Experimental assessment of phase aberration correction for breast MRgFUS therapy

Abstract

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.

Keywords:

• High intensity focussed ultrasound
• ultrasound breast therapy
• MRI
• phase aberration correction
• tissue-mimicking phantoms

Introduction

Magnetic resonance-guided focussed ultrasound (MRgFUS) surgery is an emerging therapy where ultrasonic waves converge to selectively and precisely ablate diseased tissue while preserving healthy adjacent tissues [1–5]. The excellent soft-tissue contrast of magnetic resonance imaging (MRI) enables patient-specific treatment planning, while MR temperature imaging (MRTI) allows for near real-time monitoring of the temperature changes caused by focussed ultrasound [6]. The completely non-invasive nature of MRgFUS is unique and mounting clinical evidence suggests that MRgFUS is an effective therapy for a variety of diseases [7–14].

MRgFUS commonly uses phased-array technology in which ultrasound beams from hundreds of individual ultrasound elements constructively interfere to create a highly localised ablation region [15,16]. While spherical transducers naturally generate a focus, the coordinated manipulation of time delays or phases, applied to each phased-array element can modify this focussing and enables steering of the focal zone to different locations within the target tissue. In homogeneous tissues, the phases for focussing and steering that maximise constructive interference can be calculated from simple transducer geometry-based equations [16,17]. However, when ultrasound passes through heterogeneous tissues, the ultrasound waves constructive interference is compromised, because variability in the tissue speed of sound causes the ultrasound waves from individual elements to arrive asynchronously at the focal zone. This effect, known as phase aberration, may distort, blur or shift the focal zone, decrease peak beam intensity at the target tissue or generate undesired increased ultrasound intensity at other locations, with the end result of reduced treatment efficiency and efficacy while potentially damaging sensitive healthy tissues.

Several studies have implemented methods to correct for phase aberration in transcranial applications of MRgFUS due to the large phase shifts induced when ultrasound propagates through the skull [18–28]. The need for phase aberration correction and applying correction methods in soft-tissue anatomies such as the breast has also been explored [29–33]. Breast anatomy is highly heterogeneous [34] and patient-specific [29,33,34], with fibroglandular and fatty tissues in the breast exhibiting as large as 9% variation in speed of sound [35–37]. Of note, Farrer et al. [33] demonstrated in simulations of four patient-specific MRI-based breast models that phase aberration correction can make a significant difference for a preclinical breast-dedicated MRgFUS device. Phase aberration correction in that study, based on full-wave hybrid angular spectrum (HAS) ultrasound beam-modeling simulations [24,28,38], reduced the power required to reach ablative temperatures by 13–102% in eight simulated MRgFUS trajectories.

The objective of this study is to validate experimentally that phase aberrations in breast ablation conditions can be corrected in a clinically relevant time frame using MRI-derived models. This is evaluated using a heterogeneous breast-mimicking phantom in a breast-dedicated MRgFUS device with MRI-based phase aberration correction applied using the HAS algorithm. Thermal simulations of the sonications help determine the effectiveness of the phase aberration correction implementation. It is hypothesised that applying phase aberration correction in these phantoms will generate larger temperature changes within a smaller and more accurate focus. Demonstrating that these improvements made at clinically relevant times will improve that phase aberration correction efficacy, time-efficiency and safety of breast MRgFUS therapies.

Materials and methods

Phase aberration correction overview

The phase aberration correction procedure [28] uses the HAS simulation method [38] and requires the following inputs: a three-dimensional (3 D) segmented model of the tissue, acoustic property values of density, speed of sound and attenuation coefficient for each of the segmented tissue types and the relative position of the ultrasound transducer (and its elements) with respect to the model. With these inputs, the HAS method is applied for each individual element of the phased-array transducer to calculate 3 D pressure patterns within the model, initially assuming zero phase on all element excitations. The phase correction to be imposed on each element is then the negative of the computed phase at the desired focus location. By imposing these phase corrections during sonication, constructive interference is restored at the focus location with higher ultrasound intensities and greater temperature rises than if not applied.

Procedure verification with aberrator model

To verify whether the phase correction code was implemented correctly, a phased-array ultrasound transducer built by Imasonic, Voray-sur-l’Ognon, France (256 semi-randomly positioned elements each with 4 mm diameter, 940 kHz, 14.4 × 9.8 cm aperture, 10 cm radius of curvature) was mounted vertically in a degassed water bath with a hydrophone (HNR-500, Onda Corporation, Sunnyvale, CA) scanned with two stepper motors (NRT150, Thorlabs Inc., Newton, NJ) in the plane of the transducer’s geometric focus (Figure 1). Electronics for driving the transducer were developed and constructed by Image Guided Therapy, Pessac, France. This verification experiment employed a 3 D-printed photopolymer aberrator model created in-house and were designed with randomly positioned thickness variations to induce relative phase shifts of 0–2π [28]. The 3 D pattern used for printing the aberrator was also utilised as the numerical model for phase aberration correction. Acoustic properties of the photopolymer material were determined by a through-transmission method, as described previously [28]. The phase aberration correction was evaluated by comparing the pressure patterns acquired from three hydrophone scans (0.25 mm isotropic spacing): a water-only scan (0.5 acoustic watts (W)) with no aberrator in place, and uncorrected and phase aberration-corrected scans (8 W) with the aberrator model positioned and secured at a known fixed distance and rotation with respect to the ultrasound transducer.

