⚛️ biophysics

Impact of Axon Model Complexity on Deep Brain Stimulation: A Comparative Analysis of MRG and Cohen Double-Cable Models

This study demonstrates that while both the McIntyre-Richardson-Grill (MRG) and Cohen double-cable axon models effectively predict deep brain stimulation outcomes, the more detailed Cohen model exhibits greater excitability, lower activation thresholds, and superior predictive accuracy, particularly regarding frequency-dependent responses.

Original authors: Bartels, R., Vinke, S., Rijpma, A., Nadimi, M.

Published 2026-08-27

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CC BY 4.0

Original authors: Bartels, R., Vinke, S., Rijpma, A., Nadimi, M.

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 ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed.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

Deep brain stimulation is a medical treatment that uses tiny, precise electrical pulses to calm the chaotic signals of a diseased brain, offering relief for conditions like Parkinson's disease. Imagine a surgeon placing a thin wire deep inside the brain and sending a gentle, rhythmic current through it. This current acts like a reset button for the neural circuits, smoothing out the tremors and stiffness that plague patients. However, finding the perfect settings for this current is a delicate art. If the signal is too weak, it does nothing; if it is too strong, it can cause unwanted side effects. To solve this puzzle, scientists build computer models of the brain's wiring. These models act as virtual laboratories where they can test thousands of different electrical settings without ever touching a patient. The key to these simulations is understanding how the electrical pulse travels along the microscopic wires of the nervous system, known as axons, and how it wakes them up to fire.

For years, researchers have relied on a standard computer model to predict how these axons respond to stimulation. This model, known as the MRG model, treats the insulation around the nerve fiber as a simple barrier, assuming that electricity flows primarily through the center of the wire. But recent discoveries in biology have revealed a more complex reality. Scientists found that the space between the nerve fiber and its insulating myelin sheath is not just empty or sealed off; it is a narrow, conductive channel that allows electricity to flow along the outside of the wire as well. This discovery led to the creation of a new, more detailed model called the Cohen model, which includes this hidden pathway. The question remained: does this extra layer of biological detail actually change the predictions doctors use to program brain stimulators, or is the older, simpler model good enough?

A team of researchers at Radboud University Medical Center set out to answer this by running a head-to-head comparison of the two models. They did not test this on a new group of patients but instead used high-resolution brain scans from a single individual who had already received a deep brain stimulator. Using these scans, they built a precise digital replica of that person's brain, including the exact location of the electrode and the specific bundles of nerve fibers, known as the hyperdirect pathway, that connect the brain's motor cortex to the target area. They then simulated the electrical field generated by the device and ran it through both the old MRG model and the new Cohen model to see how each predicted the nerves would react.

The results showed that while both models agreed on the general behavior of the nerves, the new model predicted that the nerves were significantly more sensitive to the electrical pulse. When the researchers applied a standard current of 2 milliamperes, the older model suggested the stimulation would activate nerve fibers up to 6 millimeters away from the electrode. The new model, however, predicted that the same current would reach out and activate fibers as far as 10 millimeters away. In nearly every single case they tested, the new model required less electrical power to wake up the nerve fibers than the old model did. This suggests that the hidden conductive channel in the insulation plays a real role in helping the nerve fire, making the brain more responsive to the treatment than previously thought.

The two models also disagreed on how the nerves reacted when the speed of the electrical pulses changed. When the researchers increased the frequency of the pulses, the new model showed that the nerves became harder to activate, requiring more power to keep firing. This behavior aligns with what happens in real biological tissue, where nerves need a moment to recover between pulses. In contrast, the older model showed the opposite trend, suggesting that faster pulses made the nerves slightly easier to activate. This difference is crucial because it implies that the older model might not accurately predict how a patient will respond if the doctor changes the stimulation speed to manage symptoms.

To make sense of these complex interactions, the researchers trained computer programs to learn the relationship between the stimulation settings and the nerve response. These programs were fed data on how far the nerve was from the electrode, how long each pulse lasted, and how fast the pulses were repeating. The programs learned to predict the activation threshold—the minimum power needed to fire the nerve—with remarkable accuracy. The new model proved slightly easier for the computer to predict, with its results matching the simulation data more closely than the older model. This indicates that the new model's behavior is more consistent and perhaps more reliable for future planning.

The study concludes that while the older model remains a useful tool for estimating the general area of brain activation, the new model offers a more realistic picture of how electricity travels through the brain's wiring. The researchers found that the distance between the electrode and the nerve fiber is the most important factor in determining whether a nerve will fire, far outweighing the effects of pulse speed or length. However, the structural details of the nerve insulation do matter. By including the conductive channel beneath the myelin, the new model captures a level of biological truth that the older model misses. For doctors and engineers designing future treatments, this means that while the simple model can provide a good starting point, the more detailed model may be necessary for fine-tuning the therapy to ensure it is both effective and safe for the individual patient.

