Skip to main content

Advertisement

Log in

Spatio-temporal Regularization in Linear Distributed Source Reconstruction from EEG/MEG: A Critical Evaluation

  • Original Paper
  • Published:
Brain Topography Aims and scope Submit manuscript

Abstract

The high temporal resolution of EEG/MEG data offers a way to improve source reconstruction estimates which provide insight into the spatio-temporal involvement of neuronal sources in the human brain. In this work, we investigated the performance of spatio-temporal regularization (STR) in a current density approach using a systematic comparison to simple ad hoc or post hoc filtering of the data or of the reconstructed current density, respectively. For the used STR approach we implemented a frequency-specific constraint to penalize solutions outside a narrow frequency band of interest. The widely used sLORETA algorithm was adapted for STR and generally used for source reconstruction. STR and filtering approaches were evaluated with respect to spatial localization error and spatial dispersion, as well as to correlation of original and reconstructed source time courses in single source and two source scenarios with fixed source locations and oscillating source waveforms. We used extensive computer simulations and tested all algorithms with different parameter settings (noise levels and regularization parameters) for EEG data. To verify our results, we also used data from MEG phantom measurements. For the investigated scenarios, we did not find any evidence that STR-based methods outperform purely spatial algorithms applied to temporally filtered data. Furthermore, the results show very clearly that the performance of STR depends very much on the choice of regularization parameters.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Notes

  1. As for the frequency ranges normally considered in EEG and MEG, the temporal derivatives in the Maxwell equations can be ignored (quasistatic assumption; Plonsey and Heppner 1967), these properties amount to the spatial distribution of the electrical conductivity.

References

  • Ahlfors SP, Simpson GV (2004) Geometrical interpretation of fMRI-guided MEG/EEG inverse estimates. Neuroimage 22(1):323–332

    Article  PubMed  Google Scholar 

  • Akhtari M, Bryant HC, Marnelak AN, Flynn ER, Heller L, Shih JJ, Mandelkern M, Matlachov A, Ranken DM, Best ED, DiMauro MA, Lee RR, Sutherling WW (2002) Conductivities of three-layer live human skull. Brain Topogr 14(3):151–167

    Article  PubMed  CAS  Google Scholar 

  • ANT S.D.G. (2003) filter design tool: xfir. ANT B.V. Advanced Neuro Technology, Enschede, Netherlands

  • Awada KA, Jackson DR, Williams JT, Wilton DR, Baumann SB, Papanicolaou AC (1997) Computational aspects of finite element modeling in EEG source localization. IEEE Trans Biomed Eng 44(8):736–752

    Article  PubMed  CAS  Google Scholar 

  • Baillet S, Garnero L (1997) A Bayesian approach to introducing anatomo-functional priors in the EEG/MEG inverse problem. IEEE Trans Biomed Eng 44(5):12

    Article  Google Scholar 

  • Brooks DH, Ahmad GF, MacLeod RS, Maratos GM (1999) Inverse electrocardiography by simultaneous imposition of multiple constraints. IEEE Trans Biomed Eng 46(1):3–18

    Article  PubMed  CAS  Google Scholar 

  • Buchner H, Knoll G, Fuchs M, Rienacker A, Beckmann R, Wagner M, Silny J, Pesch J (1997) Inverse localization of electric dipole current sources in finite element models of the human head. Electroencephalogr Clin Neurophysiol 102(4):267–278

    Article  PubMed  CAS  Google Scholar 

  • Dale M, Serano MI (1993) Improved localization of cortical activity by combining EEG and MEG with MRI cortical surface reconstruction: a linear approach. J Cogn Neurosci 5(1):15

    Google Scholar 

  • Dale AM, Liu AK, Fischl BR, Buckner RL, Belliveau JW, Lewine JD, Halgren E (2000) Dynamic statistical parametric mapping: combining fMRI and MEG for high-resolution imaging of cortical activity. Neuron 26(1):55–67

    Article  PubMed  CAS  Google Scholar 

  • Dannhauer M, Lanfer B, Wolters CH, Knösche TR (2011) Modeling of the human skull in EEG source analysis. Hum Brain Mapp 32(9):1383–1399

    Article  PubMed  Google Scholar 

  • Darvas F, Schmitt U, Louis AK, Fuchs M, Knoll G, Buchner H (2001) Spatio-temporal current density reconstruction (srCDR) from EEG/MEG-data. Brain Topogr 10(3):13

    Google Scholar 

  • de Munck J, Peters M (1993) A fast method to compute the potential in the multi sphere model. IEEE Trans Biomed Eng 40(11):1166–1174

    Article  PubMed  Google Scholar 

  • de Munck J, van Dijk BW, Spekreijse H (1988) Mathematical dipoles are adequate to describe realistic generators of human brain activity. IEEE Trans Biomed Eng 35(11):960–966

