The patient population with active implanted medical devices has a relatively high probability of needing MRI investigations and is rapidly growing. Tissue heating induced by sharply peaked scattered RF electric fields at the tip of elongated implants is a severe safety hazard. The introduction of the transfer function concept (Park et al$$$^1$$$) greatly expedited RF safety assessment studies as impinging tangential electric fields assessed by simulations could be combined with measurements of the transfer function (TF) to determine the scattered electric field at the tip. Measurements of TFs are widely used in modern safety standards (ISO TS 10974$$$^2$$$). Currently a dedicated bench setup is required to apply, sequentially repositioned, localized tangential electric field exposures along an implant and measure the scattered field around the tip, called piecewise excitation method (PWE), which is both experimentally challenging and time consuming.

Recently the reciprocate approach was shown to be equally adequate in determining the TF$$$^3$$$. Contrary to the conventional PWE method, the excitation occurs at the tip (by soldering it to a coax cable with drive signal) and the resultant electric field distribution along the structure displays the TF. We introduce a new approach to measure the TF with this second method using MRI. We exploit the ability to map induced currents on elongated implants using MRI. The proposed method can accurately determine TFs with high spatial resolution in a single relatively simple and time efficient measurement. It furthermore has the potential to measure TFs of (curved) implanted devices in hetrogeneous media allowing experimental safety assessment in more realistic scenarios, where conventional methods become inapplicable.

The relationship between the scattered electric field$$$\,\vec{E_s}(\vec{r})\,$$$in proximity of a tip and the tangential incident field $$$E_{\text{tan}}\,$$$along an implant of length $$$L$$$, whose trajectory is parameterized by $$$q,\,$$$can be generically written as$$$^1$$$,$$\vec{E_s}(\vec{r})=\int_{0}^{L}\vec{S}(q,\vec{r})E_{\text{tan} }(q)\text{d}q=\vec{E_\text{tip}}\int_{0}^{L}S(q)E_{\text{tan}}(q)\text{d}q.$$In this equation the complex quantity $$$S(q)\,$$$is known as the transfer function. The last equality is valid because the spatial pattern$$$\,\vec{E_s}(\vec{r})\,$$$around the tip is independent on the excitation along the implant.

By virtue of the principle of reciprocity an applied electric field at the tip$$$\,\vec{E_i}(\vec{r})\,$$$and measurements of the resultant $$$E_{\text{tan}}\,$$$along the implant (or induced current $$$I(q)\,$$$) allows determination of TFs.

Generic implants (insulated copper wires of 10, 20 and 30cm length), with TFs known from literature$$$^{1,3}\,$$$were placed in an elliptic ASTM phantom filled with CuSO$$$_4\,$$$doped saline (conductivity 0.47S/m and relative permittivity 78). These implants were locally excited by an open ended coax cable where the inner conductor was soldered to the insulated wire. The coax cable was connected to a 1.5T MR scanner (Achieva, Philips Healthcare) and used as a transceive antenna. Although the structures are non-matched (hence have large reflections), the induced currents on the wire generate $$$B_1^+\,$$$field distribution and, by reciprocity, also prescribe the $$$B_1^{-}\,$$$field distribution, i.e. the wire’s sensitivity pattern. The product is $$$B_1^+B_1^{-*}\,$$$is directly proportional to the MRI signal level (in the low-flip angle regime). 3D spoiled gradient echo MRI data, with 1mm isotropic resolution with 2$$$^o\,$$$flip angle was acquired for each structure. Because the spatial current trajectory is known upon visual inspection (see fig.2) the law of Biot-Savart can be applied to reconstruct the current profile along the wire.

The wire trajectories were discretized in $$$N\,$$$3mm straight line segments assuming piecewise constant currents $$$I_k\,$$$which transform the Biot-Savart integral equation in a Riemann sum. A least squares approximation minimizing the signal from the Biot-Savart law with respect to actually acquired MRI data was used to determine the current distribution in the implant and hence the TF. I.e.,$$\min_{\widetilde{I}}\left\| M_{\text{BS}}\cdot \widetilde{I}-d_{\text{meas}}\right\|_2^2,$$where $$$M_{\text{BS}}\,$$$is a matrix containing the $$$N\,$$$contributions of each $$$I_k\,$$$,contained in $$$\widetilde{I},\,$$$ to every voxel and $$$d_{\text{meas}}\,$$$ a vector with voxel signals.

To verify the measurement outcome, the TF of all structures was simulated using Sim4Life (ZMT, Zurich).The phase of the MRI data was corrected for B$$$_0\,$$$and eddy current contributions by using dual echo gradient sequences different readout polarities (Van Lier$$$^4$$$).

The equivalence between the coax excitation and the PWE method was demonstrated with simulations.The normalized TFs determined with the PWE method showed excellent agreement with the ones determined from simulations of excitation by a coax cable and with literature (fig.4).

The MRI measured TFs are in good agreement with simulations (fig.5). With the proposed method, the electric field at the tip is determined with a relative error of maximally 8% for a worst case incident electric field distribution. This research shows that TFs can accurately be determined using MRI techniques. This avoids elaborate bench setups and extensive measurement procedures. Furthermore, it allows testing of implants under relevant and more realistic MRI conditions.