Evaluation of acoustic-thermal simulations of in vivo magnetic resonance guided focused ultrasound ablative therapy.

PURPOSE: To evaluate numerical simulations of focused ultrasound (FUS) with a rabbit model, comparing simulated heating characteristics with magnetic resonance temperature imaging (MRTI) data collected during in vivo treatment. METHODS: A rabbit model was treated with FUS sonications in the biceps femoris with 3D MRTI collected. Acoustic and thermal properties of the rabbit muscle were determined experimentally. Numerical models of the rabbits were created, and tissue-type-specific properties were assigned. FUS simulations were performed using both the hybrid angular spectrum (HAS) method and k-Wave. Simulated power deposition patterns were converted to temperature maps using a Pennes' bioheat equation-based thermal solver. Agreement of pressure between the simulation techniques and temperature between the simulation and experimental heating was evaluated. Contributions of scattering and absorption attenuation were considered. RESULTS: Simulated peak pressures derived using the HAS method exceeded the simulated peak pressures from k-Wave by 1.6 ± 2.7%. The location and FWHM of the peak pressure calculated from HAS and k-Wave showed good agreement. When muscle acoustic absorption value in the simulations was adjusted to approximately 54% of the measured attenuation, the average root-mean-squared error between simulated and experimental spatial-average temperature profiles was 0.046 ± 0.019 °C/W. Mean distance between simulated and experimental COTMs was 3.25 ± 1.37 mm. Transverse FWHMs of simulated sonications were smaller than in in vivo sonications. Longitudinal FWHMs were similar. CONCLUSIONS: Presented results demonstrate agreement between HAS and k-Wave simulations and that FUS simulations can accurately predict focal position and heating for in vivo applications in soft tissue.

The influence of bone model geometries on the determination of skull acoustic properties.

In this study, we investigated the impact of various simulated skull bone geometries on the determination of skull speed of sound and acoustic attenuation values via optimization using transmitted pressure amplitudes beyond the bone. Using the hybrid angular spectrum method (HAS), we simulated ultrasound transmission through four model sets of different geometries involving sandwiched layers of diploë and cortical bone in addition to three models generated from CT images of ex-vivo human skull-bones. We characterized cost-function solution spaces for each model and, using optimization, found that when a model possessed appreciable variations in resolvable layer thickness, the predefined attenuation coefficients could be found with low error (RMSE < 0.01 Np/cm). However, we identified a spatial frequency cutoff in the models' geometry beyond which the accuracy of the property determination begins to fail, depending on the frequency of the ultrasound source. There was a large increase in error of the attenuation coefficients determined by the optimization when the variations in layer thickness were above the identified spatial frequency cutoffs, or when the lateral variations across the model were relatively low in amplitude. For our limited sample of three CT-image derived bone models, the attenuation coefficients were determined successfully. The speed of sound values were determined with low error for all models (including the CT-image derived models) that were tested (RMSE < 0.4 m/s). These results illustrate that it is possible to determine the acoustic properties of two-component models when the internal bone structure is taken into account and the structure satisfies the spatial frequency constraints discussed.

Influence of cerebrospinal fluid on power absorption during transcranial magnetic resonance-guided focused ultrasound treatment.

