Anisotropic partial volume CSF modeling for EEG source localization

Abstract

Electromagnetic source localization (ESL) provides non-invasive evaluation of brain electrical activity for neurology research and clinical evaluation of neurological disorders such as epilepsy. Accurate ESL results are dependent upon the use of patient specific models of bioelectric conductivity. While the effects of anisotropic conductivities in the skull and white matter have been previously studied, little attention has been paid to the accurate modeling of the highly conductive cerebrospinal fluid (CSF) region. This study examines the effect that partial volume errors in CSF segmentations have upon the ESL bioelectric model. These errors arise when segmenting sulcal channels whose widths are similar to the resolution of the magnetic resonance (MR) images used for segmentation, as some voxels containing both CSF and gray matter cannot be definitively assigned a single label. These problems, particularly prevalent in pediatric populations, make voxelwise segmentation of CSF compartments a difficult problem. Given the high conductivity of CSF, errors in modeling this region may result in large errors in the bioelectric model. We introduce here a new approach for using estimates of partial volume fractions in the construction of patient specific bioelectric models. In regions where partial volume errors are expected, we use a layered gray matter-CSF model to construct equivalent anisotropic conductivity tensors. This allows us to account for the inhomogeneity of the tissue within each voxel. Using this approach, we are able to reduce the error in the resulting bioelectric models, as evaluated against a known high resolution model. Additionally, this model permits us to evaluate the effects of sulci modeling errors and quantify the mean error as a function of the change in sulci width. Our results suggest that both under and over-estimation of the CSF region leads to significant errors in the bioelectric model. While a model with fixed partial volume fraction is able to reduce this error, we see the largest improvement when using voxel specific partial volume estimates. Our cross-model analyses suggest that an approximately linear relationship exists between sulci error and the error in the resulting bioelectric model. Given the difficulty of accurately segmenting narrow sulcal channels, this suggests that our approach may be capable of improving the accuracy of patient specific bioelectric models by several percent, while introducing only minimal additional computational requirements.

Figure 1. Structure MRI Images

Left to right are axial, coronal and sagittal slices for a) the collected T1 weighted image and b) the collected T2 weighted image.

Figure 2. Anisotropic Conductivity Tensors

Fiber orientation is denoted by color, with red denoting left-right, green marking anterior-posterior, and blue being superior-inferior.

Figure 3. Brain Segmentation Before/After Model Based Sulci Extraction

A) Axial, coronal and sagittal slices of collected T1 data used for segmentation. B) Original segmentation obtained using automated procedure. C) Segmentation following model based sulci extraction.

Figure 4. Construction of Partial Volume Anisotropic Conductivities

a) Multi-layer model used to construct anisotropic conductivities. Conductivity along the X-axis (Across layers) will be computed using series conductors, while conductivity along the Y and Z-axes (Parallel to the layers) will use parallel conductors. b) Graphical illustration of the relationship between neighboring normal vectors and the final tensor orientation. Disks represent estimates of cortical surface orientation at each neighboring voxel (i.e.- The plane perpendicular to the normal vector), while the red ellipse is the anisotropic conductivity tensor after rotation into the appropriate cortical plane. A partial volume fraction of f_CSF = 0.5 was chosen to enhance visibility of the tensor orientation. c) Conductivity tensors as f_CSF is varied from 0 (entirely grey matter) to 1 (entirely CSF).

Figure 5. Segmentation for High Resolution Model

a) Segmentation for “True” model used as ground truth. Narrow sulci have been added using a selective erosion procedure which created sulci. b) Histogram of CSF partial volume fractions in “true” model for voxels identified as potential sulci. Mean fraction 0.2048, standard deviation 0.2441.

Figure 6. Cross Analysis of Models with Fixed Partial Volume Fraction

Plots of RDM and MAG differences between all pairs of models with fixed volume fraction. In both plots, X and Y axes indicate the percentage of volume occupied by CSF. Curves plotted underneath the surface are isocontours. (a) Plot of magnitude error showing approximately linear relationship between change in volume fraction and MAG error. Note that MAG(a, b) = 1/MAG(b, a). (b) Linear fit to MAG data. Plotting difference in volume fraction against resulting MAG, a linear fit y = 0.002595x+1.007 with R² = 0.9774 is obtained. (c) Plot of topographic error (RDM) showing a similar nearly linear relationship between volume fraction and error. The plot is symmetric along X = Y because RDM(a, b)=RDM(b, a). (d) Plot of absolute value of difference in volume fraction against resulting RDM. A linear fit results in y = 0.00144x + 0.01321 with R² = 0.9684.

Figure 7. Magnitude Error between Models

a) Mean MAG error and standard deviation for all fixed volume fraction models (blue) and for the model with voxel specific volume fractions (red). b) Full brain and slice images of MAG error for model using original segmentation (PV Fraction = 0). Note that minimum MAG = 1, thus voxels in red overestimate signal magnitude, while those in blue underestimate it. c) Full brain and slice images for model with voxel specific partial volume fractions.

Figure 8. Histogram of Magnitude Errors

Histogram of magnitude error (MAG) for: a) Model built from original segmentation b)Anisotropic sulci with fixed volume fraction of 40% c) Anisotropic sulci with partial volume fractions set for each individual voxel.

Figure 9. Topography Error between Models

a) Mean RDM error and standard deviation for all fixed volume fraction models (blue) and for the model with voxel specific volume fractions (red). b) Full brain and slice images of MAG error for model using original segmentation (PV Fraction = 0). c) Full brain and slice images for model with voxel specific partial volume fractions.

Figure 10. Histogram of Topography Errors

Histogram of topography error (RDM) for: a) Model built from original segmentation b)Anisotropic sulci with fixed volume fraction of 30% c) Anisotropic sulci with partial volume fractions set for each individual voxel.