An augmented hybrid multibaseline and referenceless MR thermometry motion compensation algorithm for MRgHIFU hyperthermia

A hybrid principal component analysis and projection onto dipole fields (PCA‐PDF) MR thermometry motion compensation algorithm was optimized with atlas image augmentation and validated.

effects from hyperthermia can improve tumor response and treatment efficacy of radiation, 2,3 chemotherapy, 4 and immunotherapy. 5One noninvasive method of administering hyperthermia is MR-guided high intensity focused ultrasound (MRgHIFU). 6MRI is used for treatment planning and monitoring thermal changes in the tissue via MR thermometry. 7

Motion in MR thermometry during hyperthermia
One of the main challenges for the clinical translation of MR thermometry is that the thermometry is sensitive to motion artifacts.The current Food and Drug Administration (FDA) and Health Canada approved thermometry method is based on the proton resonance frequency shift, where previously acquired baseline phase images are subtracted from incoming phase images.When motion occurs, this will create a misalignment in the phase patterns resulting in motion artifacts when the subtraction calculation is done.For accurate thermometry, it is important to isolate phase changes that occur from temperature changes.Motion artifacts can greatly skew temperature calculations and decrease temperature accuracy. 7epending on the tumor location, periodic motion due to respiration or sporadic motion due to peristalsis or patient twitching can pose a challenge.Specific to thermal therapies, it was found that the swelling of the tumor in response to heating can also cause MR thermometry motion artifacts. 8Hyperthermia sessions can last tens of minutes in which accurate thermometry is required over the total duration of the hyperthermia for both the safety and efficacy of the treatment.

Thermometry-based temperature feedback control
During hyperthermia, a control system is implemented that uses MR thermometry data to regulate the sonication power output.It is common for a proportional-integral-derivative (PID) controller to be used for controlled hyperthermia with a desired target temperature. 9In the context of temperature feedback control, it is imperative for temperature measurements in the MR thermometry to be accurate.
If motion artifacts are present in the region used for temperature feedback, the PID controller will interpret these motion artifacts as heating, and will consequently reduce or even halt sonications.This may result in substantially underheating the target region due to the presence of artifacts.Implementing a motion compensation algorithm can help resolve this issue by removing thermometry motion artifacts to ensure the PID controller is passed accurate thermometry data.If the thermometry motion artifacts are not corrected, the PID controller can either under or overheat the tumor, resulting in an inaccurate therapy which could impact treatment outcome.

Principal component analysis and projection onto dipole fields
Principal component analysis and projection onto dipole fields (PCA-PDF) is a motion compensation algorithm that is a hybrid of a multibaseline and a near-referenceless technique, respectively. 10PCA is performed preoperatively, to reduce the dimensionality of the atlas of baseline images to eigenvectors to allow for a larger reference atlas while minimizing computational costs. 11To match incoming phase images with the atlas, orthogonal projection by singular value decomposition is performed.PCA is advantageous for repetitive periodic motion, such as controlled respiration, as the motion is preoperatively recorded by the atlas.After the matching with PCA is done, then PDF calculations are completed.In this method, phases are calculated using a magnetic dipole model which is based on the phase patterns in larger tissue regions. 12For this reason, PDF is ideal for correcting susceptibility artifacts that are produced during spontaneous motion.Combining PCA and PDF allows for correction of both periodic and susceptibility motion artifacts.The hybrid PCA-PDF algorithm has been tested on both porcine and human kidney MR thermometry scans by Tan et al., 10 but has not yet been prospectively tested for MRgHIFU hyperthermia applications or during controlled motion.
The objective of this work is to validate a novel augmented PCA-PDF algorithm to reduce thermometry motion artifacts under various motion schemes.The performance of the augmented PCA-PDF algorithm will be compared to the original PCA-PDF algorithm and thermometry without any motion compensation.

