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.

DEQ-MPI: A Deep Equilibrium Reconstruction With Learned Consistency for Magnetic Particle Imaging.

Magnetic particle imaging (MPI) offers unparalleled contrast and resolution for tracing magnetic nanoparticles. A common imaging procedure calibrates a system matrix (SM) that is used to reconstruct data from subsequent scans. The ill-posed reconstruction problem can be solved by simultaneously enforcing data consistency based on the SM and regularizing the solution based on an image prior. Traditional hand-crafted priors cannot capture the complex attributes of MPI images, whereas recent MPI methods based on learned priors can suffer from extensive inference times or limited generalization performance. Here, we introduce a novel physics-driven method for MPI reconstruction based on a deep equilibrium model with learned data consistency (DEQ-MPI). DEQ-MPI reconstructs images by augmenting neural networks into an iterative optimization, as inspired by unrolling methods in deep learning. Yet, conventional unrolling methods are computationally restricted to few iterations resulting in non-convergent solutions, and they use hand-crafted consistency measures that can yield suboptimal capture of the data distribution. DEQ-MPI instead trains an implicit mapping to maximize the quality of a convergent solution, and it incorporates a learned consistency measure to better account for the data distribution. Demonstrations on simulated and experimental data indicate that DEQ-MPI achieves superior image quality and competitive inference time to state-of-the-art MPI reconstruction methods.

TranSMS: Transformers for Super-Resolution Calibration in Magnetic Particle Imaging.

Magnetic particle imaging (MPI) offers exceptional contrast for magnetic nanoparticles (MNP) at high spatio-temporal resolution. A common procedure in MPI starts with a calibration scan to measure the system matrix (SM), which is then used to set up an inverse problem to reconstruct images of the MNP distribution during subsequent scans. This calibration enables the reconstruction to sensitively account for various system imperfections. Yet time-consuming SM measurements have to be repeated under notable changes in system properties. Here, we introduce a novel deep learning approach for accelerated MPI calibration based on Transformers for SM super-resolution (TranSMS). Low-resolution SM measurements are performed using large MNP samples for improved signal-to-noise ratio efficiency, and the high-resolution SM is super-resolved via model-based deep learning. TranSMS leverages a vision transformer module to capture contextual relationships in low-resolution input images, a dense convolutional module for localizing high-resolution image features, and a data-consistency module to ensure measurement fidelity. Demonstrations on simulated and experimental data indicate that TranSMS significantly improves SM recovery and MPI reconstruction for up to 64-fold acceleration in two-dimensional imaging.

A Simulation Study for Three Dimensional Tomographic Field Free Line Magnetic Particle Imaging.

Magnetic Particle Imaging (MPI) is an emerging modality that images the magnetic nanoparticle distribution inside the body. The method is based on the non-linear response of the magnetic nanoparticles to an applied magnetic field. In this study, we present simulation results for three-dimensional (3D) tomographic imaging using an open-bore MPI system that can electronically scan a field free line (FFL). A field of view with 26×26×10 mm3 volume is imaged with a relatively low gradient field of 0.5 T/m. Imaging results for two 3D phantoms are presented: a letter phantom and a vessel phantom with stenosis regions. Using the system-matrix based reconstruction approach, the images were obtained with the Algebraic reconstruction technique (ART) and alternating direction method of multipliers (ADMM) methods. The stenosis regions were visually recognizable in high SNR conditions with ADMM. The effect of low gradient strength became prominent with increasing noise level, resulting in interlayer coupling artifacts.Clinical relevance- Magnetic Particle Imaging (MPI) is a new tracer-based imaging modality with high-spatiotemporal resolution. MPI can map quantitative distribution of super-paramagnetic iron oxide nanoparticles introduced inside the body. A field free line scanning MPI system with an open configuration can enable imaging of human-size volumes for interventional operations. In this study, we present simulation results for an FFL scanning open MPI system configuration to scan 3D field of view volume electronically. We analyze 3D imaging performance for various SNR levels at a low gradient value of 0.5 T/m that is relevant for clinical-size systems.

A Generalized Split-Step Angular Spectrum Method for Efficient Simulation of Wave Propagation in Heterogeneous Media.

Angular spectrum (AS) methods enable efficient calculation of wave propagation from one plane to another inside homogeneous media. For wave propagation in heterogeneous media such as biological tissues, AS methods cannot be applied directly. Split-stepping techniques decompose the heterogeneous domain into homogeneous and perturbation parts, and provide a solution for forward wave propagation by propagating the incident wave in both frequency-space and frequency-wavenumber domains. Recently, a split-step hybrid angular spectrum (HAS) method was proposed for plane wave propagation of focused ultrasound beams. In this study, we extend these methods to enable simulation of acoustic pressure field for an arbitrary source distribution, by decomposing the source and reflection spectra into orthogonal propagation direction components, propagating each component separately, and summing all components to get the total field. We show that our method can efficiently simulate the pressure field of arbitrary sources in heterogeneous media. The accuracy of the method was analyzed comparing the resultant pressure field with pseudospectral time domain (PSTD) solution for breast tomography and hemispherical transcranial-focused ultrasound simulation models. Eighty times acceleration was achieved for a 3-D breast simulation model compared to PSTD solution with 0.005 normalized root mean-squared difference (NRMSD) between two solutions. For the hemispherical phased array, aberrations due to skull were accurately calculated in a single simulation run as evidenced by the resultant-focused ultrasound beam simulations, which had 0.001 NRMSD with 40 times acceleration factor compared to the PSTD method.

