NEURAL MECHANISMS UNDERLYING THE RECOVERY OF VOLUNTARY CONTROL OF MOTONEURONS AFTER PARALYSIS WITH SPINAL CORD STIMULATION

SUMMARY

Spinal cord stimulation (SCS) improves motor control after paralysis. This evidence led to the hypothesis that SCS facilitates residual supraspinal inputs to spinal motoneurons. Here we demonstrate that this hypothesis is not supported by experimental evidence. Instead, we show that residual supraspinal inputs modulate motoneurons’ membrane potential to transform subthreshold SCS pulses into suprathreshold action potentials, thereby entraining motoneuron activity to SCS. Despite this entrainment, residual supraspinal inputs can control motoneuron firing rates by modulating the number of subthreshold SCS pulses transformed into action potentials, resulting in volitional modulation of motor output for a restricted set of SCS parameters. Furthermore, we predict that residual supraspinal inhibitory drive can silence unwanted suprathreshold motoneuron activity, enlarging the functional set of SCS parameters. Finally, we demonstrate that this set of functional stimulation parameters is further restricted by lesion severity, highlighting an intrinsic limitation of SCS in cases of severe injury.

INTRODUCTION

In the last two decades, animal and clinical studies showed that epidural electrical spinal cord stimulation (SCS) can improve motor control in people with spinal cord injury (SCI) and stroke^1–7. The most striking observation emerging from clinical trials is that, during SCS, humans with paralysis appear able to voluntarily control previously paralyzed limbs^2,8. In other words, SCS does not generate movement per se, but rather facilitates volitional movement^2,9. In an effort to explain these results, mechanistic investigations of SCS focused either on the identification of the neural pathways that are directly recruited by SCS^10–13 or the involvement of movement-generating spinal circuits such as reflexes^11–13, synergies¹⁴ and central pattern generators^15–17. However, these studies never considered the contribution of residual supraspinal fibers, thereby failing to explain the facilitation of voluntary movements. Understanding how volitional inputs can shape motor output during SCS could lead to more effective stimulation protocols targeted to maximize volitional control.

The leading hypothesis is that SCS increases the excitability of spinal circuits and, particularly, spinal motoneurons, bringing their membrane potential closer to firing threshold and making them more responsive to supraspinal input^2,8,18. While plausible, it is difficult to conceive how pulsatile stimulation could lead to membrane modulation of motoneurons given the stimulation frequencies and membrane time constants at play. This limitation is exacerbated by the fact that this hypothesis has surprisingly never been tested experimentally.

Indeed, prior work established that SCS directly activates sensory afferents in the dorsal roots and dorsal columns^{10–12,19–21}. Importantly, these afferents form mono- and polysynaptic excitatory connections to spinal motoneurons (and other structures), thereby conveying SCS excitatory drive to motoneurons via short-duration excitatory post-synaptic potentials (EPSPs, i.e., glutamatergic synapses with decay times around 2 ms). While this synaptic input can depolarize the motoneuron membrane, its short duration coupled to the pulsatile nature of SCS would require very high stimulation frequencies to summate and tonically depolarize the membrane potential.

In fact, animal studies showed that SCS pulses can facilitate monosynaptic corticospinal motor-evoked potentials²² when the two pulses are timed to arrive at the same time on the motoneuron membrane. Similarly, supraspinal excitatory drive can modulate and increase the strength of spinal reflexes induced by SCS pulses²³ and other technologies stimulating the primary afferents²⁴, demonstrating that these two excitatory pathways can interact to modulate the neural activity of motoneurons. Here, we started from this body of evidence to study how residual supraspinal excitatory drive and SCS pulses are integrated in the motoneuron membrane to enable volitional motor control.

To do so, we built on established biophysics^25–28 to develop a model of the motoneuron membrane potential while it received excitatory inputs from sensory afferents recruited by SCS and residual supraspinal fibers. We used this model to predict motoneuron firing rates and we tested these predictions on motoneuron firing rates with motor units recordings in monkeys and humans with SCI and stroke. We found that, in the presence of residual supraspinal inputs, motoneuron action potentials are triggered by otherwise subthreshold SCS pulses, becoming effectively entrained to the stimulation interpulse interval and its integer multiples^29–31. Despite this entrainment, residual supraspinal inputs can control the overall motoneuron pool firing rate by modulating the number of SCS-mediated EPSPs that are transformed into action potentials. Thus, our results refute the hypothesis that SCS facilitates residual supraspinal inputs by tonically increasing motoneuron excitability while offering an alternative explanation to the observation that SCS facilitates voluntary movement. Moreover, we show that only a subset of SCS parameters enables volitional motor control via combined residual excitatory and inhibitory action, and that the size of this functional parameter space shrinks with lesion severity. While restricted to the analysis of motoneurons, our results are a first step towards the understanding of the mechanisms enabling the recovery of voluntary motor control with SCS.

RESULTS

Fundamental representation of the biophysics of SCS in the motoneuron membrane

To identify the membrane mechanisms underlying motoneuron activation during SCS, we started from four assumptions grounded on experimental evidence (Figure 1a) that define the validity boundary of our approach. First, SCS directly recruits large-diameter sensory afferents, particularly, Ia afferents¹¹. Second, electrical stimulation causes simultaneous depolarization in all recruited afferents thereby producing synchronized volleys of action potentials. Third, in contrast to this non-natural input, supraspinal drive can be modeled as a stochastic process of non-synchronized axon firing^32,33. Fourth, a lesion reduces the number of available supraspinal fibers, thus impacting the ability of the cortex to produce action potentials in spinal motoneurons.

Figure 1. Biophysical model with underlying assumptions.

a, Model assumptions. b, Schematic of the biophysical model. Spinal motoneurons receive excitatory inputs from supraspinal fibers and Ia-afferents recruited by SCS. Motoneurons’ membrane potential are modeled with standard Hodgkin–Huxley equations²⁶.

While other network elements are also involved in the generation of movement during SCS, we aimed at understanding how much of the behavior could be explained with the simplest possible circuit known to be recruited by SCS: the monosynaptic reflex. We designed a simple circuit including motoneurons, Ia afferents with monosynaptic connections to the motoneurons, and “supraspinal fibers”, which represent the total supraspinal input to spinal motoneurons (Figure 1a). Because the phenomenon at play depends on specific membrane relaxation timings and the durations of EPSPs, we used a Hodgkin-Huxley model²⁶ to represent the motoneuron membrane, while Ia afferents and supraspinal fibers were modeled as point processes providing excitatory inputs to the motoneuron models (see Methods). We modeled stimulation amplitude as the percentage of afferents activated by SCS (see Methods), allowing us to vary between no activation and full population recruitment²⁷. Recruited afferents elicit synchronous volleys firing at the SCS frequency, a phenomenon that holds for stimulation frequencies up to 500 Hz²⁷. Natural supraspinal inputs are modeled as Poisson processes with time-varying firing rates. Variability is introduced at the synapses from both supraspinal and sensory afferents as well as in the motoneuron size (see Methods, Figure S2). Finally, we simulated lesions of different severities by reducing the number of available supraspinal fibers.

Supraspinal inputs transform subthreshold SCS-mediated EPSPs into action potentials

Using our model, we inspected the simulated membrane potential of motoneurons before and after a lesion. Prior to a lesion, supraspinal inputs generated regular and sustained motoneurons action potentials (Figure 2a). We then simulated a lesion by suppressing activity in 80% of supraspinal fibers (Figure 2b). Residual supraspinal EPSPs produced a mean tonic depolarization of 1.4 mV, ramping up within 10 ms after the start of supraspinal activity. This tonic depolarization effectively sets the motoneuron membrane closer to firing threshold (Figure 2b). However, it was insufficient to produce action potentials, thus leading to simulated paralysis. We then simulated a train of subthreshold SCS pulses at a low frequency (10 Hz) that alone did not suffice to directly produce action potentials in motoneurons (Figure 2b). As opposed to the tonic depolarization produced by residual natural inputs, subthreshold SCS induced a pulsatile depolarization. This pulsatile depolarization occurred through discrete EPSPs in consequence of the synchronized recruitment of Ia afferents following each stimulation pulse.

Figure 2. SCS entrains motoneuron action potentials.

a, Simulation of the membrane potential of a single motoneuron driven by supraspinal fibers prior to lesion (top), raster plot of each supraspinal fiber firing stochastically (middle) b, Simulation of the membrane potential of a single motoneuron after lesion receiving only residual supraspinal inputs (white background, top), during SCS alone (10 Hz, 40% amplitude; blue background, top) and concurrent residual supraspinal inputs and SCS (gray background, top). Raster plot of each residual supraspinal fiber (middle). Raster plot of each Ia afferent firing synchronously after each SCS pulse (bottom). c, Same as b at a higher SCS frequency (40 Hz, 40% amplitude). d, Same as b and c with the leading hypothesis that SCS is a current that tonically depolarizes the membrane potential. e, Motoneuron firing rate as a function of SCS frequencies for an example motoneuron. Dashed line shows the identity line (i.e. SCS frequency equals motoneuron firing rate). f-i, Probability distribution of the number of skipped SCS pulses. We obtained the number of skipped SCS pulses normalizing the ISI by the SCS interpulse interval minus 1. Same example motoneuron in e with SCS at 10 (f) and 40 (g) Hz, motoneuron pool at 40 Hz (h), and motoneuron pool with the SCS tonic depolarization hypothesis (i). See also Figure S2.