BACKGROUND: Ultrasound beam aberration correction is vital when focusing ultrasound through the skull bone in transcranial magnetic resonance-guided focused ultrasound (tcMRgFUS) applications. Current methods make transducer element phase adjustments to compensate for the variation in skull properties (shape, thickness, and acoustic properties), but do not account for variations in the internal brain anatomy. PURPOSE: Our objective is to investigate the effect of cerebrospinal fluid (CSF) and brain anatomy on beam focusing in tcMRgFUS treatments. METHODS: Simulations were conducted with imaging data from 20 patients previously treated with focused ultrasound for disabling tremor. The Hybrid Angular Spectrum (HAS) method was used to test the effect of including cerebral spinal fluid (CSF) and brain anatomy in determining the element phases used for aberration correction and beam focusing. Computer tomography (CT) and magnetic resonance imaging (MRI) images from patient treatments were used to construct a segmented model of each patient's head. The segmented model for treatment simulation consisted of water, skin, fat, brain, CSF, diploë, and cortical bone. Transducer element phases used for treatment simulation were determined using time reversal from the desired focus, generating a set of phases assuming a homogeneous brain in the intracranial volume, and a second set of phases assigning CSF acoustic properties to regions of CSF. In addition, for three patients, the relative effect of separately including CSF speed of sound values compared to CSF attenuation values was found. RESULTS: We found that including CSF acoustic properties (speed of sound and attenuation) during phase planning compared to phase correction without considering CSF increased the absorbed ultrasound power density ratios at the focus over a range of 1.06 to 1.29 (mean of 17% ± 6%) for 20 patients. Separately considering the CSF speed of sound and CSF attenuation showed that the increase was due almost entirely to including the CSF speed of sound; considering only the CSF attenuation had a negligible effect. CONCLUSIONS: Based on HAS simulations, treatment planning phase determination using morphologically realistic CSF and brain anatomy yielded an increase of up to 29% in the ultrasound focal absorbed power density. Future work will be required to validate the CSF simulations.

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models.

Computational models of acoustic wave propagation are frequently used in transcranial ultrasound therapy, for example, to calculate the intracranial pressure field or to calculate phase delays to correct for skull distortions. To allow intercomparison between the different modeling tools and techniques used by the community, an international working group was convened to formulate a set of numerical benchmarks. Here, these benchmarks are presented, along with intercomparison results. Nine different benchmarks of increasing geometric complexity are defined. These include a single-layer planar bone immersed in water, a multi-layer bone, and a whole skull. Two transducer configurations are considered (a focused bowl and a plane piston operating at 500 kHz), giving a total of 18 permutations of the benchmarks. Eleven different modeling tools are used to compute the benchmark results. The models span a wide range of numerical techniques, including the finite-difference time-domain method, angular spectrum method, pseudospectral method, boundary-element method, and spectral-element method. Good agreement is found between the models, particularly for the position, size, and magnitude of the acoustic focus within the skull. When comparing results for each model with every other model in a cross-comparison, the median values for each benchmark for the difference in focal pressure and position are less than 10% and 1 mm, respectively. The benchmark definitions, model results, and intercomparison codes are freely available to facilitate further comparisons.

Experimental validation of acoustic and thermal modeling in heterogeneous phantoms using the hybrid angular spectrum method.

PURPOSE: The aim was to quantitatively validate the hybrid angular spectrum (HAS) algorithm, a rapid wave propagation technique for heterogeneous media, with both pressure and temperature measurements. METHODS: Heterogeneous tissue-mimicking phantoms were used to evaluate the accuracy of the HAS acoustic modeling algorithm in predicting pressure and thermal patterns. Acoustic properties of the phantom components were measured by a through-transmission technique while thermal properties were measured with a commercial probe. Numerical models of each heterogeneous phantom were segmented from 3D MR images. Cylindrical phantoms 30-mm thick were placed in the pre-focal field of a focused ultrasound beam and 2D pressure measurements obtained with a scanning hydrophone. Peak pressure, full width at half maximum, and normalized root mean squared difference (RMSDn) between the measured and simulated patterns were compared. MR-guided sonications were performed on 150-mm phantoms to obtain MR temperature measurements. Using HAS-predicted power density patterns, temperature simulations were performed. Experimental and simulated temperature patterns were directly compared using peak and mean temperature plots, RMSDn metrics, and accuracy of heating localization. RESULTS: The average difference between simulated and hydrophone-measured peak pressures was 9.0% with an RMSDn of 11.4%. Comparison of the experimental MRI-derived and simulated temperature patterns showed RMSDn values of 10.2% and 11.1% and distance differences between the centers of thermal mass of 2.0 and 2.2 mm. CONCLUSIONS: These results show that the computationally rapid hybrid angular spectrum method can predict pressure and temperature patterns in heterogeneous models, including uncertainties in property values and other parameters, to within approximately 10%.

Magnetic resonance shear wave elastography using transient acoustic radiation force excitations and sinusoidal displacement encoding.

