Impact of MRI RF coil design on the RF-induced heating of medical implants: fixed B 1 + rms exposure versus normal operating mode

A direct comparison of the impact of RF coil design under specific absorption rate and B1+rms limitations are investigated and quantified using RF coils of different geometries and topologies at 64 MHz and 128 MHz. The RF-induced in vivo electric field and power deposition of a 50 cm long pacemaker and 55 cm long deep brain stimulator (DBS) are evaluated within two anatomical models exposed with these RF coils. The associated uncertainty is quantified and analyzed under a fixed B1+rms incident and normal operating mode. For a fixed B1+rms incident, the in vivo incident field shows a much higher uncertainty (>5.6 dB) to the RF coil diameter compared to other design parameters (e.g. <2.2 dB for coil length and topology), while the associated uncertainty reduced greatly (e.g. <1.5 dB) under normal operating mode exposure. Similar uncertainties are observed in the power deposition near the pacemaker and DBS electrode. Compared to the normal operating mode, applying a fixed B1+rms field to the untested implant will lead to a large variation in the induced incident and power deposition of the implant, as a result, a larger safe margin when different coil designs (e.g. coil diameter) are considered.


Introduction
The coexistence of static and time-varying electromagnetic (EM) fields in magnetic resonance imaging (MRI) can lead to potential hazards for patients undergoing MRI scans (Norris 2011, Bottomley and Andrew 1978, Bottomley and William 1981, Bottomley et al 1985, Nyenhuis et al 2005).Extensive study has led to procedures and safety guidelines to mitigate those adverse effects (US Food and Drug Administration (FDA) 2014, 2019, International Electrotechnical Commission 2022, ASTM International 2019, International Commission on Non-Ionizing Radiation Protection 2004).However, the major focus of these guidelines are on patients not wearing and medical implantable devices.As the conductive active or passive implantable medical devices (AIMD and PIMD) may interact with the EM field, patients with medical implants usually bear additional risks during MRI examinations, among which radio-frequency (RF)-induced hazards are of the greatest concern.
Ensuring a safe MRI scanning for patients with medical implants is not trivial, as the magnitude of RFinduced hazards during MRI is due to a multitude of variables specific to the implant geometry, MRI system (e.g.RF coil design), patient anatomy, and imaging positions.The impact of implant geometry on the RF-induced hazards can be decoupled by characterizing the implant-RF interaction separately (e.g.implant transfer function as described in ISO/TS 10974 (ISO/TS 2022)), while the contribution from the remaining clinical factors (e.g.MRI system, patient anatomy, imaging positions) are directly correlated to the induced in vivo EM fields that a medical implant is exposed to during MRI scanning.
The absorption mechanism of RF energy in the human body exposed to an RF magnetic field is a superposition of two processes: RF-induced eddy currents and capacitive coupling of stray E-fields close to the capacitors of the RF coils.While clinical factors, such as the human body, may have a significant influence on the first mechanism, the RF coil geometry and design may have a higher impact on the second mechanism.Previous studies have addressed the impact of the human body and RF coil feed configurations on the RF absorption in the human body (Murbach et al 2014, Lucano et al 2018).Previous work (Yao et al 2021) also summarized the potential + B 1 rms spread under normal operating mode for different RF coils.However, none of these studies quantified the impact of RF coil geometry and design on the in vivo EM fields that medical implants are exposed to during MRI scanning, and the end-point power deposition near the implant electrode.
In addition, most investigations are conducted under the normal operating mode defined in the IEC 60601-2-33 standard (International Electrotechnical Commission 2010), which is limited by specific absorption rate (SAR) as listed in table 1.In IEC 60 601-2-33: 2010 (International Electrotechnical Commission 2010), a noncompulsory option, FIXED PARAMETER OPTION:BASIC (FPO:B), is introduced to limit RF and gradient field outputs (peak and RMS) for scanning patients with MR conditional implants, where the risk of RF-induced heating of an MR-conditional device is limited in terms of the root-mean-square (RMS) averaged + B 1 ( + B 1 rms ).This is because, unlike whole-body SAR, + B 1 rms is independent of the patient and calculated consistently by different MRI manufacturers, making it a more consistent approach to assessing RF-induced implant heating.In the latest version (International Electrotechnical Commission 2022), the MR equipment output conditioning (MROC) is introduced as mandatory functionality at 1.5 T and 3 T which allows the MR operator to specify certain output limits of the MR system, e.g.RF transmit coil type, RF polarization, maximum + B 1 rms and maximum gradient slew rate to in line with the MR-Conditional labeling of many implants.
The objective of this study is two-fold.Firstly, we aim to quantify the impact of the MRI RF coil on the in vivo tangential electric field along implant routings, as well as the in vivo power deposition near the implant electrode.Secondly, we intend to investigate the major impact of different exposure limitation strategies (fixed + B 1 rms and normal operating mode) has on the implant RF-safety labeling.The goal is to provide a scientific rational for the selection of labeling strategy during the evaluation of RF-induced heating of medical implants under MRI exposure.