Figure 1. Setup for phase aberration correction verification. Focused ultrasound passed through a photopolymer aberrator model designed to generate phase aberrations of 0–2π. A hydrophone controlled by stepper motors scanned the ultrasound pressure pattern in the plane of the transducer’s geometric focus.

Phantom design

Heterogeneous phantoms were constructed from materials with acoustic properties comparable to those of human breast tissue (Table 1) to generate phase aberrations during experimental MRgFUS heating. First, a breast-shaped mould (maximum diameter = 11 cm, length = 7 cm) was made with a soft but robust material (Plasti Dip^®, Blane, MN) as shown in Figure 2. Next, successive layers of 250-bloom gelatine with 1:1mixture of water and evaporated milk [39], representative of breast fibroglandular tissue, were poured into the phantom mould. As the gelatine cooled, latex balloons (diameter = 1.1–2.0 cm) filled with canola oil were placed in the gelatine to mimic breast fat. By alternating the pouring of gelatine and placement of balloons, allowing time for the gelatine to cool and set, each heterogeneous phantom had six balloons located at a variety of levels and positions (Figure 2). Balloons were generally positioned in the near field of the ultrasound beam path for two reasons: first, loading the near field with materials of different speed of sounds created phase aberrations and second, keeping the geometric focus location away from canola oil and in the gelatine ensured that the water-based proton resonance frequency (PRF) method [40,41] would provide accurate MRTI measurements for evaluating phase aberration in the phantoms.

Figure 2. Fabrication of breast-mimicking phantoms. (a–c) Top view of canola oil filled balloons held in place with removable supports as different layers of the gelatine cool and solidify. (d) Pouring gelatine around secured balloons. (e, f) Side views of the breast-shaped mould at different stages of phantom fabrication. The canola oil-filled balloons were placed in the near field of the breast mould to create a heterogeneous anatomy that induced phase aberrations while allowing MRTI at the geometric focus of the transducer.

Table 1. Summary of acoustic and thermal properties for the breast-mimicking phantom and related human tissues^a.

Tissue material	Speed of sound (m s^−1)	Attenuation coefficient (Np m^−1 MHz^−1)	Density (kg m^−3)	Thermal conductivity (W m^−1 °C^−1)	Specific heat (J kg^−1°C^−1)	Reference
Gelatin	1555	4.7	1057	0.55	3250	Measured [39]
Fibroglandular tissue	1505 ± 47	8.6	1041 ± 45	0.33 ± 0.02	2960	[37]
Canola oil	1469	1.25	920	0.18	1913	Measured [57]
Breast fat	1440 ± 22	4.4	911 ± 53	0.21	2348 ± 372	[37]
Plasti Dip^® mould^b	1500	90.3	1000	0.63	4178	Measured
Water	1500	0	1000	0.63	4178	[17,58]

^a Property values from the literature are presented as the mean ± standard deviation when applicable.

^b Plasti Dip^® properties were assumed equal to water.

Acoustic property measurements

Acoustic properties of the gelatine and canola oil were measured experimentally and are presented in Table 1 along with corresponding properties for human tissues found in the literature. Speed of sound was determined with the through-transmission technique [39,42,43]. Ultrasonic attenuation coefficients were computed with the insertion-loss method using a radiation force balance [44–46]. Density was measured via the water displacement method. The attenuation coefficient of the Plasti Dip^® mould was also measured, while its speed of sound and density were set to water properties under the assumption that the soft, thin (∼0.5 mm) material would have minimal reflection and refraction effects.

Experimental protocols

Experimental setup

Four different breast-mimicking phantoms were fabricated for phase aberration correction evaluation in this study. In each experiment, the phantom was mounted in a dedicated breast MRgFUS system [47]. The system included the transducer described above as well as an integrated eight-channel radiofrequency (RF) coil [48,49]. All study sonications and imaging were performed in a Siemens TIM Trio 3 T MRI scanner (Erlangen, Germany).

