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Effect of non-symmetric waveform on conduction block induced by high-frequency (kHz) biphasic stimulation in unmyelinated axon

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Abstract

The effect of a non-symmetric waveform on nerve conduction block induced by high-frequency biphasic stimulation is investigated using a lumped circuit model of the unmyelinated axon based on Hodgkin-Huxley equations. The simulation results reveal that the block threshold monotonically increases with the stimulation frequency for the symmetric stimulation waveform. However, a non-monotonic relationship between block threshold and stimulation frequency is observed when the stimulation waveform is non-symmetric. Constant activation of potassium channels by the high-frequency stimulation results in the increase of block threshold with increasing frequency. The non-symmetric waveform with a positive pulse 0.4–0.8 μs longer than the negative pulse blocks axonal conduction by hyperpolarizing the membrane and causes a decrease in block threshold as the frequency increases above 12–16 kHz. On the other hand, the non-symmetric waveform with a negative pulse 0.4–0.8 μs longer than the positive pulse blocks axonal conduction by depolarizing the membrane and causes a decrease in block threshold as the frequency increases above 40–53 kHz. This simulation study is important for understanding the potential mechanisms underlying the nerve block observed in animal studies, and may also help to design new animal experiments to further improve the nerve block method for clinical applications.

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References

  • Bowman, B. R., & McNeal, D. R. (1986). Response of single alpha motoneurons to high-frequency pulse train: firing behavior and conduction block phenomenon. Applied Neurophysiology, 49, 121–138.

    CAS  PubMed  Google Scholar 

  • Boyce WE, Diprima RC. Elementary differential equations and boundary value problems. John Wiley & Sons Inc. 6th ed: 436–457, 1997.

  • Camilleri, M., Toouli, J., Herrera, M. F., Kow, L., Pantoja, J. P., Billington, C. J., Tweden, K. S., Wilson, R. R., & Moody, F. G. (2009). Selection of electrical algorithms to treat obesity with intermittent vagal block using an implantable medical device. Surgery for Obesity and Related Diseases, 5, 224–230.

    Article  PubMed  Google Scholar 

  • Cattell, M., & Gerard, R. W. (1935). The “inhibitory” effect of high-frequency stimulation and the excitation state of nerve. Journal of Physiology, 83, 407–415.

    CAS  PubMed Central  PubMed  Google Scholar 

  • Catterall, W. A. (2012). Voltage-gated sodium channels at 60: structure, function and pathophysiology. Journal of Physiology, 590, 2577–2589.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Cuellar, J. M., Alataris, K., Walker, A., Yeomans, D. C., & Antognini, J. F. (2013). Effect of high-frequency alternating current on spinal afferent nociceptive transmission. Neuromodulation, 16, 318–327.

    Article  PubMed  Google Scholar 

  • Frankenhaeuser, B. (1960). Quantitative description of sodium currents in myelinated nerve fibres of xenopus laevis. Journal of Physiology (London), 151, 491–501.

    CAS  Google Scholar 

  • Gaunt, R. A., & Prochazka, A. (2009). Transcutaneously coupled, high-frequency electrical stimulation of the pudendal nerve blocks external urethral sphincter contractions. Neurorehab. Neural Repair, 23, 615–626.

    Article  Google Scholar 

  • Heinbockel JH. Numerical Methods for Scientific Computing. Trafford Publishing, 2005.

  • Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology (London), 117, 500–544.

    CAS  Google Scholar 

  • Jan, L. Y., & Jan, Y. N. (2012). Voltage-gated potassium channels and the diversity of electrical signalling. Journal of Physiology (London), 590, 2591–2599.

    Article  CAS  Google Scholar 

  • Joseph, L., & Butera, R. (2009). Unmyelinated aplysia nerves exhibit a nonmonotonic blocking response to high-frequency stimulation. IEEE Trans Neural Syst Rehab Eng, 17, 537–544.

    Article  Google Scholar 

  • Joseph, L., & Butera, R. (2011). High-frequency stimulation selectively blocks different types of fibers in frog sciatic nerve. IEEE Trans Neural Syst Rehab Eng, 19, 550–557.

    Article  Google Scholar 

  • Leob, G. E. (1989). Neural prosthetic interfaces with the nervous system. Trends in Neurosciences, 12, 195–201.

    Article  Google Scholar 

  • Rattay, F. (1989). Analysis of models for extracellular fiber stimulation. IEEE Transactions on Biomedical Engineering, 36, 676–682.

    Article  CAS  PubMed  Google Scholar 

  • Rattay, F., & Aberham, M. (1993). Modeling axon membranes for functional electrical stimulation. IEEE Transactions on Biomedical Engineering, 40, 1201–1209.

    Article  CAS  PubMed  Google Scholar 

  • Reboul, J., & Rosenblueth, A. (1939). The action of alternating currents upon the electrical excitability of nerve. American Journal of Physiology, 125, 205–215.

    Google Scholar 

  • Rosenblueth, A., & Reboul, J. (1939). The blocking and deblocking effects of alternating currents on nerve. American Journal of Physiology, 125, 251–264.

