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Sudden phase changes are related to cortical phase transitions, which likely change in frequency and spatial distribution as epileptogenic activity evolves. A 100 s long section of micro-ECoG data obtained before and during a seizure was selected and analyzed. In addition, nine other short-duration epileptic events were also examined. The data was collected at 420 Hz, imported into MATLAB, downsampled to 200 Hz, and filtered in the 1–50 Hz band. The Hilbert transform was applied to compute the analytic phase, which was then unwrapped, and detrended to look for sudden phase changes. The phase slip rate (counts/s) and its acceleration (counts/s2) were computed with a stepping window of 1-s duration and with a step size of 5 ms. The analysis was performed for theta (3–7 Hz), alpha (7–12 Hz), and beta (12–30 Hz) bands. The phase slip rate on all electrodes in the theta band decreased while it increased for the alpha and beta bands during the seizure period. Similar patterns were observed for isolated epileptogenic events. Spatiotemporal contour plots of the phase slip rates were also constructed using a montage layout of 8 × 8 electrode positions. These plots exhibited dynamic and oscillatory formation of phase cone-like structures which were higher in the theta band and lower in the alpha and beta bands during the seizure period and epileptogenic events. These results indicate that the formation of phase cones might be an excellent biomarker to study the evolution of a seizure and also the cortical dynamics of isolated epileptogenic events.

Effects of soft skull bone, cerebrospinal fluid (CSF) and gray matter on scalp potentials were examined with highly heterogeneous finite element models of an adult male subject. These models were constructed from segmented T1 weighted magnetic resonance images. Models had voxel resolutions of 1x1x3.2 mm with a total of about 1.5 million voxels. The scalp potentials, due to a dipolar source in the motor cortex area, were computed with an adaptive finite element solver. It was found that the scalp potentials were significantly affected by the soft bone, CSF and gray matter tissue boundaries in the models.

Abstract: We calculate the mixing of real and imaginary components of space and time under the influence of superluminal boosts in thex direction. A unique mixing is determined for this superluminal Lorentz transformation when we consider the symmetry properties afforded by the inclusion of three temporal directions. Superluminal transformations in complex six-dimensional space exhibit unique tachyonic connections which have both remote and local space-time event connections.

Abstract: The influence of volume currents on the magnetic field is an important question in magnetoencephalography since the spherical volume conductor is still widely used for source localization. In theory, the magnetic field of a radial dipole in a homogeneous sphere is zero. In realistic models of the head, the field is suppressed when compared with a tangential dipole. To determine the influence of the volume currents, this suppression ratio (magnetic field of the radial dipole divided by the field of the tangential dipole) needs to be quantified. Large-scale finite element method models of the human head and the rabbit head were constructed and the suppression ratio was computed. The computed suppression value of 0.28 in the rabbit head was similar to the previously measured experimental value. In the human head, an average suppression ratio of 0.190.07 was found for different regions and depths in the gray matter. It was found that the computed magnetic field of radial sources varied significantly with the conductivities of the surrounding tissues where the dipole was located. We also modeled the magnetic field of an epileptic interictal spike in a finite element model of the rabbit head with a single dipole and with extended sources of varying length (1–8 mm). The extended source models developed were based on invasive measurements of an interictal spike within the rabbit brain. The field patterns of the small (1–2 mm) extended sources were similar to a single dipolar source and begin to deviate significantly from a dipolar field for the larger extended sources (6–8 mm).

Muscle fiber pathways in the heart wall are described. Procedures are introduced which permit data to be standardized from cadaver and animal hearts fixed at different points of the cardiac cycle or obtained in vivo from patients with different ejection fractions and heart masses. Design criteria are also developed here to construct a hypothetical standard left ventricle to compare the data from different hearts. The equations allow the nested set of toroidal fiber-shells to be depicted with typical muscle fiberpaths. With this formulation the heart wall and typical elements in it can be shown computergraphically as they move from the contracted state to the distended. Man-made fiber structures that simulate the fail-safe shockload absorbing features of the heart can now be designed and tested computergraphically by use of the mathematical procedures described here.