Next, we combined subthreshold SCS with residual supraspinal inputs, which led to a robust production of action potentials that seemed coupled to the stimulation pulses (Figure 2b). Indeed, when calculating the interspike interval (ISI) of the motoneuron pool, we found that it coincided with the stimulation interpulse interval (Figure 2f). In other words, for each stimulation pulse, motoneurons produced an action potential (i.e., full entrainment of motoneuron firing). During SCS alone at higher stimulation frequencies (i.e. frequencies that have been shown to restore voluntary movement in clinical settings, around 40 Hz), SCS-mediated EPSPs produced a pulsatile depolarization of the membrane without generating action potentials (Figure 2c). Again, with concurrent residual supraspinal inputs, this example motoneuron generated action potentials (Figure 2c). However, above 20 Hz SCS, motoneurons were not able to generate an action potential for each SCS pulse and started “skipping” SCS pulses (Figure 2c, Figure 2e). Despite pulse-skipping³⁴, action potentials still occurred only in consequence of SCS pulses, generating characteristic peaks in ISI distributions at integers of SCS interpulse intervals (Figure 2g,h, Figure S1). The number of skipped pulses increased as a function of SCS frequency (Figure 2f-h, Figure S2f). This pulse-skipping produced a non-monotonic increase of motoneuron firing rates with SCS frequency (Figure 2e) that was variable across motoneurons (Figure S2). In summary, we observed that, with concurrent activation of residual supraspinal inputs and SCS-recruited Ia-afferents, motoneuron action potentials were triggered by otherwise subthreshold SCS pulses.

We then sought to illustrate what would happen under the leading hypothesis that SCS tonically depolarizes the motoneuron membrane potential in order to compare it with the hypothesis derived from the biophysical model that pulsatile SCS triggers motoneuron action potentials. To this end, we modeled the putative effect of SCS as a constant current that depolarizes the membrane potential without producing any action potential (Figure 2d). Again, action potentials were only produced when both SCS and supraspinal inputs were activated. However, in this case, action potentials were not triggered by SCS pulses, leading to radically different ISI distributions without the discrete peaks at integers of SCS interpulse intervals (Figure 2i). Therefore, motoneuron ISI distributions represent an experimental measure that can discriminate between these two alternative hypotheses.

Voluntary vs involuntary motoneuron activity during SCS

We then sought to explore the effects of SCS parameters on the production of volitional motoneuron activity. To this end, we quantified the firing activity in a simulated pool of motoneurons during SCS alone (Figure 3a) and during concurrent activation of SCS and residual supraspinal fibers (Figure 3b), while varying SCS amplitude (i.e., percentage of Ia afferents recruited, 10–100%) and frequency (8–400 Hz). While we found subthreshold SCS parameters that did not generate motoneuron activity (Figure 3a), we also found that, for certain parameters, SCS alone directly produced sustained motoneuron firing rate (>8 Hz)³⁵, even without supraspinal input (Figure 3a). This well-known phenomenon has been described as suprathreshold SCS^3,36,37.

Figure 3. SCS parameter regimes.

a, Simulated mean firing rates of a motoneuron pool during SCS alone (5 second simulation) for a range of frequencies and amplitudes. Solid line separates subthreshold from suprathreshold SCS parameters. b, Same as a during concurrent excitatory inputs from SCS and residual supraspinal inputs to the pool of motoneurons. The dashed line separates the combinations of parameters that produce sustained motoneuron firing rates (>8 Hz). The parameters between the gray lines represent the combination of SCS parameters that produce sustained firing rate only with concurrent SCS and residual supraspinal inputs (i.e., voluntary movement regime).

Interestingly, most of the subthreshold SCS parameters that led to sparse or no firing rates showed sustained firing with the addition of the residual supraspinal inputs (Figure 3b). This pattern presented two large “regimes’’ in the SCS-parameter space that we termed voluntary and involuntary movement regimes (Figure 3b). In the voluntary movement regime, SCS-mediated subthreshold EPSPs became suprathreshold with concurrent inputs from residual supraspinal fibers. Instead, in the involuntary movement regime, SCS dominated motoneuron firing with little influence from supraspinal inputs.

Residual supraspinal input can modulate entrained motoneuron firing rates

The fact that residual supraspinal inputs can transform subthreshold SCS pulses into action potentials could imply that residual supraspinal fibers solely act as a gating mechanism. In this case, entrained motoneuron firing rates would be fully controlled by SCS parameters and volitional modulation of forces would be impossible. Since this would contradict experimental evidence in humans³⁸, we explored the role of residual supraspinal fibers in motoneuron firing rates modulation. Specifically, we simulated motoneuron output during SCS for different firing rates of residual supraspinal fibers. We observed that the motoneuron pool firing rates linearly increased with supraspinal firing rates at SCS parameters within the voluntary regime (Figure 4a). In contrast, in the involuntary regime, motoneuron firing rates remained almost unaffected by supraspinal inputs (Figure 4a).

Figure 4. Residual supraspinal inputs can modulate motoneuron firing rate during SCS.

a, Motoneuron pool mean firing rate (5 seconds simulations) as a function of residual supraspinal fibers firing rate in the voluntary movement regime (SCS parameters: 40 Hz and 40% amplitude) and involuntary regime (SCS parameters: 40 Hz and 90% amplitude). b, Membrane potential of the same motoneuron with residual supraspinal inputs at 10 and 60 Hz. This motoneuron is recruited at 60 Hz but not at 10 Hz. c, Membrane potential of another motoneuron that skips 2 SCS pulses at 10 Hz but only 1 at 60 Hz (SCS parameters: 40 Hz and 40% amplitude). d, Percentage of motoneurons recruited (firing rate >8 Hz) as a function of the residual supraspinal fibers firing rate. e,f, Motoneuron pool ISI normalized probability distributions for residual supraspinal firing rates at 10 and 60 Hz during SCS (40 Hz, 40% amplitude). g, Normalized ISI cumulative distributions. h, To match the motoneuron firing rate with different SCS frequencies (40 and 80 Hz), we adapted the firing rate of the residual supraspinal fibers to 45 and 50 respectively. i,j, ISI normalized probability distributions for the same parameters in h. k, Normalized ISI cumulative distributions for the same parameter as in h. To maintain the same motoneuron firing rate with higher SCS frequency, motoneurons skipped more pulses. l-m, Fine movement task in the voluntary (40 Hz, 40% amplitude) and involuntary (40 Hz, 90% amplitude) movement regimes. Firing rates are computed in 100 ms bin windows. From bottom to top: Total number of supraspinal inputs to motoneurons that follow a sinusoidal wave, motoneuron firing rate and normalized force. Blue area indicates the difference in firing rate from the prelesion case (i.e., error). n, Root-mean square of the difference between the motoneuron firing rate pre- vs postlesion (light blue regions in l and m) for all simulated SCS parameters. The gray lines in the heatmap indicate the voluntary movement regime defined in the isometric task (Figure 3b).

To understand the mechanisms underlying this supraspinal control of motoneuron firing during SCS, we inspected simulated membrane potential during SCS within the voluntary regime. First, we found that, if residual supraspinal fibers firing rates were high enough, they could induce a stronger depolarization in the motoneuron membrane, thereby bringing motoneurons closer to firing threshold and increasing the number of recruited motoneurons (see an example of a motoneuron that was recruited by SCS with high residual supraspinal inputs (dark blue, Figure 4b), but not low (light blue, Figure 4b)). Over the whole motoneuron pool, the number of active motoneurons increased with higher supraspinal input (i.e., 90% recruitment probability increase from supraspinal firing at 5 Hz vs 60 Hz, Figure 4d).

Second, we found that, as the residual supraspinal firing rate increased, the motoneuron depolarization was faster, decreasing the number of skipped SCS pulses. For instance, the motoneuron in Figure 4c skipped 2 SCS pulses with residual supraspinal fibers firing at 10 Hz, but it only skipped 1 with residual supraspinal fibers firing at 60 Hz. Indeed, ISI histograms were shifted towards smaller values (i.e., fewer skipped SCS pulses) for stronger residual supraspinal inputs (Figure 4e-g).

One could test if supraspinal inputs can control pulse-skipping by asking a participant to produce a constant force while receiving SCS at different frequencies. In this case, to maintain constant force output, the participant would have to adapt their supraspinal inputs to skip more or less SCS pulses, thereby maintaining constant motoneuron firing rates. We simulated this task in our model, where we set SCS to two different stimulation frequencies (40 and 80 Hz). To qualitatively match motoneuron firing rate in both conditions, we adapted residual supraspinal input firing rate to 50 and 45 Hz, respectively (where motoneuron firing is used as a proxy of the force³⁹, Figure 4h). As expected, we found that, to maintain the same motoneuron pool firing rate, the number of skipped pulses was higher at high SCS frequencies (Figure 4i-k).

Together, these results predict that residual supraspinal fibers can modulate motoneuron firing rate, even though it is entrained to SCS. We then studied whether this modulation could produce functional fine motor control. To this end, we simulated a task where residual supraspinal inputs aimed at producing a sinusoidal target force while we estimated the force produced by a pool of motoneurons³⁹ (see Methods, Figure 4l,m). In the prelesion case, a sinusoidal force was produced by the supraspinal inputs via modulating their firing rate according to the target force (Figure 4l, grey line). Expectedly, after the lesion, the supraspinal inputs were not able to produce motoneuron activation (Figure 4l, grey dashed line). With SCS ON at parameters within the voluntary movement regime, the same supraspinal strategy (i.e. modulating the firing rate according to the force target) was enough to modulate force (Figure 4l, black line, Figure 4n). Instead, SCS parameters belonging to the involuntary movement regime impeded residual supraspinal inputs modulation of motoneuron activity, yielding high task errors (Figure 4m, black line, Figure 4n).