    Article  PubMed  Google Scholar 

  • de Peralta Grave, Menendez R, Murray MM, Andino SLG (2004) Improving the performance of linear inverse solutions by inverting the resolution matrix. IEEE Trans Biomed Eng 51(9):1680–1683

    Article  Google Scholar 

  • Fuchs M, Wagner M, Kohler T, Wischmann HA (1999) Linear and nonlinear current density reconstructions. J Clin Neurophysiol 16(3):267–295

    Article  PubMed  CAS  Google Scholar 

  • Fuchs M, Wagner M, Kastner J (2007) Development of volume conductor and source models to localize epileptic foci. J Clin Neurophysiol 24(2):101–119

    Article  PubMed  Google Scholar 

  • Güllmar D, Haueisen J, Eiselt M, Giessler F, Flemming L, Anwander A, Knösche TR, Wolters CH, Dümpelmann M, Tuch DS, Reichenbach JR (2006) Influence of anisotropic conductivity on EEG source reconstruction: investigations in a rabbit model. IEEE Trans Biomed Eng 53:1841–1850

    Article  PubMed  Google Scholar 

  • Güllmar D, Haueisen J, Reichenbach JR (2010) Influence of anisotropic electrical conductivity in white matter tissue on the EEG/MEG forward and inverse solution. A high-resolution whole head simulation study. Neuroimage 51:145–163

    Article  PubMed  Google Scholar 

  • Hämäläinen MS, Ilmoniemi RJ (1994) Interpreting magnetic fields of the brain: minimum norm estimates. Med Biol Eng Comput 32(1):8

    Article  Google Scholar 

  • Hansen PC, O’Leary DP (1993) The use of the L-curve in the regularization of discrete ill-posed problems. SIAM 14(6):17

    Google Scholar 

  • Huiskamp G, Maintz J, Wieneke G, Viergever M, van Huffelen AC (1997) The influence of the use of realistic head geometry in the dipole localization of interictal spike activity in MTLE patients. Biomed Tech 42:4

    Google Scholar 

  • Huiskamp G, Vroeijenstijn M, van Dijk R, Wieneke G, van Huffelen AC (1999) The need for correct realistic geometry in the inverse EEG problem. IEEE Trans Biomed Eng 46(11):1281–1287

    Article  PubMed  CAS  Google Scholar 

  • Jeffs B, Leahy R, Singh M (1987) An evaluation of methods for neuromagnetic image reconstruction. IEEE Trans Biomed Eng 34(11):713

    Article  PubMed  CAS  Google Scholar 

  • Klimesch W (1999) EEG alpha and theta oscillations reflect cognitive and memory performance: a review and analysis. Brain Res Rev 29:169–195

    Article  PubMed  CAS  Google Scholar 

  • Kybic J, Clerc M, Abboud T, Faugeras O, Keriven R, Papadopoulo T (2005) A common formalism for the integral formulations of the forward EEG problem. IEEE Trans Med Imaging 24(1):12–28

    Article  PubMed  Google Scholar 

  • Lew S, Wolters CH, Anwander A, Makeig S, MacLeod RS (2009) Improved EEG source analysis using low-resolution conductivity estimation in a four-compartment finite element head model. Hum Brain Mapp 30(9):2862–2878

    Article  PubMed  Google Scholar 

  • Liu AK, Belliveau JW, Dale AM (1998) Spatiotemporal imaging of human brain activity using functional MRI constrained magnetoencephalography data: Monte Carlo simulations. Neuroimage 23(14):582

    Google Scholar 

  • Lucka F, Pursiainen S, Burger M, Wolters CH (2011) Hierarchical Bayesian models for EEG inversion: depth localization and source separation for focal sources in realistic FE head models. In: Biomedical engineering, vol 56. De Gruyter, Berlin, pp 939–4990

  • Marin G, Guerin C, Baillet S, Garnero L, Meunier G (1998) Influence of skull anisotropy for the forward and inverse problem in EEG: simulation studies using FEM on realistic head models. Hum Brain Mapp 6(4):250–269

    Article  PubMed  CAS  Google Scholar 

  • Molins A, Stufflebeam SN, Brown EM, Hämäläinen MS (2008) Quantification of the benefit from integrating MEG and EEG data in minimum l(2)-norm estimation. NeuroImage 42(3):1069–1077

    Article  PubMed  CAS  Google Scholar 

  • Pascual-Marqui RD (2002) Standardized low-resolution brain electromagnetic tomography (sLORETA): technical details. Methods Find Exp Clin Pharmacol 24(1):8

    Google Scholar 

  • Pascual-Marqui RD (2007) Discrete, 3D distributed linear imaging methods of electric neuronal activity. Part 1: exact, zero error localization. Technical report: arXiv:0710.3341v2