    Google Scholar 

  • Roth, B. J. (1994). Mechanisms for electrical stimulation of excitable tissue. Critical Rev Biomed Eng, 22, 253–305.

    CAS  Google Scholar 

  • Roth, B. J. (1995). A mathematical model of make and break electrical stimulation of cardiac tissue by a unipolar anode or cathode. IEEE Transactions on Biomedical Engineering, 42, 1174–1184.

    Article  CAS  PubMed  Google Scholar 

  • Schwarz, J. R., Reid, G., & Bostock, H. (1995). Action potentials and membrane currents in the human node of Ranvier. Pflügers Archiv, 430, 283–292.

    Article  CAS  PubMed  Google Scholar 

  • Song, D., Raphael, G., Lan, N., & Loeb, G. E. (2008). Computationally efficient models of neuromuscular recruitment and mechanics. Journal of Neural Engineering, 5, 175–184.

    Article  CAS  PubMed  Google Scholar 

  • Tai, C., Roppolo, J. R., & de Groat, W. C. (2004). Block of external urethral sphincter contraction by high frequency electrical stimulation of pudendal nerve. Journal of Urology, 172, 2069–2072.

    Article  PubMed  Google Scholar 

  • Tai, C., de Groat, W. C., & Roppolo, J. R. (2005a). Simulation analysis of conduction block in unmyelinated axons induced by high-frequency biphasic electrical currents. IEEE Transactions on Biomedical Engineering, 52, 1323–1332.

    Article  PubMed Central  PubMed  Google Scholar 

  • Tai, C., de Groat, W. C., & Roppolo, J. R. (2005b). Simulation of nerve block by high-frequency sinusoidal electrical current based on the Hodgkin-Huxley model. IEEE Trans Neural Syst Rehab Eng, 13, 415–422.

    Article  Google Scholar 

  • Tai, C., Roppolo, J. R., & de Groat, W. C. (2009). Analysis of nerve conduction block induced by direct current. Journal of Computational Neuroscience, 27, 201–210.

    Article  PubMed Central  PubMed  Google Scholar 

  • Tai, C., Guo, D., Wang, J., Roppolo, J. R., & de Groat, W. C. (2011). Mechanism of conduction block in amphibian myelinated axon induced by biphasic electrical current at ultra-high frequency. Journal of Computational Neuroscience, 31, 615–623.

    Article  PubMed Central  PubMed  Google Scholar 

  • Tanner, J. A. (1962). Reversible blocking of nerve conduction by alternating-current excitation. Nature, 195, 712–713.

    Article  CAS  PubMed  Google Scholar 

  • van Buyten, J. P., Al-Kaisy, A., Smet, I., Palmisani, S., & Smith, T. (2013). High-frequency spinal cord stimulation for the treatment of chronic back pain patients: results of a prospective multicenter European clinical study. Neuromodulation, 16, 59–65.

    Article  PubMed  Google Scholar 

  • Vasylyev, D. V., & Waxman, S. G. (2012). Membrane properties and electrogenesis in the distal axons of small dorsal root ganglion neurons in vitro. Journal of Neurophysiology, 108, 729–740.

    Article  PubMed  Google Scholar 

  • Wattaja, J. J., Tweden, K. S., & Honda, C. N. (2011). Effects of high frequency alternating current on axonal conduction through the vagus nerve. Journal of Neural Engineering, 8, 056031.

    Google Scholar 

  • Waxman, S. G. (2012). Sodium channels, the electrogenisome and the electrogenistat: lessons and questions from the clinic. Journal of Physiology (London), 590, 2601–2612.

    Article  CAS  Google Scholar 

Download references

Acknowledgments

This study is supported by DOD Spinal Cord Injury Program under grant W81XWH-11-1-0819 and by NIH under grant DK-068566.

Conflict of interest

The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. Department of Urology, University of Pittsburgh, 700 Kaufmann Building, 15213, Pittsburgh, PA, USA

    Shouguo Zhao, Guangning Yang, Jicheng Wang & Changfeng Tai

  2. Department of Biomedical Engineering, Beijing Jiaotong University, Beijing, Peoples Republic China

    Shouguo Zhao & Guangning Yang

  3. Department of Pharmacology and Chemical Biology, University of Pittsburgh, Pittsburgh, PA, USA

    James R. Roppolo, William C. de Groat & Changfeng Tai

Authors
  1. Shouguo Zhao
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  2. Guangning Yang
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  3. Jicheng Wang
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  4. James R. Roppolo
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  5. William C. de Groat
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  6. Changfeng Tai
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Correspondence to Changfeng Tai.

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Action Editor: Arnd Roth

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Zhao, S., Yang, G., Wang, J. et al. Effect of non-symmetric waveform on conduction block induced by high-frequency (kHz) biphasic stimulation in unmyelinated axon. J Comput Neurosci 37, 377–386 (2014). https://doi.org/10.1007/s10827-014-0510-z

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  • DOI: https://doi.org/10.1007/s10827-014-0510-z

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