In summary, our biophysical model predicted that, although motoneuron firing rate is entrained to SCS, residual supraspinal fibers can still volitionally modulate motoneuron activity by changing the number of recruited motoneurons and controlling the number of skipped SCS pulses.

Validation of model assumptions in electrophysiological experiments in monkeys

We conducted animal experiments to validate model assumptions. We leveraged our experimental setup to perform advanced electrophysiology^40–42 in propofol⁴³ anesthetized macaque monkeys (n=2; Mk-JC, Mk-Ka). Briefly, we applied SCS at C6-C8 cervical spinal segments, while manipulating supraspinal input by means of deep-brain stimulation of the internal capsule⁴⁴ (Figure S3a). In parallel, we measured motoneuron output directly, via intraspinal neural recordings, and indirectly, via intramuscular electromyography (EMG) of the hand muscles (Figure 5a).

Figure 5. Experimental validation of model assumptions and predictions in monkeys.

a, Experimental setup in anesthetized monkeys and schematic of the spinal circuits involved during dorsal root stimulation and activation of corticospinal fibers via deep-brain stimulation of the internal capsule. b, EMG stimulation-triggered average traces of an SCS pulse with (red) and without (grey) ICS conditioning. c, EMG stimulation-triggered average traces of an ICS pulse with (blue) and without (grey) SCS conditioning. d, Peak-to-peak amplitudes EMG responses to a single SCS pulse with and without ICS conditioning for two hand muscles (FDM, APB) in both monkeys. Conditioning ICS pulse was delivered 5 ms prior to the SCS pulse. The sample size for each condition was n>60. e, Same as d when conditioning a single pulse of ICS with SCS. The sample size for each condition was n>60. To test significance, we used Kruskal-Wallis two-tailed test to test significance (*** p<0.001). Square and error bars indicate the mean distribution of the data with 95% confidence interval. f, Sample of sorted single unit action potential waveforms recorded from the ventral channels of the linear probe and its peristimulus time histogram. g, Histograms of normalized ISI probability distribution of the sorted single units during 100 Hz SCS in both monkeys.

Our prediction is that supraspinal fibers can modulate motoneuron membrane and reduce the threshold for incoming SCS-mediated EPSPs. While we can not directly test this in anesthetized monkeys, if this is true, conditioning a pulse of SCS with a single pulse of internal capsule stimulation (ICS) should facilitate SCS and produce larger SCS-triggered spinal reflexes in targeted muscles. We thus designed a stimulation protocol to condition SCS with a pulse of ICS at 5 ms delay (Figure 5c). In both monkeys, mean peak-to-peak of SCS-induced reflex amplitudes significantly increased when SCS was conditioned by a pulse of ICS, demonstrating that corticospinal inputs can facilitate SCS-induced reflexes (Figure 5c, Mk-JC: 111.3% in APB; 285.8% in FDM. Mk-Ka: 19.6% in FDM; 44.6% in APB). Another important feature of our model is that both Ia afferents and supraspinal fibers excite motoneurons through fast glutamatergic synapses, resulting in a similar effect on the motoneuron membrane. Thus, SCS-induced EPSPs should modulate corticospinal motor-evoked potentials. Indeed, corticospinal motor-evoked potentials mean peak-to-peak amplitudes significantly increased in comparison to control (i.e., ICS alone) in both monkeys, in contrast to previous reported results^22,45 (Figure 5d). Moreover, as expected, these facilitations decreased at longer latencies, given that EPSPs from monosynaptic Ia afferent-mediated and cortex-mediated excitatory inputs did not coincide in the motoneuron membrane (Figure S3b-f). These results show that, as we assumed in our model, both inputs can depolarize membrane potentials of motoneurons and facilitate a subsequent EPSP from each other.

We next validated the assumption that SCS recruits sensory afferents synchronously at a given stimulation frequency (Figure 1b). As depicted in our simulations (Figure 2), if SCS produces synchronous volleys in the recruited afferents, motoneurons should produce spikes triggered by these sensory inputs and, therefore, be aligned to SCS pulses. To test this, we inspected postsynaptic motoneuron firing when receiving SCS alone. In particular, we delivered SCS at a high frequency (100 Hz) in both monkeys and identified intraspinal single units from the ventral channels in the linear probe (Figure 5e), corresponding to the location of motoneuron pools in lamina IX^46,47. We then computed ISI distributions and detected peaks at exact integers of SCS pulses intervals (Figure 5f, Figure S3g). This not only shows that SCS inputs are highly synchronous and entrain motoneuron activity, but also that motoneurons are skipping SCS pulses at high stimulation frequencies as predicted by our simulations.

These experiments validated some of the model assumptions. However, as the monkeys were anesthetized, we could not demonstrate our central results concerning combined volitional input and SCS; namely, that supraspinal control of motoneuron activity is entrained to SCS for motor recovery.

Volitional control of spinal motor units in humans with paralysis during SCS

We conducted experiments in humans by leveraging our existing Institutional Review Board protocols. Specifically, we performed experiments in one participant with SCI (STIM01, ASIA A: sensory and motor complete) and two participants with poststroke arm hemiparesis (SCS03, SCS04). STIM01 was enrolled in the framework of an observational study for people who received an SCS implant on the lumbosacral spinal cord to reduce neuropathic pain in the lower limbs (Figure S4c,d). SCS03 and SCS04 participated in a clinical trial exploring the effects of cervical SCS on motor control of the hand and arm⁶ (Figure S4a,b). By testing our main model predictions in humans with SCI and stroke, we aimed at demonstrating that there are fundamental principles underlying the mechanisms of SCS, irrespective of the specific disease that caused the lesion to the supraspinal fibers.

We started by testing the effects of subthreshold SCS on motoneuron firing rates in STIM01, who had complete leg paralysis in consequence of a SCI; hence, a severe lesion. We asked the participant to contract his paralyzed leg in a knee extension isometric task at the maximum voluntary strength with and without SCS. Concurrently, we extracted motor units using surface EMG⁴⁸ (Figure 6a,b, see Methods), providing a direct measure of single motoneuron firing (Figure S5a). The participant could not produce any force without SCS. Instead, with SCS parameters that did not produce any force alone (i.e., in the voluntary regime), SCS led to substantial volitional force production (Figure 6c), replicating previous experimental observations^4,5.

Figure 6. Experimental validation in humans with paralysis.

a, Schematic of the experimental setup in participants with upper-limb paralysis performing a force task with their paretic arm (similar setup was adapted for the participant with lower-limb paralysis). b, Schematic of motor unit decomposition using surface EMG performing a voluntary movement along with a sample raster plot for a detected motor unit action potential waveform. c, Example of trial where STIM01 extended his leg at their maximum voluntary contraction (MVC) during 2 seconds (3 repetitions). Top: torque trace, Middle: firing rate of decomposed motor units from both extensor muscles (Vastus Lateralis, Rectus Distal, sorted by average firing rate) and Bottom: raster plot of the same units. SCS parameters: 40 Hz and 10.8 mA. d, Histogram of normalized ISI probability distribution of the highly entrained motor units in STIM01 for the same task in c (6 repetitions). e, Normalized ISI cumulative distribution of the highly entrained motor units in STIM01 during 40 and 60 Hz SCS where STIM01 held 35% of their maximum force (task torque) during 20 seconds (2 repetitions for each stimulation frequency). f, Left: Torque traces for the same task as e. Right: Motor unit firing rate in STIM01 during 40 and 60 Hz SCS. Square and error bars indicate the mean and the 95% confidence interval. Each point is the mean firing rate of single motor units. g, Example of a raster plot in STIM01 during 40 Hz SCS illustrating that the ISIs are multiple of the IPI (IPI: interpulse interval; ISI: interspike interval). h, Mean torque trace with and without stimulation in SCS04 and SCS03 during the force-modulated task (35–50% of the maximum force). i, Histograms of normalized ISI probability distribution of the highly entrained motor units in SCS04 (see Figure S6d for SCS03) for each force-modulated task with and without stimulation (18 repetitions for all for levels). j, Normalized ISI cumulative distribution of the extracted motor units during SCS in SCS04 (left) and SCS03 (right) for all force levels for all trials (18 repetitions for SCS04 for all for levels, 9 repetitions in SCS03 for 5% isometric force level, 7 for 20%, 7 for 35% and 4 for 50%). See also Figure S5, S6, and S7.

We then inspected whether motor unit action potentials were entrained to SCS and found ISI distributions with clear peaks at multiple of SCS interpulse intervals (Figure 6c-d,g and Figure S6b) with a striking similarity to simulated distributions (Figure 2h). In our model, we solely represented monosynaptic connections from Ia afferents, which led to highly entrained motoneurons that fired aligned to the stimulation pulses. Instead, in human experiments, many other neural elements such as polysynaptic pathways could relax SCS entrainment, producing some action potentials that are not directly triggered by SCS pulses. Thus, we measured single motor unit entrainment and detected that, in STIM01, all motor units were entrained: around 40% were highly entrained (i.e., 40 to 100% of the spikes triggered by SCS pulses) and around 60% were entrained (i.e., 20 to 40% of the spikes triggered by SCS pulses, Figure S7a-c). In other words, the majority of motor unit action potentials were triggered by SCS pulses (Figure 6d), as predicted by our simple model (Figure 2e,f).

