Skip to main content
SpringerLink
Log in

Three-dimensional interpolation methods to spatiotemporal EEG mapping during various behavioral states

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

This work applies a novel method called multiquadratic interpolation that represents a 3D brain activity following a spatiotemporal mode. It also develops other classical interpolation techniques (barycentric, spline), which are based on the calculation of the Euclidean distance between the estimated and measured electrodes. Then, it modifies these methods by substituting the Euclidean distance by the corresponding arc length. Starting from 19 real electrodes for generating the electroencephalogram (EEG) potential representations of healthy subjects having three different behavioral brain states, a 3D EEG mapping of 128 electrodes was obtained. The proposed multiquadratic interpolation is evaluated by comparing it with the other methods by calculating the root mean squared error and processing time means.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Abdoun, O., Joucla, S., Mazzocco, C., Yvert, B.: NeuroMap: a spline-based interactive open-source software for spatiotemporal mapping of 2D and 3D MEA data. Front. Neuroinform. 4, 119 (2011)

    Article  Google Scholar 

  2. Fletcher, E.M., Kussmaul, C.L., Mangun, G.R.: Estimation of interpolation errors in scalp topographic mapping. Electroencephalogr. Clin. Neurophysiol. 98, 422–434 (1996)

  3. Onaran, I., Ince, N.F., Cetin, A.E.: Sparse spatial filter via a novel objective function minimization with smooth \(l_{1}\) regularization. Biomed. Signal Process. Control 8, 282–288 (2013)

    Article  Google Scholar 

  4. Duffy, F.H., Bartels, P.H., Burchfiel, J.L.: Significance probability mapping: an aid in the topographic analysis of brain electrical activity. Electroencephalogr. Clin. Neurophysiol. 51, 455–462 (1981)

    Article  Google Scholar 

  5. Ashida, H., Tatsuno, J., Okamoto, J., Maru, E.: Field mapping of EEG by unbiased polynomial interpolation. J. Biomed. Inform. 17, 267–276 (1984)

    Google Scholar 

  6. Perrin, F., Pernier, J., Bertrand, O., Giard, M.H., Echallier, J.F.: Mapping of scalp potentials by surface spline interpolation. Electroencephalogr. Clin. Neurophysiol. 66, 75–81 (1987)

    Article  Google Scholar 

  7. Perrin, F., Pernier, J., Bertrand, O., Echallier, J.F.: Spherical splines for scalp potential and current density mapping. Electroencephalogr. Clin. Neurophysiol. 72, 184–187 (1989)

    Article  Google Scholar 

  8. Soufflet, L., Toussaint, M., Luthringer, R., Gresser, j, Minot, R., Macher, J.P.: A statistical evaluation of the main interpolation methods applied to 3-dimensional EEG mapping. Electroencephalogr. Clin. Neurophysiol. 79, 393–402 (1991)

    Article  Google Scholar 

  9. Srinivasan, R., Nunez, P.L., Tucker, D.M., Silberstein, R.B., Caducsh, P.J.: Spatial sampling and filtering of EEG with spline Laplacians to estimate cortical potentials. Brain Topogr. 8, 355–366 (1996)

    Article  Google Scholar 

  10. Ferree, T.C.: Spherical splines and average referencing in scalp electroencephalography. Brain Topogr. 19, 43–52 (2006)

    Article  Google Scholar 

  11. Brunet, D., Murray, M.M., Michel, C.M.: Spatiotemporal analysis of multichannel EEG: CARTOOL. Comput. Intell. Neurosci. 2011 (2011). doi:10.1155/2011/813870

  12. Lagarias, J.C., Reeds, J.A., Wright, M.H., Wright, P.E.: Convergence properties of the Nelder–Mead simplex method in low dimensions. SIAM J. Control Optim. 9, 112–147 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  13. Law, S.K., Nunez, P.L., Wijesinghe, R.S.: High-resolution EEG using spline generated surface Laplacians on spherical and ellipsoidal surfaces. IEEE Trans. Bio-Med. Eng. 40, 145–153 (1993)

    Article  Google Scholar 

  14. Ferree, T.C.: Spline Interpolation of the Scalp EEG. Electrical Geodesics, Inc.,Technical Note(2000)

  15. Yvert, B., Crouzeix-Cheylus, A., Jacques, P.: Fast realistic modeling in bioelectromagnetism using lead-field interpolation. Hum. Brain. Mapp. 14, 48–63 (2001)

    Article  Google Scholar 

  16. Franke, R., Neilson, G.: Scattered data interpolation and applications: a tutorial and survey. In: Hagen, H., Roller, D. (eds.) Geometric Modelling: Methods and Their Applications, pp. 131–160. Springer, Berlin (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. TIM Laboratory, Medicine Faculty of Monastir, 5019, Monastir, Tunisia

    Ibtihel Nouira, Asma Ben Abdallah & Mohamed Hedi Bedoui

Authors
  1. Ibtihel Nouira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Asma Ben Abdallah
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohamed Hedi Bedoui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ibtihel Nouira.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nouira, I., Abdallah, A.B. & Bedoui, M.H. Three-dimensional interpolation methods to spatiotemporal EEG mapping during various behavioral states. SIViP 10, 943–949 (2016). https://doi.org/10.1007/s11760-015-0844-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-015-0844-7

Keywords

Search

Navigation