A comparison between single and double cable neuron models applicable to deep brain stimulation

Computational models for activation assessment in deep brain stimulation (DBS) are commonly based on neuronal cable equations. The aim was to systematically compare the activation distance between a single cable model implemented in MATLAB, and a well-established double cable model implemented in NEURON. Both models have previously been used for DBS studies. The field distributions generated from a point source and a 3389 DBS lead were applied to the neuron models as input stimuli. Simulations (n = 670) were performed with intersecting axon diameters (D) between the models (2.0, 3.0, 5.7, 7.3, 8.7, 10.0 m), variation in pulse shape and amplitude settings (0 to 5 in increments of 0.5 mA or V) with the single cable model as reference. Both models responded linearly to change of input (point source: 0.93 < R2 < 0.99, DBS source: R2 > 0.98), but with a systematic extended activation distance for the single cable model. The difference for a point source ranged from −0.2 mm (D = 2.0 m) to −1.1 mm (D = 5.7 m). For the DBS lead a D = 3.2 m agreed with the commonly used double cable simulations D =5.7 m in voltage mode. Possible reasons for the deviation at larger axons are the internodal length, the ion channel selection and physiological data behind the models. The single cable model covers a continuous range of small axon diameters and calculated the internodal length for each iteration, whereas the double cable models uses fixed defined axon diameters and tabulated data for the internodal length. Despite different implementations and model complexities, both models present similar sensitivity to pulse shape, amplitude and axon diameter. With awareness of the strength and weakness both models can be used to extract activation distance used to relate a specific electric field isolevel and thus estimate the volume of tissue activated in DBS simulation studies.