Predicting neural responses to intra- and extra-cranial electric brain stimulation by means of the reciprocity theorem
Fig 6
The effect of transcranial electric stimulation (tES) on individual pyramidal cells.
A: A passive pyramidal cell model receiving a somatic current input (orange dot). B: The input current with a frequency of 10 Hz and a 1 nA amplitude. C: The z-component of the resulting current-dipole moment, perpendicular to the cortical surface. D: The amplitude of this z-component as a function of the input frequency for different cell models. E: The current-dipole (panel C) is placed in the middle frontal gyrus of the New York head model. The orange dot marks the location, the black arrow marks the orientation, and the green ellipsoid marks the nearest EEG electrode. F: The induced voltage signal of 38 pV at the nearest EEG electrode (green ellipsoid in panel E), from the single pyramidal cell at the location marked in panel E. G: The EEG signal at the time of the maximum signal (time indicated by gray dashed lines in panels B, C, and F). The location of the dipole is marked by the orange dot (partially covered by an EEG electrode). H: Through the RT we can invert the situation and calculate the somatic for the pyramidal neuron (located at the green dot) responding to tES (located at the orange ellipsoid). I: A 10 Hz, 1 mA current input through an EEG electrode (marked in panel E and H), that is, 106 times larger amplitude than the original intracellular current input. J: A cross section of the head model’s lead field, displaying the amplitude of the electric field along the cortical normal direction (
). For a tES current amplitude of 1 mA through the considered electrode (orange ellipsoid), the maximum value of
is 0.21 mV/mm. This is the unmodified lead field as given by the New York head model [52]. The somatic
response for the cell model in panel A at different locations in the cortex, in response to the tES in panels H and I, can be found by a scaling of the lead field, in this case by a factor of 186 μm. K: The somatic
response to tES for the cell model in panel A at the location marked in panel E is
38 pA = 38 μV. As a control, we also simulate the effect of a uniform electric field of amplitude 0.21 mV/mm along the z-axis of the cell model, and see that the somatic
response is indistinguishable.