Method
2.1.MRI environment simulation 2.1.1.Anatomical models and RF coil design Two high-resolution numerical patient models were used-the virtual population (ViP) (Gosselin et al 2014) adult male model Duke and the female model Ella.The anatomical properties of the two models are listed in table 2. To maintain consistency, both models were positioned in a standard posture, lying on their backs with their hearts centered at the coronal plane of the MRI bore.Two imaging positions were defined for each anatomical model: • Head imaging position: The anatomical models were positioned with the hippocampus centered at the isocentre of the MRI bore.
• Thorax imaging position: The anatomical models were positioned with the heart centered at the iso-centre of the MRI bore.
These specific positions were chosen to ensure that the images captured were standardized and representative of the respective anatomical structures.
Based on a systematic investigation of commercial MRI systems (mainly from Siemens and GE), 10 RF coils with different geometries and topologies are designed and shown in figure 1(a): • 16-rung high-pass birdcage coils with length of 50 cm, 60 cm, 70 cm and diameters of 60 cm and 70 cm; • 16-rung 50 cm long 70 cm diameter birdcage coils with low-pass, and band-pass topologies; • 50 cm long 70 cm diameter high-pass birdcage coils with 8 rungs, and 32 rungs.
The geometry of the designed birdcage coils are summarized in table 3. The birdcage coil was driven at two ports (I and Q, located 90°apart) in orthogonal mode (equal amplitude with a fixed 90°phase difference between each port excitation), also known as circular polarization mode, where the resulting + B 1 field is circularly polarized and rotating clockwise when looking in the Z-direction.There are a total of N/2 resonance modes for a birdcage coil with the number of rungs N and only in order-1 mode they can generate a high homogeneous + B 1 rms field in the birdcage as we expected (Leifer 1997).Therefore these birdcage coils were tuned to order-1 resonant mode at 64 MHz and 128 MHz based on the procedure defined in IEC standard (International Electrotechnical Commission 2018), where the + B 1 rms field homogeneity of a homogeneous sphere phantom was calculated to ensure the resonance of the RF coil.The + B 1 rms field distribution of the sphere phantom inside different RF coils are summarized in the supporting information (figure S1).In the end, to validate the impact of RF coil design has on the end-point of implant heating, the Tier 3 power deposition of two generic implants (50 cm long pacemaker and 55 cm long deep brain stimulator) are evaluated with pacemaker at thorax imaging position and DBS at head imaging position.

EM numerical implementation
EM simulations were implemented with Sim4Life V7.2 using finite-difference time domain (FDTD) computational method (Taflove and Hagness 2005).Each of the anatomical models was placed at the two predefined imaging positions and exposed with the 10 designed birdcage RF coils listed in table 3. The birdcages were tuned to the resonance frequency using a broadband quadrature excitation with two ports in one end-ring, the applied incident fields correspond to an ideal circularly polarized current distribution.
Numerical FDTD simulations of the RF exposure under different clinical scenarios defined in figure 1 were performed.For each simulation, the models were discretized with a maximum resolution of 2 × 2 × 2 mm 3 , and dielectric properties at 64 MHz and 128 MHz were assigned to the tissues according to the ITIS Tissue Database (Hasgall et al 2018).
Next, the clinical routing of a generic cardiac pacemaker and deep brain stimulator were defined and shown in figure 1(d): (1) the pacemaker routing run underneath the skin from the proximal end of the left pectoral and along the veins, and terminating in the distal end of the left heart ventricle; (2) the DBS routing run underneath the skin from the proximal ends of the left pectoral muscles, along the side of the neck behind the left ear, up to the crown of the head, through the skull, and terminating in the distal end of the thalamus; For each defined clinical routing, 30 splines with constrained random variations from the baseline are generated via IMSAFE module in Sim4Life (Sim4Life V7.2, Zurich MedTech, Zurich, Switzerland) to represent the routing variation during the surgery.

