Elsevier

NeuroImage

Volume 30, Issue 3, 15 April 2006, Pages 813-826
NeuroImage

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

https://doi.org/10.1016/j.neuroimage.2005.10.014Get rights and content

Abstract

To achieve a deeper understanding of the brain, scientists, and clinicians use electroencephalography (EEG) and magnetoencephalography (MEG) inverse methods to reconstruct sources in the cortical sheet of the human brain. The influence of structural and electrical anisotropy in both the skull and the white matter on the EEG and MEG source reconstruction is not well understood.

In this paper, we report on a study of the sensitivity to tissue anisotropy of the EEG/MEG forward problem for deep and superficial neocortical sources with differing orientation components in an anatomically accurate model of the human head.

The goal of the study was to gain insight into the effect of anisotropy of skull and white matter conductivity through the visualization of field distributions, isopotential surfaces, and return current flow and through statistical error measures. One implicit premise of the study is that factors that affect the accuracy of the forward solution will have at least as strong an influence over solutions to the associated inverse problem.

Major findings of the study include (1) anisotropic white matter conductivity causes return currents to flow in directions parallel to the white matter fiber tracts; (2) skull anisotropy has a smearing effect on the forward potential computation; and (3) the deeper a source lies and the more it is surrounded by anisotropic tissue, the larger the influence of this anisotropy on the resulting electric and magnetic fields. Therefore, for the EEG, the presence of tissue anisotropy both for the skull and white matter compartment substantially compromises the forward potential computation and as a consequence, the inverse source reconstruction. In contrast, for the MEG, only the anisotropy of the white matter compartment has a significant effect. Finally, return currents with high amplitudes were found in the highly conducting cerebrospinal fluid compartment, underscoring the need for accurate modeling of this space.

Introduction

The inverse problem in EEG and MEG aims at reconstructing the underlying current distribution in the human brain using potential differences and/or magnetic fluxes measured non-invasively directly from the head surface or from a close distance. The goal of this study was to examine the sensitivity of the associated EEG/MEG forward problem especially to conductive anisotropy within the brain. We computed forward solutions for both isotropic and anisotropic versions of realistic head models using the finite element approach and evaluated the results throughout the head using sophisticated visualization techniques as well as statistical metrics.

A major premise of this study is that there are regions of the head that do not conduct electrical current isotropically, i.e., equally in all directions, but rather they conduct preferentially in directions related to the underlying tissue structure (Geddes and Baker, 1967, Haueisen, 1996). The human skull consists of a soft bone layer (spongiosa) enclosed by two hard bone layers (compacta). Since the spongiosa has a much higher conductivity than the compacta (Akhtari et al., 2002), the skull can be described by an effective anisotropic conductivity with a ratio of up to 1:10 radially to tangentially to the skull surface (Rush and Driscoll, 1968). It is also known that brain white matter has an anisotropic conductivity with a ratio of about 1:10 (normal: parallel to fibers) (Nicholson, 1965), but no direct techniques exist for its robust and non-invasive measurement. Recently, however, formalisms have been described for relating the effective electrical conductivity tensor of brain tissue to the effective water diffusion tensor as measured by diffusion tensor magnetic resonance imaging (DT-MRI) (Basser et al., 1994b, Tuch et al., 2001). The underlying assumption is that the same structural features that result in anisotropic mobility of water molecules (detected by DT-MRI) also result in anisotropic conductivity. The quantitative expression for this assumption is that the eigenvectors of the conductivity tensor are the same as those from the water diffusion tensor (Basser et al., 1994b). Even more specifically, Tuch et al. have applied a differential effective medium approach to porous brain tissue and derived a linear relationship between the eigenvalues of the DT and the conductivity tensors (Tuch et al., 2001).

A critical component of source reconstruction is the numerical approximation method used to reach an accurate solution of the associated forward problem, i.e., the simulation of fields for known dipolar sources in the brain. Although there are several different approaches in common use for this type of problem the finite element (FE) method is able to treat both realistic geometries and inhomogeneous and anisotropic material parameters (Haueisen, 1996, Buchner et al., 1997, van den Broek et al., 1998, Marin et al., 1998, Schimpf et al., 2002) and so is the approach we employed. Previous work has not sufficiently investigated the impact of tissue anisotropy on EEG and MEG. One impediment to using the FE method – and to this type of modeling in general – has been the high computational cost of carrying out the simulations. The use of recently developed advances in the FE method in EEG/MEG inverse problems (Weinstein et al., 2000, Wolters et al., 2002, Gencer and Acar, 2004, Wolters et al., 2004b) dramatically reduces the complexity of the computations, so that the main disadvantage of FE modeling no longer exists. In realistic FE models, sensitivity studies have been carried out for the influence of skull anisotropy on EEG and MEG (van den Broek et al., 1998, Marin et al., 1998, Wolters, 2003), while, to our knowledge, only a few studies have investigated the influence of realistic white matter anisotropy (Haueisen et al., 2002, Wolters, 2003). Those studies support the hypothesis that modeling anisotropy is crucial for accurate source reconstruction. The major limit of these studies that we have addressed is that their result evaluation was restricted to scalp potentials/fields. In this study, we have computed, compared and visualized potentials and especially the return current flow throughout the volume of the head. Those additional information allows a much more detailed examination of the effects of anisotropy than is possible from the evaluation of scalp values alone.

Using our realistic, anisotropic head model and a variety of sources, we were able to compare throughout the head volume the effects of anisotropic conductivity on bioelectric fields. Our results support those from previous studies suggesting that inclusion of anisotropy can be essential to accurate modeling of electric and magnetic fields and, by extension, to accurate source localization. In addition, our results show the nature of the current flow in regions of anisotropy and provide fundamental indications of the interplay between tissue characteristics and bioelectric fields.

Section snippets

Methods

To carry out the analysis of sensitivity of brain source simulation requires the construction of detailed realistic head models, in this case, from MRI image data. Here, we outline the steps we used to construct such a model and then apply advanced numerical techniques to the solution of forward problems.

Results

The goal of this study was to evaluate the influence of anisotropic conductivity on the simulation of electric and magnetic fields from dipolar sources in the brain. We present here results from the 3 dipole source types described above and, for each case, compare the results with isotropic and anisotropic assumptions for each of the white matter and the skull. We used a source magnitude of 100 nAm and, except for the statistical metrics in Fig. 6, we compared the isotropic case with the 1:10

Discussion and conclusion

In this paper, we built a realistic finite element head volume conductor model taking into account skull and white matter anisotropy. We exploited a combined T1-/PD-MRI dataset for the construction of a five-tissue model with an anisotropic skull compartment and a whole-head DT-MRI dataset to determine white matter anisotropy. Our goal was to study the influence of anisotropic tissue conductivity on forward EEG and MEG computations. We used sophisticated high-resolution visualization techniques

Acknowledgments

The authors would like to thank A. Friederici from the MPI for Human Cognitive and Brain Sciences Leipzig, E. Zeidler and W. Hackbusch from the MPI for Mathematics in the Sciences and Seok Lew and Chris Johnson from the SCI Institute in Salt Lake City for their support and the many important and helpful comments. This work was supported by the MPI for Mathematics in the Sciences, Leipzig, by the IST-program of the European Community, project SIM-BIO (http://www.simbio.de) and the NIH NCRR

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