Model creation and segmentation

The phantom was first placed in the breast-specific MRgFUS system without coupling fluid and imaged with a two-point Dixon 3 D gradient echo sequence (repetition time (TR) = 20 ms, echo times (TE) = 2.45 and 3.675 ms, flip angle (FA) = 25 °, bandwidth (BW) = 350 Hz/pixel, field-of-view (FOV) = 152 × 256 mm, 176 slices, acquired spatial resolution (Res) = 1 mm isotropic, zero-filled interpolation (ZFI) to 0.5 mm isotropic) that enabled segmentation based on the fat- and water-separated images [50]. Using thresholding, the resulting fat and water images were automatically segmented to generate a 3 D numerical model with three media: air, canola oil and gelatine. Finally, an edge detection algorithm was used to add a single voxel layer to the edge of the phantom, creating a fourth medium approximating the Plasti Dip^® mould. A surface rendering of one of the models is shown in Figure 3(a). After segmentation was complete, the cylinder surrounding the phantom was filled with degassed water for ultrasound coupling.

Figure 3. (a) Surface rendering of 3 D breast model used for phase aberration correction. MR coordinate directions are indicated along the axes. (b) Sagittal T1-weighted MR image showing experimental setup and the positioning of oblique 3 D MRTI volume. Dashed lines trace the outer rays from the spherical transducer and converge at the location of the geometric focus as determined by positioning coils.

Aberration correction registration

The HAS algorithm computes pressure patterns in a coordinate system aligned with the direction of ultrasound beam propagation, so it is necessary to rotate the 3 D segmented model, that is generated in the MR coordinates, into a new orientation. This required knowledge of the pitch and yaw rotations of the transducer as well as its geometric focus position. Pitch and yaw for each experimental sonication position were recorded from protractors integrated in the MRgFUS system ( ± 1 ° accuracy). Other degrees of freedom in the MRgFUS system were fixed throughout. Positioning coils calibrated for the MRgFUS system, with a reported accuracy of 2.1 mm [51], were used to determine the geometric focus location. The segmented model was rotated about the geometric focus position by the pitch and yaw angles such that the z direction of the rotated model (see arrow in Figure 3(b)) was aligned with the direction of beam propagation, as required for HAS calculations and phase aberration correction.

MRgFUS heating

In the four phantoms, a total of 18 locations were evaluated with and without phase aberration correction. For each location, an uncorrected sonication (∼12.5 W for 30 s in phantom 1, ∼27 W for 20 s in phantoms 2–4) was performed at the geometric focus. These low power sonications were used to ensure that the gelatine, which melts at ∼30 °C [52], did not approach the solid-liquid transition temperature, which would alter acoustic absorption and temperature profiles. 3 D MRTI (segmented-echo planar imaging (EPI), TR = 44 ms, TE = 14 ms, FA = 20°, BW = 738 Hz/pixel, FOV = 144 × 256 mm, eight slices with 25% oversampling, Res = 2 × 2 × 3 mm, temporal resolution = 3.52 s, EPI factor = 9, with fat saturation) was performed in an oblique plane (see Figure 3(b)) aligned parallel to the ultrasound propagation axis. MR data were zero-filled to 0.5 mm isotropic spacing and temperatures were computed with a multi-baseline reference reconstruction using the PRF method. Temperature uncertainty was calculated as the average standard deviation of temperatures over time in an unheated region of interest within the gelatine.

After rotation into ultrasound coordinates, the 3 D segmented model with known acoustic properties was used to calculate phase aberration corrections for heating at the geometric focus of the ultrasound transducer. For accelerated computation, the HAS pressure pattern for each element was computed in parallel on a NVIDIA Tesla GPU (Santa Clara, CA) using Jacket (ArrayFire, Atlanta, GA) and MATLAB 2012 (MathWorks, Natick, MA). The phase aberration corrections were applied experimentally, matching the power and duration of the uncorrected sonication and by employing the MRTI and reconstruction parameters described above. Acoustic power was independently quantified for each sonication following the experiments with radiation force balance measurements [53,54]. To enable direct comparisons of experimental data, temperatures were adjusted to account for differences in the measured acoustic power between uncorrected and phase aberration-corrected sonications (<2.5 W variability).

Phase aberration correction metrics

A measure of the degree of phase aberration required at each of the 18 sonication locations was provided by calculating the phase spread metric (PSM) [33], defined as , where φ_n is the calculated phase correction for the n-th element of the n = 256 elements. A PSM value of zero indicates all transducer elements are in phase and a value of one indicates phases distributed uniformly between 0 and 2π.

Each temperature dataset had three evaluation metrics. Maximum temperature rise (°C) was defined as the peak temperature value at the end of the heating period. The focus volume (cm³) for each sonication was defined as the contiguous tissue volume in the focal region whose temperature exceeded 50% of the maximum temperature rise. Focus accuracy (mm) was determined by computing the distance between the geometric focus (as previously identified by the positioning coils) and the focus’s centre of thermal mass [55] at the end of heating. The hypotheses that phase aberration correction would generate (1) a higher maximum temperature rise, (2) a smaller focus volume and (3) a more accurate focus were each evaluated statistically using a one-tailed paired-sample t test [56].

