volume | PIER Journals

Abstract

A transient finite-element model has been presented to simulate extracellular potential stimulating in a neural tissue by a nonplanar microelectrode array (MEA). This model allows simulating the extracellular potential and transmembrane voltage by means of a single transient computation performed within single finite element (FE) software. The differential effects of the configuration and position of MEA in electrical extracellular stimulation are analyzed theoretically. 3-D models of single nerve fiber and different MEA are used for the computation of the stimulation induced field potential, whereas a cable model of a nerve fibre is used for the calculation of the transmembrane voltage of the nerve fiber. The position of MEA and the spacing of the microelectrodes are varied while mono-, bi-, tri-, and penta-polar MEAs are applied. The model predicts that the lowest stimulation voltage threshold is obtained in the stimulation with penta-polar MEA. Moreover, the relationships, which exist between the thresholds of the electrical extracellular stimulation and the parameters including position of the electrode array and the spacing of the microelectrodes in array, are studied and obtained.

1. Gaunt, R. A. and A. Prochazka, "Control of urinary bladder function with devices: Successes and failures," Progress in Brain Research, Vol. 152, 163-194, 2006.
doi:10.1016/S0079-6123(05)52011-9

2. Winfree, C. J., "Spinal cord stimulation for the relief of chronic pain," Curr. Surg., Vol. 62, No. 5, 476-481, Sep. 2005.
doi:10.1016/j.cursur.2005.03.008

3. Benabid, A. L., P. Pollak, C. Gervason, D. Hoffmann, D. M. Gao, et al. "Long term suppression of tremor by chronic stimulation of the ventral intermediate thalamic nucleus," The Lancet, Vol. 337, 403-406, Feb. 1991.
doi:10.1016/0140-6736(91)91175-T

4. Theodore, W. H., "Brain stimulation for epilepsy," Nat. Clin. Pract. Neurol., Vol. 1, No. 2, 64-65, Dec. 2005.
doi:10.1038/ncpneuro0051

5. Thomas Jr., C. A., P. A. Springer, G. E. Loeb, Y. Berwald-Netter, and L. M. Okun, "A miniature microelectrode array to monitor the bioelectric activity of cultured cells," Experiment. Cell Res., Vol. 74, No. 1, 61-66, 1972.
doi:10.1016/0014-4827(72)90481-8

6. Wise, K. D., J. B. Angell, and A. Starr, "An integrated-circuit approach to extracellular microelectrodes," IEEE Trans. Biomed. Eng., Vol. 17, No. 3, 238-247, Mar. 1970.
doi:10.1109/TBME.1970.4502738

7. Buzsaki, G., "Large-scale recording of neuronal ensembles," Nature Neurosci., Vol. 7, No. 5, 446-451, May 2004.
doi:10.1038/nn1233

8. Wang, Z. G., X. S. Gu, X. Y. Lu, Z. L. Jiang, W. Y. Li, G. M. Lu, Y. F. Wang, X. Y. Shen, X. T. Zhao, H. L. Wang, Z. Y. Zhang, and et al, "Microelectronics-embedded channel bridging and signal regeneration of injured spinal cords," Progress in Natural Science, Vol. 19, No. 10, 1261-1269, Oct. 2009.
doi:10.1016/j.pnsc.2009.02.005

9. Gross, G. W., A. N. Williams, and J. H. Lucas, "Recording of spontaneous activity with photoetched microelectrode surfaces from mouse spinal neurons in culture," J. Neurosci. Methods, Vol. 5, No. 1--2, 13-22, Jan. 1982.
doi:10.1016/0165-0270(82)90046-2

10. Novak, J. L. and B. C. Wheeler, "Multisite hippocampal slice recording and stimulation using a 32 element microelectrode array," J. Neurosci. Methods, Vol. 23, No. 2, 149-159, Mar. 1988.
doi:10.1016/0165-0270(88)90187-2

11. Charvet, G., L. Rousseau, O. Billoint, S. Gharbi, J. Rostaing, et al. "A 256-channel microelectrode array (MEA) system with integrated electronics for recording and stimulation of neural networks," Society for Neuroscience 37th Annual Meeting, San Diego, California, 171-174, USA 2007.