Calculation
For each exposure scenario, the induced in vivo electric field were evaluated and compared under two exposure conditions: • Fixed incident + B 1 rms of 1 μT at the iso-centre of the empty birdcage coil; • Normal operating mode defined in IEC standard; + B 1 rms is defined as the root-mean-square of + B 1 field with an average period (t x ) of 10 s: x where t is time, and t x is the integration time, which shall be any 10 s period over the duration of the entire sequence.In order to mitigate potential numerical uncertainties arising from the use of different grids for various human body models, the + B 1 rms value of 1 μT at the isocenter of an empty birdcage coil is adopted instead of within the human body.However, if it is desired to reference the + B 1 rms value within the human body, a scaling factor can be easily applied.This scaling factor is defined as the ratio between the + B 1 rms value at the isocenter inside the human body and that inside the empty birdcage coil.In the present study, a scaling factor of 0.9 is obtained through numerical simulations of the + B 1 rms value at the isocenter of the anatomical model 'Ella,' using an RF level equals to 1 μT + B 1 rms at the isocenter of the empty birdcage coil.For a direct comparison of the RF-induced incident field to the implant, the following dosimetry quantities are compared: • Electric field distribution at the region of interest (ROI) during MRI procedure (e.g.iso-centre slice); • Max 10g averaged electric field (E g 10 ,max , E 10g was computed using a 10g mass average approach to minimize potential numerical errors, which aligns with the definition of peak Spatial SAR 10g specified in the IEEE C95.3 standard (International Electrotechnical Commission 2022).
• Averaged tangential electric field (over the 30 splines) along each implant routing (E tan ); Next, the Tier 3 RF-induced power deposition(P dep ) near implant electrodes under all the clinical scenarios can be calculated using the following equation (ISO/TS 2022): where the calibration factor, denoted as A, represents the scaling factor of the transfer function.It can be obtained through the calibration approach described in Clause 8 of ISO/TS 10 974 standard (ISO/TS 2022).The transfer function of the implant, denoted as S(l), is numerically modeled using the traditional piece-wise excitation approach as described in Zastrow and Capstick (2014).E tan (l) represents the incident tangential electric fields under each specific clinical scenario, and L corresponds to the length of the implant.

Coil diameter and length
The  B 1 rms of 1 μT at the iso-centre of the empty birdcage coil.more than 5.6 dB higher induced E g 10 ,max compared to RF coil with a diameter of 60 cm), while the RF coil length shows a much lower impact on the in vivo induced electric field (e.g. with an averaged difference of E g 10 ,max less than 2.1 dB).
Figures 2 and 3 also compare the tangential electrical field (E tan ) averaged over the 30 predefined pacemaker routings.As show in the figure, the E tan distribution under all the selected scenarios are also divided into two groups for RF coils with different diameters, while the impact from RF coils length is negligible.It is worth noting, however, that due to the stray E-field near the birdcage coil end ring, the DBS E tan near the neck shows a much bigger difference even with the same RF coil diameter.Therefore, when the exposure is limited by a fixed + B 1 rms , considering RF coils with different diameters will lead to a much larger variation in the RF-induced incident to the implants.In addition, to confirm the trend observed in different RF coil diameters, E tan distribution of an extra coil with a diameter of 65 cm is added in supporting information (figure 5). The

Topology structure and number of rungs
Figure 8 shows the field distribution and E tan under exposure of RF coils with different rung numbers and topology structure (low-pass, band-pass, and high-pass) and the E g 10 ,max are summarized in figure 9.The results show that in general, RF coil topology has a larger impact on the pacemaker (more than 2 dB difference in E g 10 ,max ) compared to DBS, this is because at thorax imaging position (pacemaker case), the hotspot is usually at the armpit, and it can be easily affected by the near-by stray field produced by different coil topology; while the hotspot at head imaging position is much further from the RF coil wall.Similar behaviour has been seen in the anatomical mode Duke, only the results of Ella are shown here.

Power deposition
Figure 10 summarises the power deposition under + B 1 rms =1 μT and normal operating mode exposure.With a fixed + B 1 rms =1 μT, power deposition of RF coils with different diameters shows a much bigger variation (e.g.>4.6 dB for DBS, and >6.1 dB for pacemaker) compared to the normal operating mode (e.g.<3.2 dB for DBS, and <1.5 dB for pacemaker), while RF coil length shows a comparable impact of about 1 dB to both exposure conditions.

