Low dimensionality of supraspinally induced force fields

Abstract

Recent experiments using electrical and N-methyl-D-aspartate microstimulation of the spinal cord gray matter and cutaneous stimulation of the hindlimb of spinalized frogs have provided evidence for a modular organization of the frog's spinal cord circuitry. A "module" is a functional unit in the spinal cord circuitry that generates a specific motor output by imposing a specific pattern of muscle activation. The output of a module can be characterized as a force field: the collection of the isometric forces generated at the ankle over different locations in the leg's workspace. Different modules can be combined independently so that their force fields linearly sum. The goal of this study was to ascertain whether the force fields generated by the activation of supraspinal structures could result from combinations of a small number of modules. We recorded a set of force fields generated by the electrical stimulation of the vestibular nerve in seven frogs, and we performed a principal component analysis to study the dimensionality of this set. We found that 94% of the total variation of the data is explained by the first five principal components, a result that indicates that the dimensionality of the set of fields evoked by vestibular stimulation is low. This result is compatible with the hypothesis that vestibular fields are generated by combinations of a small number of spinal modules.

Figure 1

The construction of a force field. (A) Grid of ankle positions in the horizontal plane used to measure the isometric forces (dorsal view of the right leg; top is caudal and bottom is rostral). The dotted segments represent the position of the femur and the tibio-fibula in three different configurations. (B) Time course of the horizontal forces generated at different ankle locations by the same train of impulses applied to the vestibular nerve (the number on the left of each trace corresponds to the number of the location on the grid). The envelope of the stimulation train is shown in the trace labeled “stim.” (C) Time course of the normalized magnitude of the horizontal forces generated at different ankle locations by the same stimulation. The forces at the time of the maximal magnitude are used to construct the force field.

Figure 2

Sample vestibular force fields from four different animals. The asterisk indicates the position of the frog’s right hip. The forces shown are obtained by a linear interpolation of the measured forces over a dense grid. The field in A is the same detailed in Fig. 1.

Figure 3

Result of the principal component analysis and comparison with random fields. The solid line represents the fraction of the total variation explained by the first n principal components as a function of n computed for the vestibular data. The broken line represents the same quantity computed for an equal number of randomly generated fields with maximal dimensionality. The dotted lines are one SD above and below the mean.