Towards an integrated radiofrequency safety concept for implant carriers in MRI based on sensor‐equipped implants and parallel transmission

To protect implant carriers in MRI from excessive radiofrequency (RF) heating it has previously been suggested to assess that hazard via sensors on the implant. Other work recommended parallel transmission (pTx) to actively mitigate implant‐related heating. Here, both ideas are integrated into one comprehensive safety concept where native pTx safety (without implant) is ensured by state‐of‐the‐art field simulations and the implant‐specific hazard is quantified in situ using physical sensors. The concept is demonstrated by electromagnetic simulations performed on a human voxel model with a simplified spinal‐cord implant in an eight‐channel pTx body coil at 3T . To integrate implant and native safety, the sensor signal must be calibrated in terms of an established safety metric (e.g., specific absorption rate [SAR]). Virtual experiments show that E ‐field and implant‐current sensors are well suited for this purpose, while temperature sensors require some caution, and B1 probes are inadequate. Based on an implant sensor matrix Qs , constructed in situ from sensor readings, and precomputed native SAR limits, a vector space of safe RF excitations is determined where both global (native) and local (implant‐related) safety requirements are satisfied. Within this safe‐excitation subspace, the solution with the best image quality in terms of B1+ magnitude and homogeneity is then found by a straightforward optimization algorithm. In the investigated example, the optimized pTx shim provides a 3‐fold higher meanB1+ magnitude compared with circularly polarized excitation for a maximum implant‐related temperature increase ∆Timp≤1K .


Abstract
To protect implant carriers in MRI from excessive radiofrequency (RF) heating it has previously been suggested to assess that hazard via sensors on the implant. Other work recommended parallel transmission (pTx) to actively mitigate implant-related heating. Here, both ideas are integrated into one comprehensive safety concept where native pTx safety (without implant) is ensured by state-of-the-art field simulations and the implant-specific hazard is quantified in situ using physical sensors. The concept is demonstrated by electromagnetic simulations performed on a human voxel model with a simplified spinal-cord implant in an eight-channel pTx body coil at 3T. To integrate implant and native safety, the sensor signal must be calibrated in terms of an established safety metric (e.g., specific absorption rate [SAR]). Virtual experiments show that E-field and implant-current sensors are well suited for this purpose, while temperature sensors require some caution, and B 1 probes are inadequate. Based on an implant sensor matrix Q s , constructed in situ from sensor readings, and precomputed native SAR limits, a vector space of safe RF excitations is determined where both global (native) and local (implant-related) safety requirements are satisfied. Within this safe-excitation subspace, the solution with the best image quality in terms of B þ 1 magnitude and homogeneity is then found by a straightforward optimization algorithm. In the investigated example, the optimized pTx shim provides a 3-fold higher mean B þ 1 À Á magnitude compared with circularly polarized excitation for a maximum implant-related temperature increase ΔT imp ≤ 1 K.
To date, sensor-equipped implants interfaced to a pTx scanner exist as demonstrator items in research labs, but commercial devices are not yet within sight. This paper aims to demonstrate the significant benefits of such an approach and how this could channels. 50,51 Dual-drive birdcage coils have been used to mitigate RF-heating of wire-like implants, 33,52-55 but more promising results were obtained when more channels were available 29,[56][57][58] and exploited to optimize patient safety and image quality simultaneously. 39,51,[59][60][61] While most of the optimizations in former work were based on simulation data alone, there are also a few studies 30,31,35,62 where a sensor reading was used to determine the pTx settings.
Those extra degrees of freedom come at a price, however, as pTx can also generate SAR and temperature hotspots throughout the exposed body. 63,64 Specific solutions for this problem have been developed, [65][66][67] most notably in the context of 7T MRI, 50,[68][69][70][71] but native RF safety is still a field of vivid ongoing research. 72 The basic methodology (i.e., measurement assisted 73,74 vs. simulation only 70,71,75 ); the modeling approach (e.g., subject specific [76][77][78] vs. static voxel models [79][80][81]; the hazard metric (e.g. SAR 82 vs. volumetric absorption rate 83 vs. temperature 72,82 vs. thermal dose 84,85 ); the thermal model (e.g., Pennes' bioheat equation 86 vs. generic bioheat transfer model 87 ); all these and more ingredients of native RF safety assessments are still evolving and still debated. Native safety is outside the focus of the present work, however, which is why one specific and widely used 50,67,[88][89][90] approach has been adopted here. This is neither an endorsement nor a requirement, however; the framework proposed here is completely modular; the implementation of native RF safety is just one building block that can easily be exchanged or modified.
What has been missing, to date, is an integrated safety concept for in situ hazard control, locally near the implant and globally in the rest of the body, and simultaneous B þ 1 optimization. Here, such a concept is proposed, combining a state-of-the-art simulation-based safety model for the native case with sensor information quantifying the implant-related hazard. It will be shown how in situ sensor data can be processed on the fly to provide the optimal safe steering conditions for the pTx scanner.
The concept is designed as an alternative to today's Tier 3 assessments as defined in ISO/TS 10974. 5 It relies on the same assumptions as this state-of-the-art approach, most notably the applicability of the transfer function concept, 16 but offers distinct advantages. To illustrate the proposed concept in detail, an example application of a virtual experiment in a 3T scanner with an eight-channel pTx body coil is presented. For better insight into the problem and to ensure that no potential complications are overlooked, Tier 4 simulations are presented here (i.e., a human body model with the implant embedded is simulated in full). Tier 4 is typically not computationally feasible unless a very simplified implant model is treated. In the present work this is realized by a straight lead with an uninsulated tip touching the spinal cord, mimicking a stimulator device for pain treatment. Despite its simplicity, this dummy implant is fully sufficient to exhibit the problem, a thermal hotspot at a position where in reality it would cause severe damage to the central nervous system, and to investigate the efficacy of the proposed mitigation. In a practical application of the concept, the implant and its trajectory can assume all levels of complexity, because neither Tier 4 nor even Tier 3 simulations need to be performed (only the underlying assumptions of a Tier 3 approach must be fulfilled). While the majority of this paper's results has been obtained by numerical simulations, the critical underlying assumption that the calibration of the primary sensor signal against a hazard measure like temperature is independent of implant path or tip position, has been verified experimentally.