We then tested if STIM01 could voluntarily modulate SCS-entrained motor unit firing rates by adapting pulse skipping. Replicating our simulations (Figure 4h-k), we asked STIM01 to hold the same isometric force under different stimulation frequencies (Figure S6c). While STIM01 was not able to produce any force without SCS (Figure S6a), STIM01 could voluntarily control motor unit firing rates to produce the same force at 40 and 60 Hz SCS frequencies (Figure 6f). We found that highly entrained motor units skipped more pulses at 60 Hz than 40 Hz SCS (Figure 6e), showing that STIM01 controlled the number of skipped pulses to produce the same force (Figure 6f).

We then asked SCS03 and SCS04 to perform a task that they could also do without SCS. Specifically, we asked them to follow a sinusoidal force profile centered around different force levels defined in intervals of their maximal voluntary contraction (5–20%, 20–35%, and 35–50% of their maximum force). Without SCS, participants followed the force target, albeit with some difficulty (Figure 6h). As expected, motor unit firing rates followed a stochastic firing probability profile as demonstrated by the ISI distributions (Figure 6i, Figure S7h-j).

As with STIM01, with cervical SCS ON, we observed that SCS entrained motor unit activity: 60 and 81% of motor units were highly entrained in SCS03 and SCS04, respectively (Figure S7b-g). Indeed, replicating the results from STIM01, the ISI distributions of highly entrained motor units showed clear peaks at multiples of SCS interpulse intervals for all force levels (Figure 6i, Figure S6d). Despite this high SCS entrainment, participants could modulate firing to follow the sinusoidal profile (Figure 6h). As predicted by our model (Figure 4e-g), higher force levels led to less pulse skipping by shifting the ISI histogram towards smaller values (Figure 6j). These results demonstrated that humans can modulate force during SCS by changing the number of skipped pulses to finely control force output.

Subthreshold SCS efficacy may depend on lesion severity

During these experiments, we noticed that, in STM01, the stimulation amplitude required to enable the voluntary production was close to the involuntary movement regime border (i.e., suprathreshold SCS). Indeed, increasing the stimulation amplitude led to involuntary motor responses that produced detectable torques (Figure S6a). We hypothesized that this phenomenon could be related to the fact that STIM01 had a severe lesion. Thus, we sought to exploit our biophysical model to study the theoretical impact that lesion severity could have on the range of SCS parameters in the voluntary movement regime. We replicated an isometric task in our model for a range of lesion severities (80–98% reduction in supraspinal inputs) and found that increasing the lesion severity reduced the size of the voluntary movement regime (from 38% to 4.3% of possible parameters, Figure 7a-c).

Figure 7. Lesion severity reduces voluntary movement regime.

a, Simulation of the membrane potential of a single motoneuron driven by residual supraspinal fibers and SCS (10 Hz, 40%) in a mild (60 supraspinal fibers, top) and severe lesion (20 supraspinal fibers, bottom). b, Simulated heatmap indicating the combinations of SCS parameters within the voluntary movement regime for different degrees of lesion severity (mildest lesion in light red, the most severe lesion in dark red; 4 seconds simulation). c, Number of SCS parameter combinations within the voluntary movement regime for different degrees of lesion severity. d, Raw EMG to illustrate the stimulation protocol employing phasic ICS (47 Hz) during continuous subthreshold SCS (60 Hz) at increasing SCS amplitudes (APB muscle). e-f, Facilitation effect of SCS in the EMG responses during phasic ICS and continuous SCS at increasing SCS amplitudes. Square and error bars indicate the mean and 95% confidence interval.

We then tested these results in monkey Mk-JC, where we could control the amount of supraspinal inputs via internal capsule stimulation (ICS) to mimic lesion severity. We superimposed subthreshold continuous SCS to bursts of ICS while recording EMG from the APB muscle (Figure 7d). We found that low SCS amplitudes did not potentiate muscle activity produced by ICS while higher, but still subthreshold SCS amplitudes potentiated muscle activity (i.e., voluntary movement regime, Figure 7e,f). As our model predicted, the number of SCS parameters in the voluntary regime shrunk with lesion severity. For example, in the APB muscle, the SCS amplitude of 140 uA belonged to the voluntary regime in mild lesion, but not in severe lesion (Figure 7e,f).

Supraspinal inhibitory drive could enlarge effective SCS parameter range

So far, we only considered supraspinal excitatory drive. However, residual supraspinal inputs could also retain control of inhibitory neurons, which could impact our overall findings. To test the contribution of supraspinal inhibition, we added a population of inhibitory neurons (Figure 8a). We found that inhibitory drive can transform action potentials triggered by suprathreshold SCS into subthreshold EPSPs, effectively silencing unwanted motoneuron activity (Figure 8b). In consequence, the presence of inhibition enlarged the voluntary regime by expanding it into the involuntary suprathreshold movement regime (Figure 8c). However, lesion severity still reduces the voluntary regime size (Figure 8d). Moreover, we found that inhibition increases the ability to modulate motoneuron firing rate (Figure 8e) and, therefore, execute a fine motor control task (Figure 8f).

Figure 8. Supraspinal inhibitory drive enlarges the voluntary regime.

a, Biophysical model schema where motoneurons receive both residual excitatory and inhibitory supraspinal drive. b, Simulated membrane potential (top), raster plot of the inhibitory supraspinal inputs (middle) and raster plot of the Ia afferents recruited by SCS (bottom). c, Motoneuron firing rate with concurrent input from SCS and supraspinal inhibitory drive as a function of SCS parameters. Grey dash lines indicate the voluntary regime when considering only supraspinal excitatory drive (from Figure 3), grey solid line indicates the enlarged voluntary regime when considering also residual supraspinal inhibitory drive. d, SCS parameters belonging to the voluntary regime with residual supraspinal excitatory (red) and inhibitory (blue) inputs. e, Average motoneuron firing rate as a function of residual supraspinal excitatory inputs with subthreshold parameters (40% amplitude and 40 Hz, red line) and inhibitory and excitatory supraspinal drive (combined) with suprathreshold SCS parameters (70% amplitude and 60 Hz, purple line). Negative/positive values indicate inhibitory and excitatory drive respectively. f, Fine motor control task. Bottom: Excitatory and inhibitory residual supraspinal inputs follow a sinusoidal function. Grey line represents the excitatory input before the lesion. Middle: Motoneuron firing rate for pre-lesion case (grey line), motoneurons receiving only excitatory inputs with subthreshold SCS parameters (40% amplitude and 40 Hz, red line) and motoneurons receiving excitatory and inhibitory inputs with suprathreshold SCS parameters ( 70% amplitude and 60 Hz, purple line). Top: Force produced by motoneuron pool before the lesion, only excitatory supraspinal inputs and both excitatory and inhibitory supraspinal inputs. g, Spinal reflexes in antagonist muscles can be voluntarily inhibited by residual supraspinal inputs. Top: EMG response to 2 Hz SCS in the biceps during rest (black) and active elbow extension movement (blue). Bottom: Peak-to peak of each spinal reflex (dots) and mean with its 95% confidence interval (square). Significance was tested with bootstrap (N=10000). See also Figure S8.

Finally, we tested whether humans with corticospinal lesions can inhibit SCS pulses, thereby expanding the voluntary regime as predicted by our model. To this aim, we analysed data of two participants with stroke from our clinical trial (SCS07 and SCS08). They were seated in the KINARM, a robotic platform that removed the weight of their arms, either at rest with their arm extended or voluntarily extending their arm (see Methods, Figure S8). In both conditions, we chose a non-selective stimulation configuration that produced clear supra-threshold reflexes in the flexors (the biceps) at a low stimulation frequency (2 Hz). During voluntary extension of their arm, the flexor spinal reflexes were significantly suppressed compared to rest (Figure 8g). Thus, participants were able to inhibit unwanted flexor reflexes induced by SCS, thereby demonstrating their ability to volitionally inhibit suprathreshold SCS.

DISCUSSION

In this study, we combined biophysical modeling with animal and human experiments to study the neural mechanisms underlying the recovery of voluntary control of spinal motoneurons during SCS after paralysis.

SCS entrains motoneuron firing but residual supraspinal inputs can control SCS-induced motoneuron firing

It is a common tendency to name the motor-enabling effect of SCS “neuromodulation”, i.e., a bias in membrane excitability^2,8,18. However, our findings reject the possibility that SCS, delivered at frequencies below 100 Hz, is modulating the membrane of neurons in the strict sense of the term “neuromodulation”. Indeed, SCS triggers action potentials because of the pulsatile nature of the synchronous afferent volleys that it produces. Instead, residual natural activity can exert this biasing action by means of fast neurotransmitters such as glutamate, but also by serotonergic and noradrenergic systems⁴⁹. Due to summation of EPSPs from both sources and the pulsatile nature of SCS, supraspinal biasing of cell excitability then transforms discrete subthreshold SCS pulses into suprathreshold events (Figure 2). Thus, at the motoneuron membrane level, it is supraspinal inputs that “facilitate” SCS-mediated motor output. Behaviorally, both interpretations (i.e., SCS facilitation of supraspinal inputs or vice versa) are indistinguishable, since movement only occurs when intention is present. However, using our biophysical model, we were able to make specific, experimentally-testable predictions of the ISI distribution to differentiate these two hypotheses. Our results refute the leading hypothesis that SCS simply increases motoneuron excitability, making motoneurons more responsive to supraspinal inputs. Instead, we showed that, while SCS entrains motoneuron firing rate, residual supraspinal inputs can modulate the number of SCS pulses transformed into action potentials, thereby controlling motoneuron firing rates and forces. This is in contrast to other neurotechnologies that directly drive motoneurons^24,50, which would instead produce highly synchronized motoneuron firing and, in turn, result in poorly-controllable forces^3,6,9,37,51. In other words, this is one of those cases in which the simple description of behavior does not offer satisfactory explanatory power of a phenomenon that requires analysis of neural output to be correctly interpreted⁵².