Robot positioner and gelatin phantoms
An MR-compatible robot was constructed to allow movement of a phantom across the right-left and superior-inferior directions, without impeding ultrasound propagation.The robotic positioner was developed through the modification of a FUS Instruments RK-100 small animal MRgHIFU system (FUS Instruments). 13This robot utilizes ultrasonic linear motors and optical encoders for position control and measurement.The water bath and transducer of the system were removed and an opening for the HIFU window was cut into the robot's base.Support arms which could accommodate the HIFU window were laser cut out of extruded acrylic.Lastly, an attachment to couple the movement arms with the phantom was developed and tested.After modification, the translational movement error of the positioner arm was measured to be within previously reported ranges of the original system. 14The range of motion after modification allowed the phantom to be reliably translated ±5 cm in both right-left and superior-inferior axes.It was confirmed that MRI signal-to-noise ratio (SNR) was not substantially reduced. 13The SNR calculated with the positioner robot set-up in the MRI was 13.8 ± 0.1 with the motors off and 13.9 ± 0.2 with the motors on.This robot was designed to induce motion on custom phantoms fabricated using 10% gelatin, 2% silica, and 0.1% formalin (Figure 1).This formulation was ideal to simulate a tissue-like stiffness, which exhibits a speed of sound of 1540 m/s, the average speed of sound through human tissue. 15

MR thermometry sequence
The motion compensation validation was performed on a clinical MRgHIFU system consisting of a 3T Achieva MRI (Philips Healthcare) and Sonalleve V1 MRgHIFU (Profound Medical) system.Proteus, 16 a custom closed-loop hyperthermia software development environment, was used for implementing the PCA-PDF algorithm and for administering the controlled hyperthermia with a target temperature of 40.5 • C. A spoiled gradient echo MRI thermometry sequence with echo-planar fast-field echo imaging was used.The MRI sequence parameters for the thermometry acquisition were a flip angle of 19.5 • , acquisition time of 1.9 s, echo time of 19.5 ms, repetition time of 30 ms, voxel size of 1.5 mm × 1.5 mm × 5.5 mm, in-plane field of view (FOV) of 168 mm × 168 mm, phase encoding bandwidth of 79Hz and an echo-planar imaging EPR electron paramagnetic resonance factor of 9.In this sequence, four slices were acquired.A coronal, transverse and sagittal slice were all set to intersect at the HIFU focal spot.The final coronal slice was set in the near-field which is typical for in vivo applications to monitor any potential skin heating.
To ensure phase maps are accurate, especially over long thermometry sequences for applications such as hyperthermia, it is important to correct for phase drift. 17During experiments, second-order phase drift correction was performed within the Proteus software. 18,19

Motion schemes
This work aims to validate the accuracy of the augmented PCA-PDF algorithm and compare its performance to the original PCA-PDF algorithm and no motion compensation.These three reconstruction techniques will be employed on both periodic and sporadic motion profiles.Four different experiments were conducted and repeated four times each: 1. Periodic motion with no motion compensation (Periodic-noPCA-PDF) • Retrospectively analyzed with the Original PCA-PDF Algorithm • Retrospectively analyzed with the Augmented PCA-PDF Algorithm "No motion compensation" refers to the images being reprocessed where no PCA-PDF algorithm was used or the algorithm was retrospectively removed from the imaging dataset.All of the data collected was retrospectively analyzed.Real-time algorithm application was acquired to investigate the impact of thermometry motion compensation on PID temperature control.All trials were done without HIFU sonication and repeated with controlled HIFU-based hyperthermia.In all hyperthermia experiments, a single point was sonicated, and no beam steering was employed.