Phase aberration correction simulations

Following the experiments, finite-difference time-domain thermal simulations were performed using the rotated segmented tissue models (0.1 s temporal resolution and 0.5 mm isotropic spatial resolution), with adiabatic boundary conditions, a uniform initial condition and thermal properties (see Table 1) taken from the literature [39,57,58]. These simulations were performed in four scenarios: (1) uncorrected sonications, (2) phase aberration-corrected sonications, (3) sonications with electronic steering to compensate for focus shift seen in uncorrected sonications and (4) uncorrected sonications in which the phantom was artificially made homogeneous by replacing canola-oil voxels with gelatine in the segmented model. Simulation results were calibrated to the experimental maximum temperature rise for each of the 18 locations.

Results

Aberrator model verification

Hydrophone pressures in the focal region are shown in Figure 4 for water only and with the ultrasound beam passing through the photopolymer aberrator model with and without phase aberration correction. Due to absorption and reflection, larger powers are required (8 W) with the aberrator in place to achieve pressures (uncorrected maximum: 75 kPa, phase aberration corrected: 163 kPa) comparable to the water only case (0.5 W, 172 kPa). Importantly, applying phase aberration correction restores the shape and position of the focus and increases the maximum pressure by 119% when compared to uncorrected measurements. These results confirm that the phase aberration correction code has been implemented correctly for the ultrasound transducer used in this study.

Figure 4. Hydrophone pressure measurements of the focussed ultrasound beam in water (left) and after passing through a photopolymer model without (centre) and with (right) phase aberration correction. Phase aberration correction restores the shape and position of the focus and doubles the maximum pressure achieved.

Breast-mimicking phantom experiments

Unique beam path geometries create varying degrees of phase aberration in the breast-mimicking phantoms. Figure 5 presents histogram plots displaying the distribution of phases calculated for phase aberration correction at each of the 18 sonication locations. (The phases for each experiment were shifted by a uniform amount to make their mean π radians to facilitate visual comparisons.) The PSM is also shown on the histogram for each location. Overall, the PSM has mean ± standard deviation values of 0.47 ± 0.12 with a range of 0.23–0.68.

Figure 5. Histogram plots for each of the 18 sonication locations showing the distribution of phases calculated for phase aberration correction. Phases are shifted to a mean of π radians to facilitate visual comparisons. The phase spread metric is also shown on the histogram for each location.

Figure 6 presents illustrative cases of uncorrected (top row) and phase aberration-corrected (middle row) sonications in the breast-mimicking phantoms. These magnitude images are overlaid with experimental temperature rise distributions in the three orthogonal directions of the 3 D MRTI volume passing through the maximum temperature rise location. The images are masked to show temperatures only in the gelatine (where the PRF method is valid). The bottom row of Figure 6 shows temperature vs. time curves at the maximum temperature rise location for both uncorrected and phase aberration-corrected sonications.

Figure 6. 3 D experimental MR temperatures from locations five and 17 of the breast-mimicking phantoms showing uncorrected (top row) and phase aberration-corrected (middle row) sonications at the end of heating. MR orientation of the three orthogonal imaging planes is shown in the top left images and the geometric focus is identified with an × marker. The bottom row shows temperature vs. time curves at the maximum temperature rise location for both uncorrected and phase aberration-corrected sonications.

In one case illustrative of an improved focus (Figure 6, left column, location five of 18), the diffuse focus of the uncorrected sonication is intensified and sharpened by phase aberration correction, with a 33% increase in the maximum temperature rise and a 37% reduction in the focus volume. In a different case showing mixed results (Figure 6, right column, location 17 of 18), the maximum temperature rise decreases (−10%) and the focus volume increases (18%) when phase aberration correction is applied. However, the spatial accuracy of the focus is improved by 5.3 mm.

The experimental maximum temperature rise was improved by phase aberration correction in 13 of 18 locations. For these cases, maximum temperature increased by an average of 30%, focus volume was reduced by an average of 40% and the mean focus accuracy was improved from 4.6 to 3.6 mm (a shift of approximately one-third of the ultrasound beam’s full-width-at-half-maximum (FWHM) in water; see Figure 4).

At five of 18 locations, the experimental maximum temperature rise decreased (−8% average) and the mean focus volume increased (10%). For these cases, phase aberration correction improved the focus accuracy from 6.1 to 2.5 mm (a shift of approximately 1.1 times the beam’s FWHM).

