Influences of skull segmentation inaccuracies on EEG source analysis

Abstract

The low-conducting human skull is known to have an especially large influence on electroencephalography (EEG) source analysis. Because of difficulties segmenting the complex skull geometry out of magnetic resonance images, volume conductor models for EEG source analysis might contain inaccuracies and simplifications regarding the geometry of the skull. The computer simulation study presented here investigated the influences of a variety of skull geometry deficiencies on EEG forward simulations and source reconstruction from EEG data.

Reference EEG data was simulated in a detailed and anatomically plausible reference model. Test models were derived from the reference model representing a variety of skull geometry inaccuracies and simplifications. These included erroneous skull holes, local errors in skull thickness, modeling cavities as bone, downward extension of the model and simplifying the inferior skull or the inferior skull and scalp as layers of constant thickness. The reference EEG data was compared to forward simulations in the test models, and source reconstruction in the test models was performed on the simulated reference data. The finite element method with high-resolution meshes was employed for all forward simulations.

It was found that large skull geometry inaccuracies close to the source space, for example, when cutting the model directly below the skull, led to errors of 20 mm and more for extended source space regions. Local defects, for example, erroneous skull holes, caused non-negligible errors only in the vicinity of the defect. The study design allowed a comparison of influence size, and guidelines for modeling the skull geometry were concluded.

Introduction

The inverse problem of reconstructing the sources of measured EEG data always involves solving the so-called forward problem; that is, the simulation of the potentials at the EEG electrodes for a given current density distribution (de Munck et al., 1988, Sarvas, 1987) by solving the quasi-static approximation of Maxwell's equations (Plonsey and Heppner, 1967, Sarvas, 1987). Exact analytical solutions for these equations only exist for simple geometries, like multi-shell spheroids (Berg and Scherg, 1994, de Munck, 1988, Irimia, 2005). Because these analytical solutions can be very efficiently evaluated, these models are still often used in spite of the fact that they do not very accurately account for the shape and the inner structure of the head.

As shown, for example, in Acar and Makeig (2010), Gencer and Acar (2004), Güllmar et al. (2010), Haueisen et al. (1995), McVeigh et al. (2007), Ramon et al. (2004), Wendel et al., 2008, Wendel et al., 2009, it is often advisable to use more realistic models, which is only possible using advanced numerical methods. In the last decade, forward solutions based on the boundary element method (BEM) (Acar and Makeig, 2010, Kybic et al., 2005), the finite difference method (FDM) (Hallez et al., 2005) and the finite element method (FEM) (Awada et al., 1997, Bertrand et al., 1991, Buchner et al., 1997, Gencer and Acar, 2004, Marin et al., 1998, Wolters et al., 2007a) have been developed. For these solutions, it is important that the numerical error, often evaluated in studies with spherical volume conductor models where exact analytical solutions are available (see, e.g., (Kybic et al., 2005, Meijs et al., 1989, Wolters et al., 2007a, Wolters et al., 2007b)), and the model errors (see, e.g., (Bruno et al., 2004, Dannhauer et al., 2011, Haueisen et al., 1995, Li et al., 2007, Ramon et al., 2004)) are both as low as possible in order to achieve an acceptable overall forward modeling error. In addition, the computational complexity of these methods must be low enough so that forward simulations can be performed reasonably fast.

Individual, realistic head models for EEG source analysis, which describe the electrical properties of the subject's head for the solution of the forward problem, are most often created by segmenting the head into regions of different tissue types and then assigning conductivity values to each of the regions. Model errors can arise from inaccurate segmentation of the regions (e.g., skull, brain) — known as geometry errors — or by using wrong values for the tissue conductivities. Note, however, that on top of these principally avoidable errors, the inherent simplifications of these compartment models cause errors, since in reality the conductivity is different at every point of the head.

Even if significant progress has been made, for example, in electrical impedance tomography (EIT) for the human head (Abascal et al., 2008), in practice, the determination of absolute values for tissue conductivities remains difficult. Therefore, conductivity values that were measured experimentally on tissue samples and published in the literature are used. Unfortunately, measured values for tissue conductivities can differ greatly between studies and even between tissue samples within the same study. See, for example, the values reported for the compact bone conductivity in Law (1993)) and Akhtari et al. (2002).

The skull plays a special role in modeling the volume conductor (Dannhauer et al., 2011, Hämäläinen et al., 1993, Sadleir and Argibay, 2007). Its conductivity is an order of magnitude smaller than the conductivity of other brain tissues and it is situated between the source space and the sensors. Therefore, errors in modeling the skull geometry have a potentially large effect on the solution of the EEG forward problem.

Model errors caused by different ways of modeling the skull conductivity were investigated by Dannhauer et al. (2011). The skull consists of layers of compact bone encasing a layer of cancellous bone, whose thickness varies over the skull. On average, the conductivity of the compact bone has been measured to be a factor of 3.6 lower than that of the cancellous bone (Akhtari et al., 2002). Large effects were found when approximating the skull as one compartment with homogeneous isotropic or anisotropic conductivity. The authors conclude that, if compact and cancellous bone can be identified with sufficient accuracy and their conductivities can be assumed to be known, they should be modeled explicitly by assigning either compact or cancellous bone conductivity to each voxel.