Tomographic Field Free Line Magnetic Particle Imaging With an Open-Sided Scanner Configuration.

Superparamagnetic iron oxide nanoparticles (SPIONs) have a high potential for use in clinical diagnostic and therapeutic applications. In vivo distribution of SPIONs can be imaged with the Magnetic Particle Imaging (MPI) method, which uses an inhomogeneous magnetic field with a field free region (FFR). The spatial distribution of the SPIONs are obtained by scanning the FFR inside the field of view (FOV) and sensing SPION related magnetic field disturbance. MPI magnets can be configured to generate a field free point (FFP), or a field free line (FFL) to scan the FOV. FFL scanners provide more sensitivity, and are also more suitable for scanning large regions compared to FFP scanners. Interventional procedures will benefit greatly from FFL based open magnet configurations. Here, we present the first open-sided MPI system that can electronically scan the FOV with an FFL to generate tomographic MPI images. Magnetic field measurements show that FFL can be rotated electronically in the horizontal plane and translated in three dimensions to generate 3D MPI images. Using the developed scanner, we obtained 2D images of dot and cylinder phantoms with varying iron concentrations between 11 [Formula: see text]/ml and 770 [Formula: see text]/ml. We used a measurement based system matrix image reconstruction method that minimizes l1 -norm and total variation in the images. Furthermore, we present 2D imaging results of two 4 mm-diameter vessel phantoms with 0% and 75% stenosis. The experiments show high quality imaging results with a resolution down to 2.5 mm for a relatively low gradient field of 0.6 T/m.

Fast System Calibration With Coded Calibration Scenes for Magnetic Particle Imaging.

Magnetic particle imaging (MPI) is a relatively new medical imaging modality, which detects the nonlinear response of magnetic nanoparticles (MNPs) that are exposed to external magnetic fields. The system matrix (SM) method for MPI image reconstruction requires a time consuming system calibration scan prior to image acquisition, where a single MNP sample is measured at each voxel position in the field-of-view (FOV). The scanned sample has the maximum size of a voxel so that the calibration measurements have relatively poor signal-to-noise ratio (SNR). In this paper, we present the coded calibration scene (CCS) framework, where we place multiple MNP samples inside the FOV in a random or pseudo-random fashion. Taking advantage of the sparsity of the SM, we reconstruct the SM by solving a convex optimization problem with alternating direction method of multipliers using CCS measurements. We analyze the effects of filling rate, number of measurements, and SNR on the SM reconstruction using simulations and demonstrate different implementations of CCS for practical realization. We also compare the imaging performance of the proposed framework with that of a standard compressed sensing SM reconstruction that utilizes a subset of calibration measurements from a single MNP sample. The results show that CCS significantly reduces calibration time while increasing both the SM reconstruction and image reconstruction performances.

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.

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.

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.

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.

Harmonic motion microwave Doppler imaging: a simulation study using a simple breast model.

A hybrid method for tissue imaging using dielectric and elastic properties is proposed and investigated with simple bi-layered breast model. In this method, local harmonic motion is generated in the tissue using a focused ultrasound probe. A narrow-band microwave signal is transmitted to the tissue. The Doppler component of the scattered signal, which depends on the dielectric and elastic properties of the vibrating region, is sensed. A plane-wave spectrum technique is used together with reciprocity theorem for calculating the response of a vibrating electrically small spherical tumor in breast tissue. The effects of operating frequency, antenna alignment and distance, and tumor depth on the received signal are presented. The effect of harmonic motion frequency on the vibration amplitude and displacement distribution is investigated with mechanical simulations using the finite element method. The safety of the method is analyzed in terms of microwave and ultrasound exposure of the breast tissue. The results show that the method has a potential in detecting tumors inside fibro-glandular breast tissue.

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.

Harmonic Motion Microwave Doppler Imaging method for breast tumor detection.

Harmonic Motion Microwave Doppler Imaging (HMMDI) method is recently proposed as a non-invasive hybrid breast imaging technique for tumor detection. The acquired data depend on acoustic, elastic and electromagnetic properties of the tissue. The potential of the method is analyzed with simulation studies and phantom experiments. In this paper, the results of these studies are summarized. It is shown that HMMDI method has a potential to detect malignancies inside fibro-glandular tissue.