Introduction
Optimizing peripheral nerve stimulation is crucial for improving clinical outcomes in neural prosthetics and bioelectronics medicines. The effects of extracellular electrical stimulation of peripheral myelinated axons depend jointly on the stimulus amplitude, waveform, and frequency. This work shows that variation in the waveform configuration (monophasic and biphasic with and without interphase gaps) defines the baseline activation thresholds across monopolar and bipolar electrode configurations using the same cuff structure around the rat sciatic nerve. Further, we explored how pulse-train frequency influences temporal entrainment limits, subharmonic skipping patterns, and intrinsic ionic adaptation kinetics.
Methods
We used the McIntyre-Richardson-Grill model for a myelinated nerve fiber with modified adaptation kinetics [1]. Next, a mesh of a rat sciatic nerve was created with GMESH [2]. We solved spatial potential maps for both monopolar and bipolar electrode cuff setups to isolate electric field effects using the Finite Element Method in FEniCSx [3]. We mapped these potential values onto the axon in NEURON [4] to simulate the nerve behavior. Nodes contained fast transient Na+, persistent Na+ driving afterdepolarization (ADP), and slow adaptation K+ currents. Further, we evaluated baseline thresholds for 12 biphasic waveforms at 5 Hz to ensure intervals exceeded the refractory period. Lastly, frequency adaptation was tested at 5, 100, and 1000 Hz.
Results
At 5 Hz, the activation threshold was observed at 250 µA for the symmetric and 100 µA for the asymmetric pulse because the bipolar configuration constrains the current spread. However, the monopolar configuration distributes the field between source and ground, resulting in variable thresholds ranging from 250 µA to 650 µA. The reduction in activation thresholds was observed with the introduction of an interphase gap. At 100 Hz, bursting emerged due to ionic tug-of-war: ADP drove rapid firing until a slowly developing AHP suppressed activity, creating 60–180 ms silent intervals. At 1000 Hz, axons show spike-skipping (1:3 to 1:5 entrainment) due to the refractory period, with 3–5 ms intra-burst ISIs and 200–400 ms adaptation gaps.
Discussion
Symmetric cathodic-leading pulses show lower baseline thresholds due to rapid depolarization, whereas the anodic-leading pulses show higher baseline thresholds because they hyperpolarize the membrane. However, the interphase gap (IPG) lowers the thresholds further, providing extra time for sodium channels to open more before the charge-reversing phase arrives. These findings show that axonal activation is a highly dynamic process shaped by spatial coupling and stimulation rates. The progression from linear scaling at 5 Hz to bursting at 100 Hz and combined bursting and subharmonic skip firing at 1000 Hz indicates that the behavior of axons under electrical stimulation is highly dependent upon the biophysical properties of ion channels.
References
[1] McIntyre, C. C., Richardson, A. G., & Grill, W. M. (2002). Modeling the excitability of mammalian nerve fibers: Influence of afterpotentials on the recovery cycle. Journal of Neurophysiology, 87(2), 995–1006. https://doi.org/10.1152/jn.00353.2001
[2] Geuzaine, C., & Remacle, J. F. (2009). Gmsh: A three-dimensional finite element mesh generator. International Journal for Numerical Methods in Engineering, 79(11), 1309–1331. https://doi.org/10.1002/nme.2579
[3] Baratta, I. A., et al. (2023). DOLFINx: The next generation FEniCS problem solving environment. Preprint. https://doi.org/10.5281/zenodo.10447666
[4] Hines, M. L., & Carnevale, N. T. (1997). The NEURON simulation environment. Neural Computation, 9(6), 1179–1209. https://doi.org/10.1162/neco.1997.9.6.1179
Acknowledgement
This work was conducted at the Prescott Lab, University of Calgary. Computational resources and simulation infrastructure were provided by the Prescott Lab, with additional laboratory infrastructure and support from the Hotchkiss Brain Institute, University of Calgary.