A summary of experimental results from all 18 sonication locations is provided in Table 2, including the metrics of maximum temperature rise, focus volume and focus accuracy. The percent change for maximum temperature rise and focus volume compares the phase aberration correction relative to the uncorrected sonication. An absolute change in the focus accuracy is also provided. Considering all cases, on average, applying phase aberration correction increases the maximum temperature rise by 19% from 4.4 to 5.1 °C, a statistically significant increase (p = 0.0023). The average focus volume decreases significantly (p = 0.0011) from 0.44 to 0.31 cm³ (a 22% average reduction) with phase aberration correction. Finally, applying phase aberration correction changes the accuracy of the focus from 5.0 to 3.3 mm. This 1.7 mm improvement is also statistically significant (p = 0.0035).

Table 2. Metrics for experimental data including phase aberration computation time, temperature uncertainty, maximum temperature rise, focus volume and focus accuracy for uncorrected (UC) and phase aberration-corrected (PAC) sonications^a.

			Temperature uncertainty (°C)		Maximum temperature rise (°C)			Focus volume (cm^3)			Focus accuracy (mm)
Location	Phantom	Phase aberration computation time (s)	UC	PAC	UC	PAC	% Change^b	UC	PAC	% Change^b	UC	PAC	Change
1	1	97	0.13	0.12	2.2	2.9	31	0.43	0.22	−50	2.5	1.6	−0.9
2	1	92	0.17	0.15	2.0	3.0	50	0.69	0.29	−58	3.2	3.7	0.6
3	1	91	0.16	0.15	2.6	3.2	22	0.33	0.24	−28	2.5	2.9	0.4
4	1	83	0.20	0.18	2.3	3.3	44	0.51	0.24	−53	4.2	3.2	−1.0
5	2	112	0.14	0.13	3.8	5.0	33	0.44	0.28	−37	4.5	4.1	−0.5
6	2	107	0.15	0.10	4.6	5.6	22	0.40	0.29	−29	0.9	3.3	2.4
7	2	108	0.11	0.12	5.3	4.8	−10	0.27	0.33	23	8.0	2.6	−5.4
8	2	104	0.15	0.14	4.2	5.6	34	0.56	0.44	−21	4.8	4.5	−0.3
9	2	105	0.17	0.15	5.6	4.9	−11	0.27	0.28	4	3.7	1.2	−2.4
10	3	109	0.10	0.11	5.2	8.1	55	0.68	0.22	−68	3.1	1.9	−1.2
11	3	102	0.11	0.14	5.3	6.3	18	0.31	0.31	1	9.0	5.0	−4.1
12	3	105	0.12	0.12	4.5	5.0	10	0.48	0.37	−24	7.4	5.2	−2.3
13	3	104	0.12	0.13	5.0	4.9	−2	0.63	0.55	−13	5.4	3.3	−2.1
14	4	108	0.21	0.22	4.2	5.4	29	0.47	0.26	−46	4.9	3.7	−1.2
15	4	102	0.12	0.12	5.4	6.7	25	0.38	0.25	−34	2.7	3.9	1.3
16	4	100	0.14	0.14	5.1	5.8	14	0.56	0.33	−41	10.6	4.2	−6.4
17	4	100	0.14	0.14	6.2	5.6	−10	0.24	0.28	18	6.9	1.6	−5.3
18	4	97	0.14	0.14	6.5	6.1	−6	0.25	0.38	53	6.6	3.7	−2.9
Overall	–	101 ± 7	0.14 ± 0.03	0.14 ± 0.03	4.4 ± 1.4	5.1 ± 1.4	19 ± 21	0.44 ± 0.15	0.31 ± 0.09	−22 ± 32	5.0 ± 2.6	3.3 ± 1.2	−1.7 ± 2.4

^a Overall values are computed as the mean ± one standard deviation for all 18 locations.

^b % Change identifies the percentage change in a given measurement when applying phase aberration correction relative to the uncorrected sonication. For maximum temperature rise, positive changes represent improvement; for focus volume and accuracy negative changes represent improvement.

Breast-mimicking phantom simulations

Figures 7 and 8 present simulation results for the two cases shown experimentally in Figure 6. The left columns display simulated uncorrected (top left) and phase aberration-corrected (bottom left) temperature maps at the end of heating for all three directions through the geometric focus location. In the right columns are simulations in which electronic steering has been used to correct for phase aberration-induced focus shift (top right) and in which homogeneous tissue has replaced oil-filled balloons in the phantoms (bottom right).

Figure 7. 3 D simulated temperatures corresponding to experimental location 5 (left column of Figure 6). Simulation scenarios include uncorrected (top left) and phase aberration-corrected (bottom left) sonications, as well as simulations in which electronic steering has been used to correct for phase aberration-induced focus shift (top right) and in which homogeneous tissue is assumed (bottom right). Tissue interfaces in the model are identified with white outlines and all images are shown at the end of heating through the geometric focus (× marker).

Figure 8. 3 D simulated temperatures corresponding to experimental location 17 (right column of Figure 6). Simulation scenarios include uncorrected (top left) and phase aberration-corrected (bottom left) sonications, as well as simulations in which electronic steering has been used to correct for phase aberration-induced focus shift (top right) and in which homogeneous tissue is assumed (bottom right). Tissue interfaces in the model are identified with white outlines and all images are shown at the end of heating through the geometric focus (× marker).