The spread of SCS entrainment to other spinal network elements

Through the analysis of the membrane mechanisms underlying the responses of spinal motoneurons to SCS pulses, we studied the computational principles that govern the integration of SCS-mediated inputs and residual supraspinal activity in motoneurons membrane. While we focused only on spinal motoneurons, the membrane mechanisms that we identified here are likely to hold also for spinal interneurons that receive significant inputs from Ia afferents activated by SCS^53,54. For example, central pattern generators^55,56, inhibitory interneurons⁵⁷ and excitatory premotor interneurons involved in muscle synergies⁵⁸, all receive strong sensory inputs from proprioceptive afferents. Therefore, similarly to what we observed in motoneurons, residual supraspinal modulation could also bring subthreshold SCS events into suprathreshold action potentials in these network elements. In other words, the divergent connectivity of Ia-afferents towards large parts of the sensorimotor network guarantees the brain access to many crucial components that all contribute to the observed recovery of motor function with SCS. In fact, from motor units in humans, we observed that extracted units displayed different levels of entrainment to SCS, suggesting that motor units were likely activated also via polysynaptic pathways through SCS. This could explain why, despite the well-known low specificity of SCS^12,36, we can observe repeatable, strong clinical effects^4,5. In fact, we can speculate that a more selective technology that only enables control of motoneurons, or any other specific set of neurons, would fail at restoring voluntary motor control. The success of SCS does not stem from the activation of specific neural elements, but rather from the widespread projections of SCS-activated sensory afferents that enable supraspinal control of spinal networks.

Clinical implications

A critical outcome of our study for clinical application is the prediction that the parameters that optimize fine control and maximize motoneuron firing rates are slightly supra-threshold, i.e. in a region where SCS directly triggers motoneuron activity. Indeed, we showed that participants can exploit residual supraspinal inhibition to silence unwanted suprathreshold SCS motoneuron activity. These results suggest that SCS should be set slightly above threshold, and participants should be trained to sculpt motoneuron firing rate by both inhibiting unwanted SCS activity and using SCS to maximize motoneuron firing rate. In fact, it is conceivable that a person with severe paralysis could learn to sculpt suprathreshold SCS inputs either by presynaptic inhibition of the Ia afferents or postsynaptic inhibition of the motoneurons. In both cases, inhibition could suppress unwanted activity and direct SCS excitatory drive towards movement-relevant neural pathways. It is possible that this is one of the effects of physical training, which, by strengthening synaptic connectivity, can enable voluntary control of SCS.

The second finding with direct clinical impact is that the well-defined SCS parameter regime that enables volitional control of spinal motoneurons shrinks as the number of residual supraspinal inputs decreases, i.e., as the severity of the lesion increases. This is caused by the fact that, to compensate for severe loss of excitatory drive and to produce sufficient firing to enable movement, SCS amplitudes must be set to values that rapidly enter the “suprathreshold” region, which we termed the “involuntary movement” regime, meaning that motoneuron activation and, likely, muscle co-contraction, will occur even when participants try to inhibit it. This intrinsic limitation of SCS emerges when inspecting aggregated experimental human data⁵⁹ that show a clear trade-off between efficacy and lesion severity in SCI.

Finally, technology can also improve the efficacy of SCS; for example, closed-loop, spatiotemporal modulation of SCS^3,9,37,60 can help support the sculpting of SCS and facilitate the production of complex movements in people with severe injuries. While these alternatives can help increase the applicability of SCS, it is important to highlight that intrinsic limitations will eventually reduce SCS applicability and effectiveness for people with severe paralysis, irrespective of the specific condition causing paralysis. It is conceivable that these limitations will be even more relevant for the recovery of upper limb movements given the strong dependence of hand control on corticospinal drive.

Limitations

The aim of this study was not to quantitatively predict SCS parameters or motoneuron firing rates but rather to provide a qualitative understanding of how residual supraspinal inputs can recover control of motoneurons. To this aim, we built a simple model that only considered excitatory monosynaptic connections to motoneurons. Obviously, many more components are stimulated by SCS that could affect our results. For instance, while monosynaptic EPSPs cannot effectively summate in the membrane until around 100 Hz because of their short decay time, SCS-triggered polysynaptic excitatory inputs could provide more waves of EPSPs that can summate at lower SCS frequencies. However our monkey experiments suggest that the facilitatory effect of a single pulse of SCS (which includes all potential modulating sources) decays rapidly after 5 ms (Figure S3). Thus, the main driver of SCS-induced activation is still likely to be strong monosynaptic drive. Moreover, as we discussed above for motoneurons, EPSPs summation is likely to hold also when considering polysynaptic inputs and, importantly, other types of neurons that receive inputs from Ia afferents, such as Ia-inhibitory interneurons, central pattern generators, and excitatory premotor interneurons⁶¹. However, we found that our simple model with only monosynaptic connections from Ia afferents is able to explain most of the action potentials produced by motoneurons during SCS. Finally, our model only focuses on the immediate effects of SCS and cannot be used to directly predict long-term changes that occur with physical training. Future work should be directed towards modeling long-term circuit changes that represent a major driver of SCS clinical efficacy.

In conclusion, our findings demonstrate how the central nervous system can integrate artificially-induced activity to restore voluntary control over motoneuron firing during SCS. We found that neural firing rate that is highly entrained to pulsatile artificial stimulation can still be modulated by natural activity, a mechanism that likely generalizes to other pulsatile neurostimulation technologies^40,62.

RESOURCE AVAILABILITY

Lead Contact

Requests for further information and resources should be directed to and will be fulfilled by the lead contact, Marco Capogrosso (mcapo@pitt.edu).

Materials Availability

This study did not generate new materials.

STAR METHODS

EXPERIMENTAL MODEL AND STUDY PARTICIPANT DETAILS

Non-human primate model

All procedures were approved by the University of Pittsburgh Animal Research Protections and Institutional Animal Care and Use Committee (ISOOO17081). We conducted experiments in 2 anesthetized Macaca Fascicularis (Mk-JC: age 6, 7.5 kg, male; Mk-Ka: age 5, 6.8 kg, female). The animals were housed in the primate facility at the Division of laboratory Animal Resources at the University of Pittsburgh. The animals had unrestricted access to water and food as well as daily enrichments. All these experiments were part of terminal procedures during which multiple other experiments were run in addition to those described here in order to minimize the use of animals in research according to the principles of the 3Rs^63,64.

Study participant details

Trials information.

All experimental protocols were approved by the University of Pittsburgh Institutional Review Board (IRB): STUDY19090210, for the stroke participants (SCS03, SCS04, SCS07, and SCS08SCS03, and SCS04, SCS0), and STUDY22020031, for the spinal cord injury participant (STIM01). All participants provided informed consent according to the procedure approved by the IRB of the University of Pittsburgh and participants were compensated for each day of the trial and for travel and lodging during the study period.

The stroke participants (SCS03, SCS04, SCS07, and SCS08) were recruited to participate in an exploratory clinical trial (ClinicalTrials.gov: NCT04512690) to obtain preliminary evidence of safety and efficacy of SCS to improve motor control in people with chronic post-stroke upper-limb hemiparesis⁶. The spinal cord injury participant (STIM01) was recruited to participate in a basic research study enrolling people already living with an epidural spinal cord stimulator (STUDY22020031). During the experimental sessions in STIM01, we changed the stimulation parameters to perform the different tasks using the Medtronic Intellis Platform. At the end of each session, we reset the stimulation parameters to their clinical values.

Participants Information.

STIM01 (Black male, 24 years old) was diagnosed as ASIA A after a spinal cord injury at T6 vertebra level 5 years ago. He was implanted with a spinal cord stimulation to reduce pain and spasticity 4 years ago. Since the implantation, he has combined SCS and physical therapy to regain control of his lower limbs. When he enrolled in the study, he was able to voluntarily move his left leg during SCS. STIM01 was implanted with a Medtronic paddle array from the bottom of T11 to the top L1 vertebrae. SCS03 (White male, 45 years old) suffered a hemorrhagic stroke followed by craniotomy 7 years before participating in the study and was diagnosed with a Fugl-Meyer motor score of 28. SCS04 (Black male, 43 years old) suffered an ischemic stroke in the anterior frontal and temporal lobe 5 years before participating in the study and was diagnosed with a Fugl-Meyer motor score of 23. SCS07, 61 year old Black female who sustained a left hemispheric lacunar infarct ten years prior to study participation, with a past medical history including hypertension and diabetes mellitus. Her post-stroke deficits included weakness and spasticity in her right upper limb. She actively participated in physical and occupational therapy prior to the study. SCS08 60 year old Asian female who had a right-sided ischemic stroke involving the corona radiata four years prior to the study. She has a notable past medical history of hypertension. Her post-stroke deficits include persistent weakness and spasticity in the left upper and lower extremities, with preserved sensation in the affected arm. To minimize risks in SCS03, SCS04, SCS07, and SCS08, participants were temporally implanted for 29 days, after which electrodes were explanted. Following the 3R principle (Replacement, Reduction and Refinement), human participants with stroke involved in this study (SCS03, SCS04, SCS07 and SCS08) were not renamed to SCS01–04 respectively. Analysis of the influence of sex, race, socioeconomic status, or other related factors on the results of this study was not conducted as it was not deemed relevant for the mechanisms of interest studied here.

