in circuits that represent sensorimotor transformations. Sensory inputs include extrinsic information about the state of world as well as intrinsic information about our body. Extrinsic information, for example the spatial location of a target, can be provided by auditory and visual inputs. Intrinsic information includes both kinematic and kinetic information about our body.
Kinematic information includes the position, velocity, and acceleration of the hand, joint angles, and lengths of muscles without reference to the forces that cause them. Kinetic information is concerned with the forces generated or experienced by our body. These different forms of intrinsic information are provided by different sensors. For example, information about muscle lengths and their rate of change is provided mainly by muscle spindles, whereas Golgi tendon organs in the muscles and mechanoreceptors in our skin provide information about the force we are exerting.
Simple reflexes, such as a tendon-jerk reflex, involve a simple sensorimotor transformation: Sensory inputs cause motor output directly without the intervention of higher brain centers. However, voluntary movement requires multistage sensorimotor transformations. The involvement of multiple processing centers actually simplifies processing: Higher levels plan more general goals, whereas lower levels concern themselves with how these goals can be implemented.
Such a hierarchy accounts for the fact that a specific motor action, such as writing, can be performed in different ways with more or less the same result. Handwriting is structurally similar regardless of the size of the letters or the limb or body segment used to produce it (Figure 33-1). This phenomenon, termed motor equivalence, suggests that purposeful movements are represented in the brain abstractly rather than as sets of specific joint motions or muscle contractions. Such abstract representations of movement, able to drive different effectors, provide a degree of flexibility of action not practical with preset motor programs.
Figure 33-1 Motor equivalence. The ability of different motor systems to achieve the same behavior is called motor equivalence. For example, writing can be performed using different parts of the body. The examples here were written by the same person using the right (dominant) hand (A), the right hand with the wrist immobilized (B), the left hand (C), the pen gripped between the teeth (D), and the pen attached to the foot (E). (Reproduced, with permission, from Raibert 1977.)
How do sensorimotor transformations generate movement to a desired location? For a person to reach toward an object, sensory information about the target’s location must be converted into a sequence of muscle actions leading to joint rotations that will bring the hand to the target.
First, the target is localized in space relative to some part of the body such as the head or arm (egocentric space). Several sources of information are combined in this process. For example, the location of the target relative to the head is computed from the location of the target on each retina together with the direction of gaze of the eyes (Figure 33-2A). A person also needs to know the initial location of his hand or the tip of the tool that he wishes to place on the target (the end-effector or endpoint). The initial location of the endpoint can be estimated by combining visual inputs, proprioceptive signals, and tactile sensations, each of which can provide location information. Once the current configuration of the arm and location of the target are calculated, a movement can be planned. A plan typically has to specify both a particular path, the successive spatial positions of the endpoint, and also the trajectory, the time course over which these positions will be covered, and thus the accelerations and speeds of the movement (Figure 33-2B).
Figure 33-2 Sensorimotor transformations used to generate a particular movement. The task of generating a goal-directed movement is often broken down into a set of sequential stages, the details of which are still being elucidated. The figure shows one possible set of stages to generate a reaching movement, and the arrows indicate the processes required to move between the stages.
A. Spatial orientation. To reach for an object, the object and hand are first located visually in a coordinate system relative to the head (egocentric coordinates).
B. Movement planning. The direction and distance the hand must move to reach the object (the endpoint trajectory) are determined based on visual and proprioceptive information about the current locations of the arm and object.
C. Inverse kinematic transformation. The joint trajectories that will achieve the hand path are determined. The transformation from a desired hand movement to the joint trajectory depends on the kinematic properties of the arm, such as the lengths of the arm’s segments.
D. Inverse dynamic transformation. The joint torques or muscle activities that are necessary to achieve the desired joint trajectories are determined. The joint torques required to achieve a desired change in joint angles depend on the dynamic properties of the arm such as the mass of the segments.
