Journal of Computational Neuroscience

, Volume 32, Issue 1, pp 73–100 | Cite as

Dipole characterization of single neurons from their extracellular action potentials

  • Ferenc MechlerEmail author
  • Jonathan D. Victor


The spatial variation of the extracellular action potentials (EAP) of a single neuron contains information about the size and location of the dominant current source of its action potential generator, which is typically in the vicinity of the soma. Using this dependence in reverse in a three-component realistic probe + brain + source model, we solved the inverse problem of characterizing the equivalent current source of an isolated neuron from the EAP data sampled by an extracellular probe at multiple independent recording locations. We used a dipole for the model source because there is extensive evidence it accurately captures the spatial roll-off of the EAP amplitude, and because, as we show, dipole localization, beyond a minimum cell-probe distance, is a more accurate alternative to approaches based on monopole source models. Dipole characterization is separable into a linear dipole moment optimization where the dipole location is fixed, and a second, nonlinear, global optimization of the source location. We solved the linear optimization on a discrete grid via the lead fields of the probe, which can be calculated for any realistic probe + brain model by the finite element method. The global source location was optimized by means of Tikhonov regularization that jointly minimizes model error and dipole size. The particular strategy chosen reflects the fact that the dipole model is used in the near field, in contrast to the typical prior applications of dipole models to EKG and EEG source analysis. We applied dipole localization to data collected with stepped tetrodes whose detailed geometry was measured via scanning electron microscopy. The optimal dipole could account for 96% of the power in the spatial variation of the EAP amplitude. Among various model error contributions to the residual, we address especially the error in probe geometry, and the extent to which it biases estimates of dipole parameters. This dipole characterization method can be applied to any recording technique that has the capabilities of taking multiple independent measurements of the same single units.


Multisite recording Inverse problem Passive conductor model Lead field theory Finite element method (FEM) 



This work was supported by NIH grant EY9314 (JDV, FM).

We thank Qin Hu, Ifije Ohiorhenuan, Mike Repucci and Anita Schmid for their help in the data collection; Dirk Hoehl and Thomas Recording Gmbh for their consistently reliable tetrodes; Dr Stephen B. Doty and Tony Labassiere of Analytical Microscopy Core Facility, Hospital for Special Surgery New York, NY, for the scanning electron-microscopy; and Drs Partha Mitra and Alexander Polyakov for stimulating early discussions and introducing the use of Femlab.

Supplementary material

10827_2011_341_MOESM1_ESM.pdf (124 kb)
ESM 1 (PDF 124 kb)
10827_2011_341_MOESM2_ESM.pdf (108 kb)
ESM 2 (PDF 108 kb)