METHOD DETAILS

Biophysical modeling

We implemented a biophysical model of motoneurons, Ia afferents, and supraspinal fibers in Python 3.8 using NEURON 7.8⁶⁵. The following number of neurons and their properties have been validated in similar models^{11,12,27,28,33}.

Motoneuron model.

We simulated a pool of 100 motoneurons. Each motoneuron follows the standard Hodgkin-Huxley formalism described and validated previously²⁶. By doing so, we are able to study the integration of multiple synaptic sources into the motoneuron. The motoneuron membrane potential ($\mathit{V}$) is described as a function of the ion channels, as shown in equation (1):

$$\mathit{C}\frac{\mathit{d}\mathit{V}}{\mathit{d}\mathit{t}}=-{\sum }_{\mathit{x}}^{\mathit{i}\mathit{o}\mathit{n}\mathit{s}}{\mathit{I}}_{\mathit{x}}-{\sum }_{\mathit{s}}^{\mathit{s}\mathit{y}\mathit{n}\mathit{a}\mathit{p}\mathit{s}\mathit{e}\mathit{s}}{\mathit{I}}_{\mathit{s}}$$ (1)

where $\mathit{C}$ is the membrane capacity, ${\mathit{I}}_{\mathit{s}}$ is external current from afferent or supraspinal synaptic drive to the neuron, and ${\mathit{I}}_{\mathit{x}}$ is the current generated by the ionic channels. ${\mathit{I}}_{\mathit{x}}$ for each ion channel is described by equation (2):

$${\mathit{I}}_{\mathit{x}}={\mathit{g}}_{\mathit{x}}\mathrm{*}{\mathit{\omega }}_{\mathit{x}}\mathrm{*}\left({\mathit{V}-\mathit{E}}_{\mathit{x}}\right)$$ (2)

where ${\mathit{E}}_{\mathit{x}}$ and ${\mathit{g}}_{\mathit{x}}$ is the reversal potential and the maximum conductance of the ion $\mathit{x}$, respectively, and ${\mathit{\omega }}_{\mathit{x}}$ ranges between 0 and 1 and dictates the activation status of each current. The general form of the dynamics of each gating variable (represented by $\mathit{\omega }$) is described in equations (3) and (4):

$${\mathit{\tau }}_{\mathit{\omega }}=\frac{1}{{\mathit{\alpha }}_{\mathit{\omega }}+{\mathit{\beta }}_{\mathit{\omega }}}$$ (3)

$$\frac{\mathit{d}\mathit{\omega }}{\mathit{d}\mathit{t}}={\mathit{\alpha }}_{\mathit{\omega }}(1-\mathit{\omega })-{\mathit{\beta }}_{\mathit{\omega }}\mathit{\omega }=\frac{({\mathit{\omega }}_{\mathrm{\infty }}-\mathit{\omega })}{{\mathit{\tau }}_{\mathit{\omega }}}$$ (4)

Our motoneuron model describes the dynamics of multiple ion channels–namely, L-type Ca²⁺, Ca²⁺-activated K, delayed rectifier K⁺, N-type Ca²⁺, and nonlinear fast Na⁺. The equations dictating the ionic currents and gating variables are specified below, where $\mathit{m},\mathit{h},\mathit{n},\mathit{q},\mathit{l}$, $\mathit{p}$ are ion channel-specific instances of the general gating variable $\mathit{\omega }$.

Fast sodium (Na⁺) current

$${\mathit{I}}_{\mathit{N}\mathit{a}\mathit{f}}={\mathit{g}}_{\mathit{N}\mathit{a}\mathit{f}}\mathrm{*}{\mathit{m}}^{\mathbf{3}}\mathrm{*}\mathit{h}\mathrm{*}({\mathit{V}}_{\mathit{m}}-{\mathit{E}}_{\mathit{N}\mathit{a}})$$

$${\mathit{\alpha }}_{\mathit{m}}=[\mathbf{0.4}\mathrm{*}(-{(\mathit{V}}_{\mathit{m}}+\mathbf{66}))]/[{\mathit{e}}^{\{-{(\mathit{V}}_{\mathit{m}}+\mathbf{66})/\mathbf{5}\}}-\mathbf{1}]$$

$${\mathit{\beta }}_{\mathit{m}}=[\mathbf{0.4}\mathrm{*}{(\mathit{V}}_{\mathit{m}}+\mathbf{32})]/[{\mathit{e}}^{\{-{(\mathit{V}}_{\mathit{m}}+\mathbf{32})/\mathbf{5}\}}-\mathbf{1}]$$

$${\mathit{\tau }}_{\mathit{h}}=\mathbf{30}/[{\mathit{e}}^{\{{(\mathit{V}}_{\mathit{m}}+\mathbf{60})/\mathbf{15}\}}+{\mathit{e}}^{\{-{(\mathit{V}}_{\mathit{m}}+\mathbf{60})/\mathbf{16}\}}]$$

$${\mathit{h}}_{\mathrm{\infty }}=\mathbf{1}/[\mathbf{1}+{\mathit{e}}^{\{-{(\mathit{V}}_{\mathit{m}}+\mathbf{65})/\mathbf{7}\}}]$$

Delayed rectifier potassium (K⁺) current

$${\mathit{I}}_{\mathit{K}\mathit{d}\mathit{r}}={\mathit{g}}_{\mathit{K}\mathit{d}\mathit{r}}\mathrm{*}{\mathit{n}}^4\mathrm{*}({\mathit{V}}_{\mathit{m}}-{\mathit{E}}_{\mathit{K}})$$

$${\mathit{\tau }}_{\mathit{n}}=\mathbf{5}/[{\mathit{e}}^{\{{(\mathit{V}}_{\mathit{m}}+\mathbf{50})/\mathbf{40}\}}+{\mathit{e}}^{\{-{(\mathit{V}}_{\mathit{m}}+\mathbf{50})/\mathbf{50}\}}]$$

$${\mathit{n}}_{\mathrm{\infty }}=\mathbf{1}/[\mathbf{1}+{\mathit{e}}^{\{{(\mathit{V}}_{\mathit{m}}+\mathbf{38})/-\mathbf{15}\}}]$$

N-type calcium (Ca²⁺) current

$${\mathit{I}}_{\mathit{C}\mathit{a}\mathit{N}}={\mathit{g}}_{\mathit{C}\mathit{a}\mathit{N}}\mathrm{*}{\mathit{q}}^{\mathbf{2}}\mathrm{*}\mathit{l}\mathrm{*}({\mathit{V}}_{\mathit{m}}-{\mathit{E}}_{\mathit{C}\mathit{a}})$$

$${\mathit{q}}_{\mathrm{\infty }}=\mathbf{1}/[\mathbf{1}+{\mathit{e}}^{\{{(\mathit{V}}_{\mathit{m}}+\mathbf{32})/-\mathbf{5}\}}]$$

$${\mathit{l}}_{\mathrm{\infty }}=\mathbf{1}/[\mathbf{1}+{\mathit{e}}^{\{{(\mathit{V}}_{\mathit{m}}+\mathbf{50})/\mathbf{5}\}}]$$

L-type calcium (Ca²⁺) current

$${\mathit{I}}_{\mathit{C}\mathit{a}\mathit{L}}={\mathit{g}}_{\mathit{C}\mathit{a}\mathit{L}}\mathrm{*}\mathit{p}\mathrm{*}({\mathit{V}}_{\mathit{m}}-{\mathit{E}}_{\mathit{C}\mathit{a}})$$

$${\mathit{p}}_{\mathrm{\infty }}=\mathbf{1}/[\mathbf{1}+{\mathit{e}}^{\{{(\mathit{V}}_{\mathit{m}}+\mathbf{55}.\mathbf{8})/-\mathbf{3}.\mathbf{7}\}}]$$

Calcium (Ca²⁺) dynamics

$${\mathit{d}[\mathit{C}\mathit{a}]}_{\mathit{i}}/\mathit{d}\mathit{t}=\mathbf{0}.\mathbf{01}\mathrm{*}(-({\mathit{I}}_{\mathit{C}\mathit{a}\mathit{N}}+{\mathit{I}}_{\mathit{C}\mathit{a}\mathit{L}})-(\mathbf{4}\mathrm{*}[\mathit{C}\mathit{a}{]}_{\mathit{i}}))$$

$${\mathit{E}}_{\mathit{C}\mathit{a}}=[(\mathbf{1000}\mathrm{*}\mathit{R}\mathrm{*}\mathbf{309}.\mathbf{15})/(\mathbf{2}\mathrm{*}\mathit{F})]\mathrm{*}\mathit{l}\mathit{n}([\mathit{C}\mathit{a}{]}_{\mathit{o}}/[\mathit{C}\mathit{a}{]}_{\mathit{i}})$$

Calcium-activated potassium (K⁺) current

$${\mathit{I}}_{\mathit{K}(\mathit{C}\mathit{a})}={\mathit{g}}_{\mathit{K}(\mathit{C}\mathit{a})}\mathrm{*}[\mathit{C}\mathit{a}{]}_{\mathit{i}}^{\mathbf{2}}/([\mathit{C}\mathit{a}{]}_{\mathit{i}}^{\mathbf{2}}+\mathbf{0}.\mathbf{001}{\mathbf{4}}^{\mathbf{2}})\mathrm{*}({\mathit{V}}_{\mathit{m}}-{\mathit{E}}_{\mathit{K}})$$

To capture the increase in excitability in the motoneuron membrane after a lesion, we defined a model of a postlesion motoneuron with modified ionic properties. Specifically, we reduced the Ca²⁺-activated K ion channel conductance by 40%⁶⁶. We assumed that the dynamics of the supraspinal fibers are unaltered after a lesion.

