Elsevier

NeuroImage

Volume 51, Issue 1, 15 May 2010, Pages 145-163
NeuroImage

Influence of anisotropic electrical conductivity in white matter tissue on the EEG/MEG forward and inverse solution. A high-resolution whole head simulation study

https://doi.org/10.1016/j.neuroimage.2010.02.014Get rights and content

Abstract

To investigate the influence of anisotropic electrical conductivity in white matter on the forward and inverse solution in electroencephalography (EEG) and magnetoencephalography (MEG) numerical simulation studies were performed. A high-resolution (1 mm3 isotropic) finite element model of a human head was implemented to study the sensitivity of EEG and MEG source localization. In vivo information on the anisotropy was obtained from magnetic resonance diffusion tensor imaging and included into the model, whereas both a direct transformation and a direct transformation with volume normalization were used to obtain conductivity tensors. Additionally, fixed artificial anisotropy ratios were also used, while considering only the orientation information from DTI, to generate conductivity tensors. Analysis was performed using over 25,000 single dipolar sources covering the full neocortex. Major findings of the study include that EEG is more sensitive to anisotropic conductivities in white matter compared to MEG. Especially with the inverse analysis, we found that sources placed deep in sulci are located more laterally if anisotropic conductivity of white matter tissue is neglected. Overall, the single-source localization errors resulting from a neglect of anisotropy were found to be smaller compared to errors associated with other modeling errors, like misclassified tissue or the use of nonrealistic head models. In contrast to the small localization error we observed significant changes in magnitude and orientation. The latter is important since dipole orientation might be more important than absolute dipole localization in assigning, e.g., epileptic activity to the wall of the affected brain sulcal area. If high-resolution finite element models are used to perform source localization in EEG and MEG experiments and the quality of the measured data permits localization accuracy of 1 mm and below, the influence of anisotropic compartments has to be taken into account.

Introduction

EEG and MEG source reconstruction of cerebral activity has become an established tool in clinical diagnosis (Rullmann et al., Jan 2009, Waberski et al., 1998) and cognitive research (Baillet et al., 2001). Compared to functional analysis based on functional magnetic resonance imaging (fMRI), which is only indirectly related to neuronal activity through neurovascular coupling, electromagnetic source localization directly estimates the electrical activity in neuronal populations. Therewith, the spatiotemporal dynamics of neuronal currents in the brain are modeled and estimated. Unfortunately, estimation of the location and strength of the current sources is an ill-posed inverse problem. Methods for solving the inverse problem are based on solutions of the corresponding forward problem, i.e., simulation of electric potentials or magnetic field distributions for a given primary source in the brain using a volume conduction model of the human head. While the theoretical foundation of this forward problem is well established (see, e.g., the proof for existence and uniqueness of the forward problem in Wolters et al., 2007a) with many existing numerical implementations, there are still open questions with respect to the localization accuracy. In particular, investigating the effect of different forward models on source location errors has been of primary interest in a multitude of studies (Awada et al., Sep 1998, de Munck, 1988, Hämäläinen and Sarvas, Feb 1989, Ramon et al., 2006, Zanow and Peters, Jul 1995).

The forward problem requires a volume conductor model that closely mimics the electromagnetic properties of the investigated subject as accurately as possible. In case of the human head the simplest volume conductor consists of a single sphere or multilayered spheres (de Munck, 1988, de Munck and Peters, 1993) with the advantage that analytic solutions exist. To better take into account the correct shape of the scalp, skull and convoluted brain, Boundary Element Method (BEM) head models have been developed (Hämäläinen and Sarvas, 1989). With BEM models volume conductor properties are approximated by several, realistically shaped compartments that are each modeled with different, but isotropic and homogeneous, conductivities. Anisotropy of the electrical conductivity and the characteristic structure of the tissue, in which the electric sources are embedded, are, however, neglected with these models. Those features can be incorporated by using finite element methods (FEM) (Awada et al., Aug 1997, Buchner et al., Apr 1997, Haueisen, June 1996), which, however, suffer from large computational burden. A big step forward with regard to decreasing FE computational effort has been the development of efficient FEM forward modeling techniques (especially EEG and MEG transfer matrices, but also fast solver techniques) as described in the following papers (Weinstein et al., Sep 2000, Gençer and Acar, Mar 2004, Wolters et al., 2004b, Lew et al., 2009). With these improved methods and advances in computer technology FEM calculations have been facilitated, even with standard computer hardware. Several studies have already investigated the influence of anisotropic conductivity in different tissue layers on both the forward and the inverse solution by using volume conductor FEM models (Güllmar et al., Sep 2006, Haueisen et al., Jan 2002, Wolters et al., Apr 2006).

