, Volume 5, Issue 4, pp 207–222 | Cite as

Inverse Current-Source Density Method in 3D: Reconstruction Fidelity, Boundary Effects, and Influence of Distant Sources

  • Szymon ŁęskiEmail author
  • Daniel K. Wójcik
  • Joanna Tereszczuk
  • Daniel A. Świejkowski
  • Ewa Kublik
  • Andrzej Wróbel


Estimation of the continuous current-source density in bulk tissue from a finite set of electrode measurements is a daunting task. Here we present a methodology which allows such a reconstruction by generalizing the one-dimensional inverse CSD method. The idea is to assume a particular plausible form of CSD within a class described by a number of parameters which can be estimated from available data, for example a set of cubic splines in 3D spanned on a fixed grid of the same size as the set of measurements. To avoid specificity of particular choice of reconstruction grid we add random jitter to the points positions and show that it leads to a correct reconstruction. We propose different ways of improving the quality of reconstruction which take into account the sources located outside the recording region through appropriate boundary treatment. The efficiency of the traditional CSD and variants of inverse CSD methods is compared using several fidelity measures on different test data to investigate when one of the methods is superior to the others. The methods are illustrated with reconstructions of CSD from potentials evoked by stimulation of a bunch of whiskers recorded in a slab of the rat forebrain on a grid of 4×5×7 positions.


Current source density Local field potentials Evoked potentials Inverse problems Rat Thalamus Somatosensory system 

Anatomical Abbreviations


anterior pretectal nucleus


cerebral peduncle




internal capsule


medial geniculate nucleus


medial lemniscus


posterior thalamic nuclear group


reticular thalamic nucleus


substantia nigra


ventral posteromedial thalamic nucleus


zona incerta



We are grateful to Wit Jakuczun for his suggestion to investigate spatial jittering as one way to improve the CSD reconstruction. This work was partly financed from the Polish Ministry of Science and Higher Education research grants N401 146 31/3239 and 2P04C 046 27.


  1. Freeman, J. A., & Nicholson, C. (1975). Experimental optimization of current source-density technique for anuran cerebellum. Journal of Neurophysiology, 38, 369–382.PubMedGoogle Scholar
  2. 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, 413–497.CrossRefGoogle Scholar
  3. Kublik, E., Świejkowski, D. A., & Wróbel, A. (2003). Cortical contribution to sensory volleys recorded at thalamic nuclei of lemniscal and paralemniscal pathways. Acta Neurobiologiae Experimentalis (Wars), 63, 377–382.Google Scholar
  4. Lin, B., Colgin, L. L., Brücher, F. A., Arai, A. C., & Lynch, G. (2002). Interactions between recording technique and AMPA receptor modulators. Brain Research, 955, 164–173.PubMedCrossRefGoogle Scholar
  5. Mitzdorf, U. (1985). Current source-density method and application in cat cerebral cortex: Investigation of evoked potentials and eeg phenomena. Physiology Review, 65, 37–100.Google Scholar
  6. 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
  7. Novak, J. L., & Wheeler, B. C. (1989). Two-dimensional current source density analysis of propagation delays for components of epileptiform bursts in rat hippocampal slices. Brain Research, 497, 223–230.PubMedCrossRefGoogle Scholar
  8. Nunez, P. L., & Srinivasan, R. (2005). Electric fields of the brain: The neurophysics of EEG. Oxford University Press.Google Scholar
  9. Paxinos, G., & Watson, C. (1996). The rat brain in stereotaxic coordinates, compact third edition Academic.Google Scholar
  10. Pettersen, K. H. Devor, A., Ulbert, I., Dale, A. M., & Einevoll, G. T. (2006). Current-source density estimation based on inversion of electrostatic forward solution: Effects of finite extent of neuronal activity and conductivity discontinuities. Journal of Neuroscience Methods, 154, 116–133.PubMedCrossRefGoogle Scholar
  11. Plonsey, R., (1969). Bioelectric phenomena. New York: McGraw-Hill Book Company.Google Scholar
  12. Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (1992). Numerical Recipes in C: The art of scientific computing, chapter 3.3 (2nd ed.) (pp. 113–115). Cambridge University Press.Google Scholar
  13. Shimono, K., Brucher, F., Granger, R., Lynch, G., & Taketani, M. (2000). Origins and distribution of cholinergically induced beta rhythms in hippocampal slices. Journal of Neuroscience, 20, 8462–8473.PubMedGoogle Scholar
  14. Sukov, W., & Barth, D. S. (1998). Three-dimensional analysis of spontaneous and thalamically evoked gamma oscillations in auditory cortex. Journal of Neurophysiology, 79, 2875–2884.PubMedGoogle Scholar
  15. Ueno, S., & Sekino, M. (2005). Conductivity tensor MR imaging. Proceedings of the XXVIIIth URSI General Assembly in New Delhi.Google Scholar
  16. Vaknin, G., DiScenna, P. G., & Teyler, T. J.(1988). A method for calculating current source density (CSD) analysis without resorting to recording sites outside the sampling volume. Journal of Neuroscience Methods, 24, 131–135.PubMedCrossRefGoogle Scholar

Copyright information

© Humana Press Inc. 2007

Authors and Affiliations

  • Szymon Łęski
    • 1
    • 2
    Email author
  • Daniel K. Wójcik
    • 2
    • 3
  • Joanna Tereszczuk
    • 4
  • Daniel A. Świejkowski
    • 2
  • Ewa Kublik
    • 2
  • Andrzej Wróbel
    • 2
    • 3
  1. 1.Center for Theoretical PhysicsPolish Academy of SciencesWarsawPoland
  2. 2.Department of Neurophysiology, Nencki Institute of Experimental BiologyPolish Academy of SciencesWarsawPoland
  3. 3.Warsaw School of Social PsychologyWarsawPoland
  4. 4.Faculty of Mathematics and Information ScienceWarsaw University of TechnologyWarsawPoland

Personalised recommendations