## 2 Materials and Methods
### Calculation of the Power Deposition at the Tip of the Implant  
The determination of the temperature rise in the tissues caused by AIMDs during an MRI session is described in ISO TS 10974:2018 [38]. A four-tier approach has been elaborated with increased complexity and accuracy of estimation between successive tiers. The lower tiers are based on simplifications of the exposure situation, yielding an overestimation of the temperature increase and, therefore, a larger safety margin. On the contrary, the higher tiers involve the realistic implant placement of AIMDs in the human body and the accurate calculation of the incident fields, reducing the overestimation and resulting in a more realistic prediction of the temperature rise. In particular, the Tier 3 approach uses the concept of the transfer function (TF) of an implant and relates the incident tangential electric field along a path to the deposited power in the tissue surrounding the lead tip, which leads to temperature increase [43]. The Tier 4 approach combines the use of anatomical human models and detailed modelling of the implants, thus resulting in the least overestimation compared to the in vivo exposure. However, the simulation time and, in general, the computational resources for the latter evaluation are highly demanding. According to the transfer function approach, the power deposition at the tip of the implant is provided by  
\[\mathrm{P}=\mathrm{A}\left(\int_{\mathrm{L}}\mathrm{E}_{\mathrm{tan}}( \mathrm{z})\mathrm{S}(\mathrm{z})\mathrm{dz}\right)^{2} \tag{1}\]  
where S(z) is the transfer function (TF), A is a calibration factor and \(\mathrm{E}_{\mathrm{tan}}\) (z) is the tangential component of the incident electric field along the lead pathway inside the patient, without the lead in place. Hence, the TF decouples the scattered field from the incident, simplifying the computation. The aim of this work was not to calculate the absolute values of the deposited power at the tip of the lead but to compare among the different pacemaker paths inside a human \begin{table}
\begin{tabular}{c c c} \hline
**Model** & **No. of Coiling Circles** & **No. of Potential Implantation Paths** \\
**Name** & **No. of Coiling Circles** & **No. of Potential Implantation Paths** \\ \hline [PERSON] & 3 & 54 \\ [PERSON] & 2 & 36 \\ [PERSON] & 1 & 18 \\ [PERSON] & 2 & 36 \\ [PERSON] & 2 & 36 \\ [PERSON] & 4 & 72 \\ \hline \end{tabular}
\end{table} 
Table 4: Number of coiling circles and possible implantation paths per anatomical model. model under different scanning scenarios independent of the structure of the device. Thus, the square of the excitation potential across the different paths was assessed as provided by  
\[\text{W}=\left|\int_{\text{L}}\text{E}_{\text{tan}}(\text{z})\text{dz}\right|^{2} \tag{2}\]  
which is proportional to the temperature increase at the tip, as demonstrated in [44]. Equations (1) and (2) are equal for a unity transfer function S(z). Similar approaches have been used in previous works for the assessment of the impact of a high dielectric material at the tip of the implant [45; 46] or for the results of the different positions of the feeding sources on an RF coil [47]. The tangential electric field was scaled to the SAR limits of the Normal Operating Mode as defined in safety standard IEC 60601-2-33 [36]. In particular, regarding the landmarks LD\({}_{1}\) and LD\({}_{2}\), the limit of the head-averaged SAR (3.2 W/kg) was assessed and, for the rest imaging positions, the limit of the whole body averaged SAR (2 W/kg) was used. As many commercial CIEDs are labeled as MR-safe for specific maximum allowed B\({}_{1}\)+ field, the electric field was also scaled to the value of 2 uT at the iso-center of the coil. Both outcomes were chosen because they are automatically calculated and reported by a scanner and are commonly adopted in MRI conditional guidelines and labeling of devices [35].