12. Billoint, O., J. P. Rostaing, G. Charvet, and B. Yvert, "A 64-channel ASIC for in-vitro simultaneous recording and stimulation of neurons using microelectrode arrays," Conf. Proc. IEEE Eng. Med. Biol. Soc., Vol. 1, 6070-6073, 2007.

13. Branner, A., R. B. Stein, and R. A. Normann, "Selective stimulation of cat sciatic nerve using an array of varying-length microelectrodes," J. Neurophysiol, Vol. 85, 1585-1594, 2001.

14. McCreery, D., A. Lossinsky, V. Pikov, and X. D. Liu, "Microelectrode array for chronic deep-brain microstimulation and recording," IEEE Trans. Biomed. Eng., Vol. 53, No. 4, 726-737, Apr. 2006.
doi:10.1109/TBME.2006.870215

15. Smit, J. P. A., W. L. C. Rutten, and H. B. K. Boom, "Endoneural selective stimulating using wire-microelectrode arrays," IEEE Trans. Biomed. Eng., Vol. 7, No. 4, 399-412, Dec. 1999.

16. Campbell, P. K., K. E. Jones, R. J. Huber, K. W. Horch, and R. A. Normann, "A silicon-based, three-dimensional neural interface: Manufacturing processes for an intracortical electrode array," IEEE Trans. Biomed. Eng., Vol. 38, No. 8, 758-768, Aug. 1991.
doi:10.1109/10.83588

17. Song, Y. K., W. R. Patterson, C. W. Bull, J. Beals, N. Hwang, A. P. Deangelis, C. Lay, J. L. McKay, A. V. Nurmikko, M. R. Fellows, and et al, "Development of a chipscale integrated microelectrode/microelectronic de-vice for brain implantable neuroengineering applications," IEEE Tans. Neural. System and Rehabilitation Eng., Vol. 13, No. 2, 220-226, Jun. 2005.
doi:10.1109/TNSRE.2005.848337

18. Hoogerwerf, A. C. and K. D. Wise, "A three-dimensional microelectrode array for chronic neural recording," IEEE Trans. Biomed. Eng., Vol. 41, No. 12, 1136-1146, Dec. 1994.
doi:10.1109/10.335862

19. Aziz, J. N. Y., R. Genov, B. L. Bardakjian, M. Derchansky, and P. L. Carlen, "Brain-silicon interface for high-resolution in vitro neural recording," IEEE Tans. Biomedical Circuits and Systems, Vol. 1, No. 1, 56-62, Mar. 2007.
doi:10.1109/TBCAS.2007.893181

20. Wang, R. X., X. J. Huang, G. F. Liu, W. Wang, F. T. Dong, and Z. H. Li, "Fabrication and characterization of a parylene-based three-dimensional microelectrode array for use in retinal prosthesis," Journal of Microelectromechanical Systems, Vol. 19, No. 2, 367-374, Apr. 2010.
doi:10.1109/JMEMS.2009.2039773

21. Huber, D., L. Petreanu, N. Ghitani, S. Ranade, T. Hromadka, et al. "Sparse optical microstimulation in barrel cortex drives learned behaviour in freely moving mice," Nature, Vol. 451, No. 7174, 61-64, Jan. 2008.
doi:10.1038/nature06445

22. Houweling, A. R. and M. Brecht, "Behavioural report of single neuron stimulation in somatosensory cortex," Nature, Vol. 451, 65-68, Jan. 2008.
doi:10.1038/nature06447

23. Grumet, A. E., J. L. Wyatt, Jr, and J. F. Rizzo, "Multi-electrode stimulation and recording in the isolated retina," J. Neurosci. Methods, Vol. 101, No. 1, 31-42, Aug. 2000.
doi:10.1016/S0165-0270(00)00246-6

