Fig 1.
First order model for interaction of electric fields with elongated neurons.
On the left, pyramidal neuron population from the human cortex (edited from “Comparative study of the sensory areas of the human cortex” by Santiago Ramon y Cajal, published in 1899, Wikipedia Public Domain). On the right, realistic model of the electric field generated by a current a dipole located at x in the cortex. The orientation of the generating dipole or neuron population and the sensing population (at point y) both play a role.
Fig 2.
Geometry and electric field distribution in a simplified model of a sulcus.
(A) 3D view of half of the simplified volume conductor (100×100×100 mm). The different tissues are colored by their respective conductivity, in S/m. The patch of single dipole sources is placed in the central region of the model (posterior wall of the sulcus), covering an area of 60 mm2. The figure’s inset shows a sagittal view of the model (sulcus width of 1 mm) with dipole sources in its posterior wall. (B-E) Magnitude of the electric field in the GM tissue for models with different source strength and patch distributions (common color scale between plots in V/m). Also shown are vector plots of the electric field and isosurfaces of the electrostatic potential. Left/right columns represent the models with the sources scaled to a density of 0.5 and 1.0 nAm/mm2 respectively. Top/bottom rows represent multiple/single dipole distributions. The colorscale is saturated to 0.1 V/m to better show the E-field in the sulcal wall opposite to the location of the sources. The E-field in the sulcus wall with the sources is much higher (1 order of magnitude higher), but its distribution is not the focus of this work.
Fig 3.
(A) Two views of the 3D volume conductor geometry, including volumes representing the scalp (yellow), skull (red), CSF (white), GM (light-grey) and WM (light blue). Models of electrodes, placed in the 10–10 EEG positions, are also included in the model (grey). The patch used to place dipoles in the multiple-source model (posterior wall of the post-central sulcus, on the right hemisphere) is displayed in red in the GM volume. It comprises a cortical surface of 5.30 cm2. The captions provide zoomed views of the cortical patch with the dipole sources. (B-G): Electric field magnitude (color bar in V/m) and vector field direction, and isosurfaces of the electrostatic potential (mV) in a sagittal slice passing through the middle of the right hemisphere post-central sulcus. First (B-D) and second (E-F) rows: dipole density per unit area of 0.5/1.0 nAm/mm2. Columns, from left to right: model with all dipole sources, model with single dipole in narrow region of the sulcus, model with single dipole in wide region of the sulcus. The location of the individual dipoles in the middle and right-most columns are shown as blue circles in Figs C and D. The sulcus is approximately 5.5 mm wide in its wide region and 1.8 mm wide in its narrow region. For the same reasons as highlighted in Fig 2, the colorscale of the E-field's magnitude is saturated to 0.1 V/m.
Table 1.
Summary of the maximum values of the scalp electrostatic potential (V) and GM electric field (magnitude, E, and normal component, En) induced in all the source distributions used in the realistic head model.
For each quantity, two dipole densities are considered: 0.5 and 1.0 nAm/mm2.
Fig 4.
Ephaptic Modulation in the human brain.
(A) Average EMOD1. Individual EMOD1 maps are registered to Freesurfer’s common template (fsaverage) and then averaged at each vertex across subjects. For the purpose of visualization, we have thresholded the average EMOD1 map at EMOD1>50. (B) Vertex-wise correlation. At each vertex, the Pearson’s correlation coefficient between EMOD1 and cortical surface area, thickness, gyrification and subject’s age is computed. The resulting maps are then corrected for multiple comparisons using the Benjamini- Hochberg procedure (p-value <0.05). Pearson’s correlation coefficient values for vertices that passed the multiple comparison correction are overlaid on Freesurfer common template (fsaverage).
Fig 5.
EMOD1, thickness, Area and LGI–correlation with age.
(A) Vertex-wise EMOD1 values were correlated with age across the sample of 401 subjects, resulting in a weighted map displaying the cortical regions whose ephaptic modulation index is significantly affected by aging. (B) Individual data for correlation between age, EMOD1, as well as cortical morphologies are displayed. Red-yellow shows positive and blue-cyan negative correlations.