Ferdinando A. Mussa-Ivaldi

Convergent force fields organized in the frog's spinal cord

Microstimulation of the gray matter of the frogs spinal cord was used to elicit motor responses. Force responses were recorded with the frogs ankle clamped while EMG activity was monitored. The collections of force patterns elicited at different leg configurations were summarized as force fields. These force fields showed convergence to an equilibrium point. The equilibrium paths were calculated from the force fields with the leg clamped. These paths predicted free limb motion in 75% of trials. The force fields were separated into active and prestimulation resting responses. The active force field responses had a fixed position equilibrium. These active force fields were modulated in amplitude over time, although the balance and orientations of forces in the pattern remained fixed. The active fields grouped into a few classes. These included both convergent and parallel fields. The convergent force fields (CFFS) could be observed in deafferented preparations. Motoneuron (MN) activity underlying the force fields was marked using sulforhodamine. The marked activity covered several segments. Several simulations and MN stimulations show that topography, limb geometry, and random activation could not account for the results. It is likely that propriospinal interneurons distribute the activity that underlies the responses observed here. Experiments showed that CFFs that resemble those elicited by microstimulation also underlie natural behaviors. The full variety of fields revealed by microstimulation was larger than the repertoire elicited by cutaneous stimulation. It was concluded that fixed-pattern force fields elicited in the spinal cord may be viewed as movement primitives. These force fields could form building blocks for more complex behaviors.

Evaluation of robotic training forces that either enhance or reduce error in chronic hemiparetic stroke survivors.

This investigation is one in a series of studies that address the possibility of stroke rehabilitation using robotic devices to facilitate “adaptive training.” Healthy subjects, after training in the presence of systematically applied forces, typically exhibit a predictable “after-effect.” A critical question is whether this adaptive characteristic is preserved following stroke so that it might be exploited for restoring function. Another important question is whether subjects benefit more from training forces that enhance their errors than from forces that reduce their errors. We exposed hemiparetic stroke survivors and healthy age-matched controls to a pattern of disturbing forces that have been found by previous studies to induce a dramatic adaptation in healthy individuals. Eighteen stroke survivors made 834 movements in the presence of a robot-generated force field that pushed their hands proportional to its speed and perpendicular to its direction of motion — either clockwise or counterclockwise. We found that subjects could adapt, as evidenced by significant after-effects. After-effects were not correlated with the clinical scores that we used for measuring motor impairment. Further examination revealed that significant improvements occurred only when the training forces magnified the original errors, and not when the training forces reduced the errors or were zero. Within this constrained experimental task we found that error-enhancing therapy (as opposed to guiding the limb closer to the correct path) to be more effective than therapy that assisted the subject.

Controlling multijoint motor behavior.

Much can be learned about the central nervous system from a study of motor coordination, but its true richness and complexity become evident only in a multiarticular system. Despite the intrinsic complexity of multiarticular actions, they offer an unparalleled opportunity to learn about the central nervous system in a quantitative and experimentally testable way. For example, the observation that unconstrained, unperturbed arm movements are coordinated in terms of hand motion shows that motor control is organized in a hierarchy of increasing levels of abstraction. These arm motions are organized as though a disembodied hand could be moved in space; the details of how this is to be achieved must then be supplied by a different level in the hierarchy. The essence of human behavior is its adaptability. Just as the true complexity of coordination is evident only in multiarticular actions, the sophistication and subtlety of adaptive behavior are evident only in dynamic, interactive tasks. A study of movement alone is not sufficient to understand this behavior. The dynamic response of the limbs becomes the overriding concern and must be controlled by the central nervous system. The dynamic response of a limb is usually associated with its posture, rather than its movement, but in a functional task such as the use of a tool, the postural dynamics are an integral part of the action. This perspective on motor behavior leads to some useful insights. Coordination is not a problem for movement alone; in a multiarticular system, even posture requires coordination and control. Muscles do not merely act reciprocally to generate forces about the joints; the net mechanical impedance of the limb may be controlled by synergistic activation of all muscles, including antagonists. Controlling dynamic behavior is a far more demanding task than controlling motion. Consequently, features of the neuromusculoskeletal system that appear to be redundant or unnecessary for movement control can play a functional role in controlling dynamic behavior. Polyarticular muscles contribute to the mechanical impedance in a unique way. Skeletal redundancies have a profound influence on all aspects of dynamic behavior, including the apparent inertia of the limbs. Redundancies are commonly perceived as a complicating factor in the control of motion, a problem that must be solved by the central nervous system. Rather than presenting a problem requiring solution, they may present a solution to a problem. Posture is not merely the outcome of a motor act; it is one of the important preparatory stages in the production of motor behavior.

Human arm stiffness characteristics during the maintenance of posture

SummaryWhen the hand is displaced from an equilibrium position, the muscles generate elastic forces to restore the original posture. In a previous study, Mussa-Ivaldi et al. (1985) have measured and characterized the field of elastic forces associated with hand posture in the horizontal plane. Hand stiffness which describes the relation between force and displacement vectors in the vicinity of equilibrium position was measured and graphically represented by an ellipse, characterized by its size, shape and orientation. The results indicated that the shape and orientation of the stiffness ellipse are strongly dependent on arm configuration. At any given hand position, however, the values of these parameters were found to remain invariant among subjects and over time. In this study we investigate the underlying causes for the observed spatial pattern of variation of the hand stiffness ellipse. Mathematically analyzing the relation between hand and joint stiffness matrices, we found that in order to produce the observed spatial variations of the stiffness ellipse, the shoulder stiffness must covary in the workspace with the stiffness component provided by the two-joint muscles. This condition was found to be satisfied by the measured joint stiffness components. Using anatomical data and considering the effects that muscle cross-sections and changes in muscle moment arms have on the joint stiffness matrix, we found that these anatomical factors are not sufficient to account for the observed pattern of variation of joint stiffness in the workspace. To examine whether the coupling between shoulder and two-joint stiffnesses results from the coactivation of muscles contributing to these stiffnesses, EMG signals were recorded from shoulder, elbow and two-joint muscles. Our results indicated that, while some muscle coactivation may indeed exist, it can be found for only some of the muscles and in only part of the workspace.