24. Rattay, F. and S. Resatz, "Dipole distance for minimum threshold current to stimulate unmyelinated axons with microelectrodes," IEEE Trans. Biomed. Eng., Vol. 54, No. 1, 158-162, Jan. 2007.
doi:10.1109/TBME.2006.883730

25. Holsheimer, J. and W. A. Wesselink, "Optimum electrode geometry for spinal cord stimulation: The narrow bipole and tripole," Med. Biol. Eng. Comput., Vol. 35, No. 5, 493-497, Sep. 1997.
doi:10.1007/BF02525529

26. Rattay, F. and S. Resatz, "Effective electrode configuration for selective stimulation with inner eye prostheses," IEEE Trans. Biomed. Eng., Vol. 51, No. 9, 1659-1664, Sep. 2004.
doi:10.1109/TBME.2004.828044

27. Meier, J. H., W. L. Rutten, A. E. Zoutman, H. B. Boom, and P. Bergveld, "Simulation of multipolar fiber selective neural stimulation using intrafascicular electrodes," IEEE Trans. Biomed. Eng., Vol. 39, No. 2, 122-134, Feb. 1992.
doi:10.1109/10.121643

28. Schnabel, V. and J. J. Struijk, "Evaluation of the cable model for electrical stimulation of unmyelinated nerve fibers," IEEE Trans. Biomed. Eng., Vol. 48, No. 9, 1027-1033, Sep. 2001.
doi:10.1109/10.942593

29. Fromherz, P., "Sheet conductor model of brain slices for stimulation and recording with planar electronic contacts," Eur. Biophys. J., Vol. 31, No. 3, 228-231, Apr. 2002.
doi:10.1007/s00249-002-0213-7

30. Church, P., A. Leduc, R. A. Beique, and J. R. Derome, "A numerical solution of cylindrical coordinate Laplace's equation with mixed boundary conditions along the axis of symmetry: Application to intracerebral stimulating electrodes," J. Appl. Phys., Vol. 56, No. 1, 1-5, 1984.
doi:10.1063/1.333752

31. Altman, K. W. and R. Plonsey, "Development of a model for point source electrical fibre bundle stimulation," Med. Biol. Eng. Comput, Vol. 26, No. 5, 466-475, Sep. 1988.
doi:10.1007/BF02441913

32. Buitenweg, J. R., W. L. Rutten, and E. Marani, "Extracellular stimulation window explained by a geometry-based model of the neuron-electrode contact," IEEE Trans. Biomed. Eng., Vol. 49, No. 12, 1591-1599, Dec. 2002.
doi:10.1109/TBME.2002.804504

33. McIntyre, C. C., W. M. Grill, D. L. Sherman, and N. V. Thakor, "Cellular effects of deep brain stimulation: Model-based analysis of activation and inhibition," J. Neurophysiol., Vol. 91, No. 4, 1457-1469, Apr. 2004.
doi:10.1152/jn.00989.2003

34. Struijk, J. J., J. Holsheimer, and H. B. Boom, "Excitation of dorsal root fibers in spinal cord stimulation: a theoretical study," IEEE Trans. Biomed. Eng., Vol. 40, No. 7, 632-639, Jul. 1993.
doi:10.1109/10.237693

35. Laudani, A., S. Coco, and F. R. Fulginei, "Finite element model of charge transport across ionic channels," COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 32, No. 6, 1845-1854, 2013.
doi:10.1108/COMPEL-10-2012-0282

36. Buitenweg, J. R., W. L. C. Rutten, and E. Marani, "Geometry-based finite-element modeling of the electrical contact between a cultured neuron and a microelectrode," IEEE Trans. Biomed. Eng., Vol. 50, No. 4, 501-509, Apr. 2003.
doi:10.1109/TBME.2003.809486

37. Buitenweg, J. R., W. L. C. Rutten, and E. Marani, "Modeled channel distributions explain extracellular recordings from cultured neurons sealed to microelectrodes," IEEE Trans. Biomed. Eng., Vol. 49, No. 11, 1580-1590, Nov. 2002.
doi:10.1109/TBME.2002.805555