Controlled periodic motion
To recreate periodic motion, a periodic movement with a period of 4 s and an amplitude of 10 mm were used in the superior-inferior axis, which was found to be the average movement of the diaphragm in healthy adult subjects. 20This suggests that the amplitude motion of the diaphragm of 10 mm would be the largest possible motion of target organs/tissue.During atlas collection, the robot moved the phantom following the same motion profile used during the treatment, allowing the motion to be preoperatively recorded in the atlas.No motion was induced for the first 2 min once the thermometry and hyperthermia sonication started, to allow the average temperature to stabilize at 40.5 • C. For the following 2 min, the periodic motion was induced on the phantom with the robot within the MRgHIFU system, while continuing to administer controlled hyperthermia.After the motion and sonication were halted, the thermometry data were collected for 2 additional minutes.This was performed four times without any motion compensation and four times with the real-time original PCA-PDF algorithm.The PCA-PDF atlas was composed of 16 images.As the augmented PCA-PDF algorithm was designed to address sporadic motion, it was also tested retrospectively on the periodic motion set to ensure the augmented PCA-PDF algorithm remained comparable in efficacy to the original PCA-PDF algorithm during periodic motion.

Controlled sporadic motion
In creating sporadic motion, the goal was to reproduce a patient twitching or suddenly moving.To do so, the phantom was first positioned at one end of the FOV in such a way that it was still fully visible in the MR image.During atlas image acquisition, there was no motion.In doing so, any motion that occurred during the thermometry would be considered sporadic as the movement was not preoperatively recorded.Similar to the periodic motion experiment, after the atlas there was a 90-s thermometry acquisition without motion for a baseline.Next, a displacement of 2.5 cm was performed, moving the phantom to the other end of the FOV, while still being fully in the FOV.2.5 cm was chosen as it would be large enough to produce substantial MR thermometry motion artifacts, while maintaining the phantom within the FOV.After one minute the phantom was then moved back to the initial position and thermometry images were acquired for 90 additional seconds.This was done four times with the real-time original PCA-PDF algorithm and was repeated with the real-time augmented PCA-PDF algorithm four times.

Combined periodic and sporadic motion
The augmented PCA-PDF algorithm was tested under a combination of both periodic and sporadic motion.A 20-min hyperthermia sonication was administered at 40.5 • C. The periodic specifications for motion in the superior-inferior axis were the same as in Section 2.3.1.Every 2 min, a sporadic motion of a 1-cm displacement in the right-left axis was induced on the phantom.The augmented PCA-PDF algorithm was run in real-time during the hyperthermia sonication with a 160-image augmented atlas and with a 10-pixel SD.

Augmented atlas algorithm
The goal of the motion predictive augmented atlas algorithm is to help the PCA algorithm better match the phase image for a larger sporadic motion that was not recorded during the atlas acquisition.Each phase image acquired in the atlas is augmented to create a set of new images that are added to the PCA atlas (Figure 2).These images are horizontally and vertically translated in image space by a random number of pixels drawn from a Gaussian distribution centered at 0 with a specified pixel standard deviation set by the user.The new images serve to mimic motion that the subject could undergo during the treatment.After the atlas is expanded, the PCA-PDF algorithm is executed normally. 10Since computational time increases with the number of images in the atlas, a sufficiently large atlas will inhibit real-time thermometry predict motion Image acquired in atlas Augmentation of one atlas image to predict motion in the augmented principal component analysis and projection onto dipole fields (PCA-PDF) algorithm.After augmentation, the image is translated vertically and horizontally.The original atlas image is augmented to create an atlas of 25 images.Each row demonstrates a different SD of pixel displacement (5, 10, 15, 20, 25).This procedure is repeated for each atlas image acquired.
processing.In order to decrease computational time, the number of eigen images used is automatically chosen to account for at least 99% of the variance of the atlas images.This eliminates redundant data to speed up the algorithm while retaining nearly all useful information contained in the atlas.
After the augmented atlas method was developed and implemented within the PCA-PDF algorithm, a retrospective analysis was conducted on the controlled sporadic motion data sets to optimize the parameters.The two parameters that were varied were the atlas size and the pixel displacement SD.As the atlas size in the controlled sporadic motion data set was 16 images, atlas multipliers of 2, 4, 6, 8, and 10 were tested, resulting in total atlas sizes after augmentation of 32, 64, 96, 128, and 160 images, respectively.For the second parameter, the images are translated by a random number of pixels drawn from a Gaussian distribution centered at zero with a specified pixel SD.For this analysis, pixel SD values of 5, 10, 15, 20, and 25 were tested as shown in Figure 2. All combinations of atlas size and pixel standard deviation were used to retrospectively apply the augmented PCA-PDF algorithm.On each of the four datasets for each motion profile, five retrospective analyses were run where different pixel displacements were randomly selected from the Gaussian distribution to demonstrate the reproducibility of the augmentation.