Technical Summary: Impact of Axon Model Complexity on Deep Brain Stimulation

Problem Statement
Deep brain stimulation (DBS) modeling relies on biophysical neuron models to estimate neural activation thresholds and predict the volume of tissue activated (VTA). While the McIntyre–Richardson–Grill (MRG) model has long been the standard for simulating myelinated axon responses, it treats the submyelin pathway as largely passive and does not quantify periaxonal or paranodal resistivities. Recent experimental work by Cohen et al. suggests that the periaxonal and paranodal spaces form a conductive nanocircuit enabling longitudinal current flow beneath the myelin, a feature absent in classical formulations. This study addresses the gap in understanding how these structural and electrophysiological differences between the widely adopted MRG model and the more detailed Cohen double-cable model affect predicted DBS outcomes, specifically regarding excitability, activation thresholds, and sensitivity to stimulation parameters.

Methodology
The study employed a patient-specific computational framework to compare two axonal models under identical DBS conditions:

Patient Data & Imaging: A single Parkinson's disease patient (69-year-old female) underwent bilateral subthalamic nucleus (STN) DBS. Multimodal imaging (T1, T2, and diffusion-weighted imaging) was acquired intraoperatively and preoperatively. The workflow included brain extraction, segmentation of grey/white matter and the STN, and tractography to reconstruct the hyperdirect pathway (HDP).
Bioelectric Field Modeling: A finite element model (FEM) of the Boston Scientific DB-2202 directional lead and surrounding brain tissue was constructed using Gmsh and solved via Elmer FEM. The model included an encapsulation layer to account for fibrotic tissue. Electric potential distributions were computed under quasi-static approximation.
Axonal Models:
- Model I (MRG): A standard double-cable model with 21 nodes of Ranvier, treating the internode as electrically isolated with passive myelin properties.
- Model II (Cohen): A biophysically detailed double-cable model incorporating a conductive periaxonal nanocircuit (~53.7 Ω·cm) and finite myelin conductance, derived from patch-clamp and voltage-sensitive dye recordings.
Simulation Protocol: 100 axonal trajectories from the HDP were simulated using the NEURON environment. Both models were subjected to asymmetric charge-balanced biphasic pulses across varying distances (2–10 mm), pulse widths (60–120 μs), and frequencies (80–300 Hz). Activation was defined by the generation of five consecutive action potentials.
Analysis: Machine learning regressors (Linear Regression, Random Forest, Gradient Boosting) were trained to predict activation thresholds based on distance, pulse width, and frequency. Model agreement was assessed via linear regression and Bland-Altman analysis.

Key Contributions

Systematic Comparison: The study provides a direct, controlled comparison of the MRG and Cohen models within the same patient-specific DBS simulation framework, isolating the impact of submyelin current flow on activation metrics.
Quantification of Excitability Differences: It quantifies how the inclusion of a conductive periaxonal nanocircuit alters activation thresholds and spatial recruitment patterns, demonstrating that structural details significantly influence predicted DBS efficacy.
Frequency-Dependent Behavior: The research highlights a critical divergence in frequency response between the two models, challenging the assumption that all double-cable models behave similarly under high-frequency stimulation.
Predictive Modeling: The study validates the use of machine learning to predict activation thresholds from stimulation parameters, showing that the more complex Cohen model yields slightly superior predictive metrics.

Results

Activation Distance and Thresholds: At 2 mA, the Cohen model (Model II) achieved an activation distance of 10 mm, compared to 6 mm for the MRG model (Model I), indicating greater excitability. Across matched fiber tracts, the Cohen model required lower activation thresholds in 97.7% of cases, with threshold differences ranging from −1.40 mA to 0.27 mA.
Parameter Sensitivity: Both models showed a strong inverse relationship between pulse width and activation threshold. However, they exhibited opposite trends regarding frequency: the Cohen model showed increasing thresholds at higher frequencies (1.23 mA at 80 Hz to 1.51 mA at 300 Hz), while the MRG model showed a slight decrease (1.96 mA to 1.82 mA).
Machine Learning Performance: Gradient Boosting provided the best predictive accuracy. The Cohen model achieved an $R^2$ of 0.986 (RMSE = 0.045 mA) on the test set, outperforming the MRG model ( $R^2$ = 0.977; RMSE = 0.089 mA).
Model Agreement: While the models showed strong correlation ( $R^2$ = 0.780, Pearson $r$ = 0.883), a systematic bias was observed where the MRG model predicted higher thresholds (mean bias of 0.631 mA).

Significance and Claims
The authors conclude that while both models reliably estimate DBS-induced activation, structural differences—specifically the presence of a conductive periaxonal nanocircuit in the Cohen model—significantly affect excitability and frequency-dependent behavior. The study claims that the Cohen model offers a more physically realistic representation of submyelin current flow, leading to lower activation thresholds and a frequency response consistent with observed reductions in neuronal activity at higher frequencies.

The paper asserts that either model can be used to derive activation distances and estimate the volume of tissue activated in patient-specific simulations, provided their respective strengths and limitations are understood. It emphasizes that electrode distance remains the primary determinant of activation threshold, with pulse width and frequency exerting secondary effects. The authors suggest that model selection should balance computational efficiency against biophysical realism based on specific application requirements, noting that further validation with larger patient cohorts and in vivo data is necessary to advance patient-specific DBS modeling.

Technical Summary: Impact of Axon Model Complexity on Deep Brain Stimulation

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