Transient calculation of the induced currents inside the brain during magnetic stimulation

Abstract

PurposeTransient calculation of currents in brain tissue induced during a transcranial magnetic stimulation treatment.Design/methodology/approachBecause of the short pulses used in this technique a time‐harmonic approximation is no longer valid, and transient effects have to be considered. We have performed a Fourier analysis of the induced currents calculated in a high‐resolution model of the brain using the extended scalar potential finite differences (Ex‐SPFD) approach.FindingsThe peak induced currents in the transient development of the pulse are higher by a factor of approximately seven than the time harmonic solutions at the fundamental frequency. Furthermore, an analysis of the impact of the conductivity dispersion revealed an increase in the peak induced currents by 17.3 percent for white matter and by 20.8 percent for gray matter.Originality/valueUsing the numerically efficient Ex‐SPFD approach, along with a high performance cluster, the current densities inside the brain can be calculated incorporating more details than previous calculations of this type.

Magnetic stimulation of the spine: the role of tissues and their modelling

“…The standard deviation of the relative difference variation is 2%, which means that the difference is everywhere close to the quoted mean. One would expect the Fourier synthesis to give a larger value for the electric field, as in this case, since it takes also physical dispersion into account (Barchanski et al 2007). The discrepancy between the two numerical techniques can be attributed to the contribution of the displacement currents to the solution.…”

“…It was found with numerical experiments that although the fundamental frequency of the monophasic pulse generated by the coil is about 1.6 kHz, its spectral content is so rich (figure 5) that at least 800 harmonics distributed logarithmically in the frequency spectrum from 1 Hz to 100 MHz were needed to reproduce with sufficient accuracy the temporal pattern of the electric field. Barchanski et al (2007) used 300 harmonics in their work ranging from 800 Hz (their fundamental frequency) to 240 kHz. At a second step the solution was obtained in the time domain, assuming that displacement currents were negligible compared to conduction currents σ ωε 1 (see section 2.1).…”

“…With respect to the spine, there exists only one study which describes the magnetic stimulation of a simplified model, but without enough detail about the methodology used (Scivill et al 1996). In contrast, in the area of TMS there has been considerable progress in computational calculations with simplified (Wagner et al 2004(Wagner et al , 2008 or realistic (Nadeem et al 2003, Barchanski et al 2007 head models and different numerical methods. The work of Barchanski et al (2007) is of particular interest, since the authors do not solve the problem of TMS solely for the dominant frequency of the applied pulse, but perform a calculation of the resulting temporal behaviour of the induced current in the head with the help of a Fourier transform; in this way the dispersion of conductivity in biological tissues is taken into account.…”

“…In contrast, in the area of TMS there has been considerable progress in computational calculations with simplified (Wagner et al 2004(Wagner et al , 2008 or realistic (Nadeem et al 2003, Barchanski et al 2007 head models and different numerical methods. The work of Barchanski et al (2007) is of particular interest, since the authors do not solve the problem of TMS solely for the dominant frequency of the applied pulse, but perform a calculation of the resulting temporal behaviour of the induced current in the head with the help of a Fourier transform; in this way the dispersion of conductivity in biological tissues is taken into account. Nevertheless, the effect of omitting the displacement current from the calculations, albeit small (Barchanski et al 2005), was not assessed for this particular case; only the dispersion of conductivity was taken into account.…”

Induced electric field and current density patterns in bone fractures

“…The parameters for the various tissues at 1 kHz were calculated by SEMCAD-X using the Gabriel parametric data base formulation [IFAC-CNR, 2010;SPEAG, 2011]. While the Gabriel parameters, derived primarily from measurements in excised tissue, give values below those of more recent research with fresher tissue and do not reflect the anisotropy of muscle and bone, these differences and the variation in frequency over a few kHz are small compared to the differences between the tissues in Table 1 [Barchanski et al, 2007;Gabriel et al, 2009]. Therefore, although the specific values calculated and presented below may change depending on the precise mix of Fourier frequencies, field directions, and tissue geometry, the general patterns of electric field and induced current distribution and their general and relative magnitudes should not.…”