In a hierarchical model of planning the goal can be expressed in kinematic terms, such as the desired positions and velocities of the hand, or in kinetic terms, such as the force exerted by the hand. Movement can be planned as an endpoint trajectory, a desired change in the configuration of the limb expressed in coordinates intrinsic to the limb. Such a coordinate system could determine the change in joint angles or be based on a desired change in proprioceptive feedback. For example, the endpoint trajectory could be defined kinematically as the distance and direction the hand has to move to reach the target, as well as the speed along the path to the target.
Transformations can be expressed as changes in kinematic variables, such as the position of the hand and the joint angles that place the hand at that position. The calculation of an endpoint from a set of joint angles is termed forward kinematic transformation, whereas calculation of a set of joint angles that can reach an endpoint is termed inverse kinematic transformation (Figure 33-2C). This transformation must take into account the geometric parameters of the arm, such as the lengths of the upper arm and forearm (recall that kinematics considers motion without reference to the forces that cause it). The motor system controls joint angle by activating muscles that produce torques (rotational forces) at the joint.
The action of motor commands on muscles that results in a set of angular positions and velocities is known as the forward dynamic transformation. The term “dynamic” refers to the forces required to cause motion. However, to generate a desired joint angle trajectory the system must convert kinematic parameters into motor commands. That is, the system must calculate the torques at each joint necessary to achieve the motion and relate the force required to cause this motion to the desired acceleration of the limb. This transformation is known as the inverse dynamic transformation (Figure 33-2D). In general, to cause any acceleration the forces applied must exceed any resistive forces arising from the viscosity or stiffness of the limb, from gravity, and from external loads. The force not required to overcome the total resistive force will cause an angular acceleration, with the acceleration being dependant on the limb’s inertia; the lower the inertia, the higher the acceleration.
Thus through a series of sensorimotor transformations, sensory input is finally converted into muscle contractions that generate movement. Although we have described one possible series of transformations that can achieve a movement, the actual computations used by the central nervous system are still under active investigation.
The Central Nervous System Forms Internal Models of Sensorimotor Transformations
We know from cellular studies that the central nervous system contains internal representations (“neural maps”) of the various sensory receptor arrays and the musculature. Experimental and modeling studies strongly suggest that the central nervous system also maintains internal representations that relate motor commands to the sensory signals expected as a result of movement.
Given the fixed lengths of our limb segments, there is a mathematical relationship between the joint angles of the arm and the location of the hand in space. A neural representation of this relationship allows the central nervous system to estimate hand position if it knows the joint angles and segment lengths. The neural circuits that compute such sensorimotor transformations are examples of internal models (Box 33-1). Such neural representations may not exactly match true relationships because of structural differences (the models only approximate the true relationship between joint angles and hand position) or errors in the model’s parameters (incorrect estimates of segment lengths).
An internal model that represents the causal relationship between actions and their consequences is called a forward model because it estimates future sensory inputs based on motor outputs. A forward model anticipates how the motor system’s state will change as the result of a motor command. Thus, a copy of a descending motor command acting on the sensorimotor system is passed into a forward model that acts as a neural simulator of the musculoskeletal system moving in the environment. This copy of the motor command is known as an efference copy (or corollary discharge) to signify that it is a copy of the efferent signal flowing from the central nervous system to the muscles. We will see later how such simulations can be learned and used in sensorimotor control.
An internal model that calculates motor outputs from sensory inputs is known as an inverse model. Such a model can determine what motor commands are needed to produce the particular movements necessary to achieve a desired sensory consequence.
Forward and inverse models can be better understood if we place the two in series. If the structure and parameter values of each model are correct, the output of the forward model (the predicted behavior) will be the same as the input to the inverse model (the desired behavior) (Figure 33-3).
Figure 33-3 Internal models represent relationships of the body and external world. The inverse model determines the motor commands that will produce a behavioral goal, such as raising the arm while holding a ball. A descending motor command acts on the musculoskeletal system to produce the movement. A copy of the motor command is passed to a forward model that simulates the interaction of the motor system and the world and can therefore predict behaviors. If both forward and inverse models are accurate, the output of the forward model (the predicted behavior) will be the same as the input to the inverse model (the desired behavior).
