Variable Anisotropic Brain Electrical Conductivities in Epileptogenic Foci

Source localization models assume brain electrical conductivities are isotropic at about 0.33 S/m. These assumptions have not been confirmed ex vivo in humans. This study determined bidirectional electrical conductivities from pediatric epilepsy surgery patients. Electrical conductivities perpendicular and parallel to the pial surface of neocortex and subcortical white matter (n = 15) were measured using the 4-electrode technique and compared with clinical variables. Mean (±SD) electrical conductivities were 0.10 ± 0.01 S/m, and varied by 243% from patient to patient. Perpendicular and parallel conductivities differed by 45%, and the larger values were perpendicular to the pial surface in 47% and parallel in 40% of patients. A perpendicular principal axis was associated with normal, while isotropy and parallel principal axes were linked with epileptogenic lesions by MRI. Electrical conductivities were decreased in patients with cortical dysplasia compared with non-dysplasia etiologies. The electrical conductivity values of freshly excised human brain tissues were approximately 30% of assumed values, varied by over 200% from patient to patient, and had erratic anisotropic and isotropic shapes if the MRI showed a lesion. Understanding brain electrical conductivity and ways to non-invasively measure them are probably necessary to enhance the ability to localize EEG sources from epilepsy surgery patients

Nonlinearity and Topology

The interplay of nonlinearity and topology results in many novel and emergent properties across a number of physical systems such as chiral magnets, nematic liquid crystals, Bose-Einstein condensates, photonics, high energy physics, etc. It also results in a wide variety of topological defects such as solitons, vortices, skyrmions, merons, hopfions, monopoles to name just a few. Interaction among and collision of these nontrivial defects itself is a topic of great interest. Curvature and underlying geometry also affect the shape, interaction and behavior of these defects. Such properties can be studied using techniques such as, e.g. the Bogomolnyi decomposition. Some applications of this interplay, e.g. in nonreciprocal photonics as well as topological materials such as Dirac and Weyl semimetals, are also elucidated

A systematic study of head tissue inhomogeneity and anisotropy on EEG forward problem computing

In this study, we propose a stochastic method to analyze the effects of inhomogeneous anisotropic tissue conductivity on electroencephalogram (EEG) in forward computation. We apply this method to an inhomogeneous and anisotropic spherical human head model. We apply stochastic finite element method based on Legendre polynomials,Karhunen–Loeve expansion and stochastic Galerkin methods. We apply Volume and Wang’s constraints to restrict the anisotropic conductivities for both the white matter (WM) and the skull tissue compartments. The EEGs resulting from deterministic and stochastic FEMs are compared using statistical measurement techniques. Based on these comparisons, we find that EEGs generated by incorporating WM and skull inhomogeneous anisotropic tissue properties individually result in an average of 56.5 and 57.5% relative errors, respectively. Incorporating these tissue properties for both layers together generate 43.5% average relative error. Inhomogeneous scalp tissue causes 27% average relative error and a full inhomogeneous anisotropic model brings in an average of 45.5% relative error. The study results demonstrate that the effects of inhomogeneous anisotropic tissue conductivity are significant on EEG

Cortical potential imaging using L-curve and GCV method to choose the regularisation parameter

BACKGROUND: The electroencephalography (EEG) is an attractive and a simple technique to measure the brain activity. It is attractive due its excellent temporal resolution and simple due to its non-invasiveness and sensor design. However, the spatial resolution of EEG is reduced due to the low conducting skull. In this paper, we compute the potential distribution over the closed surface covering the brain (cortex) from the EEG scalp potential. We compare two methods – L-curve and generalised cross validation (GCV) used to obtain the regularisation parameter and also investigate the feasibility in applying such techniques to N170 component of the visually evoked potential (VEP) data. METHODS: Using the image data set of the visible human man (VHM), a finite difference method (FDM) model of the head was constructed. The EEG dataset (256-channel) used was the N170 component of the VEP. A forward transfer matrix relating the cortical potential to the scalp potential was obtained. Using Tikhonov regularisation, the potential distribution over the cortex was obtained. RESULTS: The cortical potential distribution for three subjects was solved using both L-curve and GCV method. A total of 18 cortical potential distributions were obtained (3 subjects with three stimuli each – fearful face, neutral face, control objects). CONCLUSIONS: The GCV method is a more robust method compared to L-curve to find the optimal regularisation parameter. Cortical potential imaging is a reliable method to obtain the potential distribution over cortex for VEP data