| METHODS
The proposed approach is modular, and its building blocks are summarized in Figure 1. Simulations of the case without the implant are used to derive a native safety limit ( Figure 1A-C). An implant sensor ( Figure 1D) is then used to generate a raw sensor matrix Q s 35 ( Figure 1E), which, in conjunction with a precalculated sensor calibration ( Figure 1F), provides an implant safety limit ( Figure 1G). Combining both the native and the implant safety limit ( Figure 1H) allows for safe B 1 shims ( Figure 1I,J). Most of the following subsections can be directly linked to the individual panels of Figure 1. This is indicated in the subsection headings, when appropriate.

| Field calculations (Figure 1A)
A static pTx shim 50 of an N ch -channel transmit system is described by a complex vector where E c is the reference electric field if only transmit channel c is excited by u c ¼ 1. Point Q-matrices Q pt r ð Þ 43,88,91 are calculated as described in Reference. 88 For any shim vector u, the point SAR is given by where σ and ϱ denote the electric conductivity and mass density of the voxels' tissue, respectively. The conjugate transpose is indicated by a † superscript. The transition from "point SAR", where "point" refers to the grid resolution of the numerical simulations, that is, a threedimensional volume in the μl range, to the more commonly used mass-averaged SAR, is then performed by averaging the Q pt matrices accordingly.
2.2 | Safety limits for the native case ( Figure 1B) As a safety model for the native case, the approach of the IEC 60601-2-33 standard 7 is adopted, where the hazard of pTx MRI is quantified in terms of local and nonlocal SAR with limit values depending on the body region.
The IEC SAR limits (6 min averages) in the "normal mode" are 10 W=kg for 10 g averaged local SAR in head/torso, 20 W=kg for local SAR in the extremities, 2 W=kg for body SAR, and 3:2 W=kg for head SAR. For a given shim vector u, mass-averaged Q-matrices Q av are constructed accordingly, that is, local matrices of every voxel are averaged over 10 g while the two global matrices are averaged across the whole head and body, respectively. Normalized matrices b Q are defined by dividing each Q av by its assigned SAR limit; they can be used to calculate the normalized SAR 10g , d SAR, analogously to Equation (1). The total number of these matrices is The human voxel model Duke 79 with tissue properties from the IT'IS 4.0 database 92 was inserted in supine position with the heart at the scanner isocenter z ¼ 0 mm ð ). The simulation region was cropped at the knees to limit the computational burden. Two simulations were carried out, one with and one without the implant.
The considered model implant was a straight wire (300 mm length, core: one-dimensional wire as perfect electric conductor 93 ; insulated [relative permittivity ε r ¼ 3] except for 10 mm at the distal tip) that was oriented parallel to the z-axis and that touched the spinal cord at coordinates  95 This neglects element-coupling effects that are not relevant for the scope of this paper.
Ten-gram averaged Q-matrices were calculated at each position r by convoluting the point matrices Q pt with a discretized spherical kernel.
For simplicity and calculation speed, a uniform tissue density of 1000 kg=m 3 was assumed for averaging, as the difference between SAR and volumetric energy absorption rate is known to be small. 83 Thermal simulations were carried out in Sim4Life exploiting Pennes' bioheat equation, 86 using the same voxel models in the same discretization as the electromagnetic simulations. Calculated electric loss density maps L r ð Þ ¼ ϱ r ð ÞSAR pt r ð Þ and published tissue metabolism 92 were used as heat sources. As is frequently done, 1,96 a constant blood pool temperature of 37 C was assumed, and heat losses to the environment and thermoregulation were neglected. 82 Subsequently, temperature maps were generated by simulating 60 min body metabolism without RF followed by 60 min of both body metabolism and constant RF exposure and were denoted as steady-state temperatures T ss . The highest observed dT dt j t¼120 min was below 3 mK/min.