Haueisen et al. demonstrated changes in the EEG and MEG forward solutions for both single dipoles and small extended sources when modeling gray and white matter tissue with anisotropic conductivities (Haueisen et al., 2002). Including anisotropy, they reported a major effect on the amplitude of EEG and MEG and concluded that this may be problematic for a correct estimation of source strengths. Wolters et al. extended these investigations by assuming, in addition, an electrically anisotropic skull layer (Wolters et al., 2006). Their major findings were (i) that anisotropic white matter conductivity caused return currents to flow in directions parallel to white matter fiber tracts, (ii) that skull anisotropy had a smearing effect on the forward potential computation, and (iii) that the influence of this anisotropy on the resulting electric and magnetic fields was larger than the deeper the source was located and the more it was surrounded by anisotropic tissue. Güllmar et al. studied the influence of anisotropic conductivity in an animal model with similar results (Güllmar et al., 2006). In addition to using realistic rabbit brain structures, an artificial brain structure was investigated with some interesting results, including findings that the effect of an anisotropic conductivity mainly depends on the orientation of the dipolar source relative to the anisotropic structure. More recently, Hallez et al. investigated the effects of white matter anisotropy on forward and inverse solutions by using the Finite Difference Method (FDM) (Hallez et al., 2009). In contrast to the other studies they compared two different anisotropic models instead of comparing an anisotropic model with an isotropic model.

One common feature of all these studies is that the anisotropy information is derived from diffusion tensor data acquired with magnetic resonance imaging (MRI). This approach is based on the assumption of a cross-property relation between the diffusion and conductivity tensor that was first proposed by Basser et al. (1994). Later, Tuch et al. (2001), using an effective medium approach, demonstrated a strong linear relationship between the conductivity and the diffusion tensor eigenvalues. A phantom validation study performed by Oh et al. (2006) with silk yarn confirmed this relationship; however, an in vitro experiment on freshly excised neocortex and subcortical white matter of epilepsy patients undergoing neurosurgery found large variations in electrical conductivities and was unable to verify linear relationships (Akhtari et al., 2006).

Therefore, it appears necessary to further investigate the impact of anisotropic conductivities on modeling in greater detail. Although the aforementioned papers addressed this problem to some extent, they all suffered from different limitations. Either, only few dipole configurations were tested, or the simulations considered only forward solutions or they only examined EEG signals. The present paper aims to overcome these limitations by using different models of anisotropy and investigating the effects of anisotropic white matter tissue on the EEG and MEG forward and inverse solution in a high-resolution human head model with a large number of dipole configurations.

Section snippets

MR data acquisition

To construct an individual, anisotropic, high-resolution volume conductor model, T1-, T2-weighted and diffusion tensor data sets were acquired on a healthy volunteer (male, 30 years) by using a Tim Trio 3T MR whole-body scanner (Siemens Medical Solutions, Erlangen, Germany). The T1-weighted scan was performed with a 3D magnetization prepared rapid gradient echo (MPRAGE) sequence (Mugler and Brookeman, 1990), which provides good contrast between gray and white matter. The following parameters

Forward simulations

RDM and MAG values were computed (Eqs. 7 and 8) using the fields and potentials derived with the anisotropic models as measurement data and those obtained from the isotropic model as reference data. Density functions were created (see Fig. 6) in the following way: The edge defining vector (bin) for the plots was set from 0 to 1 for RDM and from 0.3 to 1.4 for MAG, both with a step size of 0.0075. We observed skewed, non-Gaussian distributions for both RDM and MAG. Thus, in order to quantify the

Discussion

In this study, the sensitivity of EEG and MEG forward and inverse solutions on white matter anisotropy was investigated using high-resolution finite element volume conductor models of a human head. Information about the anisotropy of the electrical conductivity was derived from diffusion tensor data using different approaches. The results from the forward analysis indicate that with increasing anisotropy in the white matter segment the topographical error (RDM) as well as the size of magnitude

Conclusion

Despite the limitations of the present study, the potential of simulations has been demonstrated to investigate the influence of anisotropic conductivity on forward and inverse problems in EEG and MEG. The effects, which were observed, are manifold and illustrate the complexity of the problem. To the best of our knowledge, so far no other study has simulated the effect of anisotropic conductivity of white matter in such detail. In particular, mapping of the error quantities for the whole cortex

Acknowledgments

This study was supported in part by the German Ministry of Science (01 GQ 0703), the German Research Foundation (Ha 2899/6-1,7-1) and the BMBF/IZKF Jena (foreign exchange scholarship to DG).

References (87)

  • KringsT. et al.

    Accuracy of eeg dipole source localization using implanted sources in the human brain

    Clin. Neurophysiol.

    (Jan 1999)
  • LewS. et al.

    Accuracy and run-time comparison for different potential approaches and iterative solvers in finite element method based eeg source analysis

    Applied Numerical Mathematics

    (2009)
  • McIntyreC.C. et al.

    Electric field and stimulating influence generated by deep brain stimulation of the subthalamic nucleus

    Clin. Neurophysiol.

    (Mar 2004)
  • NaggaraO. et al.

    Diffusion tensor imaging in early alzheimer's disease

    Psychiatry Res.

    (Apr 2006)
  • RullmannM. et al.

