Accelerating implant RF safety assessment using a low-rank inverse update method

Abstract

Purpose: Patients who have medical metallic implants, e.g. orthopaedic implants and pacemakers, often cannot undergo an MRI exam. One of the largest risks is tissue heating due to the radio frequency (RF) fields. The RF safety assessment of implants is computationally demanding. This is due to the large dimensions of the transmit coil compared to the very detailed geometry of an implant.

Methods: In this work, we explore a faster computational method for the RF safety assessment of implants that exploits the small geometry. The method requires the RF field without an implant as a basis and calculates the perturbation that the implant induces. The inputs for this method are the incident fields and a library matrix that contains the RF field response of every edge an implant can occupy. Through a low-rank inverse update, using the Sherman-Woodbury-Morrison matrix identity, the EM response of arbitrary implants can be computed within seconds. We compare the solution from full-wave simulations with the results from the presented method, for two implant geometries.

Results: From the comparison, we found that the resulting electric and magnetic fields are numerically equivalent (maximum error of 1.35%). However, the computation was between 171 to 2478 times faster than the corresponding GPU accelerated full-wave simulation.

Conclusions: The presented method enables for rapid and efficient evaluation of the RF fields near implants and might enable situation-specific scanning conditions.

Keywords: FDTD; RF Safety; implant safety; minimization problems; simulations.

Figure 1

A representation of the S matrix for a 2D grid. The left shows the values inside the support matrix for the corresponding edges in the grid on the right. The red edges define the small domain while the red plus the black edges define the large domain. The blue arrows indicate to which edge in the grid each ‘1’ corresponds to

Figure 2

The geometry and location of the passive implant inside Duke

Figure 3

The geometry and location of the DBS lead inside Duke. Duke's position inside the birdcage coil is the same as for the setup with the orthopaedic implant

Figure 4

Comparison of the electric field components obtained by FDTD and the proposed inverse computation method from a surgical screw. The three rows show the magnitude of the $E_{x,y,z}$ components respectively. The first column shows the magnitude of the electric field if there is no implant present. The second column shows the electric fields with the implant present computed by the FDTD method. For the same implant, the third column shows the output of the computations performed with the presented methodology. The last column shows the error percentage as computed by Equation (18)

Figure 5

Comparison of the magnetic field components obtained by FDTD and the proposed inverse computation method from a surgical screw. The three rows show the magnitude of the $H_{x,y,z}$ components respectively. The first column shows the magnitude of the magnetic field if there is no implant present. The second column shows the magnetic fields with the implant present computed by the FDTD method. For the same implant, the third column shows the output of the computations performed with the presented methodology. The last column shows the error percentage as computed by Equation

Figure 6

Comparison between the RF fields computed with the FDTD and the presented method for the straight deep brain stimulator lead (aligned with grid axes). On the left, the location of the computed domain within the model is indicated with a red contour. The top row of figures shows the magnitude of the electric field for the FDTD simulation, the inverse computation and the error percentage as computed by Equation (18). Equivalent plots are shown for the magnetic field in the bottom row

Figure 7

Comparison between the RF fields computed with the FDTD and the presented method for the tilted deep brain stimulator lead (not aligned with grid axes). On the left, the location of the computed domain within the model is indicated with a red contour. The top row of figures shows the magnitude of the electric field for the FDTD simulation, the inverse computation and the error percentage as computed by Equation (18). Equivalent plots are shown for the magnetic field in the bottom row

Figure 8

Comparison between the true solution, as computed by Equation (17), and the solution found by the inverse computation, as defined by Equation (16). The current density is summed for the transverse (xy‐plane) slices. The top row shows the result for the orthopaedic implant and the second row shows the result for the straight DBS implant and the bottom row shows the result for the tilted DBS lead