F I G U R E 2
Setup of an eight-channel pTx coil (one channel is marked by a brown ring with four ports in orange), RF shield (gray), and the human voxel model Duke 79 with a dummy stimulator implant (straight wire, blue) touching the spinal cord (red). The subject is positioned with the central axial slice (z ¼ 0) through the heart. The implant is aligned along z and the tip coordinates are x, y, z ¼ 0, À 106 mm, À 130 mm ð Þ . All example simulations throughout this paper refer to this geometry. The simulation region is cropped at the knees. Left: sagittal slice; right: threedimensional view. pTx, parallel transmission; RF, radiofrequency 2.4 | Virtual observation points generation and worst-case shim vectors ( Figure 1C) The normalized matrices b Q for either simulation, with and without implant, are used for separate virtual observation point (VOP) calculations. 67 The SAR overshoot ε 67 is set to 1% of the worst possible local normalized SAR of the native case. The 7:7 Â 10 6 nonzero matrices b Q are compressed to N VOP,nat ¼ 353 VOPs for the native case and N VOP,imp ¼ 327 VOPs for the implant case, subsequently referred to as "native VOPs" and "implant VOPs", respectively.
This m d SAR r ð Þ represents an estimate for the maximum of d SAR at position r. By construction, it is guaranteed that m d SAR r ð Þ ≤ 1 everywhere in the native case, that is, the shim meets the IEC limits, but such limits can be violated, if the implant is added.

| Suitability test and calibration of possible implant sensors (Figure 1F)
Five physical quantities, the virtual "sensor readings" SAR (denoted as sensor SAR), jE z j 2 , jHj 2 , temperature change-rate dT=dt and induced RF current I RF , were investigated in terms of their ability to provide a measure for implant safety in MRI by exploring how these quantities respond to different pTx shim vectors. To this end, the circularly polarized (CP) mode was applied as a universal reference plus 99 randomly selected shim vectors, all scaled to hit the IEC limits in the native case. A selection of 100 shim vectors is clearly insufficient to scan the 14-dimensional (seven phase differences and seven relative amplitudes after scaling) parameter space and it cannot be ruled out that particularly pathologic cases were not included in the selection. Still, this selection will span the relevant sensor readings and thus can be used to investigate the feasibility of calibrating the sensor and to evaluate if more shim vectors are required.
The sensor readings for SAR, jE z j 2 , jHj 2 , and dT=dt were computed for each shim vector by averaging the simulation results over a cube with edge length 4 mm (2 3 voxels) centered at the implant tip. The induced RF current I RF in the implant was simulated by applying Ampère's circuital law to a quadratic loop of 2 Â 2 voxels around the wire. Two positions were investigated for this sensor, either close to (10 mm) or relatively far away (250 mm) from the tip.
The sensor readings were plotted against four established safety measures, namely, point SAR (SAR pt ), SAR 10g , implant-induced temperature increase ΔT imp (difference between steady-state temperatures with and without implant), and steady-state temperature T ss . All safety measures were evaluated as their respective maximum value within the tip region of interest (ROI), a 40 mm Â 40 mm Â 80 mm cuboid aligned along the implant and centered at its tip. The ROI was chosen such that it incorporates the full volume around the implant where m d SAR > 1 is possible (see below).
To speed up the computations, the thermal simulations were confined to a 100 mm Â 100 mm Â 140 mm box centered at the implant tip.
For 15 shim vectors, additional full-space thermal simulations were performed for comparison, and the resulting steady-state temperatures always agreed within 0:1 K everywhere in the ROI ( Figure S2). For the maximum temperature that always occurred at the implant tip, differences were below 0:01 K.