Do neurons in the motor cortex encode movement direction? An alternative hypothesis.

Previous investigations by Georgopoulos et al. of cell activities in the primate motor cortex during the execution of voluntary arm movements have shown that these cells are characterized by tuning properties related to the direction of hand trajectories. Here, it is demonstrated that these findings do not necessarily imply that cortical cells encode spatial features of hand movements and an alternative hypothesis is considered according to which cortical cells encode muscle state variables. It is shown that this hypothesis would lead both to the single-cell activities and to the population behaviors observed by Georgopoulos et al.

Integrable solutions of kinematic redundancy via impedance control

Problems arising when kinematically redundant manipula tors are controlled using the Jacobian pseudoinverse are related to the nonintegrability of the standard pseudoin verse. This article presents a class of generalized inverses that have the property of being integrable within any sim ply connected, nonsingular region of the work space. Inte grability is obtained by deriving the equations that describe an externally imposed motion, with the hypothe sis that a compliance function is associated with each degree of freedom of the manipulator. The result is a weighted pseudoinverse containing a term that accounts for the nonlinear features of the forward kinematics. The relation of this integrable weighted pseudoinverse to the standard Moore-Penrose and other weighted pseudo- inverses is discussed.

Vector field approximation: a computational paradigm for motor control and learning

Recent experiments in the spinalized frog (Bizzi et al. 1991) have shown that focal microstimulation of a site in the premotor layers in the lumbar grey matter of the spinal cord results in a field of forces acting on the frogs ankle and converging to a single equilibrium position. These experiments suggested that the neural circuits in the spinal cord are organized in a set of control modules that “store” a few limb postures in the form of convergent force fields acting on the limbs end-point. Here, we investigate how such postural modules can be combined by the central nervous system for generating and representing a wider repertoire of control patterns. Our work is related to some recent investigations by Poggio and Girosi (1990a, b) who have proposed to represent the task of learning scalar maps as a problem of surface approximation. Consistent both with this view and with our experimental findings in the spinal frog, we regard the issue of generating motor repertoires as a problem of vector-field approximation. To this end, we characterize the output of a control module as a “basis field” (Mussa-Ivaldi 1992), that is as the vectorial equivalent of a basis function. Our theoretical findings indicate that by combining basis fields, the central nervous system may achieve a number of goals such as (1) the generation of a wide repertoire of control patterns and (2) the representation of these control patterns with a set of coefficients that are invariant under coordinate transformations.

Modular organization of motor behavior in the frog's spinal cord

The complex issue of translating the planning of arm movements into muscle forces is discussed in relation to the recent discovery of structures in the spinal cord. These structures contain circuitry that, when activated, produce precisely balanced contractions in groups of muscles. These synergistic contractions generate forces that direct the limb toward an equilibrium point in space. Remarkably, the force outputs, produced by activating different spinal-cord structures, sum vectorially. This vectorial combination of motor outputs might be a mechanism for producing a vast repertoire of motor behaviors in a simple manner.

The control of stable postures in the multijoint arm

The stiffness that is measured at the hand of a multijoint arm emerges from the combined effects of the elastic properties of the muscles and joints, the geometry of the linkages and muscle attachments, and the neural control circuits that act on the arm. The effective stiffness of a nonlinear linkage such as a two-joint arm depends on the force acting on the system as well as the intrinsic stiffness of the actuators. This paper presents an analysis of the factors that affect limb stiffness, including the effects of external forces. Three potential strategies for controlling the stability of the limb are proposed and demonstrated by computer simulations. The predictions from the simulations are then compared experimentally with measured stiffness values for human subjects working against an external force. These experiments were directed toward understanding what strategies are used by the CNS to control limb stiffness and stability. The experimental evidence showed that human subjects must increase the stiffness at the joints in order to maintain limb stability in the presence of applied external forces at the hand. In the process we identified a precise role for muscles which span two or more joints in the control of overall limb stiffness. A local strategy may be used to achieve limb stability, in which the muscle stiffness increases with muscle force. Multijoint muscles are shown to provide mechanical couplings which are necessary for the maintenance of stability. By utilizing these muscles, the neuro-musculo-skeletal system can control a global property of the system (stability) with a passive local strategy.

Does the motor control system use multiple models and context switching to cope with a variable environment

Studies of arm movements have shown that subjects learn to compensate predictable mechanical perturbations by developing a representation of the relation between the state of motion of the arm and the perturbing forces. Here, we tested the hypothesis that subjects construct internal representations of two different force fields and switch between them when presented with an alternating sequence of these fields. Our results do not support this hypothesis. Subjects performed reaching movements in four sessions over 4 days. On the 1st day the robotic manipulandum perturbed the movement by perpendicular force that alternated its direction after each movement. Subjects were unable to construct the two underlying models and switch between them. On the 2nd day only one field was applied and well learned. On the 3rd day only the other field was applied and well learned. Then the experiment of the 1st day was repeated on the 4th day. Even after this extensive training subjects showed no signs of improved performance with alternating fields. This result combined with previous studies suggests that the central nervous system has a strong tendency to employ a single internal model when dealing with a sequence of perturbations.