The Importance of Robotized TMS: Stability of Induced Electric Fields - Robotized Transcranial Magnetic Stimulation - page 33

combine hold with freely for measurement as the head motion in freely is too large
for a static positioning scenario (cf. Sect. 2.3.1 ).

2.2.4 Error Calculation

We cannot assume that the sensor to coil distance or the sensor position are exactly
the same for each single measurement. As this may change the absolute induced
electric field magnitude, we cannot apply an absolute error measure. Instead, we
calculate the decrease in the magnitude of the induced electric field as a relative
error measure. At each timestamp t we compute the error relative to the initial
field. The change in magnitude is defined as:

2
E ð 0 Þ

err rel ð t Þ¼ 1

;

E ð t Þ

2 err rel ð t Þ2½ 0 ; 1 ; ð 2 : 1 Þ

where kk 2 represents the Euclidean norm.
Our field sensor additionally measures the in-plane orientation of the electric
field (see Sect. 3.1 for the importance of coil orientation and direction of the
induced electric field). We obtain the change in the angle as
r ð t Þ¼ arctan E y ð 0 Þ

E x ð 0 Þ arctan E y ð t Þ

ð 2 : 2 Þ

E x ð t Þ

based on the x and y component of the electric field E.

2.2.5 Statistical Analysis

Statistical analysis is carried out with IBM SPSS Statistics version 20 (IBM
Deutschland GmbH, Ehningen, Germany).
As we are interested in the effect of robotized TMS compared to standard TMS
scenarios, we perform an analysis of variance (ANOVA) comparing the means of
hold-and-restrain, hold-and-rest and robot-freely for statistical analysis. Note that a
two-factorial ANOVA cannot be used as we cannot measure free with a coil holder.

2.3 Impact of Head Motion on TMS

2.3.1 Head Motion

Figure 2.7 visualizes the head motion of the three basic scenarios over time for all
subjects. In the two subplots the mean amplitude of translational and rotational