| Experiments on the robustness of the sensor calibration
In real-life applications, the sensor calibration would be performed ex ante by the implant manufacturer. It is thus crucial to ensure that this calibration is robust and universally valid for all patient and implant geometries. To test this, experiments in a pTx testbed 31 with an eight-channel 7Thead coil 97 and a cylindrical (200 mm diameter, 198 mm height) polyvinylpyrrolidone (PVP) phantom (relative permittivity ε r ¼ 43:8, electrical As a dummy implant, a loop of a semirigid coaxial cable (5 mm uninsulated inner conductor, 12 mm uninsulated outer conductor) was submerged into the phantom according to Figure 3A. An E-field sensor (E1TDSz SNI, SPEAG, Zurich, Switzerland) radial to the coaxial cable and a fiber-optic temperature sensor (FBG/FBG-TEMP-XXS with CANFDX/L-FBG-T8, imc, Berlin, Germany) were attached to the tip ( Figure 3C). Thousand RF pulses were fired with 0:1 ms duration and random voltage vectors (but cautiously staying within the linear regime of the E-field probe).
The voltage between the inner and outer conductor was measured at the remote end of the implant and recorded together with the corresponding E-field near the tip. Ten shim vectors, covering the full range of possible sensor values, were then selected and successively applied for 60 s to measure the temperature increase. This process was repeated for a second configuration where the "implant" tip was bent $50 mm away from the E-field sensor ( Figure 3B,D). The temperature increase was defined as the difference between the mean temperature 5 s before heating and mean temperature from 58 s to 62 s after the start of the heating.
2.7 | Generation of the implant sensor matrix Q s ( Figure 1E) To integrate the sensor readings into a comprehensive safety assessment combining native and implant related hazards, an implant sensor matrix Q s is constructed, 35,59 such that u † Q s u quantifies the implant-related patient hazard associated with a shim vector u.
To determine Q s for an N ch -channel pTx system with a RMS sensor, N 2 ch linear independent shim vectors u a (1 ≤ a ≤ N 2 ch ) are applied sequentially 35 ; a possible set of vectors is given in the supporting information C. Q s is then obtained by solving the linear equation system u † a Q s u a ¼ q a , where q a denotes the respective sensor reading. Q s is given in units of q a , such as K, W/kg, or A. For the case of a temperature sensor, Q s would be identical to the already known T-matrix. 98,99 Conceptually new is the idea to measure such matrix in situ by a point-like sensor. In analogy to F I G U R E 3 Experimental setup to measure correlation between the tip voltage, radial E-field, and temperature. (A) The dummy implant forming a loop within the phantom with attached fiber-optic sensor. (C) Zoom of (A) with schematic radial E-field sensor orientation. (B) Setup submerged in a cylindrical PVP phantom in position 1 with the implant tip near the E-field probe. (D) The same for position 2 with $50 mm between the implant tip and field probe. PVP, polyvinylpyrrolidone the native case, a normalized, dimensionless implant sensor matrix b Q s ¼ Q s =q limit is introduced, such that any safe shim is described by u † b Q s u ≤ 1.
Unlike the native case, however, the IEC SAR 10g limits are not suitable, 55 see also below, and universally accepted limit values q limit for implants do not yet exist. Different choices for q limit are therefore investigated in the following.
2.8 | Shim vector optimization for B þ 1 quality ( Figure 1H,J) Once the hazard matrices b Q k ð Þ VOP,nat and sensor matrix b Q s are known, the derivation of a static B 1 -shim for implant heating mitigation 29,89,100 is a straightforward optimization problem. In this work, the Nelder-Mead algorithm 101 was applied to minimize a cost function C based on the simulated complex B þ 1 r ð Þ maps for each pTx channel: where λ 0,1, 2,3, 5,10,20,80, ∞ f g is a regularization parameter, To illustrate how different choices of the sensor limit q limit affect the resulting mean B þ 1 À Á performance of CP and pTx modes, a point-SAR sensor was selected as an example and the optimization was performed for different q limit values. The optimization details are provided in the supporting information D.
In a practical application of the concept, the only computational steps to be performed in situ are the normalization and diagonalization of Q s , typically an 8 Â 8 matrix, and the solving of the optimization problem. The additional computational load to incorporate the implant is negligible.

| Single-sided safety assessments
The need for a comprehensive safety assessment, implant plus residual body, is best illustrated by "single-sided" assessments. Figure 4A shows an example of a shim vector designed to keep ΔT imp ≤ 0:1 K but without a native safety constraint. In the arms (i.e., far away from the implant), a maximum SAR 10g of 950 W=kg is found in this case, vastly exceeding any acceptable limit. Only adhering to the native IEC SAR limits, on the other hand, also fails in the presence of an implant. Figure 4B-D shows SAR 10g , SAR pt , and T ss near the implant tip for CP shim. While, by construction, SAR 10g meets the 10 W=kg limit everywhere (i.e., also at the implant tip), the point SAR exceeds 400 W=kg, resulting in a hazardous steady-state temperature of T ss ¼ 41 C at the implant tip touching the spinal cord.