A magnetic resonance (MR) shear wave elastography technique that uses transient acoustic radiation force impulses from a focused ultrasound (FUS) transducer and a sinusoidal-shaped MR displacement encoding strategy is presented. Using this encoding strategy, an analytic expression for calculating the shear wave speed in a heterogeneous medium was derived. Green's function-based simulations were used to evaluate the feasibility of calculating shear wave speed maps using the analytic expression. Accuracy of simulation technique was confirmed experimentally in a homogeneous gelatin phantom. The elastography measurement was compared to harmonic MR elastography in a homogeneous phantom experiment and the measured shear wave speed values differed by less than 14%. This new transient elastography approach was able to map the position and shape of inclusions sized from 8.5 to 14 mm in an inclusion phantom experiment. These preliminary results demonstrate the feasibility of using a straightforward analytic expression to generate shear wave speed maps from MR images where sinusoidal-shaped motion encoding gradients are used to encode the displacement-time history of a transiently propagating wave-packet. This new measurement technique may be particularly well suited for performing elastography before, during, and after MR-guided FUS therapies since the same device used for therapy is also used as an excitation source for elastography.

Development and characterization of a tissue mimicking psyllium husk gelatin phantom for ultrasound and magnetic resonance imaging.

Purpose: To develop and characterize a tissue-mimicking phantom that enables the direct comparison of magnetic resonance (MR) and ultrasound (US) imaging techniques useful for monitoring high-intensity focused ultrasound (HIFU) treatments. With no additions, gelatin phantoms produce little if any scattering required for US imaging. This study characterizes the MR and US image characteristics as a function of psyllium husk concentration, which was added to increase US scattering.Methods: Gelatin phantoms were constructed with varying concentrations of psyllium husk. The effects of psyllium husk concentration on US B-mode and MR imaging were evaluated at nine different concentrations. T1, T2, and T2* MR maps were acquired. Acoustic properties (attenuation and speed of sound) were measured at frequencies of 0.6, 1.0, 1.8, and 3.0 MHz using a through-transmission technique. Phantom elastic properties were evaluated for both time and temperature dependence.Results: Ultrasound image echogenicity increased with increasing psyllium husk concentration while quality of gradient-recalled echo MR images decreased with increasing concentration. For all phantoms, the measured speed of sound ranged between 1567-1569 m/s and the attenuation ranged between 0.42-0.44 dB/(cm·MHz). Measured T1 ranged from 974-1051 ms. The T2 and T2* values ranged from 97-108 ms and 48-88 ms, respectively, with both showing a decreasing trend with increased psyllium husk concentration. Phantom stiffness, measured using US shear-wave speed measurements, increased with age and decreased with increasing temperature.Conclusions: The presented dual-use tissue-mimicking phantom is easy to manufacture and can be used to compare and evaluate US-guided and MR-guided HIFU imaging protocols.

Efficient shear wave elastography using transient acoustic radiation force excitations and MR displacement encoding.

PURPOSE: To present a novel MR shear wave elastography (MR-SWE) method that efficiently measures the speed of propagating wave packets generated using acoustic radiation force (ARF) impulses. METHODS: ARF impulses from a focused ultrasound (FUS) transducer were applied sequentially to a preselected set of positions and motion encoded MRI was used to acquire volumetric images of the propagating shear wavefront emanating from each point. The wavefront position at multiple propagation times was encoded in the MR phase image using a train of motion encoding gradient lobes. Generating a transient propagating wavefront at multiple spatial positions and sampling each at multiple time-points allowed for shear wave speed maps to be efficiently created. MR-SWE was evaluated in tissue mimicking phantoms and ex vivo bovine liver tissue before and after ablation. RESULTS: MR-SWE maps, covering an in-plane area of ~5 × 5 cm, were acquired in 12 s for a single slice and 144 s for a volumetric scan. MR-SWE detected inclusions of differing stiffness in a phantom experiment. In bovine liver, mean shear wave speed significantly increased from 1.65 ± 0.18 m/s in normal to 2.52 ± 0.18 m/s in ablated region (n = 581 pixels; P-value < 0.001). CONCLUSION: MR-SWE is an elastography technique that enables precise targeting and excitation of the desired tissue of interest. MR-SWE may be particularly well suited for treatment planning and endpoint assessment of MR-guided FUS procedures because the same device used for therapy can be used as an excitation source for tissue stiffness quantification.

