Modeling the interactions between stimulation and physiologically induced APs in a mammalian nerve fiber: dependence on frequency and fiber diameter
Electrical stimulation of nerve fibers is used as a therapeutic tool to treat neurophysiological disorders. Despite efforts to model the effects of stimulation, its underlying mechanisms remain unclear. Current mechanistic models quantify the effects that the electrical field produces near the fiber but do not capture interactions between action potentials (APs) initiated by stimulus and APs initiated by underlying physiological activity. In this study, we aim to quantify the effects of stimulation frequency and fiber diameter on AP interactions involving collisions and loss of excitability. We constructed a mechanistic model of a myelinated nerve fiber receiving two inputs: the underlying physiological activity at the terminal end of the fiber, and an external stimulus applied to the middle of the fiber. We define conduction reliability as the percentage of physiological APs that make it to the somatic end of the nerve fiber. At low input frequencies, conduction reliability is greater than 95% and decreases with increasing frequency due to an increase in AP interactions. Conduction reliability is less sensitive to fiber diameter and only decreases slightly with increasing fiber diameter. Finally, both the number and type of AP interactions significantly vary with both input frequencies and fiber diameter. Modeling the interactions between APs initiated by stimulus and APs initiated by underlying physiological activity in a nerve fiber opens opportunities towards understanding mechanisms of electrical stimulation therapies.
KeywordsAction potential interactions Conduction reliability Nerve fiber Mechanistic model Electrical stimulation
Work supported by NIH R01 AT009401 to S.V.S, Y.G., and W.S.A., and by NPRI postdoctoral fellowship awarded to P.S. We would like to thank Dr. Michael Caterina, Neurosurgery Pain Research Institute, The Johns Hopkins University School of Medicine for valuable and insightful discussions.
Compliance with Ethical Standards
Conflict of interests
The authors declare that they have no conflict of interest.
- Agarwal, R., & Sarma, S.V. (2012). Performance limitations of relay neurons. PLoS computational biology, 8 (8), e1002,626.Google Scholar
- Baron, R. (2009). Neuropathic pain: a clinical perspective. In Canning, B.J., & Spina, D. (Eds.) Sensory Nerves (pp. 3–30). Springer.Google Scholar
- Bruns, T.M., Bhadra, N., Gustafson, K.J. (2009). Bursting stimulation of proximal urethral afferents improves bladder pressures and voiding. Journal of Neural Engineering, 6(6), 1–8.Google Scholar
- Crago, P.E., & Makowski, N.S. (2014). Alteration of neural action potential patterns by axonal stimulation: the importance of stimulus location. Journal of Neural Engineering, 11(5), 1–9.Google Scholar
- Foutz, T.J., & McIntyre, C.C. (2010). Evaluation of novel stimulus waveforms for deep brain stimulation. Journal of neural engineering, 7(6), 1–10.Google Scholar
- Groves, D.A., & Brown, V.J. (2005). Vagal nerve stimulation: a review of its applications and potential mechanisms that mediate its clinical effects. Neuroscience & Biobehavioral Reviews, 29(3), 493–500.Google Scholar
- van den Honert, C., & Mortimer, J.T. (1981). A technique for collision block of peripheral nerve: Frequency dependence. IEEE Transactions on Biomedical Engineering, 5(28), 379–382.Google Scholar
- Hursh, J.B. (1939). Conduction velocity and diameter of nerve fibers. American Journal of Physiology, 127 (1), 131–139.Google Scholar
- Kralj, A.R., & Bajd, T. (1989). Functional electrical stimulation: standing and walking after spinal cord injury. Boca Raton: CRC Press.Google Scholar
- McIntyre, C.C., & Grill, W.M. (1999). Model-based design of stimulus waveforms for selective microstimulation in the central nervous system. In Proceedings of the First Joint BMES/EMBS Conference, (Vol. 1 p. 384).Google Scholar
- Medtronic Neuromodulation. (2007). Technical design summary: Model 39565 specify 5-6-5 surgical lead.Google Scholar
- Mortimer, J.T., & Bhadra, N. (2004). Peripheral nerve and muscle stimulation. In Neuroprosthetics: Theory and Practice, World Scientific (pp. 638–682).Google Scholar
- Olin, J.C., Kidd, D.H., North, R.B. (1998). Postural changes in spinal cord stimulation perceptual thresholds. Neuromodulation: Technology at the Neural Interface, 1(4), 171–175.Google Scholar
- Sacré, P, Sarma, S.V., Guan, Y., Anderson, W.S. (2015). Electrical neurostimulation for chronic pain: on selective relay of sensory neural activities in myelinated nerve fibers. In Proceeding of the 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) (pp. 4705–4708).Google Scholar
- Sadashivaiah, V. (2018). Modeling the interactions in a mammalian nerve fiber. https://github.com/vjysd/nerve-fiber-modeling.
- Sadashivaiah, V., Sacré, P, Guan, Y., Anderson, W.S., Sarma, S.V. (2017). Modeling electrical stimulation of mammalian nerve fibers: a mechanistic versus probabilistic approach. In Proceeding of the 39th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) (pp. 3868–3871).Google Scholar
- Sadashivaiah, V., Sacré, P, Guan, Y., Anderson, W.S., Sarma, S.V. (2018). Studying the interactions in a mammalian nerve fiber: a functional modeling approach. In Proceeding of the 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). https://doi.org/10.1109/EMBC.2018.8512975, https://ieeexplore.ieee.org/document/8512975 (pp. 3525–3528).
- Sadashivaiah, V., Sacré, P, Guan, Y., Anderson, W.S., Sarma, S.V. (2018). Selective relay of afferent sensory-induced action potentials from peripheral nerve to brain and the effects of electrical stimulation. In Proceeding of the 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). https://doi.org/10.1109/EMBC.2018.8513029, https://ieeexplore.ieee.org/document/8513029 https://ieeexplore.ieee.org/document/8513029 (pp. 3606–3609).
- Schwarz, J.R., Reid, G., Bostock, H. (1995). Action potentials and membrane currents in the human node of ranvier. Pflü,gers Archiv, 430(2), 283–292.Google Scholar
- Shealy, C.N., Mortimer, J.T., Reswick, J.B. (1967). Electrical inhibition of pain by stimulation of the dorsal columns: preliminary clinical report. Anesthesia & Analgesia, 46(4), 489–491.Google Scholar
- Shechter, R., Yang, F., Xu, Q., Cheong, Y.K., He, S.Q., Sdrulla, A., Carteret, A.F., Wacnik, P.W., Dong, X., Meyer, R.A., et al. (2013). Conventional and kilohertz-frequency spinal cord stimulation produces intensity-and frequency-dependent inhibition of mechanical hypersensitivity in a rat model of neuropathic pain. Anesthesiology, 119(2), 422–432.PubMedPubMedCentralGoogle Scholar