Excitatory synapses.

Each motoneuron received excitatory inputs onto the soma from all Ia afferents (N=60) and all supraspinal fibers (the number of which depends on the lesion severity, with N=300 in the intact model). We modeled SCS with two parameters: the number of pulses per second (SCS frequency) and the percentage of Ia afferent fibers recruited. The percentage of fibers recruited encompasses the effect of both pulse width and amplitude—for simplicity, we named it SCS amplitude. For each pulse of stimulation, Ia afferents were synchronously activated with a random delay (mean 0.67 ms and standard deviation 0.25 ms)¹². Each supraspinal fiber was modeled as a random Poisson process with a variable firing rate from 0 to 60Hz, and the number of supraspinal fibers in the intact model was selected in order to produce a biophysically-reasonable firing rate in the motoneuron pool.

Both activation sources were assumed to produce EPSPs through fast, glutamatergic synapses with the same synaptic dynamics. The EPSPs were modeled as a sudden increase in synaptic conductance at the time of a spike, followed by an exponential decay in conductance. The current generated at the synapse (${\mathit{I}}_{\mathit{s}}$) is described in equation (5) and the decay in the synaptic conductance (${\mathit{g}}_{\mathit{s}}$) is shown in equation (6):

$${\mathit{I}}_{\mathit{s}}={\mathit{g}}_{\mathit{s}}\mathrm{*}(\mathit{V}-{\mathit{E}}_{\mathit{s}})$$ (5)

$${\mathit{g}}_{\mathit{s}}={\mathit{w}}_{\mathit{s}}\mathrm{*}{\mathit{e}}^{(-\mathit{t}/{\mathit{\tau }}_{\mathit{s}})}$$ (6)

where ${\mathit{E}}_{\mathit{s}}$ is the synaptic reversal potential (0.0 mV), ${\mathit{\tau }}_{\mathit{s}}$ is the decay time constant (2 ms), and ${\mathit{w}}_{\mathit{s}}$ is the synaptic weight. The synaptic weight of both supraspinal and SCS inputs followed a gamma distribution, the parameters of which were chosen so that the evoked EPSP had an average amplitude of 80μV, which is in the range of experimental values⁶⁷.

Inhibitory synapses.

Inhibitory supraspinal fibers (N=60) were also modeled as point processes with a firing rate ranging between 0 and 60 Hz. All motoneurons received inputs from all inhibitory supraspinal fibers. The IPSPs produced were modeled by a change in synaptic current as described in equation (5), but with a synaptic reversal potential (${\mathit{E}}_{\mathit{s}}$) of −75mV. The change in conductance (${\mathit{g}}_{\mathit{s}}$) at inhibitory synapses is described by equation (7):

$${\mathit{g}}_{\mathit{s}}={\mathit{w}}_{\mathit{s}}\mathrm{*}{\mathit{f}\mathrm{*}(\mathit{e}}^{(-\mathit{t}/{\mathit{\tau }}_{\mathit{d}})}-{\mathit{e}}^{(-\mathit{t}/{\mathit{\tau }}_{\mathit{r}})})$$ (7)

where ${\mathit{\tau }}_{\mathit{r}}$ is the rise time constant (1.5 ms), ${\mathit{\tau }}_{\mathit{d}}$ is the decay time constant (2 ms), and $\mathit{f}$ is an arbitrary weighting factor so that the normalized peak is 1⁶⁵. Similar to the excitatory synapses, the synaptic weight of the IPSP followed a gamma distribution.

Force model.

To estimate the force from the motoneuron pool firing rate, we used the model proposed in³⁹. Here, we described the main equations (Equations 8–11). The twitch force generated for a spike from neuron $\mathit{i}$ at time $\mathit{t}$ is modeled as:

$${\mathit{f}}_{\mathit{i}}(\mathit{t})={\mathit{g}}_{\mathit{i}}\frac{{\mathit{P}}_{\mathit{i}}\mathit{t}}{{\mathit{T}}_{\mathit{i}}}\mathit{e}\mathit{x}\mathit{p}(\mathbf{1}-\mathit{t}/{\mathit{T}}_{\mathit{i}})$$ (8)

The peak twitch is defined as ${\mathit{P}}_{\mathit{i}}=\mathit{e}\mathit{x}\mathit{p}(\mathit{b}\cdot \mathit{i})$ and the contraction time is ${\mathit{T}}_{\mathit{i}}=\mathbf{90}(\mathbf{1}/{\mathit{P}}_{\mathit{i}}{)}^{\mathbf{1}/\mathbf{4}.\mathbf{2}}$. Finally, the gain, ${\mathit{g}}_{\mathit{i}}$ was modeled depending on the normalized mean interspike interval of neuron $\mathit{i}$ $(\mathit{I}\mathit{S}{\mathit{I}}_{\mathit{i}})$ and the contraction time ${\mathit{T}}_{\mathit{i}}$:

For ${\mathit{T}}_{\mathit{i}}/\mathit{I}\mathit{S}{\mathit{I}}_{\mathit{i}}<\mathbf{0}.\mathbf{4}$:

$${\mathit{g}}_{\mathit{i}}=\mathbf{1},$$ (9)

otherwise:

$${\mathit{g}}_{\mathit{i}}=\frac{\mathit{S}({\mathit{T}}_{\mathit{i}}/\mathit{I}\mathit{S}{\mathit{I}}_{\mathit{i}})}{{\mathit{T}}_{\mathit{i}}/\mathit{I}\mathit{S}{\mathit{I}}_{\mathit{i}}},$$ (10)

where $\mathit{S}(\mathit{x})$ is the sigmoidal function $\mathit{S}(\mathit{x})=\mathbf{1}-\mathit{e}\mathit{x}\mathit{p}(\mathbf{2}{\mathit{x}}^{\mathbf{3}}).$

Finally, the total normalized force is:

$$\mathit{F}(\mathit{t})={\sum }_{\mathit{i}=\mathbf{1}}^{\mathit{N}}{\sum }_{\mathit{j}=\mathbf{1}}^{{\mathit{N}}_{\mathit{i}}}{\mathit{f}}_{\mathit{i},\mathit{j}}(\mathit{t}-{\mathit{t}}_{\mathit{i},\mathit{j}}),$$ (11)

where $\mathit{N}$ is the number of motoneurons and ${\mathit{N}}_{\mathit{i}}$ is the number of spikes in neuron $\mathit{i}$. We always report the force normalized with the maximum prelesion force.

Experimental procedures in monkeys

Surgical procedures.

Animals underwent two surgical procedures. First, in a survival procedure, we acquired in vivo structural magnetic-resonance imaging and computed tomography for each animal. Collected imaging data was used to plan the trajectories of the deep-brain probe that stimulated the posterior limb of the internal capsule, which innervates the hand muscles. We further describe this procedure in⁶⁸. Second, in a terminal procedure, certified neurosurgeons performed muscle implantation, robotic deep probe implantation and spinal probe implantation (described below in detail) while the monkeys had continuous ventilation support and were under full anesthesia induced with ketamine (10 mg/kg, i.m.) and under continuous intravenous infusion of propofol (1.8–5.4 ml/kg/h) and fentanyl (0.2–1.7 ml/kg/h). Anesthesia conditions were maintained until the conclusion of the experiments, where animals were euthanized with a single injection of pentobarbital (86 mg/kg, i.v.).

We inserted a pair of EMG needle electrodes (disposable single 7mm Subdermal needle electrode, Rhythmlink) into the hand muscles (abductor pollicis brevis (APB), flexor digiti minimi (FDM)). The reference was inserted in the lower back or the tail with a needle electrode. Subsequently, we fixed the monkey’s head in a stereotactic frame (Kopf, Model 1530, Tujunga, CA, USA) with the cervical spine fixed in a prone position.

We proceeded with the robotic deep probe implantation (ROSA robot)⁶⁸. To accurately implant a probe in the hand area of the internal capsule (AC-PC level), a frontal insertion trajectory was guided by the robot software (ROSA One(R) Robot Assistance Platform). Trajectory planning was achieved due to previously collected imaging data⁶⁸. The probe positioning was contralateral to the muscle implants. We precisely drilled a penetration hole in the skull for the implantation of a fixation bolt. Next we inserted a radiofrequency electrode (RF-SE-10 Reusable Stainless Steel Electrode, Abbott). We confirmed the correct position of the probe by inspecting the hand muscles’ EMG activity in response to ICS (2 Hz, 0.8–2 mA) that should produce monosynaptic activation of the cervical motoneurons.