| Validation of implant hazard confinement and optimum sensor placement
For the given exposure geometry (see Figure 2), maximum intensity projections of m d SAR r ð Þ, see Equation (2), are shown in Figure 5. In the native case ( Figure 5A-C), IEC SAR limits are, by construction, nowhere exceeded (i.e., m d SAR r ð Þ ≤ 1 everywhere), while in the implant case ( Figure 5D-I), the same shim vectors produce SAR 10g values overrunning the IEC limits by factors of up to seven, near the implant.
The zoomed images show that this is indeed confined to a single region of $ 15 mm radius around the tip. This method allows to identify/ confirm hazard-prone regions with their possible SAR overshoot severity and size, and to verify the correct sensor position. In the depicted case, the only critical area is at the uninsulated implant tip, which was used as the point sensor location in the subsequent analysis. If, for a different implant, a secondary hotspot did exist (e.g., further up the device), its presence and location could be revealed by such an analysis and a second sensor might be needed to control that location. The maximum normalized SAR differences m d SAR imp À m d SAR nat , depicted on a magnified scale in Figure 5J-L, also reveal some non-local implant effects. The changes of less than 10% away from the implant are safety-wise not relevant; they illustrate that the scattered E-field from the implant slightly alters the field distribution in the entire upper body.

| Suitability test of possible sensors
For five conceivable sensor types, it was investigated how their output relates to different safety measures ( Figure 6).
SAR and jE z j 2 (columns I and II) are linearly correlated to all safety measures and can easily be calibrated in those terms. Such a calibration is not possible with the scatter of jHj 2 (column III). The dT=dt sensors (column IV) can be calibrated equally well for a background heating of T 0 ¼ 37:2 C (e.g., prior to an MR examination). However, if the background temperature increases, as it might do during prolonged RF exposure, the curves shift, which needs to be considered. The implant current I RF (column V) correlates well with all safety measures when measured close to the implant tip. If the distance between sensor and implant tip increases, the sensor's sensitivity decreases, and the noise level increases. A linear correlation still persists, however, even 250 mm away from the tip. It is an interesting side result of Figure 6 that significant differences exist only between the sensor types (columns I-V), while all four safety measures (SAR pt , SAR 10g , ΔT imp , T ss ) (rows a-d) turn out to behave in a largely equivalent manner.
More quantities considered as field sensors are shown in Figure S3.
F I G U R E 6 Correlation of five virtual sensor readings, that is, simulated values of (in principle) measurable physical quantities (columns I-V), with four possible hazard quantifiers (rows a-d). The implant current I RF (V) was determined at the two indicated distances, all other readings directly at the tip (cf. Methods section for details). The different curves for the dT=dt sensor (IV) correspond to different base temperatures T 0 of the surrounding tissue. All data are based on 100 different shim vectors (CP mode and 99 randomly chosen) satisfying the IEC normal mode SAR limits of the native case. CP, circularly polarized; SAR, specific absorption rate

| Experimental validation of sensor calibration robustness
The experimental calibration curve of the radial E-field as a function of the sensor signal (voltage between inner and outer conductor) for 1000 random shim vectors with a maximum single channel voltage of 0:55 V is shown in Figure 7A. The signals are linearly correlated with the Pearson correlation coefficient r ¼ 0:969. Shim vectors exist that result in a near zero E-field at the tip.
The correlation between the measured temperature rise ΔT imp and the squared sensor signal for 10 selected shim vectors with maximum single channel voltage of 2:75 V at two different positions is shown in Figure 7B. While the maximum temperature difference at position 2 is approximately twice as high as for position 1, all the measurements follow the same linear fit with r ¼ 0:992, independently of the position of the implant tip.

| Comparison of B 1 -shims for the native case and implant case
For any given native-safe shim, the sensor reading determines the safety state completely and allows to separate unsafe from safe shims. For the example of a SAR sensor, this is shown in Figure 8A with red and orange dots, respectively. But even within the "safe" manifold where the maximum spatial normalized SAR, max r d SAR r ð Þ ≈ 1 (all vectors were scaled to fully exploit the IEC limits in the native case), different classes can be distinguished. All tested shim vectors with a RF-induced temperature increase of ΔT imp ≤ 2 K, for example, form a compact subclass within all safe shims.
Only minor differences in B þ 1 performance ( ≤ 10% in the CV and ≤ 5% in the mean of the B þ 1 distribution) are found when applying the same shim vector with and without implant, while max r d SAR r ð Þ can increase by a factor of 8 when the implant is inserted ( Figure 8B-E). Safe shim vectors with ΔT imp ≤ 2 K fill nearly the entire available shim subspace for the implant case, however. This indicates that "nearby" any unsafe shim a safe one with similar B þ 1 homogeneity and mean B þ 1 À Á can be found. The best achievable mean B þ 1 À Á for implant-safe shims, for instance, is only $ 8% below the overall maximum of the native case.

