MRI-based transfer function determination through the transfer matrix by jointly fitting the incident and scattered B1+ field

Abstract

Purpose: A purely experimental method for MRI-based transfer function (TF) determination is presented. A TF characterizes the potential for radiofrequency heating of a linear implant by relating the incident tangential electric field to a scattered electric field at its tip. We utilize the previously introduced transfer matrix (TM) to determine transfer functions solely from the MR measurable quantities, that is, the $\left(B_1^{+}\right)$ and transceive phase distributions. This technique can extend the current practice of phantom-based TF assessment with dedicated experimental setup toward MR-based methods that have the potential to assess the TF in more realistic situations.

Theory and methods: An analytical description of the $B_1^{+}$ magnitude and transceive phase distribution around a wire-like implant was derived based on the TM. In this model, the background field is described using a superposition of spherical and cylindrical harmonics while the transfer matrix is parameterized using a previously introduced attenuated wave model. This analytical description can be used to estimate the transfer matrix and transfer function based on the measured $B_1^{+}$ distribution.

Results: The TF was successfully determined for 2 mock-up implants: a 20-cm bare copper wire and a 20-cm insulated copper wire with 10 mm of insulation stripped at both endings in respectively 4 and 3 different trajectories. The measured TFs show a strong correlation with a reference determined from simulations and between the separate experiments with correlation coefficients above 0.96 between all TFs. Compared to the simulated TF, the maximum deviation in the estimated tip field is 9.4% and 12.2% for the bare and insulated wire, respectively.

Conclusions: A method has been developed to measure the TF of medical implants using MRI experiments. Jointly fitting the incident and scattered $B_1^{+}$ distributions with an analytical description based on the transfer matrix enables accurate determination of the TF of 2 test implants. The presented method no longer needs input from simulated data and can therefore, in principle, be used to measure TF's in test animals or corpses.

Keywords: EM simulations; RF heating; active implantable medical device (AIMD); safety; transfer function; transfer matrix.

Figure 1

The TM is constructed in simulations by application of a localized incident electric fields of 1 V/m created with 2 plane waves that have constructively interfering electric and destructively interfering magnetic field components. This excitation is repositioned along the entire length of the implant. The resultant current distributions for the various excitations describe the rows of the TM. The width of the excitation determines the resolution to which the TM is resolved. Given an implant with a certain TM and some incident electric field, the induced current in the implant is computed with a matrix multiplication, that is, I = ME

Figure 2

The elliptical ASTM phantom in which the dummy implants are placed is shown on the right. The wires are located on a thin sewing thread stung between 4.5‐cm‐long plastic screws. The wires are positioned approximately 13 cm away from the center of the phantom and submerged under 5 cm of phantom liquid. The setup of the phantom in the birdcage body coil is shown on the left together with the 5 bare wires that are used in simulations

Figure 3

The simulated $B_1^{+}$ magnitude and transceive phase distribution around the bare 20‐cm wire in orientations (A), (B), (C), (D), and (E) are shown on the left. These fields are fitted with Equations 8 and 9 using the minimization given in Equation 10. The results from these fits are shown in the third and fourth columns. The absolute error shown on the right is small compared to the $B_1^{+}$ magnitude

Figure 4

The simulated $B_1^{+}$ magnitude and transceive phase distribution around the insulated 20‐cm wire in orientations (Ai), (Bi), (Ci), and (Di) are shown on the left. These fields are fitted with Equations 9 and 10 using the minimalization given in Equation 11. The results from these fits are shown in the third and fourth columns. The absolute error shown on the right is small compared to the $B_1^{+}$ magnitude. The screws that keep the implant afloat are not captured by the SPACY harmonics and show up as bright spots in the absolute error map

Figure 5

Two examples of the TF and TM that follow from the fit of the fields shown in Figures 3 and 4. The results for the straight wire aligned with the z‐axis are displayed here, that is, from distribution (a) and (ai) in Figures 3 and 4, respectively. Ideally, the TMs that follow from the full field fit should be identical to the reference TMs and lie the line x = y in the outmost right figures. This is not exactly the case, but Pearson correlations are high, with R = 0.983 and R = 0.962 for the bare and insulated wire, respectively

Figure 6

The normalized TFs that follow from the fits of the simulated fields displayed for the bare wires and insulated wires in Figures 3 and 4, respectively. The TFs found from fitting the fields for the different wire trajectories resemble the gold‐standard TF

Figure 7

The measured $B_1^{+}$ magnitude and transceive phase distribution around the bare 20‐cm wire in orientations (A), (B), (C), and (D) are shown on the left. These fields are fitted with Equations 8 and 9 using the minimization given in Equation 10. The results from these fits are shown in the third and fourth columns. The absolute error is shown on the right. Despite the evident similarity between the distributions, some discrepancies, especially around the wire, remain present

Figure 8

The measured $B_1^{+}$ magnitude and transceive phase distribution around the insulated 20‐cm wire in orientations (Ai), (Bi), and (Ci) are shown on the left. These fields are fitted with Equations 8 and 9 using the minimization given in Equation 10. The results from these fits are shown in the third and fourth columns. The absolute error is shown on the right. Again, some discrepancies, especially around the wire, remain present

Figure 9

Two examples of the TF and TM that follow from the fit of the fields shown in Figures 3 and 4. The results for the straight wire aligned with the z‐axis are displayed here, that is, from distribution (A) and (Ai) in Figures 3 and 4, respectively. Ideally, the TMs that follow from the full field fit should be identical to the reference TMs and lie the line x = y in the outmost right figures. This is not exactly the case, but Pearson correlations are high, with R = 0.983 and R = 0.962 for the bare and insulated wire, respectively

Figure 10

The normalized TFs that follow from the fits of the measured fields displayed for the bare wires and insulated wires in Figures 8 and 9, respectively. The TFs found from fitting the fields for the different wire trajectories resemble the gold‐standard TF and each other. The correlation coefficients are above 0.98 for the bare and above 0.94 for the insulated wires. The agreement found between the TFs can be viewed as a validation of the measurements