A computational model for epidural electrical stimulation of spinal sensorimotor circuits

Abstract

Epidural electrical stimulation (EES) of lumbosacral segments can restore a range of movements after spinal cord injury. However, the mechanisms and neural structures through which EES facilitates movement execution remain unclear. Here, we designed a computational model and performed in vivo experiments to investigate the type of fibers, neurons, and circuits recruited in response to EES. We first developed a realistic finite element computer model of rat lumbosacral segments to identify the currents generated by EES. To evaluate the impact of these currents on sensorimotor circuits, we coupled this model with an anatomically realistic axon-cable model of motoneurons, interneurons, and myelinated afferent fibers for antagonistic ankle muscles. Comparisons between computer simulations and experiments revealed the ability of the model to predict EES-evoked motor responses over multiple intensities and locations. Analysis of the recruited neural structures revealed the lack of direct influence of EES on motoneurons and interneurons. Simulations and pharmacological experiments demonstrated that EES engages spinal circuits trans-synaptically through the recruitment of myelinated afferent fibers. The model also predicted the capacity of spatially distinct EES to modulate side-specific limb movements and, to a lesser extent, extension versus flexion. These predictions were confirmed during standing and walking enabled by EES in spinal rats. These combined results provide a mechanistic framework for the design of spinal neuroprosthetic systems to improve standing and walking after neurological disorders.

Keywords: computational model; electrical epidural stimulation; finite element model; spinal cord injury; spinal cord stimulation; spinal reflexes.

Figures

Figure 1.

Characteristics of the computational model. A, Anatomically realistic volume conductor model with explicit, color-coded representation of the gray and white matter, CSF, and epidural fat. B, Meshing of the FEM structure with tetrahedral elements, and cross sections of spinal segments L2 (a) and S1 (b). C, Axon cable model of afferent and efferent fibers with realistic geometrical representation of efferent and afferent fibers, alpha motoneurons, and interneurons. Membrane potentials were calculated through Hodgkin–Huxley equations. Afferent fibers entered the spinal cord below the spinal segment S1 and ran longitudinally before bending in the gray matter of their target segment, as depicted in the pictorial representation. Interneurons were located in laminae I–III and VII, with efferent axons expanding dorsoventrally, or crossing the spinal cord midline, respectively. Alpha motoneurons were located based on our anatomical evaluations (Fig. 2). Their efferent axons ran longitudinally toward the S1 segment before exiting the spinal cord.

Figure 2.

Anatomical features implemented in the computational model. A, Neuronal nuclei (NeuN) staining revealing the shape of the gray matter along the rostrocaudal extent of the lumbosacral spinal cord. Scale bar, 500 μm. B, The retrograde tracer Fluorogold (FG) was injected into the medial gastrocnemius (MG, ankle extensor) and the tibialis anterior (TA, ankle flexor) muscles to label MG and TA motoneurons, respectively (n = 3 rats). Scale bar, 30 μm. C, The 3D location of MG (blue) and TA (red) motoneurons was evaluated based on the analysis of serial spinal cord sections in the software Neurolucida. Angled and cross-sectional projections of the reconstructed motoneuron columns are shown. D, Dorsal; V, ventral; L, left; R, right.

Figure 3.

Currents generated by EES and effects on membrane potential of cells. A, Color-coded electrical potentials and generated currents following a single pulse of EES applied on the dorsal aspect of the spinal cord. The length and orientation of the arrows represent the intensity and direction of the induced current density, respectively. B, Effect of the extracellular field induced by a 500 μs duration pulse of EES applied at L4 with an intensity of 600 μA on the somatic membrane potential of laminae I–III interneurons (a), lamina VII interneurons (b), and motoneurons (c). The dotted horizontal lines indicate the threshold to elicit action potentials. Even at large intensities, EES did not affect the resting membrane potential of the modeled cells. Alpha motoneurons were stimulated synaptically via the excitatory EPSP resulting from the direct recruitment of Group Ia fibers with EES.

Figure 4.

Threshold current for the recruitment of afferent and efferent axons following EES applied at various lumbosacral locations. A, Bar graphs reporting the threshold for the recruitment of motor axons, Group Ia/Ib fibers, and Group II fibers in each spinal segment when delivering a cathodal square EES pulse of 500 μs at spinal segments L2, L4, and S1. Thresholds were computed as the necessary current to recruit 10% of the total number of fibers in a given segment. Currents exceeding 600 μA were not considered. B, Scheme representing the location of TA and MG motor columns. To facilitate the visualization of current thresholds for each fiber and segment, the data reported in A are displayed using a color map overlaid onto a schematic representation of spinal segments. The red arrow indicates the location of the stimulation.