| Optimization
So far, the parameter space has been explored with random shim vectors. In the following, optimized shims are investigated. In this example, we describe the simplest possible case of static pTx ("B 1 shimming") where, except for a global amplitude modulation, the complex voltage vector is kept constant during the RF pulse. The optimization goal is an intense but spatially homogeneous B þ 1 field, here characterized by only two parameters, the mean and CV of B þ 1 in a given ROI. Please note that this is an example, not a restriction. Different pTx applications or more complex optimization goals could easily be incorporated. À Á for the corresponding optimized shims. For comparison, the CP mode results are also indicated. Note that, for the same image homogeneity, the pTx solution for the most stringent sensor limit (black curve) still allows more mean B þ 1 À Á than the CP mode for the most lenient case (orange dot). The four shim vectors used in Figure 10 are marked by numbers. CP, circularly polarized; pTx, parallel transmission; SAR, specific absorption rate Four example shims are investigated in more detail in Figure 10. Near the implant, the local B þ 1 -homogeneity is lower for shims with high tip SAR (columns II and IV, "SAR 10g ≤ 10 W=kg") compared with low tip SAR shims (columns I and III, "ΔT imp ≤ 0:1 K"). Areas with temperatures exceeding 40 C can be found in the arms (Figure 10IIIc,IVc), even in IEC normal mode. Generally, it is observed that B 1 -shims optimized for high homogeneity require larger variations in the individual channel voltages compared with shims optimized for high mean B þ 1 À Á (Figure 10IIId,IVd).

| Point sensor limitations
In Figure 11 it is investigated how well the optimized pTx shims follow the calibration curves for a point-SAR sensor, which were derived based on completely random shims. For the hazard parameter ΔT imp , the data agree well ( Figure 11A), but for T ss a deviation occurs ( Figure 11B): for sensor-SAR values ≤ 60 W=kg (ΔT imp ≤ 1 K), the maximum steady-state temperature lies above the calibration curve (but below 38:5 C). Note that we previously defined T ss as the maximum steady-state temperature within a 40 mm Â 40 mm Â 80 mm volume around the tip. If we look directly at the tip, instead, the deviation vanishes ( Figure 11C).

