Transceive phase corrected 2D contrast source inversion-electrical properties tomography

Abstract

Purpose: To remove the necessity of the tranceive phase assumption for CSI-EPT and show electrical properties maps reconstructed from measured data obtained using a standard 3T birdcage body coil setup.

Methods: The existing CSI-EPT algorithm is reformulated to use the transceive phase rather than relying on the transceive phase assumption. Furthermore, the radio frequency (RF)-shield is numerically implemented to accurately model the RF fields inside the MRI scanner. We verify that the reformulated two-dimensional (2D) CSI-EPT algorithm can reconstruct electrical properties maps given 2D electromagnetic simulations. Afterward, the algorithm is tested with three-dimensional (3D) FDTD simulations to investigate if the 2D CSI-EPT can retrieve the electrical properties for 3D RF fields. Finally, an MR experiment at 3T with a phantom is performed.

Results: From the results of the 2D simulations, it is seen that CSI-EPT can reconstruct the electrical properties using MRI accessible quantities. For 3D simulations, it is observed that the electrical properties are underestimated, nonetheless, CSI-EPT has a lower standard deviation than the standard Helmholtz based methods. Finally, the first CSI-EPT reconstructions based on measured data are presented showing comparable accuracy and precision to reconstructions based on simulated data, and demonstrating the feasibility of CSI-EPT.

Conclusions: The CSI-EPT algorithm was rewritten to use MRI accessible quantities. This allows for CSI-EPT to fully exploit the benefits of the higher static magnetic field strengths with a standard quadrature birdcage coil setup.

Keywords: EPT; MRI; RF-shield; contrast source inversion; dielectric tissue mapping; electrical properties tomography; transceive phase.

FIGURE 1

The top left shows the conductivity of the phantom and the top right shows the relative permittivity. The bottom left shows the geometry of the phantom where the inner compartment will be referred to as the tube and the other compartment is referred to as the background. On the bottom right, the table shows the conductivity and permittivity values that were used in simulations as well as the dimensions of the phantom

FIGURE 2

The top row shows the setup of the line sources (left) and the resulting incident electric field amplitude (middle) and the reconstructed conductivity when this incident RF‐field is used (right). The bottom row shows the same for the numerical implementation of the PEC with mirror sources. The same current is running through the line sources in both cases

FIGURE 3

The top row shows the conductivity reconstructions with the corresponding absolute error maps below them. The reconstructions were performed with the TPA and the newly proposed method, indicated with TPC, both at 3T and 7T. The third row shows the permittivity reconstructions with the corresponding error maps below them

FIGURE 4

The top left shows an example of a simulated noisy $B_1^{+}$ amplitude map at 3T. The top middle figure shows the corresponding simulated noisy transceive phase. The top right figure shows where the mean absolute error was computed. The bottom row shows the mean absolute error in the conductivity and permittivity on a log scale vs the static magnetic field strength, where the left figure is without noise in the simulation and the right figure is with noise. The 3T and 7T reconstructions of these data points can be seen in Figure 3

FIGURE 5

The top left figure shows the reconstruction of the conductivity in the center of the birdcage coil for the 3D FDTD simulations. The seven subsequent figures are reconstructions each 1 cm more out of the center slice of the birdcage coil. The bottom figure shows the value of the actual conductivity and the reconstructed value at the red cross marked in the top left figure

FIGURE 6

On the left is a picture of the phantom that was made for the measurements. The top left shows the conductivity reconstruction for the CSI‐EPT reconstruction with an NSA of 2, the top right shows the reconstruction for NSA = 10. The bottom two figures show the standard Helmholtz MR‐EPT reconstruction. The left shows the NSA = 2 reconstruction while the right shows the NSA = 10 reconstruction

FIGURE 7

The top left shows the transceive phase from the 2D simulation. The top right shows the transceive phase measured with MRI. The middle left shows the simulated transmit phase and the middle right shows the transmit phase reconstructed by CSI‐EPT from the measurement. The bottom row shows the simulated and reconstructed receive phase