    Eeg source analysis of epileptiform activity using a 1 mm anisotropic hexahedra finite element head model

    Neuroimage

    (Jan 2009)
  • SalayevK.A. et al.

    Spike orientation may predict epileptogenic side across cerebral sulci containing the estimated equivalent dipole

    Clin. Neurophysiol.

    (Aug 2006)
  • SchlösserR.G.M. et al.

    White matter abnormalities and brain activation in schizophrenia: a combined dti and fmri study

    Schizophr. Res.

    (Jan 2007)
  • SégonneF. et al.

    A hybrid approach to the skull stripping problem in mri

    Neuroimage

    (Jul 2004)
  • van den BroekS.P. et al.

    Volume conduction effects in eeg and meg

    Electroencephalogr. Clin. Neurophysiol.

    (Jun 1998)
  • VanrumsteB. et al.

    Comparison of performance of spherical and realistic head models in dipole localization from noisy eeg

    Med. Eng. Phys.

    (Jul 2002)
  • WeiD. et al.

    Comparison of body surface potential maps simulated with isotropic and anisotropic computer heart models

    J. Electrocardiol.

    (Oct 1995)
  • WoltersC.H. et al.

    Influence of tissue conductivity anisotropy on eeg/meg field and return current computation in a realistic head model: a simulation and visualization study using high-resolution finite element modeling

    Neuroimage

    (Apr 2006)
  • YounT. et al.

    Altered hemispheric asymmetry and positive symptoms in schizophrenia: equivalent current dipole of auditory mismatch negativity

    Schizophr. Res.

    (Feb 2003)
  • YvertB. et al.

    A systematic evaluation of the spherical model accuracy in eeg dipole localization

    Electroencephalogr. Clin. Neurophysiol.

    (May 1997)
  • AkhtariM. et al.

    Electrical conductivities of the freshly excised cerebral cortex in epilepsy surgery patients; correlation with pathology, seizure duration, and diffusion tensor imaging

    Brain Topogr.

    (2006)
  • AlexanderD.C. et al.

    Spatial transformations of diffusion tensor magnetic resonance images

    IEEE Trans Med. Imaging

    (2001)
  • AnwanderA. et al.

    Influence of realistic skull and white matter anisotropy on the inverse problem in eeg/meg-source localization

  • AwadaK.A. et al.

    Computational aspects of finite element modeling in eeg source localization

    IEEE Trans. Biomed. Eng.

    (Aug 1997)
  • AwadaK.A. et al.

    Effect of conductivity uncertainties and modeling errors on eeg source localization using a 2-d model

    IEEE Trans Biomed. Eng.

    (Sep 1998)
  • BailletS. et al.

    Electromagnetic Brain Mapping

    (2001)
  • BammerR. et al.

    Magnetic resonance diffusion tensor imaging for characterizing diffuse and focal white matter abnormalities in multiple sclerosis

    Magn. Reson. Med.

    (Oct 2000)
  • BaumannS.B. et al.

    The electrical conductivity of human cerebrospinal fluid at body temperature

    IEEE Trans Biomed. Eng.

    (Mar 1997)
  • BaysalU. et al.

    Use of a priori information in estimating tissue resistivities–application to human data in vivo

    Physiol. Meas.

    (Jun 2004)
  • ChauveauN. et al.

    Effects of skull thickness, anisotropy, and inhomogeneity on forward eeg/erp computations using a spherical three-dimensional resistor mesh model

    Hum. Brain Mapp.

    (Feb 2004)
  • CuffinB.N.

    Effects of modeling errors and eeg measurement montage on source localization accuracy

    J. Clin. Neurophysiol.

    (Jan 2001)
  • CuffinB.N. et al.

    Tests of eeg localization accuracy using implanted sources in the human brain

    Ann. Neurol.

    (Feb 1991)
  • de MunckJ.

    The potential distribution in a layered anisotropic spheroidal volume conductor

    J. Appl. Phys.

    (1988)
  • de MunckJ.C. et al.

    A fast method to compute the potential in the multi sphere model

    IEEE Trans Biomed. Eng.

    (1993)
  • DouJ. et al.

    Cardiac diffusion mri without motion effects

    Magn. Reson. Med.

    (Jul 2002)
  • FilippiM. et al.

    Diffusion tensor magnetic resonance imaging in multiple sclerosis

    Neurology

    (Feb 2001)
  • GaoN. et al.

    Estimation of electrical conductivity distribution within the human head from magnetic flux density measurement

    Phys. Med. Biol.

    (Jun 2005)
  • GençerN.G. et al.

    Sensitivity of eeg and meg measurements to tissue conductivity

    Phys. Med. Biol.

    (Mar 2004)
  • GüllmarD. et al.

    Influence of anisotropic conductivity on eeg source reconstruction: investigations in a rabbit model

    IEEE Trans Biomed. Eng.

    (Sep 2006)
  • Cited by (174)

    View all citing articles on Scopus
    View full text