  1. Ainsworth, A., Dostrovsky, J. O., Merrill, E. G., & Millar, J. (1977). An improved method for insulating tungsten micro-electrodes with glass [proceedings]. Journal of Physiology, London, 269, 4P–5P.Google Scholar
  2. Aur, D., & Jog, M. S. (2006). Building spike representation in tetrodes. Journal of Neuroscience Methods, 157, 364–373.PubMedCrossRefGoogle Scholar
  3. Aur, D., Connolly, C. I., & Jog, M. S. (2005). Computing spike directivity with tetrodes. Journal of Neuroscience Methods, 149, 57–63.PubMedCrossRefGoogle Scholar
  4. Bartho, P., Hirase, H., Monconduit, L., Zugaro, M., Harris, K. D., & Buzsaki, G. (2004). Characterization of neocortical principal cells and interneurons by network interactions and extracellular features. Journal of Neurophysiology, 92, 600–608.PubMedCrossRefGoogle Scholar
  5. Bédard, C., & Destexhe, A. (2009). Macroscopic models of local field potentials and the apparent 1/f noise in brain activity. Biophysical Journal, 96, 2589–2603.PubMedCrossRefGoogle Scholar
  6. Bédard, C., Kroger, H., & Destexhe, A. (2004). Modeling extracellular field potentials and the frequency-filtering properties of extracellular space. Biophysical Journal, 86, 1829–1842.PubMedCrossRefGoogle Scholar
  7. Bédard, C., Kroger, H., & Destexhe, A. (2006). Model of low-pass filtering of local field potentials in brain tissue. Physical Review. E: Statistical, Nonlinear, and Soft Matter Physics, 73, 051911.CrossRefGoogle Scholar
  8. Blanche, T. J., Spacek, M. A., Hetke, J. F., & Swindale, N. V. (2005). Polytrodes: High-density silicon electrode arrays for large-scale multiunit recording. Journal of Neurophysiology, 93, 2987–3000.PubMedCrossRefGoogle Scholar
  9. Blanche, T. J., Hetherington, P. A., Rennie, C. J., Spacek, M. A., Swindale, N. V. (2003). Model-based 3d cortical neuron localization and classification with silicon electrode arrays. 2003 Abstract Viewer/Itinerary Planner Washington, DC: Society for Neuroscience, 2003 Online: Program No. 429.419Google Scholar
  10. Butson, C. R., & McIntyre, C. C. (2006). Role of electrode design on the volume of tissue activated during deep brain stimulation. Journal of Neural Engineering, 3, 1–8.PubMedCrossRefGoogle Scholar
  11. Buzsaki, G. (2004). Large-scale recording of neuronal ensembles. Nature Neuroscience, 7, 446–451.PubMedCrossRefGoogle Scholar
  12. Buzsaki, G., & Kandel, A. (1998). Somadendritic backpropagation of action potentials in cortical pyramidal cells of the awake rat. Journal of Neurophysiology, 79, 1587–1591.PubMedGoogle Scholar
  13. Chelaru, M. I., & Jog, M. S. (2005). Spike source localization with tetrodes. Journal of Neuroscience Methods, 142, 305–315.PubMedCrossRefGoogle Scholar
  14. Cohen, I., & Miles, R. (2000). Contributions of intrinsic and synaptic activities to the generation of neuronal discharges in in vitro hippocampus. Journal of Physiology, London, 524(Pt 2), 485–502.CrossRefGoogle Scholar
  15. Csicsvari, J., Henze, D. A., Jamieson, B., Harris, K. D., Sirota, A., Bartho, P., et al. (2003). Massively parallel recording of unit and local field potentials with silicon-based electrodes. Journal of Neurophysiology, 90, 1314–1323.PubMedCrossRefGoogle Scholar
  16. Destexhe, A., Contreras, D., & Steriade, M. (1999). Spatiotemporal analysis of local field potentials and unit discharges in cat cerebral cortex during natural wake and sleep states. The Journal of Neuroscience, 19, 4595–4608.PubMedGoogle Scholar
  17. Drake, K. L., Wise, K. D., Farraye, J., Anderson, D. J., & Bement, S. L. (1988). Performance of planar multisite microprobes in recording extracellular single-unit Intracortical activity. IEEE Transactions on Biomedical Engineering, 35, 719–732.PubMedCrossRefGoogle Scholar
