Journal of Computational Neuroscience

, Volume 29, Issue 3, pp 423–444 | Cite as

Intrinsic dendritic filtering gives low-pass power spectra of local field potentials

  • Henrik Lindén
  • Klas H. Pettersen
  • Gaute T. Einevoll
Article

Abstract

The local field potential (LFP) is among the most important experimental measures when probing neural population activity, but a proper understanding of the link between the underlying neural activity and the LFP signal is still missing. Here we investigate this link by mathematical modeling of contributions to the LFP from a single layer-5 pyramidal neuron and a single layer-4 stellate neuron receiving synaptic input. An intrinsic dendritic low-pass filtering effect of the LFP signal, previously demonstrated for extracellular signatures of action potentials, is seen to strongly affect the LFP power spectra, even for frequencies as low as 10 Hz for the example pyramidal neuron. Further, the LFP signal is found to depend sensitively on both the recording position and the position of the synaptic input: the LFP power spectra recorded close to the active synapse are typically found to be less low-pass filtered than spectra recorded further away. Some recording positions display striking band-pass characteristics of the LFP. The frequency dependence of the properties of the current dipole moment set up by the synaptic input current is found to qualitatively account for several salient features of the observed LFP. Two approximate schemes for calculating the LFP, the dipole approximation and the two-monopole approximation, are tested and found to be potentially useful for translating results from large-scale neural network models into predictions for results from electroencephalographic (EEG) or electrocorticographic (ECoG) recordings.