Validation of hybrid angular spectrum acoustic and thermal modelling in phantoms.

In focused ultrasound (FUS) thermal ablation of diseased tissue, acoustic beam and thermal simulations enable treatment planning and optimization. In this study, a treatment-planning methodology that uses the hybrid angular spectrum (HAS) method and the Pennes' bioheat equation (PBHE) is experimentally validated in homogeneous tissue-mimicking phantoms. Simulated three-dimensional temperature profiles are compared to volumetric MR thermometry imaging (MRTI) of FUS sonications in the phantoms, whose acoustic and thermal properties are independently measured. Additionally, Monte Carlo (MC) uncertainty analysis is performed to quantify the effect of tissue property uncertainties on simulation results. The mean error between simulated and experimental spatiotemporal peak temperature rise was +0.33°C (+6.9%). Despite this error, the experimental temperature rise fell within the expected uncertainty of the simulation, as determined by the MC analysis. The average errors of the simulated transverse and longitudinal full width half maximum (FWHM) of the profiles were -1.9% and 7.5%, respectively. A linear regression and local sensitivity analysis revealed that simulated temperature amplitude is more sensitive to uncertainties in simulation inputs than in the profile width and shape. Acoustic power, acoustic attenuation and thermal conductivity had the greatest impact on peak temperature rise uncertainty; thermal conductivity and volumetric heat capacity had the greatest impact on FWHM uncertainty. This study validates that using the HAS and PBHE method can adequately predict temperature profiles from single sonications in homogeneous media. Further, it informs the need to accurately measure or predict patient-specific properties for improved treatment planning of ablative FUS surgeries.

Experimental assessment of phase aberration correction for breast MRgFUS therapy.

PURPOSE: This study validates that phase aberrations in breast magnetic resonance-guided focussed ultrasound (MRgFUS) therapies can be corrected in a clinically relevant time frame to generate more intense, smaller and more spatially accurate foci. MATERIALS AND METHODS: Hybrid angular spectrum (HAS) ultrasound calculations in an magnetic resonance imaging (MRI)-based tissue model, were used to compute phase aberration corrections for improved experimental MRgFUS heating in four heterogeneous breast-mimicking phantoms (n = 18 total locations). Magnetic resonance(MR) temperature imaging was used to evaluate the maximum temperature rise, focus volume and focus accuracy for uncorrected and phase aberration-corrected sonications. Thermal simulations assessed the effectiveness of the phase aberration correction implementation. RESULTS: In 13 of 18 locations, the maximum temperature rise increased by an average of 30%, focus volume was reduced by 40% and focus accuracy improved from 4.6 to 3.6 mm. Mixed results were observed in five of the 18 locations, with focus accuracy improving from 6.1 to 2.5 mm and the maximum temperature rise decreasing by 8% and focus volume increasing by 10%. Overall, the study demonstrated significant improvements (p < 0.005) in maximum temperature rise, focus volume and focus accuracy. Simulations predicted greater improvements than observed experimentally, suggesting potential for improvement in implementing the technique. The complete phase aberration correction procedure, including model generation, segmentation and phase aberration computations, required less than 45 min per sonication location. CONCLUSION: The significant improvements demonstrated in this study i.e., focus intensity, size and accuracy from phase aberration correction have the potential to improve the efficacy, time-efficiency and safety of breast MRgFUS therapies.

Rapid full-wave phase aberration correction method for transcranial high-intensity focused ultrasound therapies.