While it is clear that many individually variable features of the head play a crucial role in the forward modeling of EEG/MEG, individual head model generation, and especially modeling the complex skull geometry, is still not a trivial task in practice. One important reason for this is that in many applications, T1 weighted magnetic resonance images (MRIs) are the only modality available for anatomical information. These MRIs are suboptimal for skull segmentation because they show low contrast between the skull and surrounding tissues. Moreover, many of the practically used MRIs, especially in clinical environments, suffer from low signal-to-noise ratio, especially in inferior regions of the head, and artifacts, for example, the water-fat-shift or the shading artifact. In addition, the resolution of commonly available MRIs is often quite low when compared to the size of the relevant anatomical structures, for example, the compact bone layers. Therefore, segmentation methods using MRIs as input data might produce results with geometric errors. Because of the thinness of the skull and its sub-layers, this structure is most vulnerable to such errors and often simplifications have to be applied. Therefore, and due to the important role of the skull, in this study, we will focus on the impact of unintentional (errors) and intentional (simplification) inaccuracies in skull models on forward solution and source localization accuracy.

A commonly occurring type of skull geometry inaccuracies comprises holes and local errors in skull thickness. A problem in segmenting the skull is the intricate internal structure of the bone. Due to noise, low resolution on the order of magnitude of the compact bone thickness, and water-fat-shift artifacts, it might be that a segmentation algorithm is not able to discern the thin compact bone layer and to differentiate between cancellous bone and the surrounding muscle or brain tissue, which do have similar intensities in the MRI. Erroneous labeling of compact and cancellous bone as scalp or brain tissue would lead to a locally underestimated skull thickness or, in extreme cases, even holes. In T1-weighted images, where there is nearly no contrast between compact bone and cerebrospinal fluid (CSF), it might be that CSF is erroneously modeled as skull, which then would lead to a head model with locally overestimated skull thickness.

Besides these unintentional errors, intentional simplifications of the skull geometry play a role. Such simplifications might be necessary, for example, for the sinus cavities, as commonly available MRIs show nearly no contrast between air and compact bone, and therefore do not allow the shape and position of the sinus cavities to be determined.

Further simplifications are often necessary when modeling the skull base. The geometry of the skull base is quite complicated. It is very thin above the orbitae and very thick where it encases the sinus cavities. In addition, the signal-to-noise ratio in inferior regions of the head is often reduced, for example, due to MR coil sensitivity. It is therefore almost impossible to automatically and accurately segment the complicated geometry of the skull base, and simplifications are necessary.

Another interesting aspect concerning the generation of individual volume conductor models is the modeling of the inferior head regions. Here, segmentation is especially hard due to a limited field-of-view, a low signal-to-noise ratio and the complex anatomy in these regions. Simplifications, for example, cutting the model along an axial plane below the skull or modeling the inferior parts as an homogeneous region with a single conductivity value, might thus be necessary.

Because of the great importance of the skull in realistic volume conductor modeling, previous studies have already dealt with the influence of skull geometry defects on the EEG. Bénar et al. (Benar and Gotman, 2002) performed simulations using the BEM to investigate the effect of burr holes in the skull on source reconstruction. Localization errors of up to 20 mm caused by a burr hole were found, depending on location and orientation of the simulated source. Another study concerning the influence of a skull hole on the EEG was conducted by Vanrumste et al. (2000), who performed simulations in spherical volume conductors and found large localization errors when the hole was not incorporated into the volume conductor. Further investigations on the influence of skull holes on the EEG with similar results can also be found in the literature (Li et al., 2007, Oostenveld and Oostendorp, 2002, van den Broek et al., 1998).

Effects of local errors in skull thickness are also dealt with in previous studies (Cuffin, 1993, Roche-Labarbe et al., 2008, Yan et al., 1991), pointing out the sensitivity of EEG source analysis to this specific parameter. In Bruno et al., 2003, Bruno et al., 2004, the influence of the downward extension of the volume conductor was studied and large errors were reported when the model was cut at a plane intersecting the inferior part of the skull.

Results of previous studies on the influence of different skull geometry deficiencies cannot be compared directly, as many aspects of the designs of the studies differ. Volume conductors with different levels of detail are used: Some studies employ spherical three layer models, others use three compartment realistically shaped models incorporating the scalp, skull, and brain, and only a few use more detailed, realistic models. Furthermore, studies differ in, for example, their choice of conductivities for the volume conductor model and in the placement and number of electrodes.

In the computer simulation study presented here, the influence of a wide range of skull geometry deficiencies on the EEG forward simulation and source reconstruction are investigated, including skull holes, local errors in skull thickness, sinus cavities modeled as compact bone, the downward extension of the volume conductor model, simplification of the inferior skull and modeling the inferior skull and scalp as layers of constant thickness. A detailed and anatomically plausible reference model with 1 mm geometry-adapted hexahedral finite element meshes and the accurate FEM (Rullmann et al., 2009, Wolters et al., 2007b) are employed for the generation of reference EEG data. Forward simulation and source reconstruction errors in test models representing the skull geometry deficiencies are evaluated for probe sources across the whole brain volume. Finally, based on the comparable results found for the influences of a range of skull geometry deficiencies, we are able to draw guidelines on how to model the skull geometry for the generation of accurate individual volume conductor models. Segmentation procedures can be designed and evaluated taking these guidelines into account.