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2017-07-04
Modelling Dispersive Behavior of Excitable Cells
By
Progress In Electromagnetics Research M, Vol. 58, 73-86, 2017
Abstract
Most of the materials have nearly constant electromagnetic characteristics at low frequencies. Nonetheless, biological tissues are not the same; they are highly dispersive, even at low frequencies. Cable theory is the most famous method for analyzing nerves though a common mistake when studying the model is to consider a constant parameter versus frequency. This issue is discussed in the present article, and the analysis of how to model the dispersion in the cable model is proposed and explained. The proposed dispersive model can predict the behavior of excitable cells versus stimulations with single frequency or wide band signals. In this article, the nondestructive external stimulation by a coil is modeled and computed by finite difference method to survey the dispersion impact. Also, 5% to 80% difference is shown between the results of dispersive and nondispersive models in the 5 Hz to 4 kHz investigation. The disagreement expresses the dispersion notability. The proposed dispersive method assists in accurate device design and signal form optimization. Noise analysis is also achieved by this model, unlike the conventional models, which is essential in the analysis of single neurons or central nervous system, EEG and MEG records.
Citation
Soheil Hashemi Ali Abdolali , "Modelling Dispersive Behavior of Excitable Cells," Progress In Electromagnetics Research M, Vol. 58, 73-86, 2017.
doi:10.2528/PIERM17030102
http://www.jpier.org/PIERM/pier.php?paper=17030102
References

1. Hodgkin, A. L. and A. F. Huxley, "A quantitative description of membrane current and its application to conduction and excitation in nerve," The Journal of Physiology, Vol. 117, No. 4, 500, 1952.
doi:10.1113/jphysiol.1952.sp004764

2. Gabbiani, F. and S. J. Cox, Mathematics for Neuroscientists, Academic Press, 2010.

3. Koch, C., I. Segev, and eds., Methods in Neuronal Modeling: From Ions to Networks, MIT Press, 1998.

4. Roth, B. J. and P. J. Basser, "A model of the stimulation of a nerve fiber by electromagnetic induction," IEEE Transactions on Biomedical Engineering, Vol. 37, No. 6, 588-597, 1990.
doi:10.1109/10.55662

5. Bernardi, P. and G. D’Inzeo, "A nonlinear analysis of the effects of transient electromagnetic fields on excitable membranes," IEEE Transactions on Microwave Theory and Techniques, Vol. 32, No. 7, 670-679, 1984.
doi:10.1109/TMTT.1984.1132752

6. Goetz, S. M., C. N. Truong, M. G. Gerhofer, A. V. Peterchev, H.-G. Herzog, and T.Weyh, "Analysis and optimization of pulse dynamics for magnetic stimulation," PloS One, Vol. 8, No. 3, e55771, 2013.
doi:10.1371/journal.pone.0055771

7. Holt, G. R., "A critical reexamination of some assumptions and implications of cable theory in neurobiology,", Ph.D. diss., California Institute of Technology, 1997.

8. Rattay, F., "Analysis of models for extracellular fiber stimulation," IEEE Transactions on Biomedical Engineering, Vol. 36, No. 7, 676-682, 1989.
doi:10.1109/10.32099

9. Joucla, S. and B. Yvert, "Modeling extracellular electrical neural stimulation: From basic understanding to MEA-based applications," Journal of Physiology-Paris, Vol. 106, No. 3, 146-158, 2012.
doi:10.1016/j.jphysparis.2011.10.003

10. Basser, P. J. and B. J. Roth, "Stimulation of a myelinated nerve axon by electromagnetic induction," Medical and Biological Engineering and Computing, Vol. 29, No. 3, 261-268, 1991.
doi:10.1007/BF02446708

11. Hirata, A., J. Hattori, I. Laakso, A. Takagi, and T. Shimada, "Computation of induced electric field for the sacral nerve activation," Physics in Medicine and Biology, Vol. 58, No. 21, 7745, 2013.
doi:10.1088/0031-9155/58/21/7745

12. Warman, E. N., W. M. Grill, and D. Durand, "Modeling the effects of electric fields on nerve fibers: Determination of excitation thresholds," IEEE Transactions on Biomedical Engineering, Vol. 39, No. 12, 1244-1254, 1992.
doi:10.1109/10.184700

13. Pashut, T., S. Wolfus, A. Friedman, M. Lavidor, I. Bar-Gad, Y. Yeshurun, and A. Korngreen, "Mechanisms of magnetic stimulation of central nervous system neurons," PLoS Computational Biology, Vol. 7, No. 3, e1002022, 2011.
doi:10.1371/journal.pcbi.1002022

14. King, R. W. P., "Nerves in a human body exposed to low-frequency electromagnetic fields," IEEE Transactions on Biomedical Engineering, Vol. 46, No. 12, 1426-1431, 1999.
doi:10.1109/10.804570