BACKGROUND: Non-invasive high-intensity focused ultrasound (HIFU) can be used to treat a variety of disorders, including those in the brain. However, the differences in acoustic properties between the skull and the surrounding soft tissue cause aberrations in the path of the ultrasonic beam, hindering or preventing treatment. METHODS: We present a method for correcting these aberrations that is fast, full-wave, and allows for corrections at multiple treatment locations. The method is simulation-based: an acoustic model is built based on high-resolution CT scans, and simulations are performed using the hybrid angular spectrum (HAS) method to determine the phases needed for correction. RESULTS: Computation of corrections for clinically applicable resolutions can be achieved in approximately 15 min. Experimental results with a plastic model designed to mimic the aberrations caused by the skull show that the method can recover 95 % of the peak pressure obtained using hydrophone-based time-reversal methods. Testing using an ex vivo human skull flap resulted in recovering up to 70 % of the peak pressure at the focus and 61 % when steering (representing, respectively, a 1.52- and 1.19-fold increase in the peak pressure over the uncorrected case). Additionally, combining the phase correction method with rapid HAS simulations allows evaluation of such treatment metrics as the effect of misregistration on resulting pressure levels. CONCLUSIONS: The method presented here is able to rapidly compute phases required to improve ultrasound focusing through the skull at multiple treatment locations. Combining phase correction with rapid simulation techniques allows for evaluation of various treatment metrics such as the effect of steering on pressure levels. Since the method computes 3D pressure patterns, it may also be suitable for predicting off-focus hot spots during treatments-a primary concern for transcranial HIFU. Additionally, the plastic-skull method presented here may be a useful tool in evaluating the effectiveness of phase correction methods.

MR thermometry for focused ultrasound monitoring utilizing model predictive filtering and ultrasound beam modeling.

BACKGROUND: A major challenge in using magnetic resonance temperature imaging (MRTI) to monitor focused ultrasound (FUS) applications is achieving high spatio-temporal resolution over a large field of view (FOV). This is important to accurately monitor all ultrasound (US) power depositions. Magnetic resonance (MR) subsampling in conjunction with thermal model-based reconstruction of the MRTI utilizing Pennes bioheat transfer equation (PBTE) is one promising approach. The thermal properties used in the thermal model are often estimated from a pre-treatment, low-power sonication. METHODS: In this proof-of-concept study we investigate the use of US simulations computed using the hybrid angular spectrum (HAS) method to estimate the US power deposition density Q, thereby avoiding the pre-treatment sonication and any potential tissue damage. MRTI reconstructions are performed using a thermal model-based reconstruction method called model predictive filtering (MPF). Experiments are performed in a homogeneous gelatin phantom and in a gelatin phantom with embedded plastic skull. MPF reconstructions are compared to separate sonications imaged with fully sampled data over a smaller FOV. Temperature root-mean-square errors (RMSE) and focal spot positions and shapes are evaluated. RESULTS: HAS simulations accurately predict the location of the focal spot (to within 1 mm) in both phantoms. Accurate temperature maps (RMSE below 1 °C), where the location of the focal spot agrees well with fully sampled "truth" (to within 1 mm), are also achieved in both phantoms. CONCLUSIONS: HAS simulations can be used to accurately predict the focal spot location in homogeneous media and when focusing through an aberrating plastic skull. The HAS simulated power deposition (Q) patterns can be used in the MPF thermal model-based reconstruction to obtain accurate temperature maps with high spatio-temporal resolution over large FOVs.

Development and validation of a MRgHIFU non-invasive tissue acoustic property estimation technique.

MR-guided high-intensity focussed ultrasound (MRgHIFU) non-invasive ablative surgeries have advanced into clinical trials for treating many pathologies and cancers. A remaining challenge of these surgeries is accurately planning and monitoring tissue heating in the face of patient-specific and dynamic acoustic properties of tissues. Currently, non-invasive measurements of acoustic properties have not been implemented in MRgHIFU treatment planning and monitoring procedures. This methods-driven study presents a technique using MR temperature imaging (MRTI) during low-temperature HIFU sonications to non-invasively estimate sample-specific acoustic absorption and speed of sound values in tissue-mimicking phantoms. Using measured thermal properties, specific absorption rate (SAR) patterns are calculated from the MRTI data and compared to simulated SAR patterns iteratively generated via the Hybrid Angular Spectrum (HAS) method. Once the error between the simulated and measured patterns is minimised, the estimated acoustic property values are compared to the true phantom values obtained via an independent technique. The estimated values are then used to simulate temperature profiles in the phantoms, and compared to experimental temperature profiles. This study demonstrates that trends in acoustic absorption and speed of sound can be non-invasively estimated with average errors of 21% and 1%, respectively. Additionally, temperature predictions using the estimated properties on average match within 1.2 °C of the experimental peak temperature rises in the phantoms. The positive results achieved in tissue-mimicking phantoms presented in this study indicate that this technique may be extended to in vivo applications, improving HIFU sonication temperature rise predictions and treatment assessment.