| DISCUSSION
This work describes a possible new approach to ensure safety for patients with implant in MRI. To use implant sensors for MRI safety purposes has been proposed and implemented previously [11][12][13][14][15]28,31,33,35,38 ; the novelty of the present study is that (i) a variety of conceivable sensors were investigated, and not just a single one; (ii) safety and image quality are consistently treated as an inseparable optimization goal; and (iii) global "native safety" requirements (determined by state-of-the-art precalculations) and local "implant safety" requirements (determined in situ by a sensor on the implant) are integrated within a single concept. The latter is achieved by introducing normalized (and dimensionless) quantities for the native or implant case, which can then be combined to ensure full patient safety, even if different safety measures are used in either subdomain.
It was shown that, in addition to providing a subject-specific safety assessment, the sensor data can be exploited for B þ 1 -optimization on pTx systems. The feasibility of the concept is exemplarily demonstrated in silico for body imaging at 3T using an eight-channel pTx body coil and a dummy implant resembling a neurostimulator touching the spinal cord as a critical application.
F I G U R E 1 0 Simulated parameter maps for the four selected shim vectors (columns I to IV) marked in Figure 9. (Row a) jB þ 1 j in the imaging slice (z ¼ 0 mm) with optimization ROI (axial slice through torso without arms) delineated by a white border. (Row b) SAR 10g in "tip slice" at z ¼ À130 mm. (Row c) Steady-state temperature T ss in the tip slice. (Row d) Amplitudes of the shim vector u c . The white arrows point to the implant's x/y position. ROI, region of interest; SAR, specific absorption rate Tier 4 simulations according to ISO/TS 10974 5 are straightforward to perform for simple straight wires as dummy implants but rapidly become unfeasible when realistic implants with very detailed geometries and a variety of possible trajectories in the body are to be studied. Consequently, a Tier 3-based approach is widely used in real-life safety assessments of AIMDs, 102 which is permissible if and only if the following preconditions are fulfilled: (a) the dominating, implant-related safety hazard must be known to occur at the implant tip; and (b) the transferfunction concept must be applicable, that is, noticeable changes to the preexisting E-field distribution are confined to the vicinity of the implant.
For the sensor-based assessment described here, the same conditions apply. A Tier 3 assessment typically consists of the following steps: (i) the implant's transfer function is measured or simulated, and (ii) it is validated by measuring the response to RF exposure (e.g., in an automated test system 103 ); (iii) thousands of possible trajectories are analyzed in precomputed field distributions of multiple possible subject models and various birdcage coils; and finally (iv) a worst-case analysis is carried out by simulating the temperature increase in tissue for the worst SAR cases. The corresponding assessment for sensor-equipped implants would be (I) to calibrate the sensor, that is, to determine the relationship between sensor reading and E-field at the tip in phantom experiments with a dedicated implant testbed (e.g., as described in 31 ), corroborated by simulations. An appropriate measurement system would need to incorporate pTx and measure a few implant exposure scenarios. In step (II), detailed simulations of the implant tip region (alternatively: animal experiments) are performed to establish the link between the hazard metric of interest (temperature increase, local SAR, etc.) and the incident E-field. Obviously, step (I) corresponds to the combined steps (i) and (ii) of the Tier 3 assessment, while step (II) corresponds to step (iv).
Step (iii) is not needed anymore, with an in situ assessment. In summary, this results in a much simpler safety assessment for the implant manufacturer.
As a side result, the present work confirms that the universally applied safety measure for the native case, SAR 10g , 7 fails to ensure safety for implants with their locally excessive E-field. 39 This is more than the practical problem of determining SAR 10g at the critical position; as demonstrated in Figure 4, the metric itself is no longer appropriate because implant heating varies on shorter length scales than native RF heating. On the other hand, it was shown that a concept focusing on the implant alone is also inadequate, as unacceptable tissue heating can occur elsewhere in the body. The implant's response to the actual exposure conditions is determined in situ by measuring the sensor Q-matrix Q s in a low-power prescan.
For eight-channel pTx, this process takes less than 20 ms with a diode-sensor. 35 Q s can be compared with the widely applied implant transfer function, 16 which is measured in a phantom or determined by simulations. Once known, the transfer function allows to compute the E-field at the tip by a weighted integration of the tangential E-field along the implant trajectory. Unfortunately, in most cases, neither the E-field distribution nor the implant trajectory is precisely known. Q s provides the same information, only the (analog) computation is already performed for all possible shim vectors; and as Q s is measured in situ, it accounts for the actual E-fields and the actual implant trajectory.
The proposed safety concept is modular and kept as general as possible: it is not restricted to a specific sensor type or native safety assessment. For the latter, the maximum product max i u † M i u of shim vector u and matrices M i was constrained by one. Normalized SAR-VOPs 67 b Q i were used in this work because the IEC SAR limits are currently the most widely used safety metric. SAR could easily be replaced or combined with other metrics, for example, pTx channel power, [104][105][106] normalized temperature matrices 99 b T i , or temperature correlation matrices. 107 The integration of a thermal dose concept, for example, cumulative equivalent minutes at 43 C (CEM43), 84,85,108,109 would not be impossible but less straightforward, as integration over time has to be implemented. More uncertainties like anatomical variance, 70,110 patient position, 106 or breathing 71 need to be considered. The implementation of such an overarching native safety concept is certainly important, but this is beyond the scope of the present work.
Temperature simulations in this work were based on Pennes' bioheat equation, 86 which is widely used but has known shortcomings. 111,112 It can be extended, if needed, by vascular tree simulations [113][114][115] or discrete vasculature models. 116,117 Another alternative is the generic bioheat transfer model, 87,118 which has been shown to still work well, even when the blood pool temperature increases continuously. 119,120 While different thermal modeling approaches are likely to result in different steady-state temperatures, the presented concept itself is not expected to change.
The optimization module is another independent block within the concept and can easily be exchanged with a different one, if desired.
Dynamic pTx applications like Transmit SENSE, 42,43 Spokes, 121,122 or kT-points 123 can be implemented, as well as more elaborate cost functions.
It is important to note that the concept does not depend on any details of the implant. Trajectory, 124,125 structural details, 126,127 proximal termination, 128,129 etc., will all affect the numerical values within Q s , but not the validity and applicability of the concept. In this study we chose the straight wire dummy for its computational simplicity, but in real life Q s will be measured, 35 not computed, and no additional difficulties or uncertainties arise if the sensor is attached to a more complex, realistic device.
Of the investigated virtual sensor readings, SAR, jE z j 2 , dT=dtj T¼37:2 C , and I 2 RF offer good linear correlation with the tested hazard measures. While a direct SAR sensor represents a theoretical construct, an jE z j 2 RMS sensor is representable as a diode. 35 For current sensors on wire-like implants, the distance between the sensor and the tip needs to be considered 130 to avoid problems with null-modes. 29 The dT=dt sensor calibration depends on the heating history and thus is not constant over time, which needs to be considered when applied in a safety concept. Regardless of this, temperature sensors have an additional value as an independent watchdog 38 and would allow implant tip temperatures to be monitored over time, which could be used in more sophisticated safety concepts, for example, applying CEM43 thermal dose thresholds. 84,85,108,109 This is also supported by the underlying data of Figure 11. The heating rate dT=dt at the sensor tip can be accurately used for pTx-based mitigations of RF heating showing good linearity ( Figure 11A). The highest absolute steady-state temperatures (T ss ) below 38.5 C might be influenced by nonimplant background heating ( Figure 11B), making a direct correlation of the measured sensor signal ( Figure 11C) to SAR challenging; however, above temperatures of 39 C, which is a critical threshold for tissue damage based on the CEM43 concept, a linear relationship is found.
While the principal possibility of an implant safety concept based on precalculated native safety limits and an implant limit derived from measurements of a calibrated sensor was demonstrated in this work, more steps are necessary for a practical implementation. Many of the virtual sensors investigated in this work can be translated to realistic implants. It was shown that small RMS sensors such as diodes with dimensions of, for example, ð1:0 Â 0:6 Â 0:65Þ mm 3 , can potentially be embedded in an implant and used successfully for pTx mitigation. 35 Similarly, negative temperature coefficient (NTC) thermistors are of small size, for example, ð0:4 Â 0:2 Â 0:2Þ mm 3 and commercial RF ablation catheters are already available with multiple thermocouples placed at the 7:5 Fr (2:5 mm diameter) tip. 131 Presumably even easier to implement, however, would be a sensor that is located in the AIMD's generator but still senses at the tip. In Figure 7 it is shown that this is indeed feasible if either the implant lead itself can be utilized as a transmit cable or a suitable cable can be added to the lead. These phantom experiments showed that the sensor signal measured at the generator end of the lead correlated well with the temperature rise and E-field as measured by reference probes near the tip.
While the implementation of such a "remote" sensor is expected to be much simpler compared with a position right at the tip, additional care must be taken in the calibration process and shielding needs to be considered to avoid measuring stray fields not originating from the tip. Wireless communication between implant and MRI scanner, for example via Bluetooth, 33 needs to be standardized and the respective (cheap) hardware must be integrated. Finally, the software of the MRI scanner must be rewritten to read and to utilize the information from the implant.

