Muscle Maps in Frog Force Muscle Relationships

Maps of both forces and muscle recruitment by microstimulation have been collected at fine spatial in unanaesthetized spinal frogs. Force maps are presented in Tresch et al.43 and Giszter et al.34 In Giszter et al.34 we focused on measurement of force samples at a fixed limb configuration and mapped the entire lumbar enlargement of the frog. We chose a limb configuration at which several two-dimensional force-fields characterized in earlier work could be distinguished using a single measurement. This restriction of data collection to single force vectors rather than complete fields was necessary to make the extensive mapping experiments feasible. Full force-field collection at the density of sampling and current variations used here would not have been possible. This is due to the data explosion of at least an order of magnitude that is required for two-dimensional field description. Stimulation sites were arrayed in a three-dimensional grid of 200-micron mediolateral separation, 200-micron depth variation and 1mm rostrocaudal separation throughout the spinal grey. Locations were later visualized using iron deposition stained using Prussian blue. The grid completely spanned the three segments comprising the majority of the lumbar spinal cord in the frog. Each site was stimulated at 1, 2, 4 and 8 microAmps using 0.5-ms pulses in 300-ms trains of 40 Hz.

Forces and EMG patterns recruited across the grid of spinal cord we sampled were examined by generating regular lattices of scalar or vector data using Delaunay tes-selation of the space and piecewise linear interpolation. Figure 4.1 shows areas of high force production in one such map. Muscle patterns underlying such field responses have not been presented in detail for these data and are briefly discussed here.

Mechanically antagonistic muscles are often coactivated in the frog reflex behaviors. This coactivation was also observed in most microstimulation. Regions of low force activation that were observed by microstimulation do not therefore always imply a corresponding low muscle activation. We therefore first analyzed EMG magnitudes regardless of force magnitudes.

Chapter 4, Color Figure 1* shows the variation of activation of individual muscles in a single frog, expressed as contours at the parasagittal surface 400 microns from the midline. We examined contours in parasagittal planes at 200, 400 and 600 microns lateral to the midline, but only display the contours for the 400-micron surface. While these planes differed in detail, the 400-micron plane characterizes all three planes for the purpose of these analyses. Peaks of activation of individual muscles appeared to be arranged in repeating or segmentally localized regions. Patterns of activation in dorsal and ventral spinal cord differed. The differences we observed are exemplified by the activation of biceps or iliofibularis muscles (BI). The rostrocaudal pattern of muscle recruitment obtained from the stimulation map altered with depth. Ventral horn regions of cord are expected to represent more direct motoneuron recruitment by stimulation. In some regions of ventral cord, and continuing up to the lower intermediate zone (900-1000 microns), muscles were activated strongly over broad regions probably representing motor pools. In dorsal horn regions of cord we observed that activation could be staggered or more rapidly

* Chapter 4, Color Figure 1 follows page 112.

FIGURE 4.1 A. High force sites (>0.67 N) with stimulation magnitude of 8 microAmps. The force magnitude surface drawn contains all stimulation sites >0.67 N. The surface was calculated in the Explorer software package (Numerical Algorithms Group). B. Peak forces at 500 ms after stimulation onset, in lateral view. Force vectors are shown in the figure as grey and white lines in 3D. Each force is drawn radiating from a base located at the point in the spinal cord at which it was recruited by the stimulation. The vector tips are white and the bases grey. Forces in several directions can be seen. The Z axis is upwards and the Y axis is directed along the rostroaudal axis of the spinal cord's coordinate system. (Data re-plotted from Giszter et al. 2000.)

FIGURE 4.1 A. High force sites (>0.67 N) with stimulation magnitude of 8 microAmps. The force magnitude surface drawn contains all stimulation sites >0.67 N. The surface was calculated in the Explorer software package (Numerical Algorithms Group). B. Peak forces at 500 ms after stimulation onset, in lateral view. Force vectors are shown in the figure as grey and white lines in 3D. Each force is drawn radiating from a base located at the point in the spinal cord at which it was recruited by the stimulation. The vector tips are white and the bases grey. Forces in several directions can be seen. The Z axis is upwards and the Y axis is directed along the rostroaudal axis of the spinal cord's coordinate system. (Data re-plotted from Giszter et al. 2000.)