15. Liston, A., R. Bayford, and D. Holder, "A cable theory based biophysical model of resistance change in crab peripheral nerve and human cerebral cortex during neuronal depolarisation: Implications for electrical impedance tomography of fast neural activity in the brain," Medical & Biological Engineering & Computing, Vol. 50, No. 5, 425-437, 2012.
doi:10.1007/s11517-012-0901-0

16. Howell, B., L. E. Medina, and W. M. Grill, "Effects of frequency-dependent membrane capacitance on neural excitability," Journal of Neural Engineering, Vol. 12, No. 5, 056015, 2015.
doi:10.1088/1741-2560/12/5/056015

17. Eleiwa, M. A. and A. Z. Elsherbeni, "Debye constants for biological tissues from 30 Hz to 20 GHz," ACES Journal, Vol. 16, No. 3, 2001.

18. Takashima, S. and H. P. Schwan, "Passive electrical properties of squid axon membrane," The Journal of Membrane Biology, Vol. 17, No. 1, 51-68, 1974.
doi:10.1007/BF01870172

19. Cole, K. S., "Electrical properties of the squid axon sheath," Biophysical Journal, Vol. 16, No. 2, 137-142, 1976.
doi:10.1016/S0006-3495(76)85670-6

20. Cole, K. S., "Rectification and inductance in the squid giant axon," The Journal of General Physiology, Vol. 25, No. 1, 29-51, 1941.
doi:10.1085/jgp.25.1.29

21. Cole, K. S. and R. F. Baker, "Longitudinal impedance of the squid giant axon," The Journal of General Physiology, Vol. 24, No. 6, 771-788, 1941.
doi:10.1085/jgp.24.6.771

22. Cole, K. S. and R. F. Baker, "Transverse impedance of the squid giant axon during current flow," The Journal of General Physiology, Vol. 24, No. 4, 535-549, 1941.
doi:10.1085/jgp.24.4.535

23. Cole, K. S. and G. Marmont, "The effect of ionic environment upon the longitudinal impedance of the squid giant axon," Fed. Proc., Vol. 1, 15-16, 1942.

24. Cole, K. S., Membranes, Ions, and Impulses: A Chapter of Classical Biophysics, Vol. 5, Univ. of California Press, 1968.

25. Grant, P. F. and M. M. Lowery, "Effect of dispersive conductivity and permittivity in volume conductor models of deep brain stimulation," IEEE Transactions on Biomedical Engineering, Vol. 57, No. 10, 2386-2393, 2010.
doi:10.1109/TBME.2010.2055054

26. Nagarajan, S. S., D. M. Durand, and E. N. Warman, "Effects of induced electric fields on finite neuronal structures: A simulation study," IEEE Transactions on Biomedical Engineering, Vol. 40, No. 11, 1175-1188, 1993.
doi:10.1109/10.245636

27. Miranda, P. C., L. Correia, R. Salvador, and P. J. Basser, "Tissue heterogeneity as a mechanism for localized neural stimulation by applied electric fields," Physics in Medicine and Biology, Vol. 52, No. 18, 5603, 2007.
doi:10.1088/0031-9155/52/18/009

28. Silva, S., P. J. Basser, and P. C. Miranda, "Elucidating the mechanisms and loci of neuronal excitation by transcranial magnetic stimulation using a finite element model of a cortical sulcus," Clinical Neurophysiology, Vol. 119, No. 10, 2405-2413, 2008.
doi:10.1016/j.clinph.2008.07.248

29. Platkiewicz, J. and R. Brette, "A threshold equation for action potential initiation," PLoS Computational Biology, Vol. 6, No. 7, 2010.
doi:10.1371/journal.pcbi.1000850

30. Ying, W. and C. S. Henriquez, "Hybrid finite element method for describing the electrical response of biological cells to applied fields," IEEE Transactions on Biomedical Engineering, Vol. 54, No. 4, 611-620, 2007.
doi:10.1109/TBME.2006.889172

31. McIntyre, C. C., et al., "Modeling the excitability of mammalian nerve fibers: Influence of afterpotentials on the recovery cycle," Journal of Neurophysiology, Vol. 87, No. 2, 995-1006, 2002.
doi:10.1152/jn.00353.2001

32. McIntyre, C. C. and W. M. Grill, "Extracellular stimulation of central neurons: Influence of stimulus waveform and frequency on neuronal output," Journal of Neurophysiology, Vol. 88, No. 4, 1592-1604, 2002.
doi:10.1152/jn.2002.88.4.1592

33. Oughstun, K. E. and N. A. Cartwright, "On the Lorentz-Lorenz formula and the Lorentz model of dielectric dispersion," Optics Express, Vol. 11, No. 13, 1541-1546, 2003.
doi:10.1364/OE.11.001541

34. Kandel, E. R., J. H. Schwartz, T. M. Jessell, and (Eds.), Principles of Neural Science, Vol. 4, 71-171, McGraw-Hill, New York, 2000.