Simon F. Giszter

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.

Does the nervous system use equilibrium-point control to guide single and multiple joint movements?

The hypothesis that the central nervous system (CNS) generates movement as a shift of the limbs equilibrium posture has been corroborated experimentally in studies involving single- and multijoint motions. Posture may be controlled through the choice of muscle length-tension curve that set agonist-antagonist torque-angle curves determining an equilibrium position for the limb and the stiffness about the joints. Arm trajectories seem to be generated through a control signal defining a series of equilibrium postures. The equilibrium-point hypothesis drastically simplifies the requisite computations for multijoint movements and mechanical interactions with complex dynamic objects in the environment. Because the neuromuscular system is springlike, the instantaneous difference between the arms actual position and the equilibrium position specified by the neural activity can generate the requisite torques, avoiding the complex inverse dynamic problem of computing the torques at the joints. The hypothesis provides a simple, unified description of posture and movement as well as contact control task performance, in which the limb must exert force stably and do work on objects in the environment. The latter is a surprisingly difficult problem, as robotic experience has shown. The prior evidence for the hypothesis came mainly from psychophysical and behavioral experiments. Our recent work has shown that microstimulation of the frog spinal cords premotoneural network produces leg movements to various positions in the frogs motor space. The hypothesis can now be investigated in the neurophysiological machinery of the spinal cord.

Transforming plans into actions by tuning passive behavior: a field-approximation approach

The issue of transforming motor plans into actions as a field-approximation problem is considered. The approach is based on the idea that planning and control processes may use force fields for representing the interactions of a manipulator with its environment. On one hand, it is assumed that planning specifies targets, obstacles and other features as patterns of vectors over a manipulators workspace. On the other hand, a manipulator operated by a set of impedance controllers acting in parallel is considered. Each controller modulates an output-force field according to a predefined law. The problem of setting the controller inputs is solved as a least-squares approximation of the planned vector field. The fields generated by the controllers are considered as basis fields, that is, as the vectorial equivalent of basis functions. In this context, the approximation problem is equivalent to finding which element of the functional space spanned by the basis fields is closest to the planned field. The relevance of this approach with respect to biological and artificial systems is discussed.<<ETX>>

Movement Primitives in the Frog Spinal Cord

We present evidence for the generation of stable convergent force field patterns and muscle synergies in the spinal cord of the frog. These synergies may form the bases of postural and trajectory adjustments. We present recent analyses which show that (1) similarly structured force fields underlie natural behaviors (2) the active fields underlying both microstimulation and natural behavioral force fields are structurally invariant but may be modulated in overall force amplitude and stiffness (3) these fields are drawn from a limited set of such fields (4) these invariant fields can be used to predict the termination position of limb endpoint trajectories in the unrestrained limb (5) in those instances tested multiple stimulations resulted in fields proportional to the vectorial summation of the fields resulting from single stimulations. This recent body of work suggests that we may view the spinal cord as possessing a small number of movement primitives: circuits that may specify invariant force fields which may be combined in a more or less flexible manner to produce adjustable behaviors.

Equilibrium point mechanisms in the spinal frog

The frog spinal cord has been shown to be capable of precise positioning and complex multi-joint trajectory generation (Fukson et al. 1980, Giszter et al. 1989, Schotland et al. 1989). It is well known, for example, that the spinal frog is capable of generating a coordinated sequence of multi-joint hindlimb movements directed to the removal of a noxious stimulus from the skin. This “wiping reflex” requires complex information-processing. Thus, the spinal cord must contain circuitry that coordinates the motion of multiple limb segments (see figure 1A). While this ability has been revealed utilizing wiping behaviors, we hypothesize that these and other behaviors may use a general limb positioning mechanism residing in the spinal cord. Such a mechanism might be expected to combine information from several sources: spinal pattern generators, higher centers in the central nervous system, and peripheral feedback. Computation in the positioning mechanism must depend on the form of final output pattern utilized. An ongoing framework for both theoretical and experimental investigation in motor control has been the concept that the viscoelastic properties of the muscles determine the type of computations needed within the central nervous system in order to plan and execute movements. This has led in particular to the equilibrium point hypothesis (Feldman, 1974, Bizzi, 1976, Bizzi et al., 1984, Hogan, 1984, Flash, 1987). We will examine the idea that general positioning by the spinal cord utilizes such a mechanism.

Motor Organization in the Frog’s Spinal Cord

We activated the spinal cord by microstimulation and recorded the forces elicited at the ankle. By moving the leg throughout the workspace and repeating this measurement we obtained an estimate of a time-varying force field resulting from the stimulation. In lateral neuropil regions, stimulation elicited force fields that consistently converged to single equilibria. Stimulation of lateral neuropil also consistently elicited a balanced activation of muscles. Equilibria were found inflexion or extension of the leg depending on the site in the lateral area of the lumbar cord that was stimulated. In contrast, force fields elicited from stimulation of motor nuclei were often divergent or parallel. While afference seems to play a role in the structuring of the force fields, most such fields could be accounted for largely by coactivation of muscles. We found partial deafferentation did not abolish the convergence of the force fields. Using a simple model, we explored the hypothesis that motoneuron spatial frequency in the cord is alone sufficient to explain the results of microstimulation. We concluded that other mechanisms must also be invoked to explain the experimental results.

The case of the missing CVs: Multi-joint primitives

The search for simplifying principles in motor control motivates the target article. One method that the CNS uses to simplify the task of controlling a limbs mechanical properties is absent from the article. Evidence from multi-joint, force-field measurements and from kinematics that points to the existence of multi-joint primitives as control variables is discussed.