Metrics and statistics
The thermometry data is evaluated by calculating the pixel-wise spatial SD and temporally averaging over the movement.The spatial SD of the temperature is taken over the region of interest shown in Figure 3, to avoid influence from hyperthermia administered in the center of the phantom.The calculated pixel-wise spatial standard deviation is then averaged over the trials conducted to obtain an experimental average and standard deviation for the periodic and sporadic motion experiments.
In proton resonance frequency thermometry, the temperature uncertainty can be estimated using the following equation 21 : where ΔT is the temperature uncertainty, SNR is the signal-to-noise ratio, B 0 is the main magnetic field and TE is the echo time.Over all experiments, the average SNR was calculated, giving a temperature uncertainty of 0.1 • C.
To evaluate statistically significant differences in the temperature SD across different processing methods, the Wilcoxon signed-rank test was used, comparing two non-parametric paired samples.The null hypothesis of this test is that the samples share the same distribution. 22n all cases,  = 0.05 was used to determine statistical significance.
A one sample lower tailed t-test was done to demonstrate that the augmented PCA-PDF algorithm was able to maintain temperature SD <1 • C. The null hypothesis is the temperature standard deviation is equal to 1 • C and the alternative hypothesis is that the temperature standard deviation is <1 • C.

Sonication power modulation
Proteus, the custom-controlled hyperthermia software, implements a PID controller that adjusts delivered sonication power based on the temperature measured within the heating region.The PID controller attempts to maintain the average temperature within the region at a predefined value, at the target temperature, which was set at 40.5 • C in all treatments performed.An example of the thermometry region used as input for the PID controller can be seen with the yellow circle in Figures 3, 4, and 7.The sonication power graphs were plotted in comparison to the graph of temperature measurements in the heating region in the phantom to examine the impact of motion artifacts and the PCA-PDF algorithm on sonication power.
The yellow box indicates a fixed region in the phantom from which temperature SD is calculated over the course of phantom movement.Location was chosen to be outside of the heated area while contained in the phantom during motion, to ensure the background is not included in the calculations.The thermometry images are the original (A) and augmented (B) principal component analysis and projection onto dipole fields (PCA-PDF) processing of sporadic motion, with plots corresponding to different retrospective processing methods on the right.

F I G U R E 4
T1W MRIs with thermometry overlaid during controlled periodic motion.

PCA-PDF capabilities during periodic motion
The average temperature SD in the periodic datasets without motion compensation was 1.1 ± 0.1 • C. The average temperature SD with the retrospective and real-time PCA-PDF were both reduced to 0.5 ± 0.1 • C using the same experimental setup and methodology.The removal of motion artifacts using the original PCA-PDF algorithm during hyperthermia can be seen in Figure 4D,E.Augmentation of the PCA-PDF algorithm did not reduce the temperature standard deviation further than the original motion compensation power movement temperature temperature percentile temperature percentile temperature Periodic motion real-time temperature measurements (average, 10th percentile and 90th percentile temperature) within the predefined region in the yellow circle and corresponding sonication powers.Left: Periodic-noPCA-PDF Right: Periodic-origPCA-PDF.
PCA-PDF algorithm, with a value of 0.5 ± 0.1 • C.There was a significant reduction in temperature SD from no motion compensation, to both the original and augmented PCA-PDF algorithm (p < 0.001).Both the original and augmented PCA-PDF algorithm had a temperature standard deviation within 1 • C, with statistical significance (p < 0.001).
Without PCA-PDF processing, severe motion artifacts as seen in Figure 4D, interfere with accurate delivery of HIFU hyperthermia.Once the phantom begins moving, the average temperature is recorded as high as 60 • C, which is a false reading caused by artifacts (Figure 5).The PID controller responds by dropping the sonication power to zero as it interprets the data as the phantom being overheated and no further power is delivered for the remainder of the treatment.When the PCA-PDF algorithm is applied in real-time, accurate temperature measurements are supplied to the PID controller maintaining an average temperature within a few degrees to 40.5 • C. In this case, the controller responds appropriately with oscillatory sonication power.This results in the average temperature being maintained near the target temperature, despite constant periodic motion.