Phase aberration simulation study of MRgFUS breast treatments.

PURPOSE: This simulation study evaluates the effects of phase aberration in breast MR-guided focused ultrasound (MRgFUS) ablation treatments performed with a phased-array transducer positioned laterally to the breast. A quantification of these effects in terms of thermal dose delivery and the potential benefits of phase correction is demonstrated in four heterogeneous breast numerical models. METHODS: To evaluate the effects of varying breast tissue properties on the quality of the focus, four female volunteers with confirmed benign fibroadenomas were imaged using 3T MRI. These images were segmented into numerical models with six tissue types, with each tissue type assigned standard acoustic properties from the literature. Simulations for a single-plane 16-point raster-scan treatment trajectory centered in a fibroadenoma in each modeled breast were performed for a breast-specific MRgFUS system. At each of the 16 points, pressure patterns both with and without applying a phase correction technique were determined with the hybrid-angular spectrum method. Corrected phase patterns were obtained using a simulation-based phase aberration correction technique to adjust each element's transmit phase to obtain maximized constructive interference at the desired focus. Thermal simulations were performed for both the corrected and uncorrected pressure patterns using a finite-difference implementation of the Pennes bioheat equation. The effect of phase correction was evaluated through comparison of thermal dose accumulation both within and outside a defined treatment volume. Treatment results using corrected and uncorrected phase aberration simulations were compared by evaluating the power required to achieve a 20 °C temperature rise at the first treatment location. The extent of the volumes that received a minimum thermal dose of 240 CEM at 43 °C inside the intended treatment volume as well as the volume in the remaining breast tissues was also evaluated in the form of a dose volume ratio (DVR), a DVR percent change between corrected and uncorrected phases, and an additional metric that measured phase spread. RESULTS: With phase aberration correction applied, there was an improvement in the focus for all breast anatomies as quantified by a reduction in power required (13%-102%) to reach 20 °C when compared to uncorrected simulations. Also, the DVR percent change increased by 5%-77% in seven out of eight cases, indicating an improvement to the treatment as measured by a reduction in thermal dose deposited to the nontreatment tissues. Breast compositions with a higher degree of heterogeneity along the ultrasound beam path showed greater reductions in thermal dose delivered outside of the treatment volume with correction applied than beam trajectories that propagated through more homogeneous breast compositions. An increasing linear trend was observed between the DVR percent change and the phase-spread metric (R(2) = 0.68). CONCLUSIONS: These results indicate that performing phase aberration correction for breast MRgFUS treatments is beneficial for the small-aperture transducer (14.4 × 9.8 cm) evaluated in this work. While all breast anatomies could benefit from phase aberration correction, greater benefits are observed in more heterogeneous anatomies.

Kinetics of Ultrasonic Drug Delivery from Targeted Micelles.

To minimize the adverse side effects of conventional chemotherapy, a targeted micellar drug carrier was investigated that retains hydrophobic drugs in its core and then releases the drug via ultrasonic activation. This paper compares the percent drug release from folated versus non-folated micelles by insonation at 70 kHz and different acoustic power densities. The encapsulated drug is Doxoru- bicin (Dox). A physical model of zero-order release with first-order re-encapsulation was used to fit the experimental kinetic data. Additionally, the acoustic activation power density and Gibbs free energy were introduced and calculated for folated and non-targeted micelles. The data suggests an important role of inertial cavitation in drug release and the presence of a power density threshold for inertial cavitation.

Characterization and evaluation of tissue-mimicking gelatin phantoms for use with MRgFUS.

