## 4 Analysis  
Brain Vision Analyzer 2 (Version 2.0.1.3417) from BrainProducts and MATLAB (The MathWorks, Natick, MA, USA) were used to analyze the EEG data. Each gradient pulse in the customized EPI sequence commenced with a 10 ms period during which the gradient ramped up linearly to a value of 20 mT m\({}^{-1}\) giving a rate of change of gradient, dG/dt, of 2 Tm\({}^{-1}\)s\({}^{-1}\). This was followed 10 ms later by a 10 ms period during which the gradient ramped down to zero with dG/dt = \(-2\) Tm\({}^{-1}\)s\({}^{-1}\) (Figure 6). Thus, equal and opposite artefact voltages (in \(\upmu\)V) were induced during both periods. The induced GAs were averaged over 30 pulses (Figure 6) to measure the artefact voltage of each electrode, and then we evaluated the average voltage over the central 5 ms of each ramp period, before taking the difference between the positive and negative values. In this way, the effect of any baseline offset and high-frequency fluctuations were eliminated. The severity of the GA depending on the phantom shape was characterized by calculating the root-mean-square (RMS) amplitude of the artefact voltage for each orthogonal gradients across the 31 electrodes (excluding the EOG electrode) located on the phantoms' or subjects' head and, finally, by averaging these measures over the phantom trials and human subjects. To graphically depict the difference between the effects of the phantom shape on the GA, spatial voltage maps of average RMS artefact voltages, for each gradient (RL, AP, and FH), were produced using Brain Vision Analyzer 2 for the different phantoms and human subjects. Additionally, the structural similarity (SSIM) was also calculated for the head-shaped phantom and the spherical phantom spatial maps in comparison to the subjects' spatial maps for each gradient. The SSIM index is a standard method to evaluate the similarity between two images (test and reference images). SSIM assesses [22] the visual impact of three characteristics of an image: luminance \(l(x,y)\), contrast \(c(x,y)\), and structure \(s(x,y)\) with respect to a reference image. The overall index is a multiplicative combination of the three terms:  
\[SSIM(x,y)=[I(x,y)]^{\alpha}.[c(x,y)]^{\delta}.[s(x,y)]^{\gamma} \tag{5}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Subjects** & **Age** & **Sex** & **Height (cm)** & **Weight (lb)** \\ \hline
**Sub1** & 29 & M & 177 & 160 \\ \hline
**Sub2** & 24 & F & 160 & 140 \\ \hline
**Sub3** & 31 & M & 180 & 150 \\ \hline
**Sub4** & 35 & M & 165 & 154 \\ \hline
**Sub5** & 22 & F & 180 & 135 \\ \hline
**Sub6** & 25 & F & 158 & 120 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the six human subjects tested in the study. where \(\alpha\), \(\delta\), and \(\gamma\) are exponents with the value of 1. _I(x,y)_, _c(x,y)_, and _s(x,y)_ are calculated from the local means, standard deviations, and cross-covariance for images \(x\), \(y\). In this work, the SSIM index was computed to quantify how close or different the spatial maps are. The EEG artefact waveform of each channel in the study 2 was acquired for a 100 ms (slice) duration. Each waveform was baseline-corrected by subtracting the average channel artefact voltage in the corresponding slice duration. The baseline-corrected voltages were averaged over the slices while excluding the periods of the EEG signal with unacceptable head movements for the subject data. To assess the effect of the phantom shape on the induced GA, the RMS over the slice acquisition period was then calculated for the average artefact on each lead. The average and standard deviation of the EEG data over phantom trials and subjects were also calculated. A paired \(t\)-test was applied to the phantoms' and subjects' data to assess if there were significant differences between the GAs, which were induced by the EPI sequence due to the variation of the geometric shapes. The MR data were realigned by using SPM8 [23] to check the head movement, so to keep them stable during the repeated MRI acquisitions.