Keywords

Local field potential Single neuron Forward modeling Frequency dependence EEG 

References

  1. Arieli, A. (1992). Novel strategies to unravel mechanisms of cortical function: From macro- to micro-electrophysiological recordings. In A. Aertsen, & V. Braitenberg (Eds.), Information processing in the cortex. New York: Springer.Google Scholar
  2. Bedard, C., Kröger H., & Destexhe A. (2004). Modeling extracellular field potentials and the frequency-filtering properties of extracellular space. Biophysical Journal, 86, 1829–1842.CrossRefPubMedGoogle Scholar
  3. Bedard, C., Kröger, H., & Destexhe, A. (2006a). Model of low-pass filtering of local field potentials. Physical Review E, 73, 051911.CrossRefGoogle Scholar
  4. Bedard, C., Kröger, H., & Destexhe, A. (2006b). Does the 1/f frequency scaling of brain signals reflect self-organized critical states? Physical Review Letters, 97, 118102.CrossRefPubMedGoogle Scholar
  5. Bedard, C., & Destexhe, A. (2009) Macroscopic models of local field potentials and the apparent 1/f noise in brain activity. Biophysical Journal, 96, 2589–2603.CrossRefPubMedGoogle Scholar
  6. Beggs, J. M., & Plenz, D. (2003). Neuronal avalanches in neocortical circuits. Journal of Neuroscience, 23, 11167–11177.PubMedGoogle Scholar
  7. Berens, P., Keliris, G. A., Ecker, A. S., Logothetis, N., & Tolias, A. S. (2008). Comparing the feature selectivity of the gamma-band of the local field potential and the underlying spiking activity in primate visual cortex. Frontiers in Systems Neuroscience, 2(2). doi:10.3389/neuro.06/002.2008.PubMedGoogle Scholar
  8. Buzsáki, G. (2004). Large-scale recording of neuronal ensembles. Nature Neuroscience, 7, 446–451.CrossRefPubMedGoogle Scholar
  9. Buzsáki, G. (2006). Rhythms of the brain. New York: Oxford University Press.CrossRefGoogle Scholar
  10. Carnevale, N. T., & Hines, M. L. (2006). The NEURON book. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
  11. Church, P., Leduc, A., & Beique, R. A. (1985). Sensitivity analysis of depth EEG electrodes to dipolar electric sources. IEEE Transactions on Biomedical Engineering, 32, 554–560.CrossRefPubMedGoogle Scholar
  12. Coombes, S. (2005). Waves, bumps, and patterns in neural field theories. Biological Cybernetics, 93, 91–108.CrossRefPubMedGoogle Scholar
  13. Di, S., Baumgartner, C., & Barth, D. S., (1990). Laminar analysis of extracellular field potentials in rat vibrissa/barrel cortex. Journal of Neurophysiology, 63, 832–840.PubMedGoogle Scholar
  14. Einevoll, G. T., Pettersen, K. H., Devor, A., Ulbert, I., Halgren, E., & Dale, A. M. (2007). Laminar population analysis: Estimating firing rates and evoked synaptic activity from multielectrode recordings in rat barrel cortex. Journal of Neurophysiology, 97, 2174–2190.CrossRefPubMedGoogle Scholar
  15. Freeman, W. J. (1980). Use of spatial deconvolution to compensate distortion of EEG by volume conduction. IEEE Transactions on Biomedical Engineering, 27, 421–429.CrossRefPubMedGoogle Scholar
  16. Freeman, W. J., Holmes, M. D., Burke, B. C., & Vanthalo, S. (2003). Spatial spectra of scalp EEG and EMB from awake humans. Clinical Neurophysiology, 114, 1053–1068.CrossRefPubMedGoogle Scholar
  17. Gabriel, S., Lau, R. W., & Gabriel, C. (1996). The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. Physics in Medicine & Biology, 41, 2271–2293.CrossRefGoogle Scholar
  18. Godey, B., Schwartz, D., de Graaf, J. B., Chauvel, P., & Liegeois-Chauvel, C. (2001). Neuromagnetic source localization of auditory evoked fields and intracerebral evoked potentials: A comparison of data in the same patients. Clinical neurophysiology, 112, 1850–1859.CrossRefPubMedGoogle Scholar
  19. Grech, R., Cassar, T., Muscat, J., Camilleri, K. P., Fabri, S. G., Zervakis, M., et al. (2008). Review on solving the inverse problem in EEG source analysis. Journal of Neuroengineering and Rehabilitation 5, 25.CrossRefPubMedGoogle Scholar
  20. Hämäläinen, M., Hari, R., Ilmoniemi, R. J., Knuutila, J., & Lounasmaa, O. V. (1993). Magnetoencephalography theory, instrumentation, and applications to noninvasive studies of the working human brain. Reviews of Modern Physics, 65, 413–449.CrossRefGoogle Scholar
  21. Hines, M. L, Davison, A. P. & Muller E. (2009). NEURON and Python. Frontiers in Neuroinformatics, 3, 1.CrossRefPubMedGoogle Scholar
  22. Holt, G. R. & Koch, C. (1999). Electrical interactions via the extracellular potential near cell bodies. Journal of Computational Neuroscience, 6, 169–184.CrossRefPubMedGoogle Scholar
  23. Jackson, J. (1998). Classical Electrodynamics. NJ: Wiley, Hoboken.Google Scholar
  24. Jirsa, V. K., & Haken, H. (1997). A derivation of a macroscopic field theory of the brain from the quasi-microscopic neural dynamics. Physica D, 99, 503–526.CrossRefGoogle Scholar
  25. Jirsa, V. K., Jantzen, K. J., Fuchs, A., & Kelso, J. A. S. (2002). Spatiotemporal forward solution of the EEG and MEG using network modeling. IEEE Transactions on Medical Imaging, 21, 493–504.CrossRefPubMedGoogle Scholar
  26. Johnston, D., & Wu, S. M.-S. (1995) Foundations of cellular neurophysiology, (Chapter 14). Cambridge, MA: MIT Press.Google Scholar
  27. Katzner, S., Nauhaus, I., Benucci, A., Bonin, V., Ringach, D. L., & Carandini, M. (2009). Local origin of field potentials in visual cortex. Neuron, 61, 35–41.CrossRefPubMedGoogle Scholar
  28. Koch, C. (1998). Biophysics of computation. New York, NY: Oxford.Google Scholar