Optimization of augmented atlas parameters
Figure 6 shows a retrospective parametric sweep of the number of atlas images and image displacement.For periodic motion, Periodic-noPCA-PDF and Periodic-origPCA-PDF, the augmented PCA-PDF algorithm did not result in any improvement in temperature SD across any set of parameters tested (Figure 6A,C).For sporadic motion, Sporadic-origPCA-PDF and Sporadic-augPCA-PDF, the augmented algorithm altered the temperature SD differently depending on the parameters selected (Figure 6B,D).For the tested sporadic motion profile of 2.5 cm, a 160-image atlas with a displacement SD of 10 pixels, equivalent to 15 mm with a 1.5-mm voxel size, consistently yielded a temperature SD of <1 • C across all tests.With these values, the atlas can predict 3 cm of motion within two SDs, which can capture motion that includes the 2.5-cm displacement induced on the phantom.For different motion profiles, the optimal parameters to minimize motion artifacts will likely be different.
The image reconstruction computation time increased with atlas size.The computational time for the 16-image Average temperature standard deviation of five trails with hyperthermia across differing principal component analysis (PCA) atlas parameters for retrospective augmented principal component analysis and projection onto dipole fields (PCA-PDF) analysis.Mean values are displayed with the experimental SDs below in parentheses.Data was originally collected as: (A) Periodic-noPCA-PDF; (B) Sporadic-origPCA-PDF; (C) Periodic-origPCA-PDF; (D) Sporadic-augPCA-PDF.
NO motion compensation h h atlas was within 25 ms and was as high as 250 ms for the 160-image atlas.All computations were well within the temporal resolution of the MRI thermometry sequence, which in these experiments was 1.9 s.

Augmented PCA-PDF capabilities during sporadic motion
Using a total atlas size of 160 and a displacement SD of 10 pixels, the resultant thermometry images are shown in Figure 7, where a reduction in the severity of motion artifacts is evident.For the four runs with the sporadic motion using the real-time original PCA-PDF algorithm, Sporadic-origPCA-PDF, a temperature SD of 8.8 ± 0.5 • C was calculated.Retrospective analysis with the augmented PCA-PDF algorithm on this data set reduced temperature standard deviation to 0.7 ± 0.1 • C (p < 0.001).When the augmented PCA-PDF algorithm was run in real-time, Sporadic-augPCA-PDF, the average temperature SD over the four trials was 0.7 ± 0.1 • C. It is important to note that with the original PCA-PDF algorithm, the HIFU focal spot is not apparent due to the limitations of the algorithm.However, with the augmentation, the HIFU focal spot is visible and distinguishable from the low-temperature artifacts that remain (Figure 7).The

