On the utilization of the adjoint method in microwave tomography

In microwave imaging, the adjoint method is widely used for the efficient calculation of the update direction, which is then used to update the unknown model parameter. However, the utilization and the formulation of the adjoint method differ significantly depending on the imaging scenario and the applied optimization algorithm. Because of the problem-specific nature of the adjoint formulations, the dissimilarities between the adjoint calculations may be overlooked. Here, we have classified the adjoint method formulations into two groups: the direct and indirect methods. The direct method involves calculating the derivative of the cost function, whereas, in the indirect method, the derivative of the predicted data is calculated. In this review, the direct and indirect adjoint methods are presented, compared, and discussed. The formulations are explicitly derived using the two-dimensional wave equation in frequency and time domains. Finite-difference time-domain simulations are conducted to show the different uses of the adjoint methods for both single source-multiple receiver, and multiple transceiver scenarios. This study demonstrated that an appropriate adjoint method selection is significant to achieve improved computational efficiency for the applied optimization algorithm.

Trajectory analysis for field free line magnetic particle imaging

PURPOSE

Magnetic particle imaging (MPI) is a relatively new method to image the spatial distribution of magnetic nanoparticle (MNP) tracers administered to the body with high spatial and temporal resolution using an inhomogeneous magnetic field. The spatial information of the MNP's is encoded using a field free point (FFP), or a field free line (FFL), in which the magnetic field vanishes at a point, or on a line, respectively. FFL scanning has the advantage of improved sensitivity compared to FFP scanning as a result of higher signal-to-noise ratio. The trajectory traversed by the FFL or FFP is an important parameter of the MPI system and should be selected to achieve the best imaging quality in minimum scan time, while considering hardware constraints and patient safety. In this study, we analyzed the image quality of different FFL trajectories for a large field of view (FOV) using simulations, to provide a baseline information for FFL scanning MPI system design.

METHODS

We simulated a human-sized FFL scanning MPI configuration to image a circular FOV with 160 mm diameter, and compared Radial, Spiral, Uniform Spiral, Flower, and Lissajous trajectories with different trajectory densities scanned by the FFL for constant scan time. We analyzed the system matrices of the trajectories in terms of mutual coherence and homogeneity of the spatial sensitivity. We calculated the maximum electric fields induced on a homogeneous conductive body by the selection field (SF) and the focus field (FF) to compare the trajectories based on the nerve stimulation threshold. The images were obtained using the system matrix reconstruction approach with two different image reconstruction methods. In the first one, we used the conventional image reconstruction method, algebraic reconstruction technique (ART), which gives a regularized least-squares solution. In the second one, we used the state-of-the-art alternating direction method of multipliers (ADMM), which minimizes a weighted sum of the l₁ -norm and the total variation (TV) of the images.

RESULTS

The Radial and Spiral trajectories resulted in a poor imaging performance at low trajectory densities due to relatively high coherency and poor sensitivity of the measurements, respectively. For ART reconstruction, the highest image quality with the lowest trajectory density was achieved with the Uniform Spiral trajectory. Uniform Spiral, Flower, and Lissajous trajectories yielded comparable performance with ADMM reconstruction. The rotating SF induced higher electric field amplitude compared to the FF. Consequently, maximum allowable gradient at the same trajectory density was greater for the Radial trajectory compared to the other trajectories.

CONCLUSIONS

For a large FOV coverage, the Uniform Spiral trajectory offers a good compromise between image quality and imaging time, taking safety and hardware limitations into account. The Radial trajectory, especially using l₁ -norm and TV priors in the reconstruction, may be favorable in case the SF induced electric field is higher than that of the FF at the same frequency (e.g., relatively small FOV coverage). In general, ADMM reconstruction resulted in higher contrast and resolution compared to ART, leading to lighter requirements on the density of the trajectory.