varying in relation to the variations in the motor pools in ventral horns. We believe this variation in upper cord areas represented the repeating segmental organization of the lumbar cord and the dorsal root entry zones. The upper intermediate zone from 400-600 microns frequently showed higher thresholds and lower responses and exhibited a different pattern from corresponding depths in dorsal or ventral horns. This can be seen in the two separate rostrocaudal regions of biceps recruitment by stimulation at this depth. Prior force-field collection was from 600-800 microns depth, usually 300 microns from the midline. This region usually showed more frequent EMG variation rostrocaudally compared to ventral horn or upper intermediate zone but with good muscle activation. It also differed from the dorsal horn. To us, these variations in upper dorsal and intermediate zone and the higher threshold or lower response region separating them make it unlikely that the patterns elicited in the intermediate zone represent simply the direct activation of motoneuron dendrites, or primary afferents processes. While muscle recruitment shows clear topography, points of highest recruitment of individual muscles do not correspond to sites of maximum force. Maps in Chapter 4, Color Figure 2* show the distributions in the stimulated spinal cord volumes of two primitive force directions extracted from the ensemble map data by statistical means using A"-means clustering. Thus each region represents recruitment of forces with directions close to the direction of a statistically identified force-field primitive. From comparison of the muscle maps in Color Figure 1 and the maps in Color Figure 2, it appears that the relation between force pattern and muscle activity may be complex and redundant.

We have used factor analysis,47 A"-means,48 and independent component analysis4950 of these force and muscle maps to examine how muscle patterns and forces relate to one another. In this presentation we focus on the results of factor analysis. We sought to discover if the maps show mixtures of statistically separable component muscle patterns at each site, and whether there were sites at which components could be obtained in pure form. Finally we sought to discover if there were sites generating patterning following microstimulation. N-methyl-D-asportic acid (NMDA) iontophoresis coupled with microstimulation studies suggested that stimulation of some sites might elicit temporally patterned activity.51

Factor analysis finds a small set of factors which explain the variance of the data. In contrast to principal component analysis, factor analysis does not require the component factors be orthogonal. In the Varimax analysis we used, we chose not to attempt to constrain factor components or weightings to purely positive values. Because each factor could contribute to EMG in both a positive or a negative fashion, the factors extracted could not be considered to represent muscle synergies per se. However the factors could be thought of as pre-motoneuronal excitatory and inhibitory drives.

In this analysis we found that more than 80% of the variance of the EMG patterns throughout the cord could be explained by either five or six factors in each frog. Using the factor weightings we could predict assignment to a force direction cluster. The factor weightings successfully predicted force/torque class in 68% of the force samples collected at 8 microAmp currents in our largest map. This was equivalent to the success of the full rank EMG. Further, we found that force direction and magnitude could be directly predicted by the extracted EMG factors using median least squares linear regression (r-squared of 0.62).

Our results from this analysis suggested that most sites represented mixtures of the factors we obtained. This is in keeping with many stimulation sites in the spinal cord representing activation of a mixture of distributed circuitry associated with one or more primitives. Most sites represented combinations of factors in the intermediate layers in the frog. It remains possible that appropriate sets of constraints on the analysis or rotations of the extracted factors might allow a purely positive set of factors to be used to capture the data, thereby representing "synergies."43 The EMG activity itself can clearly only be positive (i.e., excitatory to muscle).

* Chapter 4, Color Figure 2 follows page 112. © 2001 by CRC Press LLC

What was remarkable was that despite the mixture of component muscle activities and factor weights at most sites, the maps of force-fields or force directions showed clear segregation into a few types seen in Color Figure 2. Loeb et al.52 showed in Monte Carlo simulations that some muscle groups generate very robust fields. Thus the force stability in the face of muscle mixtures may be due to the robustness of force-fields generated by some muscle groups. However, it must be acknowledged that Saltiel's work51 suggests some pure sites may exist.

Obtaining pure recruitment of the primitives (i.e., the biological functional muscle groups and controls) organized naturally by spinal cord is clearly ideal for an FES system. How many such pure sites are accessible remains to be seen. Microstimulation in the frog activates cells near the electrode which are both excitatory and inhibitory but also excites axons and dendrites of remote cells which are passing close by the stimulation site. It therefore may not be surprising that mixtures of effects are observed when the data is examined at the muscle level. However it is also worth noting that mixtures of primitives may represent the spinal cord's normal output when interpreting sensory input and generating flexion withdrawal movements43 or aimed trajectories for wiping.33,42

Possibly the more restricted dendritic arbors of motoneurons and the more clearly laminated organization of mammalian spinal cord will allow for purer recruitment of individual primitives by microstimulation.

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