Discussion
This work investigates the potential impact that the RF coil has on the RF-induced in vivo electric field and power deposition near the implant electrode via two labeling strategies: fixed + B 1 rms incident and normal operating mode.The major contributions of this work includes: (1) It quantifies the implant incident field uncertainty associated with the RF coil design (e.g.coil length, diameter, rung numbers and topology) under two exposure limitations: fixed + B 1 rms field and normal operating mode.The results show that in general, RF coil design has a significant impact on the RF-induced heating evaluation under a fixed incident + B 1 rms exposure compared to exposures limited by normal operating mode.For a fixed + B 1 rms exposure, the implant incident electric field uncertainty caused by the RF coil diameter and length are about 5.6 dB and 2.1 dB, and the difference from the RF coil topology is about 2.2 dB.In comparison, when exposed under normal operating mode, the incident electric field uncertainty caused by the RF coil diameter and length are about 1.4 dB and 1.5 dB, while the difference from RF coil topology is less than 1.1 dB.
However, it is worth noticing that the impact from RF coil rung number and topology can be much bigger for patients wearing superficial devices near the coil end-ring or larger size patients with arms very close to the coil end-ring, as the stray field near the end-ring capacitors may change dramatically with different rung number and topology.
(2) It reveals the major impact of the two exposure limitation strategies have on the implant RF-safety labeling.
• When the exposure is defined by a fixed + B 1 field: As RF-induced in vivo E tan shows a pretty good correlation with RF coil diameter, a much larger variation of in vivo E tan or SAR will be expected for RF coils with different diameters.For tested implants, labeling with a fixed + B 1 value might be a good strategy, since it is a solid measured value which can be applied universally across different MRI manufacturers and human bodies.For non-labeled implants or off-label use, the strong variation in the in vivo incident field might amplify the current challenge for clinical personnel to assess implant safety correctly since additional information on the RF coil used is needed and safety recommendations are less 'universal' based on the current normal operating mode.
On the other hand, it might hypothetically happen that a + B 1 setting (e.g. 3.2 μT as previously suggested in the FPO:B) might used for untested implants under the assumption that its safe (e.g.cardiac pacemakers as suggested in current literature (Sohns and Sommer 2021, Nazarian et al 2017, Navarro-Valverde et al 2022)).From table 4, it is easy to see that applying a fixed + B 1 strategy will lead to a more conservative exposure compared to normal operating mode (e.g. for cardiac pacemaker inside Ella at 64 MHz, applying a fixed + B 1 rms of 3 μT will lead to a wbSAR of less than 0.5 W kg −1 for RF coils with diameter of 60 cm, while applying a whole body SAR limits of 2 W −1 regardless of RF coil will lead to a potentially four times higher SAR for RF coils with diameter of 60 cm).
• When the exposure is defined by normal operating mode: As the impact from RF coil diameter decreases, much less variation of in vivo E tan or SAR will be expected for different RF coils.For implants labeled by normal operating mode, the impact of RF coil design can be potentially ignored as the dominating impact factor will be the human body (e.g. more than 8.5 dB P dep difference of pacemaker are observed in the literature (Yao et al 2019)).On the other hand, as discussed above, the safety margin of exposure with a fixed SAR limits (e.g.normal operating mode) will be much less compared to a fixed + B 1 strategy (e.g. 3-4times higher wbSAR), but with a potential beneficial of better imaging signal- noise ratio (e.g.1-2 times higher + B 1 field strength) as indicated in table 4. As these exposure limits represent the in vivo incident to the implant, they can be applied naturally to the condition when there is no presence of implants.
Finally, we also want to point out that the RF coil design has a direct impact on the in vivo electric field, but higher in vivo electric field does not necessarily mean higher power deposition, as the implant design itself (e.g.electrical length, electrode, etc) will also greatly affect the in vivo power deposition and temperature.Therefore, the uncertainty of power deposition derived from this work cannot be applied directly to implants with different transfer function.Instead the derived uncertainty of in vivo electric field can be applied and integrated with implant transfer function for a comprehensive uncertainty analysis.,max of Ella with different RF coil topologies and rung ΔR is maximum difference of the E g 10 value when the number of the birdcage coil rungs is 8, 16, or 32.ΔT is the maximum difference of the E g 10 ,max value when the topology structure of the birdcage coil is high pass, low pass, or band pass.