Electronically rotated and translated field-free line generation for open bore magnetic particle imaging

PURPOSE

We propose a coil arrangement for open bore field-free line (FFL) magnetic particle imaging (MPI) system, which is suitable for accessing the subject from the sides. The purpose of this study is twofold, to show that the FFL can be rotated and translated electronically in a volume of interest with this arrangement and to analyze the current, voltage and power requirements for a 1 T/m gradient human sized scanner for a 200 mm diameter × 200 mm height cylindrical field of view (FOV).

METHODS

We used split coils side by side with alternating current directions to generate a field-free line. Employing two of these coil groups, one of which is rotated 90 degrees with respect to the other, a rotating FFL was generated. We conducted numerical simulations to show the feasibility of this arrangement for three-dimensional (3D) electronical scan of the FFL. Using simulations, we obtained images of a two-dimensional (2D) in silico dot phantom for a human size scanner with system matrix-based reconstruction.

RESULTS

Simulations showed that the FFL can be generated and rotated in one plane and can be translated in two axes, allowing for 3D imaging of a large subject with the proposed arrangement. Human sized scanner required 63-215 kW power for the selection field coils to scan the focus inside the FOV.

CONCLUSIONS

The proposed setup is suitable for FFL MPI imaging with an open bore configuration without the need for mechanical rotation, which is preferable for clinical usage in terms of imaging time and patient access. Further studies are necessary to determine the limitations imposed by peripheral nerve stimulation, and to optimize the system parameters and the sequence design.

Two-dimensional multi-frequency imaging of a tumor inclusion in a homogeneous breast phantom using the harmonic motion Doppler imaging method

Harmonic motion microwave Doppler imaging (HMMDI) is a novel imaging modality for imaging the coupled electrical and mechanical properties of body tissues. In this paper, we used two experimental systems with different receiver configurations to obtain HMMDI images from tissue-mimicking phantoms at multiple vibration frequencies between 15 Hz and 35 Hz. In the first system, we used a spectrum analyzer to obtain the Doppler data in the frequency domain, while in the second one, we used a homodyne receiver that was designed to acquire time-domain data. The developed phantoms mimicked the elastic and dielectric properties of breast fat tissue, and included a [Formula: see text] mm cylindrical inclusion representing the tumor. A focused ultrasound probe was mechanically scanned in two lateral dimensions to obtain two-dimensional HMMDI images of the phantoms. The inclusions were resolved inside the fat phantom using both experimental setups. The image resolution increased with increasing vibration frequency. The designed receiver showed higher sensitivity than the spectrum analyzer measurements. The results also showed that time-domain data acquisition should be used to fully exploit the potential of the HMMDI method.

Nonthermal ablation of deep brain targets: A simulation study on a large animal model

PURPOSE

Thermal ablation with transcranial MRI-guided focused ultrasound (FUS) is currently limited to central brain targets because of heating and other beam effects caused by the presence of the skull. Recently, it was shown that it is possible to ablate tissues without depositing thermal energy by driving intravenously administered microbubbles to inertial cavitation using low-duty-cycle burst sonications. A recent study demonstrated that this ablation method could ablate tissue volumes near the skull base in nonhuman primates without thermally damaging the nearby bone. However, blood-brain disruption was observed in the prefocal region, and in some cases, this region contained small areas of tissue damage. The objective of this study was to analyze the experimental model with simulations and to interpret the cause of these effects.

METHODS

The authors simulated prior experiments where nonthermal ablation was performed in the brain in anesthetized rhesus macaques using a 220 kHz clinical prototype transcranial MRI-guided FUS system. Low-duty-cycle sonications were applied at deep brain targets with the ultrasound contrast agent Definity. For simulations, a 3D pseudospectral finite difference time domain tool was used. The effects of shear mode conversion, focal steering, skull aberrations, nonlinear propagation, and the presence of skull base on the pressure field were investigated using acoustic and elastic wave propagation models.