| Limitations
As long as the sensor calibration remains valid, the proposed safety concept applies to all patients, body sizes, and implant trajectories. Nevertheless, up to now we only demonstrated this for a single body model and a single implant geometry. In the results presented so far, hardware constraints were not considered. These can straightforwardly be incorporated, however, and in Figure S4 an optimization L-curve (cf. Figure 9) is exemplarily calculated for the case of limited RF power.
Because of their additional degrees of freedom, the pTx-optimized shims tolerate stricter sensor limits with less sacrifice in image quality. This effect itself is a general trait of pTx, but the practical benefit depends on many parameters and cannot be predicted from the single investigated exposure scenario. The sensor concept is designed to handle an implant-related hotspot. If this hotspot does not exist (e.g., is prevented by very restrictive sensor limits), the optimization may find solutions that will still be safe, because native safety is built in, but possibly no longer be optimal in terms of B þ 1 . In this work, sensors were treated on a purely conceptual level. For possible implementations, including the important aspect of measurement uncertainties and the resulting safety margins, the reader is referred to dedicated, sensor-specific publications on this subject. [11][12][13][14][15]28,31,33,35 An example of how imperfect sensor measurements would affect the predictions of the safety concept is also presented and discussed in Figure S5.
The intention of the present work is to point out the benefits that sensor-equipped implants communicating with a pTx-capable scanner could have and to formalize a conceptual approach to combine native safety and implant safety. This concept benefits the patients, because of a subject-and exposure-specific safety assessment, the MR operators, because the safe scan conditions are now determined automatically and are no longer their responsibility, and the implant and scanner manufacturers, because their mutual responsibilities are well defined and clearly separated, limited to their respective product. The crucial question of the extra costs to equip future AIMDs with such sensors and to establish a communication interface to the scanner must be left to the manufacturers.

| CONCLUSION
This work presents an RF-safety concept for implant carriers, separating native from implant-caused hazards. Point-like RMS sensors, calibrated in terms of an accepted hazard metric, enable quantifying the implant-related hazard in situ, for the given patient in the scanner. The combination of fast sensor measurement and precalculated native limits can be exploited in a pTx-shim to achieve the best possible performance under a preselected safety condition. Ultimately, the shim conditions for the safe and efficient scanning of an implant patient would be computed and set automatically, and the MRI operators would no longer be responsible for the RF safety of the scan.