  18. Du, J., Riedel-Kruse, I. H., Nawroth, J. C., Roukes, M. L., Laurent, G., & Masmanidis, S. C. (2009). High-resolution three-dimensional extracellular recording of neuronal activity with microfabricated electrode arrays. Journal of Neurophysiology, 101, 1671–1678.PubMedCrossRefGoogle Scholar
  19. Gabriel, S., Lau, R. W., & Gabriel, C. (1996). The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. Physics in Medicine and Biology, 41, 2251.PubMedCrossRefGoogle Scholar
  20. Gerstein, G. L., & Clark, W. A. (1964). Simultaneous studies of firing patterns in several neurons. Science, 143, 1325–1327.CrossRefGoogle Scholar
  21. Gold, C., Henze, D. A., & Koch, C. (2007). Using extracellular action potential recordings to constrain compartmental models. Journal of Computational Neuroscience, 23, 39–58.PubMedCrossRefGoogle Scholar
  22. Gold, C., Henze, D. A., Koch, C., & Buzsaki, G. (2006). On the origin of the extracellular action potential waveform: A modeling study. Journal of Neurophysiology, 95, 3113–3128.PubMedCrossRefGoogle Scholar
  23. Gray, C. M., Maldonado, P. E., Wilson, M., & McNaughton, B. (1995). Tetrodes markedly improve the reliability and yield of multiple single-unit isolation from multi-unit recordings in cat striate cortex. Journal of Neuroscience Methods, 63, 43–54.PubMedCrossRefGoogle Scholar
  24. Hansen, P. C., & Oleary, D. P. (1993). The use of the L-curve in the regularization of discrete ill-posed problems. SIAM Journal of Scientific Computing, 14, 1487–1503.CrossRefGoogle Scholar
  25. Helmholtz H (1853a) Ueber einige Gesetze der Vertheilung electrischer Stroeme in Koerperlichen Leitern mit Anwendung auf die thierisch-elektrischen Versuche (I).,". Ann der Phys und Chemie (Leipzig, 3rd ser) 89:211–233Google Scholar
  26. Helmholtz H (1853b) Ueber einige Gesetze der Vertheilung electrischer Stroeme in Koerperlichen Leitern mit Anwendung auf die thierisch-elektrischen Versuche (II),". Ann der Phys und Chemie (Leipzig, 3rd ser) 89:353–377Google Scholar
  27. Henze, D. A., Borhegyi, Z., Csicsvari, J., Mamiya, A., Harris, K. D., & Buzsaki, G. (2000). Intracellular features predicted by extracellular recordings in the hippocampus in vivo. Journal of Neurophysiology, 84, 390–400.PubMedGoogle Scholar
  28. Hubel, D. H. (1957). Tungsten microelectrode for recording from single units. Science, 125, 549–550.PubMedCrossRefGoogle Scholar
  29. Jog, M. S., Connolly, C. I., Kubota, Y., Iyengar, D. R., Garrido, L., Harlan, R., et al. (2002). Tetrode technology: Advances in implantable hardware, neuroimaging, and data analysis techniques. Journal of Neuroscience Methods, 117, 141–152.PubMedCrossRefGoogle Scholar
  30. Lee, C. W., Dang, H., & Nenadic, Z. (2007). An efficient algorithm for current source localization with tetrodes. Conference Proceedings of the IEEE Engineering in Medicine and Biology Society, 2007, 1282–1285.Google Scholar
  31. Li, C. L., Bak, A. F., & Parker, L. O. (1968). Specific resistivity of the cerebral cortex and white matter. Experimental Neurology, 20, 544–557.PubMedCrossRefGoogle Scholar
  32. Logothetis, N. K., Kayser, C., & Oeltermann, A. (2007). In Vivo measurement of cortical impedance spectrum in monkeys: Implications for signal propagation. Neuron, 55, 809–823.PubMedCrossRefGoogle Scholar
  33. Lopez-Aguado, L., Ibarz, J. M., & Herreras, O. (2001). Activity-dependent changes of tissue resistivity in the CA1 region in vivo are layer-specific: Modulation of evoked potentials. Neuroscience, 108, 249–262.PubMedCrossRefGoogle Scholar
  34. Maldonado, P. E., Godecke, I., Gray, C. M., & Bonhoeffer, T. (1997). Orientation selectivity in pinwheel centers in cat striate cortex. Science, 276, 1551–1555.PubMedCrossRefGoogle Scholar
  35. Malmivuo, J., & Plonsey, R. (1995). Bioelectromagnetism. New York: Oxford University Press.Google Scholar
  36. McIntyre, C. C., Grill, W. M., Sherman, D. L., & Thakor, N. V. (2004). Cellular effects of deep brain stimulation: Model-based analysis of activation and inhibition. Journal of Neurophysiology, 91, 1457–1469.PubMedCrossRefGoogle Scholar
