🧠 neuroscience

Spinal Recurrent Inhibition Shapes the Dynamics of TMS-induced Motor-Evoked Potentials: A Computational Modeling Study

This study introduces a biologically plausible computational model that fits individual TMS-induced motor-evoked potential waveforms, revealing that spinal recurrent inhibition is critical for reproducing their temporal dynamics and enabling the extraction of detailed, subject-specific parameters about the corticospinal pathway's integrity.

Original authors: Chien, V. S. C., Bernasconi, E., Müller, E., Wang, P., Lowery, M., Wendt, K., O'Shea, J., Denison, T., Hlinka, J., Knösche, T. R., Weise, K., Schmidt, H.

Published 2026-09-16

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CC BY 4.0

Original authors: Chien, V. S. C., Bernasconi, E., Müller, E., Wang, P., Lowery, M., Wendt, K., O'Shea, J., Denison, T., Hlinka, J., Knösche, T. R., Weise, K., Schmidt, H.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

When a doctor wants to check how well a person's brain talks to their muscles, they often use a technique called transcranial magnetic stimulation. This involves placing a coil over the scalp that sends a brief, painless magnetic pulse into the brain. This pulse wakes up the motor cortex, the part of the brain that plans movement. The signal then travels down a long highway of nerve fibers called the corticospinal tract, reaches the spinal cord, and finally tells the muscles in the hand to twitch. By recording this twitch with electrodes on the skin, scientists can see a wave of electrical activity known as a motor-evoked potential. This wave is a vital sign of the nervous system's health, used to diagnose conditions like stroke or spinal cord injury. However, for a long time, scientists have only looked at the height of this wave to judge its strength. They have largely ignored the wave's shape and the tiny bumps and dips within it, assuming that the complex machinery of the spinal cord and muscles was too difficult to model or that these details didn't matter much.

A team of researchers has now built a detailed computer model that changes this perspective, showing that the shape of the wave holds a wealth of hidden information. The scientists created a digital simulation that spans the entire journey of the signal, from the brain's cortex down through the spinal cord and into the hand muscles. They tested this model against real data collected from ten healthy volunteers. In the experiment, magnetic pulses of varying strengths were applied to the participants' brains, and the resulting electrical waves in their hand muscles were recorded. The researchers then adjusted their computer model to match these real-world recordings as closely as possible. The model included a specific feature that had been missing from many previous attempts: a group of inhibitory cells in the spinal cord called Renshaw cells. These cells act as a brake, receiving signals from the motor neurons and sending a quick inhibitory signal back to stop them from firing too rapidly.

The results were striking. The model that included these braking cells could reproduce the fine, complex details of the electrical waves with remarkable accuracy, matching about 90 percent of the variations seen in the real data. When the researchers removed the braking cells from their simulation, the model failed to capture the wave's true shape, even though it could still predict the overall size of the response. This suggests that the braking mechanism is essential for creating the precise timing and structure of the signal. The study demonstrates that the spinal cord is not just a passive wire passing signals along; it actively sculpts the signal before it reaches the muscle. By fitting the model to each person's unique data, the researchers could also estimate hidden properties of that individual's nervous system, such as the size of their motor neurons and the speed at which signals travel along their nerves. These estimates fell within known biological ranges, confirming that the model is grounded in reality.

The researchers found that without the braking cells, the model had to rely on unrealistic adjustments to other parts of the system to make the numbers work, such as changing the balance of chemical signals in ways that do not match biological evidence. This indicates that the braking cells are not just a minor detail but a fundamental component of how the motor system responds to stimulation. The study suggests that looking beyond simple measurements of wave height to analyze the full shape of the signal could provide a much richer understanding of spinal health. It opens the door to using these detailed waveforms to detect subtle problems in the spinal cord that might otherwise go unnoticed, offering a more nuanced tool for understanding how the brain and body communicate.

Technical Summary: Spinal Recurrent Inhibition Shapes the Dynamics of TMS-induced Motor-Evoked Potentials

Problem Statement
Transcranial magnetic stimulation (TMS) of the motor cortex elicits motor-evoked potentials (MEPs) in peripheral muscles, which serve as a primary readout for corticospinal tract integrity in both basic neuroscience and clinical practice. While the generation of MEPs involves a complex cascade from cortical activation to spinal integration and peripheral muscle contraction, the specific contributions of spinal mechanisms—particularly recurrent inhibition—to the observed MEP waveform remain poorly understood. Existing computational models have largely focused on cortical mechanisms (DI-waves) or simplified spinal components consisting solely of motor neuron (MN) populations. These models typically prioritize input-output (IO) curves (peak-to-peak amplitude) over the fine temporal structure of the MEP waveform and often omit inhibitory interneurons like Renshaw cells (RCs). Consequently, there is a lack of biologically plausible, computationally efficient models capable of fitting individual MEP waveforms to disentangle the contributions of spinal and peripheral mechanisms.