38. Heuschkel, M. O., M. Fejtl, M. Raggenbass, D. Bertrand, and P. Renaud, "A three-dimensional multi-electrode array for multisite stimulation and recording in acute brain slices," J. Neurosci. Methods, Vol. 114, 135-148, 2002.
doi:10.1016/S0165-0270(01)00514-3

39. Joucla, S. and B. Yvert, "Improved focalization of electrical microstimulation using microelectrode arrays: A modeling study," PLOS ONE, Vol. 4, No. 3, e4828, 2009.
doi:10.1371/journal.pone.0004828

40. Joucla, S., P. Branchereau, D. Cattaert, and B. Yvert, "Extracellular neural microstimulation may activate much larger regions than expected by simulations: A combined experimental and modeling study," PLOS ONE, Vol. 7, No. 8, 41324, 2012.
doi:10.1371/journal.pone.0041324

41. Moulin, C., A. Gliµere, D. Barbier, S. Joucla, B. Yvert, P. Mailley, and R. Guillemaud, "A new 3-D finite-element model based on thin-film approximation for microelectrode array recording of extracellular action potential," IEEE Trans. Biomed. Eng., Vol. 55, No. 2, 683-692, Feb. 2008.
doi:10.1109/TBME.2007.903522

42. Hodgkin, A. L. and A. F. Huxley, "A quantitative description of membrane current and its application to conduction and excitation in nerve," J. Physiol., Vol. 117, 500-544, 1952.

43. Mainen, Z. F., J. Joerges, J. R. Huguenard, and T. J. Sejnowski, "A model of spike initiation in neocortical pyramidal neurons," Neuron, Vol. 15, 1427-1439, 1995.
doi:10.1016/0896-6273(95)90020-9

44. Lindsay, K. A., J. R. Rosenberg, and G. Tucker, "From Maxwell's equations to the cable equation and beyond," Progr. Biophys. Molecul. Biol., Vol. 85, No. 1, 71-116, May 2004.
doi:10.1016/j.pbiomolbio.2003.08.001

45. Mofftt, M. A. and C. C. McIntyre, "Model-based analysis of cortical recording with silicon microelectrodes," Clin. Neurophysiol., Vol. 116, No. 9, 2240-2250, Sep. 2005.
doi:10.1016/j.clinph.2005.05.018

46. Holt, G. R. and C. Koch, "Electrical interactions via the extracellular potential near cell bodies," J. Comput. Neurosci., Vol. 6, No. 2, 169-184, Mar. 1999.
doi:10.1023/A:1008832702585

47. Claverol-Tinture, E. and J. Pine, "Extracellular potentials in low-density dissociated neuronal cultures," J. Neurosci. Methods, Vol. 117, 13-21, 2002.
doi:10.1016/S0165-0270(02)00043-2

48. Brown, P. N., A. C. Hindmarsh, and L. R. Petzold, "Using Krylov methods in the solution of large-scale differential-algebraic systems," SIAM J. Scientif. Comput., Vol. 15, No. 6, 1467-1488, 1994.
doi:10.1137/0915088

49. McHardy, J., D. Geller, and S. B. Brummer, "An approach to corrosion control during electrical stimulation," Ann. Biomed. Eng., Vol. 5, No. 2, 144-149, Jun. 1977.
doi:10.1007/BF02364014

50. McCreery, D. B., W. F. Agnew, T. G. Yuen, and L. Bullara, "Charge density and charge per phase as cofactors in neural injury induced by electrical stimulation," IEEE Trans. Biomed. Eng., Vol. 37, No. 10, 996-1001, Oct. 1990.
doi:10.1109/10.102812

51. Pudenz, R. H., L. A. Bullara, S. Jacques, and F. T. Hambrecht, "Electrical stimulation of the brain. III. The neural damage model," Surg. Neurol., Vol. 4, No. 4, 389-400, Oct. 1975.

Dr. Xin-Tai Zhao

Dr. Zhi-Gong Wang

Dr. Xiao-Ying Lv