The utility of numerical models in the physical sciences has a long history. Numerical models are abstract quantitative representations of complex physical systems. Some start with equations and parameters that represent initial conditions and run forward, either in time or space, to generate physical variables at some future state. For example, we can construct a model of the weather that predicts wind speed and temperature two weeks from now. In general, the algorithms and parameters of the model should lead to one correct answer.
Other models start with a state, a set of physical variables with specific values, and operate in the inverse direction to determine what parameters in the system account for that state. When we fit a straight line to a set of data points, we are constructing an inverse model that estimates slope and intercept based on the equations of the system being linear. An inverse model may thus inform us how to set the parameters of the system to obtain desired outcomes.
Over the last 50 years the idea that the nervous system has similar predictive models of the physical world to guide behavior has become a major issue in neuroscience. The idea originated in Kenneth Craik’s notion of internal models for cognitive function. In his 1943 book, The Nature of Explanation, Craik was perhaps the first to suggest that organisms make use of internal representations of the external world:
“If the organism carries a ‘small-scale model’ of external reality and of its own possible actions within its head, it is able to try out various alternatives, conclude which is the best of them, react to future situations before they arise, utilize the knowledge of past events in dealing with the present and future, and in every way to react in a much fuller, safer, and more competent manner to the emergencies which face it.”
In this view an internal model allows an organism to contemplate the consequences of current actions without actually committing itself to those actions.
Considering the human body from the viewpoint of sensorimotor control, we should ask two fundamental questions. First, how can we generate actions on the system so as to control its behavior? Second, how can we predict the consequences of our actions?
The central nervous system must exercise both control and prediction to achieve skilled motor performance. Prediction and control are two sides of the same coin, and the two processes map exactly onto forward and inverse models. Prediction turns motor commands into expected sensory consequences, whereas control turns desired sensory consequences into motor commands.
Movement Inaccuracies Arise from Errors and Variability in the Transformations
Motor control is often imprecise. Indeed, society celebrates those who can throw a dart into a small area of a board or hit a small white ball into a hole with a club. However, even the movements of the most skilled players show some degree of variability. In the 1890s the psychologist Robert Woodworth showed that fast movements are less accurate than slow ones. People slow their movements when accuracy is demanded. Inaccuracy can arise either from variability in the sensory inputs and motor outputs or from errors in the internal representations of this information.
An important component of sensorimotor variability is the intrinsic variability of our sensors and motor neurons because of fluctuations in their membrane potential. Because of these fluctuations, known as neural noise, the level of input signals required to trigger postsynaptic action potentials also varies. On the input side, neural noise limits the accuracy of estimates of the location of a target or limb (how near an estimate is to the true value) as well as their precision (how accurate the estimate is when repeated). On the output side, neural noise limits the accuracy and precision with which we contract our muscles. Moreover, the amount of noise in motor commands tends to increase with larger motor commands, limiting our ability to move rapidly and accurately at the same time. This increase in variability is caused by random variation in both the excitability of motor neurons and the recruitment of the additional motor units needed to produce increases in force.
Incremental increases in force are produced by progressively smaller sets of motor neurons, each of which produces disproportionately greater increments of force (see Chapter 34). Therefore, as force increases, fluctuations in the number of motor neurons lead to greater fluctuations in force. The consequences of this can be observed experimentally by asking subjects to generate a constant force or a force pulse of fixed amplitude. Not only are subjects unable to maintain constant force, but the variability of force also increases with the level of the force. Over a large range this increase in variability is captured by a constant coefficient of variation (the standard deviation divided by the mean force). This dependence of variability on force corresponds to the increase in the variability of pointing movements with the average speed of movement. The decrease in accuracy of movement with increasing speed is known as the speed-accuracy trade-off (Figure 33-4).