T A B L E 1
Average temperature SD in region of interest across different hyperthermia treatments and processing methods.
PCA-PDF algorithm with the augmented atlas removed the high-temperature artifacts that resulted from sporadic motion with the original PCA-PDF algorithm.The augmented PCA-PDF algorithm had a temperature SD within 1 • C, with statistical significance (p < 0.001).Table 1 displays a summary of the temperature SD calculations for experiments conducted under periodic and sporadic motion with various thermometry algorithms.
Using the original PCA-PDF implementation, MR thermometry is corrupted by motion artifacts after the phantom moves, causing the measured temperature to vary unpredictably between 30 and 50 • C (Figure 8).The PID controller responds by delivering high or no power, rapidly switching between the two.With the augmented PCA-PDF algorithm, the temperature is measured accurately after the phantom moves, returning to the initial temperature as a previously unheated region of the phantom is sonicated, before climbing to the target temperature of 40.5 • C once again.The PID controller is able to accurately deliver higher sonication power when far from the target temperature and gradually decrease the power as the target is being heated.

Augmented PCA-PDF for combined periodic and sporadic motion during hyperthermia
Over the 20-min hyperthermia treatment, the augmented PCA-PDF algorithm maintained a temperature standard deviation of 0.8 ± 0.3 • C during the combination of both periodic and sporadic motion.Figure 9 displays the calculated temperature standard deviation over time, where the first sporadic motion occurs just before the 200-s time point.The average temperature maintained in the region of interest over the 20-min hyperthermia treatment was 39.6 ± 1.9 • C.

DISCUSSION
Using a robot positioner for the phantom, reproducible periodic and sporadic motion profiles can be created on gelatin phantoms for validation of the PCA-PDF motion compensation algorithm.Preliminary results demonstrated that the PCA-PDF algorithm compensated for periodic motion, significantly reducing motion artifacts.
When hyperthermia was administered, the PCA-PDF algorithm maintained the focal spot while removing surrounding motion artifacts.Even when substantial motion artifacts were present in the magnitude MRIs, the PCA-PDF algorithm was able to compensate successfully (Figure 4C).The temperature standard deviation was reduced to 0.5 • C with the original PCA-PDF method during real-time application and retrospective processing.These results verified that the PCA-PDF algorithm is comparable in both retrospective and real-time conditions, as expected.The augmented PCA-PDF algorithm resulted in a temperature standard deviation of 0.5 • C. As expected, this was not an improvement from the original PCA-PDF algorithm for periodic motion.
The motivation for developing the augmented atlas was due to preliminary results with the original PCA-PDF algorithm during large sporadic motion.Although these results were an improvement from the original proton resonance frequency subtraction thermometry method, there were still substantial artifacts present that produced inaccurate temperature maps and suppressed the temperature measured at the sonication hot spot.It was deduced that these artifacts were caused when the PCA matching occurred, as there were no images in the atlas similar to the motion, the PCA algorithm had to settle for a suboptimal match.The augmented atlas was created to predict bulk sporadic motion, where the image was translated horizontally and vertically by a number of pixels drawn from a Gaussian distribution with a user determined standard deviation.By varying the total augmented atlas size and the image displacement SD, the optimal parameters to counter the sporadic motion were an atlas size of 160 and a displacement standard deviation of 10 pixels.The augmented PCA-PDF algorithm was also tested with periodic motion, which showed no significant difference from the original PCA-PDF implementation, indicating that the augmented algorithm can adequately compensate for a variety of different motions.It is important to note that the optimal displacement SD will vary depending on the type and degree of motion.Future work should include automating the choice of displacement SD and further power movement temperature temperature percentile temperature percentile temperature

F I G U R E 8
Sporadic motion real-time temperature measurements (average, 10th percentile and 90th percentile temperature) and corresponding sonication powers.Left: Sporadic-origPCA-PDF Right: Sporadic-augPCA-PDF.