In Figure 7 (location five of 18), the simulated uncorrected focus is intensified and sharpened when phase aberration correction is applied (98% increase in maximum temperature rise and 86% reduction in focus volume), trends found experimentally in Figure 6. Electronically steering the ultrasound beam to the geometric focus in the simulation has only a small impact, since the focus position is relatively unaffected by phase aberrations for this sonication. The homogeneous tissue simulation demonstrates that phase aberration correction in essence removes the aberration effects caused by oil-filled balloons in the near field.

In Figure 8 (location 17 of 18), the simulation shows an uncorrected focus that is misplaced toward the oil-filled balloons (as seen experimentally in Figure 6). Phase aberration correction restores the simulated focus to the intended target location (6.5 mm improvement) and unlike the experiments, increases the maximum temperature rise by 67% and decreases the focus volume by 76%. Electronic steering also moves the focus toward the intended target location (1.7 mm improvement), but reduces the maximum temperature rise by 27% and increases the focus volume by 51% when compared with the uncorrected simulation. As in Figure 7, the phase aberration-corrected simulation in Figure 8 is very similar to that for a homogeneous tissue model.

Figure 9 summarises improvements gained in different scenarios with respect to simulations of uncorrected sonications. Changes in maximum temperature rise (left), focus volume (centre) and focus accuracy (right) are plotted against the phase spread metric for each of the 18 locations. Overall, simulations with phase aberration correction (× markers) yield 50 ± 25% improvement in maximum temperature rise, 62 ± 16% reduction in focus volume and a 2.8 ± 1.5 mm improvement in focus accuracy. Steering the beam electronically to compensate for focus shift (+ markers) does result in a 1.8 ± 1.3 mm improvement in focus accuracy, but also decreases the maximum temperature rise by 11 ± 9% and increases the focus volume by 19 ± 24%. Simulations of the 18 sonications in homogeneous tissue (o markers) reveal changes similar to those seen with phase aberration correction, with the maximum temperature rise increasing by 56 ± 32%, focus volume decreasing by 57 ± 16% and focus accuracy improving by 2.3 ± 1.5 mm.

Figure 9. Simulated improvements from phase aberration correction (× markers), electronic steering to the geometric focus (+ markers) and homogeneous tissue (o markers) with respect to simulations of uncorrected sonications. The changes in maximum temperature rise (left), focus volume (centre) and focus accuracy (right) are plotted against the phase spread metric for each of the 18 locations.

Discussion

A primary argument for the use of phase aberration correction in breast MRgFUS is an associated reduction in near-field thermal accumulation [33], because a smaller, more intense and more accurate focus will reduce the power and/or time necessary for ablation of the target tissue. At many of the locations in this study, including the first case in Figure 6 (left column), the focus was sharpened, intensified and more accurate. Such improvements would be of particular clinical interest when the targeting strategy is to ablate a small region of interest near sensitive tissues.

However, in five of the 18 locations, phase aberration correction did not yield a smaller, more intense focus (average 8% decrease in maximum temperature rise and 10% increase in focal volume). Location 17, the case shown in the right column of Figure 6, is representative of these locations. It is important to note that the uncorrected heating was quite close to a canola oil-filled balloon and applying phase aberration correction moved the focus away from the balloon and closer to the intended target location. It is possible that the apparent decline in maximum temperature rise and focus volume for these five cases was not from poor focussing with phase aberration correction, but was a result of concentrated heating at or near the oil-filled balloons. A very localised temperature maximum observed near the balloon shrinks the calculated focus volume (defined by temperatures exceeding 50% of the maximum temperature rise), thus making it smaller than when phase aberration correction was applied and the focus moved further into the gelatine and closer to the target location. Interestingly, simulations of this case (and all others) generated greater temperature increases and smaller focus volumes. Whatever the explanation may be for these five cases, from a clinical perspective, the large improvements in accuracy (averaging 3.6 mm) could outweigh modest losses to focus intensity and size.

Overall, the statistically significant (p < 0.005) improvements in all three phase aberration correction metrics (maximum temperature rise (19% increase), focus volume (22% decrease) and focus accuracy (1.7 mm better)) indicate that the HAS-correction algorithm with a MRI-derived model can generate a more intense, smaller and more accurate focus in breast ablation conditions and could have a strong clinical impact on MRgFUS treatments.

The simulations performed for this study also demonstrated that phase aberration correction yields a more intense (50% greater maximum temperature rise), smaller (62% reduction in focus volume) and more accurate (2.8 mm improvement) focus. Figures 7–9 highlight that these improvements make the focus comparable to the scenario of a completely homogeneous breast.