RESULTS

The simulation results were in agreement with the experimental findings in the prefocal region. In the postfocal region, however, side lobes were predicted by the simulations, but no effects were evident in the experiments. The main beam was not affected by the different simulated scenarios except for a shift of about 1 mm in peak position due to skull aberrations. However, the authors observed differences in the volume, amplitude, and distribution of the side lobes. In the experiments, a single element passive cavitation detector was used to measure the inertial cavitation threshold and to determine the pressure amplitude to use for ablation. Simulations of the detector's acoustic field suggest that its maximum sensitivity was in the lower part of the main beam, which may have led to excessive exposure levels in the experiments that may have contributed to damage in the prefocal area.

CONCLUSIONS

Overall, these results suggest that case-specific full wave simulations before the procedure can be useful to predict the focal and the prefocal side lobes and the extent of the resulting bioeffects produced by nonthermal ablation. Such simulations can also be used to optimally position passive cavitation detectors. The disagreement between the simulations and the experiments in the postfocal region may have been due to shielding of the ultrasound field due to microbubble activity in the focal region. Future efforts should include the effects of microbubble activity and vascularization on the pressure field.

Preclinical evaluation of a low-frequency transcranial MRI-guided focused ultrasound system in a primate model

This study investigated thermal ablation and skull-induced heating with a 230 kHz transcranial MRI-guided focused ultrasound (TcMRgFUS) system in nonhuman primates. We evaluated real-time acoustic feedback and aimed to understand whether cavitation contributed to the heating and the lesion formation. In four macaques, we sonicated thalamic targets at acoustic powers of 34-560 W (896-7590 J). Tissue effects evaluated with MRI and histology were compared to MRI-based temperature and thermal dose measurements, acoustic emissions recorded during the experiments, and acoustic and thermal simulations. Peak temperatures ranged from 46 to 57 °C, and lesions were produced in 5/8 sonicated targets. A linear relationship was observed between the applied acoustic energy and both the focal and brain surface heating. Thermal dose thresholds were 15-50 cumulative equivalent minutes at 43 °C, similar to prior studies at higher frequencies. Histology was also consistent with earlier studies of thermal effects in the brain. The system successfully controlled the power level and maintained a low level of cavitation activity. Increased acoustic emissions observed in 3/4 animals occurred when the focal temperature rise exceeded approximately 16 °C. Thresholds for thermally-significant subharmonic and wideband emissions were 129 and 140 W, respectively, corresponding to estimated pressure amplitudes of 2.1 and 2.2 MPa. Simulated focal heating was consistent with the measurements for sonications without thermally-significant acoustic emissions; otherwise it was consistently lower than the measurements. Overall, these results suggest that the lesions were produced by thermal mechanisms. The detected acoustic emissions, however, and their association with heating suggest that cavitation might have contributed to the focal heating. Compared to earlier work with a 670 kHz TcMRgFUS system, the brain surface heating was substantially reduced and the focal heating was higher with this 230 kHz system, suggesting that a reduced frequency can increase the treatment envelope for TcMRgFUS and potentially reduce the risk of skull heating.

Data acquisition system for harmonic motion microwave Doppler imaging

Harmonic Motion Microwave Doppler Imaging (HMMDI) is a hybrid method proposed for breast tumor detection, which images the coupled dielectric and elastic properties of the tissue. In this paper, the performance of a data acquisition system for HMMDI method is evaluated on breast phantom materials. A breast fat phantom including fibro-glandular and tumor phantom regions is produced. The phantom is excited using a focused ultrasound probe and a microwave transmitter. The received microwave signal level is measured on three different points inside the phantom (fat, fibro-glandular, and tumor regions). The experimental results using the designed homodyne receiver proved the effectiveness of the proposed setup. In tumor phantom region, the signal level decreased about 3 dB compared to the signal level obtained from the fibro-glandular phantom area, whereas this signal was about 4 dB higher than the received signal from the fat phantom.