BACKGROUND: A tissue-mimicking phantom that accurately represents human-tissue properties is important for safety testing and for validating new imaging techniques. To achieve a variety of desired human-tissue properties, we have fabricated and tested several variations of gelatin phantoms. These phantoms are simple to manufacture and have properties in the same order of magnitude as those of soft tissues. This is important for quality-assurance verification as well as validation of magnetic resonance-guided focused ultrasound (MRgFUS) treatment techniques. METHODS: The phantoms presented in this work were constructed from gelatin powders with three different bloom values (125, 175, and 250), each one allowing for a different mechanical stiffness of the phantom. Evaporated milk was used to replace half of the water in the recipe for the gelatin phantoms in order to achieve attenuation and speed of sound values in soft tissue ranges. These acoustic properties, along with MR (T1 and T2*), mechanical (density and Young's modulus), and thermal properties (thermal diffusivity and specific heat capacity), were obtained through independent measurements for all three bloom types to characterize the gelatin phantoms. Thermal repeatability of the phantoms was also assessed using MRgFUS and MR thermometry. RESULTS: All the measured values fell within the literature-reported ranges of soft tissues. In heating tests using low-power (6.6 W) sonications, interleaved with high-power (up to 22.0 W) sonications, each of the three different bloom phantoms demonstrated repeatable temperature increases (10.4 ± 0.3 °C for 125-bloom, 10.2 ± 0.3 °C for 175-bloom, and 10.8 ± 0.2 °C for 250-bloom for all 6.6-W sonications) for heating durations of 18.1 s. CONCLUSION: These evaporated milk-modified gelatin phantoms should serve as reliable, general soft tissue-mimicking MRgFUS phantoms.

A simulation technique for 3D MR-guided acoustic radiation force imaging.

PURPOSE: In magnetic resonance-guided focused ultrasound (MRgFUS) therapies, the in situ characterization of the focal spot location and quality is critical. MR acoustic radiation force imaging (MR-ARFI) is a technique that measures the tissue displacement caused by the radiation force exerted by the ultrasound beam. This work presents a new technique to model the displacements caused by the radiation force of an ultrasound beam in a homogeneous tissue model. METHODS: When a steady-state point-source force acts internally in an infinite homogeneous medium, the displacement of the material in all directions is given by the Somigliana elastostatic tensor. The radiation force field, which is caused by absorption and reflection of the incident ultrasound intensity pattern, will be spatially distributed, and the tensor formulation takes the form of a convolution of a 3D Green's function with the force field. The dynamic accumulation of MR phase during the ultrasound pulse can be theoretically accounted for through a time-of-arrival weighting of the Green's function. This theoretical model was evaluated experimentally in gelatin phantoms of varied stiffness (125-, 175-, and 250-bloom). The acoustic and mechanical properties of the phantoms used as parameters of the model were measured using independent techniques. Displacements at focal depths of 30- and 45-mm in the phantoms were measured by a 3D spin echo MR-ARFI segmented-EPI sequence. RESULTS: The simulated displacements agreed with the MR-ARFI measured displacements for all bloom values and focal depths with a normalized RMS difference of 0.055 (range 0.028-0.12). The displacement magnitude decreased and the displacement pattern broadened with increased bloom value for both focal depths, as predicted by the theory. CONCLUSIONS: A new technique that models the displacements caused by the radiation force of an ultrasound beam in a homogeneous tissue model theory has been rigorously validated through comparison with experimentally obtained 3D displacement data in homogeneous gelatin phantoms using a 3D MR-ARFI sequence. The agreement of the experimentally measured and simulated results demonstrates the potential to use MR-ARFI displacement data in MRgFUS therapies.

Adaptive model-predictive controller for magnetic resonance guided focused ultrasound therapy.

PURPOSE: Minimising treatment time and protecting healthy tissues are conflicting goals that play major roles in making magnetic resonance image-guided focused ultrasound (MRgFUS) therapies clinically practical. We have developed and tested in vivo an adaptive model-predictive controller (AMPC) that reduces treatment time, ensures safety and efficacy, and provides flexibility in treatment set-up. MATERIALS AND METHODS: The controller realises time savings by modelling the heated treatment cell's future temperatures and thermal dose accumulation in order to anticipate the optimal time to switch to the next cell. Selected tissues are safeguarded by a configurable temperature constraint. Simulations quantified the time savings realised by each controller feature as well as the trade-offs between competing safety and treatment time parameters. In vivo experiments in rabbit thighs established the controller's effectiveness and reliability. RESULTS: In all in vivo experiments the target thermal dose of at least 240 CEM43 was delivered everywhere in the treatment volume. The controller's temperature safety limit reliably activated and constrained all protected tissues to <9 CEM43. Simulations demonstrated the path independence of the controller, and that a path which successively proceeds to the hottest untreated neighbouring cell leads to significant time savings, e.g. when compared to a concentric spiral path. Use of the AMPC produced a compounding time-saving effect; reducing the treatment cells' heating times concurrently reduced heating of normal tissues, which eliminated cooling periods. CONCLUSIONS: Adaptive model-predictive control can automatically deliver safe, effective MRgFUS treatments while significantly reducing treatment times.