Conclusions
This work quantified the incident field uncertainty associated with RF coil design for patients wearing medical implants during MRI, and reveals the impact the two exposure strategies have on the implant RF-heating labeling: fixed + B 1 rms field and normal operating mode.Ten RF coils with different geometry and topology designs are used, the RF-induced in vivo electric field and the resulting power deposition of two typical active implants (Pacemaker and DBS) within two anatomical models are calculated, the associated variation and correlation are quantified and analyzed.
Our results show that compared to normal operating mode, the RF coil design can cause large uncertainty in the RF-induced in vivo electric field and power deposition near the implant when exposed to a fixed incident + B 1 rms field.In this case, the RF coil diameter shows a direct correlation with the induced in vivo electric field, where a larger coil diameter can double the in vivo electric field and potentially more than four times higher power deposition near the implant electrode.Therefore, when exposed to a fixed incident + B 1 rms field, it is recommended that a wide range of RF coils with different diameters be considered during the RF-induced heating evaluation.

Figure 1 .
Figure 1.Designed birdcage coils (a), sphere phantom and its three views in birdcage coil (b), used anatomical models and imaging positions (c), the implantation trajectories of DBS and cardiac pacemaker (d).
in vivo field distribution difference of Ella and Duke inside different RF coils under a fixed + B 1 rms of 1 μT exposure are shown in figure 2 (for throax imaging position) and figure 3 (for head imaging position).The maximum induced 10g averaged electric field (E g 10 ,max ) are summarized in figure 4. The results show that RF coil with different diameters shows a quite different field distribution (e.g.RF coil with a diameter of 70 cm leads to

Figure 2 .
Figure2.RF-induced in vivo electric field distribution at thorax imaging position and corresponding E tan along pacemaker routing under RF coils with different frequencies, lengths and diameters.The exposure condition is defined by a fixed incident + B 1 rms of 1 μT at the iso-centre of the empty birdcage coil.

Figure 3 .
Figure3.RF-induced in vivo electric field distribution at head imaging position and E tan along deep brain stumulator (DBS) routing under RF coils with different frequencies, lengths and diameters.The exposure condition is defined by a fixed incident + B 1 rms of 1 μT at the iso-centre of the empty birdcage coil.

Figure 4 .
Figure 4. Summary of E g 10 ,max , psSAR, and associated uncertainty of RF coils with different lengths and diameters.ΔD is the minimum difference of the E g 10 ,max or psSAR value across birdcage coils with different diameters.ΔL is the maximum difference of the E g 10 ,max or psSAR value across birdcage coils with different lengths.

Figure 6 .
Figure 6.RF-induced in vivo electric field distribution at thorax imaging position and E tan along pacemaker routing under RF coils with different frequencies, lengths and diameters.The exposure condition is defined by normal operating mode.

Figure 7 .
Figure 7. RF-induced in vivo electric field distribution at head imaging position and E tan along deep brain stimulator (DBS) routing under RF coils with different frequencies, lengths and diameters.The exposure condition is defined by normal operating mode.

Figure 8 .
Figure 8. RF-induced in vivo electric field distribution and E tan along deep brain stumulator (DBS) routing under RF coils with different topologies.

Figure 9 .
Figure9.Summary E g ,max of Ella with different RF coil topologies and rung ΔR is maximum difference of the E g 10 value when the number of the birdcage coil rungs is 8, 16, or 32.ΔT is the maximum difference of the E g 10 ,max value when the topology structure of the birdcage coil is high pass, low pass, or band pass.

Figure 10 .
Figure 10.Summary of P dep of the generic pacemaker and DBS exposure with fixed +B 1 rms = 1 μT and normal operating mode.ΔD is the minimum difference of the P dep value across birdcage coils with different diameters.ΔL is the maximum difference of the P dep value across birdcage coils with different lengths.

Table 1 .
SAR limits for body coils defined in IEC standard (International Electrotechnical Commission 2022).

Table 2 .
Summary of anatomical properties of the anatomical models.

Table 3 .
Design details of the RF coils used in this work.

Table 4 .
Resulting SAR limits (whole body SAR at thorax imaging position and head SAR at head imaging position) of exposure with fixed + B 1 rms =1 μT and corresponding + B 1 rms at normal operating mode.Those values are applicable to both patients with and without implants.