  29. Kreiman, G., Hung, C. P, Kraskov, A., Quiroga, R. Q., Poggio, T., & DiCarlo, J. J. (2006). Object selectivity of local field potentials and spikes in the macaque inferior temporal cortex. Neuron, 49, 433–445.CrossRefPubMedGoogle Scholar
  30. Lindén, H., Pettersen, K. H., & Einevoll, G. T. (2008). Frequency scaling in local field potentials: A neuron population forward modelling study Frontiers in Neuroinformatics. Conference Abstract: Neuroinformatics, 2008. doi:10.3389/conf.neuro.11.2008.01.026.Google Scholar
  31. Lindén, H., Pettersen, K. H., Tetzlaff, T., Potjans, T., Denker, M., Diesmann, M., et al. (2009a). Estimating the spatial range of local field potentials in a cortical population model. BMC Neuroscience, 10(1), 224.CrossRefGoogle Scholar
  32. Lindén, H., Potjans, T. C., Einevoll, G. T., Grün, S., & Diesmann, M. (2009b). Modeling the local field potential by a large-scale layered cortical network model. Frontiers in Neuroinformatics, Conference Abstract: 2nd INCF Congress of Neuroinformatics. doi:10.3389/conf.neuro.11.2009.08.046.
  33. Liu, J., & Newsome, W. T. (2006). Local field potential in cortical area MT. Stimulus tuning and behavioral correlations. Journal of Neuroscience, 26, 7779–7790.CrossRefPubMedGoogle Scholar
  34. 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.CrossRefPubMedGoogle Scholar
  35. Lorente de Nó, R. (1947). Action potential of the motoneurons of the hypoglossus nucleus. Journal of Cellular and Comparative Physiology, 29, 207–287.CrossRefGoogle Scholar
  36. Mainen, Z. F., & Sejnowski, T. J. (1996). Influence of dendritic structure on firing pattern in model neocortical neurons. Nature, 382, 363–366.CrossRefPubMedGoogle Scholar
  37. Mazzoni, A., Panzeri, S., Logothetis, N. K., & Brunel, N. (2008). Encoding of naturalistic stimuli by local field potential spectra in networks of excitatory and inhibitory neurons. PLoS Computers in Biology, 4, e1000239.CrossRefGoogle Scholar
  38. Miller, K. J., Sorensen, L. B., Ojemann, J. G., & den Nijs, M. (2009). Power-law scaling in the brain surface electric potential. PLoS Computers in Biology, 5, e1000609.CrossRefGoogle Scholar
  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.CrossRefPubMedGoogle Scholar
  40. Milstein, J., Mormann, F., Fried, I., & Koch., C (2009). Neuronal shot noise and Brownian 1/f2 behavior in the local field potential. PLoS ONE, 4, e4338.CrossRefGoogle Scholar
  41. Mitzdorf, U. (1985). Current source-density method and application in cat cerebral cortex: Investigation of evoked potentials and EEG phenomena. Physiological Reviews, 65, 37–99.PubMedGoogle Scholar
  42. Murakami, S., & Okada, Y. (2006). Contributions of principal neocortical neurons to magnetoencephalography and electroencephalography signals. Journal of Physiology, 575, 925–936.CrossRefPubMedGoogle Scholar
  43. Nauhaus, I., Busse, L., Carandini, M., & Ringach, D. L. (2009). Stimulus contrast modulates functional connectivity in visual cortex. Nature Neuroscience, 12, 70–76.CrossRefPubMedGoogle Scholar
  44. Nicholson, C., & Freeman, J. A. (1975). Theory of current source-density analysis and determination of conductivity tensor for anuran cerebellum. Journal of Neurophysiology, 38, 356–368.PubMedGoogle Scholar
  45. Normann, R. A., Maynard, E. M., Rousche, P. J., & Warren, D. J. (1999). A neural interface for a cortical vision prosthesis. Vision Research, 39, 2577–2587.CrossRefPubMedGoogle Scholar
  46. Nunez, P. L., & Srinavasan, R. (2006). Electric fields of the brain: The neurophysics of EEG. Oxford: Oxford University Press.CrossRefGoogle Scholar
  47. Pettersen, K. H., & Einevoll, G. T. (2008). Amplitude variability and extracellular low-pass filtering of neuronal spikes. Biophysical Journal, 94, 784–802.CrossRefPubMedGoogle Scholar
  48. Pettersen, K. H., Hagen, E., & Einevoll, G. T. (2008). Estimation of population firing rates and current source densities from laminar electrode recordings. Journal of Computational Neuroscience, 24, 291–313.CrossRefPubMedGoogle Scholar
  49. Pettersen, K. H., Lindén, H., Dale, A. M., & Einevoll, G. T. (2010). Extracellular spikes and current-source density. In R. Brette, & A. Destexhe (Eds.), Handbook of neural activity measurements. Cambridge, UK: Cambridge University Press.Google Scholar
  50. Plonsey, R. (1969). Bioelectric phenomena. New York: McGraw-Hill.Google Scholar
  51. Plonsey, R., & Barr, R. C. (2007). Bioelectricity: A quantitative approach. New York: Springer.Google Scholar
  52. Pritchard, W. S. (1992). The brain in fractal time: 1/f-like power spectrum scaling of the human electroencephalogram. International Journal of Neuroscience, 66, 119–129.CrossRefPubMedGoogle Scholar
  53. Rall, W. (1962). Electrophysiology of a dendritic neuron model. Biophysical Journal, 2, 145–167.CrossRefPubMedGoogle Scholar
  54. Xing, D., Yeh, C.-I., & Shapley, R. M. (2009). Spatial spread of the local field potential and its laminar variation in visual cortex. Journal of Neuroscience, 29, 11540–11549.CrossRefPubMedGoogle Scholar
  55. Yvert, B., Fischer, C., Bertrand, O., & Pernier, J. (2001). Localization of human supratemporal auditory areas from intracerebral auditory evoked potentials using distributed source models. NeuroImage, 28, 140–153.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Henrik Lindén
    • 1
  • Klas H. Pettersen
    • 1
  • Gaute T. Einevoll
    • 1
    • 2
  1. 1.Department of Mathematical Sciences and TechnologyNorwegian University of Life SciencesÅsNorway
  2. 2.Center for Integrative GeneticsNorwegian University of Life SciencesÅsNorway

Personalised recommendations