  37. McNaughton, B. L., O'Keefe, J., & Barnes, C. A. (1983). The stereotrode: A new technique for simultaneous isolation of several single units in the central nervous system from multiple unit records. Journal of Neuroscience Methods, 8, 391–397.PubMedCrossRefGoogle Scholar
  38. Mechler, F., Hu, Q., Ohiorhenuan, I. E., Schmid, A. M., Victor, J. D. (2011). Three-dimensional localization of neurons in cortical tetrode recordings. J Neurophysiol. doi: 10.1152/jn.00515.2010.
  39. Milstein, J. N., & Koch, C. (2008). Dynamic moment analysis of the extracellular electric field of a biologically realistic spiking neuron. Neural Computation, 20, 2070–2084.PubMedCrossRefGoogle Scholar
  40. Mitzdorf, U. (1985). Current source-density method and application in cat cerebral cortex: Investigation of evoked potentials and EEG phenomena. Physiological Reviews, 65, 37–100.PubMedGoogle Scholar
  41. Moffitt, M. A., & McIntyre, C. C. (2005). Model-based analysis of cortical recording with silicon microelectrodes. Clinical Neurophysiology, 116, 2240–2250.PubMedCrossRefGoogle Scholar
  42. Musial, P. G., Baker, S. N., Gerstein, G. L., King, E. A., & Keating, J. G. (2002). Signal-to-noise ratio improvement in multiple electrode recording. Journal of Neuroscience Methods, 115, 29–43.PubMedCrossRefGoogle Scholar
  43. Nordhausen, C. T., Maynard, E. M., & Normann, R. A. (1996). Single unit recording capabilities of a 100 microelectrode array. Brain Research, 726, 129–140.PubMedCrossRefGoogle Scholar
  44. Pettersen, K. H., & Einevoll, G. T. (2008). Amplitude variability and extracellular low-pass filtering of neuronal spikes. Biophysical Journal, 94, 784–802.PubMedCrossRefGoogle Scholar
  45. Plonsey, R. (1963). Reciprocity applied to volume conductors and Ecg. IEEE Transactions on Biomedical Engineering, 10, 9–12.PubMedGoogle Scholar
  46. Plonsey, R., & Heppner, D. B. (1967). Considerations of quasi-stationarity in electrophysiological systems. The Bulletin of Mathematical Biophysics, 29, 657–664.PubMedCrossRefGoogle Scholar
  47. Rall, W. (1962). Electrophysiology of a dendritic neuron model. Biophysical Journal, 2, 145–167.PubMedCrossRefGoogle Scholar
  48. Ranck, J. B., Jr. (1963). Specific impedance of rabbit cerebral cortex. Experimental Neurology, 7, 144–152.PubMedCrossRefGoogle Scholar
  49. Robinson, D. A. (1968). Electrical properties of metal microelectrodes. Proceedings of Institute of Electrical and Electronics Engineers, 56, 1065–1071.Google Scholar
  50. Rosenthal, F., Woodbury, J. W., & Patton, H. D. (1966). Dipole characteristics of pyramidal cell activity in cat postcruciate cortex. Journal of Neurophysiology, 29, 612–625.PubMedGoogle Scholar
  51. Sholl, D. A. (1953). Dendritic organization in the neurons of the visual and motor cortices of the cat. Journal of Anatomy, 87, 387–406.PubMedGoogle Scholar
  52. Somogyvari, Z., Zalanyi, L., Ulbert, I., & Erdi, P. (2005). Model-based source localization of extracellular action potentials. Journal of Neuroscience Methods, 147, 126–137.PubMedCrossRefGoogle Scholar
  53. Tikhonov, A. N., & Arsenin, V. Y. (1977). Solutions of ill-posed problems. Washington: Winston & Sons.Google Scholar
  54. Vigmond, E. J., Perez Velazquez, J. L., Valiante, T. A., Bardakjian, B. L., & Carlen, P. L. (1997). Mechanisms of electrical coupling between pyramidal cells. Journal of Neurophysiology, 78, 3107–3116.PubMedGoogle Scholar
  55. Wei, X. F., & Grill, W. M. (2005). Current density distributions, field distributions and impedance analysis of segmented deep brain stimulation electrodes. Journal of Neural Engineering, 2, 139–147.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Neurology and NeuroscienceMedical College of Cornell UniversityNew YorkUSA

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