A quantitative physical model of the TMS-induced discharge artifacts in EEG
Fig 4
Representative example of TMS artifacts on a human head and assessment of the artifact model.
(A) Example of raw EEG traces displaying TMS-induced artifacts recorded from a human head. Magnetic stimulation was applied at time 0 at electrode Cz on a 64-electrode cap with 32 electrodes on the right hemisphere. The artifacts appear in every electrode trace at different strength or shape. Inset: On the uV scale of physiological brain waves, some traces exhibit an artifact duration of more than 100 ms. (B) The fast initial artifact dynamics related to the magnetic pulse. (C) Averaging out noise using five trials shows the long-lasting artifact decay to baseline. (D) On a log-log scale, the tails in the decay of the artifacts (from C) follow a power-law with an exponent on the order of 2 (red dashed lines). (E) TMS-EEG traces on a human knee. Shown are raw data (gray) of a single recording from 28 electrodes covering the knee following TMS. The artifacts reconstructed with the model are shown in green. (F) Log-log plot. (G) Data after subtraction of the reconstructed artifacts followed by subtraction of average of all traces to remove the common mode. As expected from TMS on a knee, the stimulation does not evoke neuronal activity, such that the artifact-removed traces are flat up to continuation of the typical very slow and small electrode drifts. The area shaded in gray indicates where the artifacts could not be reconstructed. (H) To assess the goodness of fit, we use the χ2-test with significance level α = 5%. Shown is the maximal time span for which the test accepts the fit. Beyond this time, the fit is rejected. Small electrode drifts and noise due to TMS-device recharging can shorten this time, however never below 20 ms. (I-J) Fits of sums of two exponentials. (K) Subtraction of the fits introduces both fast and slow distortions of the data in almost all traces. (L) Correspondingly, the fits are generally not accepted, except mainly in noisy and drifting electrodes. (M) The difference of data reconstructed by the model and by the sum of two exponentials. This equals the difference of the respective reconstructed artifacts. (N) For almost all fits by a sum of two exponentials, the quotients of the decay constants are approximately equal and have the same order of magnitude (a, b, c, d constants, t time).