Methodology
The authors developed a biologically grounded, computationally efficient spinal-peripheral model designed to fit individual MEP waveforms across a range of TMS intensities. The model comprises two main components:

Spinal Cord Component: This module simulates the interaction between 100 alpha motor neurons (αMNs) and a common population of Renshaw cells (RCs).
- αMNs: Modeled as leaky integrate-and-fire (LIF) neurons with membrane resistances ( $R$ ) decreasing monotonically to reflect the size principle. They receive descending corticospinal volleys (DI-waves) as excitatory input.
- RCs: Modeled as a single rate-based population receiving excitatory input from MN collaterals and providing rapid inhibitory feedback to the MN pool.
- Synaptic Dynamics: The model incorporates specific synaptic kernels for AMPA, NMDA, and Glycinergic transmission. The balance between AMPA and NMDA currents ( $\alpha_{AMPA}$ ) is a free parameter.
- Input: Synthetic DI-wave inputs were generated based on group-level IO curves, deconvolved to estimate underlying firing rates, and used as input to the spinal circuit.
Hand Muscle Component: This module translates MN spiking into surface EMG signals.
- Motor Units (MUs): 100 MUs correspond to the 100 MNs.
- MUAPs: A repertoire of 100 motor unit action potentials (MUAPs) was generated using a finite-element method (FEM) volume-conductor model of the first dorsal interosseous (FDI) muscle, informed by diffusion tensor imaging (DTI) data to capture anatomical fiber trajectories.
- Output: The final MEP is computed as the summation of time-delayed MUAPs, accounting for axonal conduction delays and MU refractory periods.

Experimental Design and Comparison
The model was fitted to MEP datasets from 10 healthy participants recorded at varying TMS intensities (Sorkhabi et al., 2022). To evaluate the necessity of RC recurrent inhibition, two variants of the spinal-peripheral model were compared:

RC+ Model: Includes the full spinal circuit with RC recurrent inhibition.
RC− Model: Excludes RCs, relying solely on MN dynamics and excitatory inputs.

Both were benchmarked against a Phenomenological Model that bypasses spinal circuitry entirely. The phenomenological model generates MEPs by summing MUAPs based on firing times derived from a gamma distribution, allowing for maximum flexibility in fitting IO curves and waveforms without biological constraints.

Key Results

Waveform Reproduction: The RC+ model successfully reproduced individual MEP waveforms, accounting for approximately 90% of the observed variance ( $R^2 \approx 0.9$ ) across participants. This performance was comparable to the phenomenological benchmark ( $R^2 \approx 0.91$ ).
Necessity of RC Inhibition: The RC− model showed a significant reduction in waveform goodness-of-fit ( $R^2 \approx 0.79$ ), despite maintaining relatively accurate IO curve fits in some cases. The RC− model failed to capture secondary peaks and the fine temporal structure of the MEP, particularly at lower TMS intensities.
Mechanism of Stability: The RC+ model provided a physiological explanation for the stability of MEP peak latencies across TMS intensities. In the RC+ model, recurrent inhibition ensures that while MU activation onset may shift, the decay of activity is regulated to maintain a consistent peak latency. The RC− model lacked this regulatory mechanism, resulting in delayed waveforms.
Parameter Estimation: The fitted RC+ model yielded interpretable estimates of latent neural dynamics, including MN size distribution (via membrane resistance), synaptic receptor balance (AMPA/NMDA ratio), axonal conduction delays, and MU refractoriness. These estimates fell within known biological ranges.
Compensation in RC− Model: In the absence of RC inhibition, the RC− model compensated by increasing the AMPA weight ( $\alpha_{AMPA}$ ) and altering membrane resistances, but these adjustments were insufficient to replicate the full temporal dynamics of the MEP.

Significance and Claims
The paper claims that individual MEP waveforms, when analyzed using a biologically grounded model, carry substantially more information about spinal and peripheral motor pathway integrity than conventional amplitude-based measures (IO curves) alone.

The primary contribution is the demonstration that recurrent inhibition of Renshaw cells is indispensable for reproducing the fine temporal structure of TMS-evoked MEP waveforms. Even when IO curve fitting appears adequate without it, the omission of RCs leads to a loss of critical temporal features. The study establishes that a simplified spinal-peripheral model incorporating a lumped RC population is sufficient to capture these dynamics, balancing biological plausibility with computational efficiency.

The authors conclude that their model enables the inference of participant-specific latent neural dynamics and pathway parameters (e.g., MN size distribution, synaptic balance) that are consistent with biological constraints. This suggests the model is a promising tool for developing individualized motor pathway models, potentially aiding in the identification of abnormalities in corticospinal transmission, cortical dysfunction, or peripheral muscle factors, though the paper notes that further validation regarding parameter identifiability and clinical utility is required.

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