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

Abstract

Deep brain stimulation (DBS) modeling relies heavily on biophysical neuron models to estimate neural activation thresholds and predict stimulation spread. In this study, we systematically compared a widely adopted axon model, the McIntyre-Richardson-Grill (MRG) model (Model I), with a more detailed biophysical model, the Cohen model (Model II), to assess how structural and electrophysiological differences affect predicted DBS outcomes. Electric field distributions generated by 2202 DBS lead were applied to the neuron models as extracellular input stimuli. Both models were simulated under biphasic pulse stimulation across varying axon-electrode distances, pulse widths, and stimulation frequencies. Activation distances ranged from approximately 2 to 10 mm depending on stimulation parameters and contact location. At 2 mA, Model I achieved an activation distance of 6 mm, whereas Model II reached 10 mm, indicating greater excitability. Across matched fiber tracts, threshold differences ranged from -1.40 mA to 0.27 mA, with Model II requiring lower thresholds in 97.7% of cases. Both models showed a strong inverse relationship between pulse width and activation threshold. However, frequency responses differed: Model II exhibited increasing thresholds at higher frequencies, while Model I showed a slight decrease. Machine learning regressors trained on distance, pulse width, and frequency achieved high predictive accuracy, with Gradient Boosting performing best. Model II demonstrated superior prediction metrics (R^2 = 0.986; RMSE = 0.045 mA; MAE = 0.034 mA) compared to Model I (R^2 = 0.977; RMSE = 0.089 mA; MAE = 0.068 mA). Overall, both models reliably estimate DBS-induced activation, but structural differences significantly affect excitability and frequency-dependent behavior. With appropriate awareness of their respective strengths and limitations, either model can be used to derive activation distances for estimating electric field isolevels and the volume of tissue activated in patient-specific DBS simulations.