Figure 33-4 Accuracy of movement varies in direct proportion to its speed. Subjects held a stylus and were required to try and hit a target line lying perpendicular to the direction in which they moved. Each subject started from three different initial positions and was required to complete the movement within three different times (140, 170, or 200 ms). A successful trial was one in which the subject completed the movement within 10% of the required time. Only successful trials were used for analysis. Subjects were informed if their movements were more than 10% different from the required duration. The plot shows the variability in the motion of the subjects’ arm movements as the standard deviation of the extent of movement versus average speed (for each of three movement starting points and three movement times, giving nine data points). The variability in movement increases in proportion to the speed and therefore to the force producing the movement. (Reproduced, with permission, from Schmidt et al. 1979.)
Errors can also arise from inaccuracy in the internal models that compute sensorimotor transformations. Neural representations of the musculature cannot easily capture the complex biomechanical properties of the musculoskeletal system, and this in turn significantly complicates the ability of the brain to compute accurate sensorimotor transformations. Indeed, the dependence of muscle force on the motor command is itself highly complex. A model prescribing motion in a system with just a single joint must not only estimate the muscle force (or torque) but also take into account inertia (the mass resisting acceleration), viscosity (resistive forces proportional to velocity), stiffness (elastic forces proportional to displacement) produced by the muscles and tendons opposing movement, and gravity.
The dynamic relationship between segments of limbs further complicates sensorimotor transformations. The motion of each segment produces torques, and potentially motions, at all other segments through mechanical interactions. For example, flexion of the upper arm through shoulder rotation can lead to either extension or flexion of the elbow depending on the initial elbow angle. In general, because of the interactions between linked segments, the torques needed to produce a specific change in angle at a particular joint depend not only on the muscles acting directly at this joint but also on the configurations and the motions of all other joints, and especially their acceleration. The brain develops an internal model of these complex mechanical interactions through learning early in childhood. We will see later that this learning is updated throughout life and depends critically on proprioception, which provides the brain with information about changes in muscle length and joint angles.
Different Coordinate Systems May Be Employed at Different Stages of Sensorimotor Transformations
Different coordinate systems are used in sensorimotor transformations and are encoded in several brain regions. Coordinate systems are either extrinsic or intrinsic to the body. Extrinsic coordinate systems relate objects in the outside world to other objects (allocentric coordinates) or to our body (egocentric coordinates) using exteroceptive information, usually visual or auditory (Figures 33–5A and B). Intrinsic coordinate systems, such as the set of muscle lengths or set of joint angles (Figure 33-5C), are based on information provided primarily by proprioceptive systems.
Figure 33-5 The location of the finger in space can be specified in different egocentric coordinate systems.
A. Cartesian coordinates centered on the eyes.
B. Spherical polar coordinates centered on the shoulder (distance γ, azimuth ϕ, and elevation θ).
C. An intrinsic coordinate system based on shoulder angles α1 and α2), which relate the orientation of the upper arm to the Cartesian axes, and elbow angle (α3), which specifies the angle between the upper and lower arm.
Elucidating the coordinate systems used in sensorimotor transformations is a major endeavor in neuroscience. We will see in later chapters that this issue can be fruitfully studied by examining how the firing patterns of neurons in different parts of the brain encode task features or movement parameters. Such studies aim to determine the variables (such as position or velocity) or type of coordinate system (such as allocentric or egocentric) that the neurons encode.
Behavioral studies also have used a variety of methods to examine the coordinate systems used in directing movement. One way has been to examine the details of the errors made during movement in different tasks. When subjects are asked to reach rapidly and repeatedly to a target, the error in the movements can be measured in different ways. If we average the final location of the hand across many trials, we may find a constant error or bias in the movement. We can examine the distribution of the final locations of the hand about this average position and infer from the patterns of constant and variable error the coordinate system used in the movement (Box 33-2).
Stereotypical Patterns Are Employed in Many Movements
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