Figure 5.

Simulated and experimental modulations of early-, medium-, and late-latency motor responses. A, Plots reporting the change in amplitude of the early-, medium-, and late-latency motor responses as a function of current applied at S1 for the computational model compared with experimental recordings. The shaded areas indicate the SEM of response amplitude for the experimental rats. B, Correlation plots between the normalized amplitudes of experimental and simulated motor responses. R2 values are reported in each graph. C, Histogram plots reporting the average current values for the threshold and saturation of the early-, medium-, and late-latency motor responses in the TA and MG muscles for experiments and simulations. Significant differences at *p < 0.05.

Figure 6.

Electrophysiological and pharmacological evaluations of fibers and circuits engaged by EES in vivo. A, Scheme illustrating the putative afferent fibers innervating proprioceptors and mechanoreceptors, and their associated reflex circuits activated by EES. In, Interneuron. Mn, motoneuron. B, Representative recordings of the early-, medium-, and late-latency motor responses recorded in the TA muscle following EES applied at S1. The responses were differentiated based upon their respective latencies. C, Theoretical schemes illustrating which neurons, fibers, and/or circuits were likely inhibited (gray) in response to each experimental manipulation in anesthetized rats. D, Representative waveforms recorded in the same rat during baseline, concurrently to Achilles' tendon vibration, during repeated (10 Hz) stimulation, and after the administration of tizanidine or TTX, from top to bottom. Each waveform is the average (±SD) of 10 stimuli. E, Histogram plots reporting, for each experimental condition, the relative change in the integral of the recruitment curve for each motor response compared with baseline. Significant differences at **p < 0.01 and ***p < 0.0001, respectively.

Figure 7.

Recruitment of selective sensorimotor circuits with EES. A, Color maps representing the current threshold for the recruitment of the medium-latency response following stimulation applied at spinal segment L2, L4, and S1 at a distance of 750 μm from the spinal cord midline in the computational compared with experimental rats. Current threshold for nonstimulated segments were obtained through linear interpolation. B, Selectivity in the recruitment of TA and MG muscles were computed for EES applied at spinal segment L2, L4, and S1 in the computational model compared with experimental rats.

Figure 8.

Lateralized EES promotes unilateral facilitation of stepping in spinal rats. A, Schematic of the complete SCI, electrode positioning, and robotic system providing adjustable body weight support during stepping on a treadmill (9 cm/s). Reflective markers were positioned overlying bony landmarks to monitor hindlimb joint motion. The limb was defined as a virtual segment reflecting whole-hindlimb oscillation. B, Representative stick diagram of decomposition of left and right hindlimb movements together with the successive, color-coded trajectories of the limb endpoint extracted from a continuous sequence of stepping movements without stimulation, and during EES applied at 0 or 750 μm from the midline (left) of spinal segment S1. Stick diagrams were extracted from the time window highlighted by the dotted squares in C. C, The oscillations of the left and right limbs are displayed at the bottom together with the stance (filled) and swing (empty) phases of gait, and the concurrent pattern of EES.

Figure 9.

Modulation of medium- and late-latency reflexes during gait. A, Continuous sequence of EMG activity recorded from the left MG and TA muscles during stepping enabled by EES. B, Detailed EMG activity extracted from the time window highlighted by the red, dotted line in A. During locomotion, each pulse of EES induces a reflex response locked to the stimulation. C, Color-coded medium- and late-latency responses evoked in the ipsilateral MG and TA muscles during stance (C1) versus swing (C2). D, The plots report modulation of mean (n = 10 responses per rat) amplitude (±SD) of medium- and late-latency responses over the course of the stance phase for the MG muscle, and the swing phase for the TA muscle.

Figure 10.

Site-specific EES promotes extension versus flexion of the hindlimb during standing in spinal rats. A, Robotic postural neuroprosthesis providing adjustable body weight support in the vertical and mediolateral directions during bipedal standing. Scheme showing the lateralized location of stimulating electrodes at spinal segment L2 and S1. B, Representative stick diagram of decomposition of hindlimb movements before (black) and during (red) the application of continuous EES at S1 versus L2 during standing. EMG activity of left ankle muscles and vertical ground reaction forces before, during (shaded area), and after delivering continuous EES at L2 versus S1 during standing. C, Color-coded medium- and late-latency motor responses recorded in the left MG and TA muscles following EES applied at S1 versus L2, respectively. The displayed temporal windows (a, b) were extracted from the middle of the stimulating period shown in B.