Treatment envelope evaluation in transcranial magnetic resonance-guided focused ultrasound utilizing 3D MR thermometry.

BACKGROUND: Current clinical targets for transcranial magnetic resonance-guided focused ultrasound (tcMRgFUS) are all located close to the geometric center of the skull convexity, which minimizes challenges related to focusing the ultrasound through the skull bone. Non-central targets will have to be reached to treat a wider variety of neurological disorders and solid tumors. Treatment envelope studies utilizing two-dimensional (2D) magnetic resonance (MR) thermometry have previously been performed to determine the regions in which therapeutic levels of FUS can currently be delivered. Since 2D MR thermometry was used, very limited information about unintended heating in near-field tissue/bone interfaces could be deduced. METHODS: In this paper, we present a proof-of-concept treatment envelope study with three-dimensional (3D) MR thermometry monitoring of FUS heatings performed in a phantom and a lamb model. While the moderate-sized transducer used was not designed for transcranial geometries, the 3D temperature maps enable monitoring of the entire sonication field of view, including both the focal spot and near-field tissue/bone interfaces, for full characterization of all heating that may occur. 3D MR thermometry is achieved by a combination of k-space subsampling and a previously described temporally constrained reconstruction method. RESULTS: We present two different types of treatment envelopes. The first is based only on the focal spot heating-the type that can be derived from 2D MR thermometry. The second type is based on the relative near-field heating and is calculated as the ratio between the focal spot heating and the near-field heating. This utilizes the full 3D MR thermometry data achieved in this study. CONCLUSIONS: It is shown that 3D MR thermometry can be used to improve the safety assessment in treatment envelope evaluations. Using a non-optimal transducer, it is shown that some regions where therapeutic levels of FUS can be delivered, as suggested by the first type of envelope, are not necessarily safely treated due to the amount of unintended near-field heating occurring. The results presented in this study highlight the need for 3D MR thermometry in tcMRgFUS.

The accuracy and precision of two non-invasive, magnetic resonance-guided focused ultrasound-based thermal diffusivity estimation methods.

PURPOSE: The use of correct tissue thermal diffusivity values is necessary for making accurate thermal modelling predictions during magnetic resonance-guided focused ultrasound (MRgFUS) treatment planning. This study evaluates the accuracy and precision of two non-invasive thermal diffusivity estimation methods, a Gaussian temperature method and a Gaussian specific absorption rate (SAR) method. MATERIALS AND METHODS: Both methods utilise MRgFUS temperature data obtained during cooling following a short (<25 s) heating pulse. The Gaussian SAR method can also use temperatures obtained during heating. Experiments were performed at low heating levels (ΔT∼10 °C) in ex vivo pork muscle and in vivo rabbit back muscle. The non-invasive MRgFUS thermal diffusivity estimates were compared with measurements from two standard invasive methods. RESULTS: Both non-invasive methods accurately estimated thermal diffusivity when using MR temperature cooling data (overall ex vivo error <6%, in vivo <12%). Including heating data in the Gaussian SAR method further reduced errors (ex vivo error <2%, in vivo <3%). The significantly lower standard deviation values (p < 0.03) of the Gaussian SAR method indicated that it had better precision than the Gaussian temperature method. CONCLUSIONS: With repeated sonications, either MR-based method could provide accurate thermal diffusivity values for MRgFUS therapies. Fitting to more data simultaneously likely made the Gaussian SAR method less susceptible to noise, and using heating data helped it converge more consistently to the FUS fitting parameters and thermal diffusivity. These effects led to the improved precision of the Gaussian SAR method.