Copyright © 1999 Massachusetts Institute of Technology
To specify a plan of action, the central nervous system (CNS) must first transfer sensory inputs into motor goals such as the direction, amplitude, and velocity of the intended movement. Then, to execute movements, the CNS must convert these desired goals into signals controlling the muscles that are active during the execution of even the simplest kind of limb trajectory. Thus, the CNS must transform information about a small number of variables (direction, amplitude, and velocity) into a large number of signals to many muscles. Any transformation of this type is "ill-posed" in the sense that an exact solution may be either not available or not unique. How the nervous system computes these transformations has been the focus of recent studies.
Specifically, to plan an arm trajectory toward an object, the CNS first must locate the position of the object with respect to the body and represent the initial position of the arm. Recordings from single neurons in the parietal cortex and superior colliculus in awake monkeys have significantly contributed to our understanding of how space is represented. There is some evidence that in the parietal cortical areas there are retinotopic neurons whose activity is tuned by signals derived from somatosensory sources. Their visual receptive field is modified by signals representing both eye and head position. This result suggests that parietal area 7a contains a representation of space in body-centered space. Neurons representing object location in body-independent (allocentric) coordinates have also been found in the parietal cortex and in the HIPPOCAMPUS (Andersen et al. 1993).
To specify the limb's trajectory toward a target, the CNS must locate not only the position of an object with respect to the body but also the initial position of the arm. The conventional wisdom is that proprioception provides information about arm configuration to be used in the programming of the arm's trajectory. However there is experimental evidence indicating that information about the initial position of the limb derives from a number of sources, including the visual afferences (Ghez, Gordon, and Ghilardi 1993).
The current view on the formation of arm trajectories is that the CNS formulates the appropriate command for the desired trajectory on the basis of knowledge about the initial arm position and the target's location. Recent psychophysical evidence supports the hypothesis that the planning of limbs' movements constitutes an early and separate stage of information processing. According to this view, during planning the brain is mainly concerned with establishing movement kinematics, a sequence of positions that the hand is expected to occupy at different times within the extrapersonal space. Later, during execution, the dynamics of the musculoskeletal system are controlled in such a way as to enforce the plan of movement within different environmental conditions.
There is evidence indicating that the planning of arm trajectories is specified by the CNS in extrinsic coordinates. The analysis of arm movements has revealed kinematic invariances (Abend, Bizzi, and Morasso, 1982; Morasso 1981). Remarkably, these simple and invariant features were detected only when the hand motion was described with respect to a fixed Cartesian reference frame, a fact suggesting that CNS planning takes place in terms of the hand's motion in space (Flash and Hogan 1985). Even complex curved movements performed by human subjects in an obstacle-avoidance task displayed invariances in the hand's motion and not in joint motion (Abend et al. 1982). The data derived from straight and curved movements indicate that the kinematic invariances could be derived from a single organizing principle based on optimizing endpoint smoothness (Flash and Hogan 1985). It follows that if actions are planned in spatial or extrinsic coordinates, then for the execution of movement, the CNS must convert the desired direction and velocity of the limb into signals that control muscles.
Investigators of motor control have been well aware of the computational complexities involved in the production of muscle forces. A variety of proposals have been made to explain these complexities. In theory, in a multijoint limb, the problem of generation forces may be addressed only after the trajectory of the joint angles has been derived from the trajectory of the endpoint -- that is, after an inverse kinematics problem has been solved. Investigations in robot control in the late 1970s and early 1980s have shown that both the inverse kinematic and inverse dynamic problems may be efficiently implemented in a digital computer for many robot geometries. On the basis of these studies, investigators have argued that the brain may be carrying out inverse kinematic and dynamic computations when moving the arm in a purposeful way.
One way to compute inverse dynamics is based on carrying out explicitly the algebraic operations after representing variables such as positions, velocity acceleration, torque, and inertia. This hypothesis, however, is unsatisfactory because there is no allowance for the inevitable mechanical vagaries associated with any interaction with the environment.
Alternative proposals have been made that do not depend on the solution of the complicated inverse-dynamic problem. Specifically, it has been proposed that the CNS may transform the desired hand motion into a series of equilibrium positions (Bizzi et al. 1984). The forces needed to track the equilibrium trajectory result from the intrinsic elastic properties of the muscles (Feldman 1974).
According to the equilibrium-point hypothesis, as first proposed by Feldman, limb movements result from a shift in the neurally specified equilibrium point. Studies of single and multijoint movements have provided experimental evidence that supports the equilibrium-point hypothesis (Bizzi et al. 1984). The equilibrium-point hypothesis has implications both for the control and for the computation of movements. With respect to control, the elastic properties of the muscles provide instantaneous correcting forces when a limb is moved away from the intended trajectory by some external perturbation. With respect to computation, the same elastic properties offer the brain an opportunity to deal with the inverse-dynamics problem. Once the brain has achieved the ability to represent and control equilibrium postures, it can master movements as temporal sequences of such postures. In this context, a representation in the CNS of the inertial, viscous, and gravitational parameters contained in the equations of motion is no longer necessary.
Recently, a set of experiments performed in frogs with spinal cords that were surgically disconnected from the brain stem has provided neurophysiological support for the equilibrium-point hypothesis. Microstimulation of the spinal cord demonstrated that this region is organized to produce the neural synergies necessary for the expression of equilibrium points. These experiments have indicated that the spinal cord contains circuitry that, when activated, produces precisely balanced contractions in groups of muscles. These synergistic contractions generate forces that direct the limb toward an equilibrium point in space (Bizzi, Mussa-Ivaldi, and Giszter 1991).
Experimental evidence also indicates that microstimulation of the lumbar gray results in a limited number of force patterns. More importantly, the simultaneous stimulation of two sites, each generating a force field, results in a force field proportional to the vector sum of the two fields (Mussa-Ivaldi, Giszter, and Bizzi 1994). Vector summation of force fields implies that the complex nonlinearities that characterize the interactions both among neurons and between neurons and muscles are in some way eliminated. This result has led to a novel hypothesis for explaining movement and posture based on combinations of a few basic elements. The limited-force pattern may be viewed as representing an elementary alphabet from which, through superimposition, a vast number of movements could be fashioned by impulses conveyed by supraspinal pathways. With mathematical modeling, experimenters have verified that this novel view of the generation of movement and posture has the competence required for controlling a wide repertoire of motor behaviors.
The hypothesis that the premotor zones in the spinal gray may be the structures underlying the transformation from extrinsic to intrinsic coordinates is consistent with the results obtained by other groups of investigators, who have demonstrated the existence of a few separate circuits for controlling horizontal and vertical head movements in the owl. These structures, which are located in the brain stem, receive inputs from the tectum and transform the tectal movement vectors into the neck motor-neural activation.
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Copyright © 1999 Massachusetts Institute of Technology