Lastly, we performed a laminectomy from C3 to T1 vertebrae and exposed the cervical spinal cord to the nerves that innervated targeted muscles. After opening the dura matter, we placed a stimulator (bipolar, 73602–190/10, Ambu Neuroline, Denmark) on the cervical dorsal roots (Mk-JC: C8, Mk-Ka: C8). We confirmed its positioning by verifying EMG responses in the target muscles. Furthermore, we implanted a 32-channel linear probe (A1×32–15mm-100–177-CM32 Linear Probe with 32 pin Omnetics Connector, NeuroNexus, Ann Arbor, MI, USA) at the cervical spinal segment rostral to the stimulation site (Mk-JC: C7, Mk-Ka: C7) using Kopf micromanipulators (Kopf, Model 1760, Tujunga, CA, USA). To do so, we pierced the pia using a surgical needle to ensure safety probe penetration. Its placement was ~1.2 mm parallel to midline (ipsilateral to the muscle implants) due to the flow of sensory information of Ia afferent in the dorsoventral direction consistent with the placement of the probe. Its length (3.1 mm) is designed to cover the gray matter of the monkey’s spinal cord and record extracellular potentials as well as intraspinal spiking activity. The reference was inserted under the skin next to the probe insertion site.

Data acquisition and electrophysiology.

We employed an AM stimulator (model 2100 A-M Systems, Sequim, WA, USA) for the stimulation of the dorsal roots and internal capsule as biphasic symmetric square pulses in the form of single or train of pulses and detailed pulse widths (Mk-JC: 0.40 ms for SCS, 1 ms for ICS; Mk-Ka: 0.45 ms for SCS, 0.8 ms for ICS). Specific stimulation configurations and parameters are defined in each figure. After data amplification (Nano2-HV headstage) and digital processing, neural recordings (EMG and intraspinal spiking data) were recorded (Ripple Neuro Grapevine Neural Interface 1.14.3) at 30 kHz sampling frequency along with the force/torque data (same sampling frequency). Through the data acquisition platform (Trellis), we developed an in-house interface that computed the EMG stimulation-trigger averaged responses in real-time to determine the stimulation amplitude for motor threshold responses for each muscle.

Analysis of muscle activity.

EMG signal was calculated for each muscle differentially between the two needle electrodes and was bandpass filtered between 30 and 800 Hz with a 2nd order Butterworth filter. We then identified the peak-to-peak amplitude of reflex-mediated responses evoked by the paired stimulation in a window of 25 ms after the SCS pulse. Moreover, we computed the root-mean square of the response during phasic ICS alone and concurrent phasic ICS and continuous SCS. We then computed SCS facilitation as the normalized root-mean square of the EMG response during concurrent ICS and SCS minus ICS alone. Analogously, SCS facilitation for SCS alone was measured as the normalized root-mean square of the EMG response during SCS alone minus no stimulation. This analysis was performed offline in MATLAB (version R2019b).

Analysis of single unit activity.

We sorted spikes from the 8 most ventral channels of the 32-channel linear probe. Previously, we applied a comb filter of the raw signal to remove artifacts at 60 Hz. We then applied a high-pass filter of 250 Hz (consisting of 52 samples, 1.7 ms, non-overlapping). Spikes were detected by waveform threshold crossing. All intraspinal recordings were concatenated by channel for comparison purposes across performed experiments. Using a spike sorting software (Plexon Offline Sorter, Dallas, Texas), we identified single motoneurons by channel with semi-automatic k-means clustering. Regarding the histograms of the normalized ISI probability distribution of the sorted units, we used a bin width of 0.1 ms. Previously, we noticed that the application of continuous SCS resulted in an initial short hyperexcitable period; thus, we discarded the first 5 seconds of spiking data after the start of the stimulation to perform our analysis on stationary conditions. This analysis was performed offline in MATLAB (version R2019b).

Experimental procedures in humans

Torque experiments.

We performed the torque experiments in all subjects using a robotic torque dynamometer (HUMAC NORM, CSMi) that can be set to measure torque in different joints⁶.

For STIM01, we measured his maximum torque during knee extension for 6 repetitions of 2 seconds (Figure S6a). We also asked STIM01 to hold a torque level of 35% of his maximum torque during 30 seconds (Figure S6c). In both tasks, we placed a 4-channel EMG sensor (Trigno Galileo Sensor, Delsys) to record EMG activity on the vastus lateralis and rectus femoris.

SCS03 performed an isometric force-modulated task for elbow flexion where he was asked to follow a predefined force trace ranging from 5–20%, 20–35%, and 35–50% of his maximum voluntary contraction force with and without SCS (Figure 6i; Figure S6d). This experiment was repeated with and without SCS. A 64-channel high-density EMG grid (TMSi, The Netherlands) was placed over Bicep Brachii to record muscle activation during the experiment.

Because of SCS04’s inability to perform the force-modulated task at the elbow, he performed a similar task of grasp force-modulated task at different force levels, ranging from 5–20%, 20–35%, and 35–50% of his maximum torque, both with and without SCS (Figure 6i). The grasp force data was measured with a 6-axis low-profile force and torque (F/T) sensor (Mini40, ATI Industrial Automation, North Carolina). A 32-channel high-density EMG grid (TMSi,The Netherlands) was placed over the anterior forearm (specifically, Flexor Carpi Radialis) to record muscle activity during the task.

Motor unit decomposition.

In STIM01, we used the Neuromap software (Delsys) to decompose the EMG activity into single motoneuron action potentials. For the experiments with SCS03 and SCS04, single motor unit firing rates were identified from high-density EMG signals using the Convolution Kernel Compensation (CKC) technique⁶⁹. The high-density EMG signals were first bandpass filtered between 20 and 500 Hz with a 3rd order Butterworth filter. Additionally, the SCS artifact was removed by notch filtering at the SCS frequency. SCS harmonics were also removed using notch filtering by identifying peaks in the power spectrum associated with SCS. The filtered high-density EMG signals were decomposed by the DEMUSE software (v6.1; The University of Maribor, Slovenia)^70,71. The decomposed motor unit spike trains were processed to identify single motor units and calculate their firing rates. During this step, physiologically irregular motor unit firings (<5 Hz and >50 Hz) were discarded^72,73. The irregular motor unit firings were identified by following the guidelines in literature and accuracy of identified motor units was determined by the Pulse-to-Noise Ratio (>25 dB)^74,75 (Figure S5b,c,e).

Analysis of torque.

To account for the weight of the paretic limb in STIM01, torque responses were baseline corrected with the mean resting torque for the first 60 ms. Moreover, given the fluctuations in the responses, we smoothed the data by applying a moving window of 100 ms. Lastly, we computed the maximum torque during the maximum voluntary contraction periods for each repetition. Only for SCS04, given that the force-modulated task was performed with a grip dynamometer, torque responses were corrected with the mean resting torque for the first 3.33 seconds. This analysis was performed offline in MATLAB (version R2019b).

Analysis of firing rate activity.

In SCS03 and SCS04 we computed the firing rate in a 50 ms window with a sliding window of 5 ms over the entire duration of the trial, and zeropadded for 45 ms and smoothed it by applying a moving window of 100 ms. We identified firing rates for each unit during a constant force level, i.e., a constant supraspinal innervation (replicating what we did in our biophysical model). Like in the monkey normalized ISI probability distributions, we used a bin width of 0.1 ms. Importantly, we included those motor units whose spiking at the stimulation pulse +/− 10% represented at least 40% of their total spiking activity. As indicated in the captions, data included in the figures correspond to all the repetitions under the same conditions and session. This analysis was performed offline in MATLAB (version R2019b).

Voluntary inhibition of spinal reflexes task.

Participants were seated in the KINARM (KINARM End-Point Lab, BKIN Technologies Ltd., Kingston, ON, Canada), which is a planar robot that enables reaching movement exercises by removing the weight of participants’s arms and records two dimensional arm kinematics. When participants were resting, their elbow was in a flexed position. In this rest condition, we passively extended their elbow to a comfortable position and kept it extended. Instead, in the voluntary extension condition, we set a target at the same comfortable elbow extended position and asked participants to reach and keep their arm in the target position for 500 ms. Note that even if the KINARM removes the weight of their arms, participants in the voluntary extension condition had to activate their elbow extensors to keep their arm extended. In both conditions, we delivered SCS at 2 Hz; although the stimulation was targeting the triceps (the agonist muscle), it was also stimulating the biceps (the antagonist muscle). Using EMGs, we recorded the spinal reflexes in the antagonist muscle during the voluntary extension and the rest condition. While we were continuously stimulating at 2 Hz, we only used the reflexes delivered when participants were keeping their arm in the target position, as defined as ±5% of the target.

QUANTIFICATION AND STATISTICAL ANALYSIS

All statistical comparisons were performed using the Kruskal-Wallis two-tailed test, which is a nonparametric approach to the one-way ANOVA. Subsequently, follow-up multiple comparison tests on pairs of sample medians were performed. Data points outside 1.5 times the interquartile range plus the 25th/75th percentile were classified as outliers and discarded. For illustration purposes, the mean distribution of the data with 95% confidence interval was indicated for each distribution. This analysis was performed offline in MATLAB (version R2019b).

Data and Code Availability

The main data supporting the results in this study are available within the paper. All data generated in this study will be uploaded in a public repository upon acceptance of the manuscript. Raw data will be available upon reasonable request to the corresponding author. The code for analyzing data and performing the neural simulations is available at Zenodo DOI: 10.5281/zenodo.16820440. Any additional information required to reanalyze the data reported in this work paper is available from the Lead Contact upon request.