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