When phase aberration induces shifts in the focus position, it seems plausible to use electronic steering to move the focus back to the target location. This could be done easily without requiring calculations for phase aberration correction. Our simulations indicated that this is possible (1.8 mm improvement in focus accuracy), though it was not as effective in restoring the beam to the target location as phase aberration correction (2.8 mm improvement). There are two additional disadvantages to this approach. First, adjusting the beam with electronic steering would still require an initial sonication to recognise how much the beam has shifted and must be steered; this takes time and contributes to unnecessary energy deposition at the shifted focus location and in the near field. Second, as seen in Figures 7–9, the steered beam would still be phase aberrated, with a lower intensity and larger focus than when employing phase aberration correction. In fact, the steered beam would also experience losses inherent to electronic steering [17,47,59], explaining why Figure 9 shows that the maximum temperature rise and focus volume were poorer when steered to the geometric focus than in uncorrected sonications.

The simulations in Figure 9 also show trends indicating that the benefits of phase aberration correction increase with a larger phase spread metric. While this is consistent with theory, the same trends were not uniformly observed in the experimental data (data not shown). The amount of improvement observed in experiments (maximum temperature rise: +19%, focus volume: −22% and focus accuracy: 1.7 mm improvement) was also less than predicted by simulations (maximum temperature rise: +50%, focus volume: −62% and focus accuracy: 2.8 mm improvement).

These discrepancies underscore the fact that the effectiveness of model-based phase aberration correction depends upon the accuracy of the inputs used to generate the corrected phases. For our study, we included the accuracy of the segmented model, tissue property measurements, transducer-to-model registration and the HAS algorithm. Errors in any of these inputs will reduce the effectiveness of phase aberration correction experimentally, but would not be apparent in simulations.

Our segmented model neglected any effects of the latex balloons and the possibility of air bubbles in the phantom (potential sources of the concentrated hot spots identified in some experimental cases) and approximated the Plasti Dip^® mould as a uniform single-voxel (0.5 mm) thick layer with its impedance matched to water. While the acoustic properties of the gelatine and canola oil were measured independently, these properties and those of real tissues are known to change with temperature [36,60–64], which could alter the effectiveness of phase aberration correction, particularly in ablative therapies. Errors from the positioning coils, whose reported accuracy is 2.1 mm [51] or from physical positioning of the transducer and its yaw and pitch rotations, lead to nonregistration of the transducer to the segmented model. In spite of these potential errors, the significant improvements observed in this study are encouraging and suggest that the HAS-based phase aberration correction method is robust to input errors while having the potential for further improvement.

The results of this study are similar to those found by Mougenot et al. [32], who used ray-trace algorithms based on a MRI-derived model to correct for phase aberrations in both simulations (stochastic ray-tracing method [65]) and MRgFUS experiments (straight-line ray-tracing method [33]). Using a different MRgFUS system and a distinct heterogeneous breast mimicking-phantom, their alternate phase aberration correction technique led to increases in the maximum measured focus temperature rise of 23% and reductions to the FWHM of the focal temperatures of 22%, but the study did not assess focus accuracy.

The present study shows that phase aberration correction can have a wide range of effects with some locations experiencing great improvements to the focus and others demonstrating only mild changes. Clinically, the need for phase aberration correction will depend upon the target tissue and its location, nearby sensitive tissues, heating strategy and degree of tissue heterogeneity among other factors. Some metrics for addressing a priori the necessity of phase aberration correction, such as the phase spread metric, have been suggested [33], but evaluating the value of those measures in the clinic is beyond the scope of this study. However, if corrections can be computed in a clinically relevant time frame, the results of this study suggest there is minimal risk and potentially great benefit in applying phase aberration correction.

While the phantom materials and structure were selected to mimic breast tissue, results from this study should apply to other soft-tissue anatomies treated by MRgFUS, such as uterine fibroids [7] and desmoid tumours [66]. However, increases in the complexity and number of tissue types may necessitate more advanced segmentation algorithms [67] for generating the 3 D numerical tissue model than those employed herein.

A long-term goal is to develop a model-based phase-correction algorithm that can be incorporated into patient treatment planning. Thus, if the physicist and/or physician performing a MRgFUS treatment is concerned about phase aberration, a model could quickly be generated and simulations could also be run to determine the effect of phase aberration on MRgFUS efficiency. With this long-term aim in mind, one goal of the study was to demonstrate phase aberration correction in a clinically relevant time frame. Each phantom experiment lasted 3–4 h with phase aberration correction performed at 4–5 distinct locations. The experiment workflow included creation of the 3 D segmented tissue model and (for each location) imaging and uncorrected sonications, computation of phase aberration corrections and phase aberration corrected-sonications.

