Effective electric fields along realistic DTI-based neural trajectories for modelling the stimulation mechanisms of TMS

Abstract

In transcranial magnetic stimulation (TMS), an applied alternating magnetic field induces an electric field in the brain that can interact with the neural system. It is generally assumed that this induced electric field is the crucial effect exciting a certain region of the brain. More specifically, it is the component of this field parallel to the neuron's local orientation, the so-called effective electric field, that can initiate neuronal stimulation. Deeper insights on the stimulation mechanisms can be acquired through extensive TMS modelling. Most models study simple representations of neurons with assumed geometries, whereas we embed realistic neural trajectories computed using tractography based on diffusion tensor images. This way of modelling ensures a more accurate spatial distribution of the effective electric field that is in addition patient and case specific. The case study of this paper focuses on the single pulse stimulation of the left primary motor cortex with a standard figure-of-eight coil. Including realistic neural geometry in the model demonstrates the strong and localized variations of the effective electric field between the tracts themselves and along them due to the interplay of factors such as the tract's position and orientation in relation to the TMS coil, the neural trajectory and its course along the white and grey matter interface. Furthermore, the influence of changes in the coil orientation is studied. Investigating the impact of tissue anisotropy confirms that its contribution is not negligible. Moreover, assuming isotropic tissues lead to errors of the same size as rotating or tilting the coil with 10 degrees. In contrast, the model proves to be less sensitive towards the not well-known tissue conductivity values.

Modeling transcranial magnetic stimulation from the induced electric fields to the membrane potentials along tractography-based white matter fiber tracts

“…Contrary to previous research (De Geeter et al 2014), the effect of stimulation on the membrane potential is investigated instead of the stimulation mechanisms E l l 2 , E l and E 2 . The membrane potential V l t , ( ) is calculated with equation (1) of section 2.3 on the basis of the induced effective electric field E l t , l ( ), computed in section 2.2.…”

“…The time variation of this magnetic field induces an electric field in the material below the coil. For the considered case study, the induced electric field in the whole brain is computed using the anisotropic independent impedance method (De Geeter et al 2014).…”

“…Those tracts that traverse this box are identified from the whole-brain tractogram, and reduced to a total of 54 neural fiber tracts, shown in figure 1. For more details on the applied selection criteria, we refer to (De Geeter et al 2014). (Cole andCole 1941, Gabriel et al 1996).…”

“…After 20 μs, a single biphasic pulse with a pulse width of 230 μs is applied. First, the peak excitation current's time derivative is set to 21.87 A μs −1 , analogous to the TMS pulse simulated in (De Geeter et al 2014). We gradually increase this stimulator output and the resulting spatio-temporal distributions of the membrane potential are shown in figure 5.…”

“…The induced electric field is calculated (Thielscher and Kammer 2004, Salinas et al 2007, De Geeter et al 2012, Janssen et al 2013, Krieg et al 2015 and, related to this field, the activation function and stimulation mechanisms are studied (Lu et al 2008, Opitz et al 2011, Pashut et al 2011, Salvador et al 2011, De Geeter et al 2014, Shahid et al 2014. However, we believe that these electromagnetic computations are not sufficient to fully understand the observed clinical response to TMS, to explain its reported variability and thus to optimize the currently existing devices.…”