F I G U R E 9
Temperature standard deviation over a 20-minute hyperthermia treatment.
exploring how this parameter can be optimized for different motion profiles.
Throughout all heatmaps showing augmented PCA-PDF performance on sporadic motion (Figure 5B,D), a distinct diagonal trend emerges in which a greater standard deviation of displacement and smaller atlas size results in higher temperature SD, indicating worse performance.It is possible that with atlases larger than 160 images, a larger or smaller than ideal standard deviation of displacement could adequately represent the predicted motion of the phantom.In order to minimize computational time, a small atlas is most desirable, leading to the best parameter set inhabiting a "sweet spot" of the correct displacement paired with an atlas size that is sufficiently large to predict the motion of the phantom while keep computational times low.This insight will assist future work into automating parameter selection for optimal performance across a variety of motion profiles.
For the large sporadic motion data collected, an atlas size of 160 images and 10 pixel SD resulted in a significantly lower temperature SD, indicating that artifacts resulting from sporadic motion were minimized as a result of atlas augmentation.Additionally, the time to reduce an atlas of 160 images to eigen images required approximately 0.25 s, which is well within the MR thermometry temporal resolution.This computation is only completed once, after atlas acquisition is complete and before the thermometry images are calculated.The qualitative effects of the motion compensation with the original PCA-PDF method have random, high temperature artifacts scattered throughout the entirety of the phantom.The augmented PCA-PDF method resulted in reducing the degree of temperature artifacts, resulting in artifacts that are distinguishable from the induced focused ultrasound hyperthermia.Although there are still some motion artifacts present, the temperature accuracy is still acceptable as it is <1 • C.
To further improve hyperthermia, future work could focus on incorporating electronic HIFU beam steering to correct for any misalignment between the region used for temperature feedback (yellow circle) and the HIFU focal spot. 23An example of this misalignment can be seen in Figure 7F.

CONCLUSION
The results demonstrate that the PCA-PDF algorithm's real-time capabilities were comparable to retrospective analysis, where the algorithm improved temperature accuracy to <1 • C during periodic motion with HIFU hyperthermia.This was a significant improvement in temperature SD than the thermometry without any motion compensation.The results from the large sporadic motion indicate that supplementing the PCA-PDF method with an augmented atlas improved temperature accuracy to <1 • C during sporadic motion in real-time MR thermometry.The augmented PCA-PDF algorithm demonstrated significant improvement in reducing temperature SD from the original PCA-PDF algorithm during sporadic motion.This work would allow hyperthermia treatments using MRgHIFU to continue despite a large patient movement or respiratory motion rather than being forced to stop the treatment due to thermometry artifacts.Future work will involve further optimization of the augmented PCA-PDF algorithm to minimize computation time and further eliminate artifacts, incorporating HIFU electronic beam steering, as well as further validation in ex vivo and in vivo studies.
U R E 1 MR compatible robot positioner which induces motion on custom gelatin phantoms.(A) Top-down view of positioner with movement axis defined over high intensity focused ultrasound (HIFU) window.(B) Setup with positioner, phantom and MRI coil on the HIFU table.

2 . 3 . 4 .
Periodic motion with the Original PCA-PDF Algorithm (Periodic-origPCA-PDF)• Retrospectively analyzed removing the Motion Compensation Algorithm • Retrospectively analyzed with the Augmented PCA-PDF Algorithm Sporadic motion with the original PCA-PDF algorithm (Sporadic-origPCA-PDF)• Retrospectively analyzed removing the Motion Compensation Algorithm • Retrospectively analyzed with the Augmented PCA-PDF Algorithm Sporadic motion with the augmented PCA-PDF algorithm (Sporadic-augPCA-PDF)• Retrospectively analyzed removing the Motion Compensation Algorithm • Retrospectively analyzed with the Original PCA-PDF Algorithm (A-C) No Heating, (D-F) high intensity focused ultrasound (HIFU) controlled hyperthermia.(A,D) No motion compensation, (B,E) Original principal component analysis and projection onto dipole fields (PCA-PDF), (C,F) Augmented PCA-PDF.
Thermometry during controlled sporadic motion.(A-C) No heating, (D-F) high intensity focused ultrasound (HIFU) controlled hyperthermia at a target temperature of 40.5 • C. (A,D) No motion compensation, (B,E) Original principal component analysis and projection onto dipole fields (PCA-PDF), (C,F) Augmented PCA-PDF.