Creating the 3 D segmented-tissue model required 15–25 min, including time for the MRI scan, image reconstruction, manual data transfer to a laptop, reformatting for MATLAB, threshold refinement and segmentation, registration verification and data transfer back to the FUS computer. This process could be automated, streamlined and expedited for faster and more accurate model generation. The segmented tissue model only needs to be created once for each patient and clinically this could be accomplished in parallel with other tasks of the treatment-planning phase. Obtaining the necessary model resolution (0.5 mm isotropic) for phase aberration correction requires MR signal strength beyond current anatomic imaging protocols for MRgFUS. Thus, performing phase aberration correction with FDA-approved body systems would require improved RF coils or multiple averages to ensure the image quality required for model segmentation [55].

The process for applying phase aberration correction took 20–30 min for each location. Adjusting the position of the transducer for each new location can be performed manually in less than a minute with easy adjustments and readouts on the transducer/cylinder assembly [47]. At each location, the scan for positioning coils to identify the geometric focus takes less than one second [51]. MR imaging for verifying the model-to-transducer registration and performing the uncorrected sonication took 4–5 min. Transferring data, updating and visually confirming parameters to accurately register the model with the transducer geometry lasted several minutes and the parallelised HAS calculation of the correction phases took 101 ± 7 s (Table 2). Again, with automatic data transfers and process automation, the time required for phase aberration correction could be streamlined significantly. Uncorrected sonications and imaging to verify the registration could be eliminated in the clinic. Additionally, our study only performed sonications at the geometric focus of the transducer. Once the transducer is positioned appropriately, phase aberration correction can be utilised to implement electronic steering for additional treatment locations or for treating a larger volume of tissue, with negligible time increases for each new location beyond the initial ∼100 s phase aberration correction computation. These aberration-corrected, steered treatment locations would still be subject to amplitude drop-offs that occur with geometry-based electronic steering [17,47,59], but phase aberration correction would minimise those losses by ensuring maximal phase coherence at the target location.

The metrics utilised in this study are not optimised for characterising the ultrasound focus. Absorption of the ultrasound along the beam path tends to move the maximum temperature rise a few millimetres proximal to the geometric focus, so even a perfect phase aberration correction might not have a focus accuracy of 0 mm. Both maximum temperature rise and the 50% temperature profile used as a surrogate for focus volume are subject to thermal conduction effects that will lower the magnitude and spread the distribution of temperatures. More precise and direct metrics might include the magnitude of the ultrasonic specific absorption rate and its distribution, but the most accurate methods for characterising those quantities require a very fast temporal acquisition rate (<1 s per image) or assume a radially symmetric beam pattern [68], which is not applicable for this non-circular transducer (see Figure 4). However imperfect, the metrics used for this study are approximations to the ideal metrics of interest and because the limitations stated above obscure the effects of phase aberration correction, it is likely that those ideal metrics would show even greater improvements than found in this study.

Finally, the heterogeneous phantom developed for this study does not accurately replicate true breast anatomy. Our previous simulation study demonstrated that phase aberrations would be caused in realistic human anatomies and that the HAS-based correction algorithm could correct for those aberrations [33]. This study showed that HAS-based phase aberration correction can be used effectively in the experimental setting with this MRgFUS system and in tissues with properties similar to those of the human breast. Thus, these two studies in combination suggest that phase aberration correction for breast MRgFUS therapies are both important and clinically feasible.

Conclusion

We have demonstrated experimentally that phase aberrations in breast tissue ablation conditions can be corrected in a clinically relevant time frame using MRI-derived models and the HAS-correction algorithm, yielding significant improvements in the focal temperature rise, size and accuracy. Simulations showed similar trends and also indicate the potential for additional progress in the experimental implementation of this phase aberration correction technique. Applied in the clinic, these improvements in the beam size, intensity and accuracy will have great potential to improve the efficacy, time-efficiency and safety of breast MRgFUS therapies.

Abbreviations
3D	=	three-dimensional
BW	=	band width (Hz/pixel)
EPI	=	echo planar imaging
FA	=	Flip angle (°)
FOV	=	field of view (mm)
FWHM	=	full width at half maximum (mm)
GF	=	geometrics focus
HAS	=	hybrid angular spectrum
MR	=	magnetic resonance
MRgFUS	=	magnetic resonance-guided focussed ultrasound
MRI	=	magnetic resonance imaging
MRTI	=	magnetic resonance temperature imaging
PAC	=	phase aberration corrected
PRF	=	proton resonance frequency
PSM	=	phase spread metric
Res	=	spatial resolution (mm)
RF	=	radiofrequency
TE	=	echo time (ms)
TR	=	repetition time (ms)
UC	=	uncorrected
W	=	acoustic watts
ZFI	=	zero-filled interpolation

Acknowledgements

The authors thank Dennis Parker for his thoughtful and critical suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was funded by the National Cancer Institute, Grant R01 CA172787 and the National Institute of Child Health and Human Development, Grant F32 HD085685.