  • Pascual-Marqui RD, Michel CM, Lehmann D (1994) Low resolution electromagnetic tomography: a new method for localizing electrical activity in the brain. Int J Psychophysiol 18(1):49–65

    Article  PubMed  CAS  Google Scholar 

  • Plonsey R, Heppner DB (1967) Considerations of quasi-stationarity in electrophysiological systems. Bull Math Biophys 29(1):8

    Google Scholar 

  • Ramon C, Schimpf PH, Haueisen J (2006) Influence of head models on EEG simulations and inverse source localizations. Biomed Eng Online 5:10

    Article  PubMed  Google Scholar 

  • Sarvas J (1987) Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem. Phys Med Biol 32(1):11–22

    Article  PubMed  CAS  Google Scholar 

  • Scherg M (1990) Fundamentals of dipole source potential analysis. In: auditory evoked magnetic fields and electric potentials. Adv Audiol 6(1):30

    Google Scholar 

  • Scherg M, Berg P (1991) Use of prior knowledge in brain electromagnetic source analysis. Brain Topogr 4(2):8

    Article  Google Scholar 

  • Scherg M, von Cramon D (1986) Evoked dipole source potentials of the human auditory cortex. Electroencephalogr Clin Neurophysiol 65(5):16

    Google Scholar 

  • Schmitt U, Louis AK (2002) Efficient algorithms for the regularization of dynamic inverse problems: I. Theory. Inverse Probl 18(1):14

    Google Scholar 

  • Schmitt U, Louis AK, Darvas F, Buchner H, Fuchs M (2001) Numerical aspects of spatio-temporal current density reconstruction from EEG-/MEG-data. IEEE Trans Med Imaging 20(4):11

    Article  Google Scholar 

  • Schmitt U, Louis AK, Wolters CH, Vauhkonen M (2002) Efficient algorithms for the regularization of dynamic inverse problems: II. Applications. Inverse Probl 18(1):18

    Google Scholar 

  • Schmitt U, Wolters CH, Anwander A, Knösche T (2004) STR: a new spatio-temporal approach for accurate and efficient current density reconstruction. In: Halgren E, Ahlfors S, Hämäläinen M, Cohen D (eds) BIOMAG 2004, proceedings of the 14th international conference on biomagnetism. Biomag, Boston, pp 591–592

    Google Scholar 

  • Vallaghe S, Papadopoulo T (2010) A trilinear immersed finite element method for solving the electroencephalography forward problem. Siam J Sci Comput 32(4):2379–2394. doi:10.1137/09075038X

    Google Scholar 

  • van den Broek SP, Reiders F, Donderwinkel M, Peters MJ (1998) Volume conduction effects in EEG and MEG. Electroencephalogr Clin Neurophysiol 106(6):13

    Google Scholar 

  • Wagner M, Fuchs M, Kastner J (2004) Evaluation of sLORETA in the presence of noise and multiple sources. Brain Topogr 16(4):277–280

    Article  PubMed  Google Scholar 

  • Wolters CH, Anwander A, Berti G, Hartmann U (2007a) Geometry-adapted hexahedral meshes improve accuracy of finite-element-method-based EEG source analysis. IEEE Trans Biomed Eng 54(8):1446–1453

    Article  PubMed  Google Scholar 

  • Wolters CH, Köstler H, Möller C, Härdtlein J, Grasedyck L, Hackbusch W (2007b) Numerical mathematics of the subtraction method for the modeling of a current dipole in EEG source reconstruction using finite element head models. Siam J Sci Comput 30(1):24–45.

    Article  Google Scholar 

  • SimBio (2011) SimBio: a generic environment for bio-numerical simulations. https://www.mrt.uni-jena.de/simbio. Accessed 2 July 2012.

  • Zanow F (1997) Realistically shaped models of the head and their application to EEG and MEG. PhD thesis. University of Twente, Enschede

  • Zhang YH, Ghodrati A, Brooks DH (2005) An analytical comparison of three spatio-temporal regularization methods for dynamic linear inverse problems in a common statistical framework. Inverse Probl 21(1):357–382

    Article  Google Scholar 

Download references

Acknowledgments

This work was kindly supported by the Deutsche Forschungsgemeinschaft (contract Grant Numbers KN 588/2-1,4-1 and WO 1425/1-1,3-1). None of the authors has any conflict of interest, financial or otherwise, related to the submitted.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Thomas R. Knösche.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dannhauer, M., Lämmel, E., Wolters, C.H. et al. Spatio-temporal Regularization in Linear Distributed Source Reconstruction from EEG/MEG: A Critical Evaluation. Brain Topogr 26, 229–246 (2013). https://doi.org/10.1007/s10548-012-0263-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10548-012-0263-9

Keywords

Navigation