Sliding window prior data assisted compressed sensing for MRI tracking of lung tumors

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2 Sliding window prior data assisted compressed sensing for MRI tracking of lung tumors Eugene Yip Department of Oncology, Medical Physics Division, University of Alberta, University Avenue, Edmonton, AB T6G 1Z2, Canada Jihyun Yun Department of Oncology, Medical Physics Division, University of Alberta, University Avenue, Edmonton, AB T6G 1Z2, Canada Department of Physics, University of Alberta, Avenue, Edmonton, AB T6G 2G7, Canada Keith Wachowicz Department of Oncology, Medical Physics Division, University of Alberta, University Avenue, Edmonton, AB T6G 1Z2, Canada Department of Medical Physics, Cross Cancer Institute, University Avenue, Edmonton, AB T6G 1Z2, Canada Zsolt Gabos Department of Radiation Oncology, Cross Cancer Institute, University Avenue, Edmonton, AB T6G 1Z2, Canada Department of Oncology, Radiation Oncology Division, University of Alberta, University Avenue, Edmonton, AB T6G 1Z2, Canada Satyapal Rathee Department of Oncology, Medical Physics Division, University of Alberta, University Avenue, Edmonton, AB T6G 1Z2, Canada Department of Medical Physics, Cross Cancer Institute, University Avenue, Edmonton, AB T6G 1Z2, Canada B.G. Fallone a) Department of Oncology, Medical Physics Division, University of Alberta, University Avenue, Edmonton, AB T6G 1Z2, Canada Department of Physics, University of Alberta, Avenue, Edmonton, AB T6G 2G7, Canada Department of Medical Physics, Cross Cancer Institute, University Avenue, Edmonton, AB T6G 1Z2, Canada MagnetTx Oncology Solutions, Ltd, PO Box 52112, Edmonton, AB, Canada (Received 11 January 2016; revised 7 November 2016; accepted for publication16 November 2016; published 19 January 2017) Purpose: Hybrid magnetic resonance imaging and radiation therapy devices are capable of imaging in real-time to track intrafractional lung tumor motion during radiotherapy. Highly accelerated magnetic resonance (MR) imaging methods can potentially reduce system delay time and/or improves imaging spatial resolution, and provide flexibility in imaging parameters. Prior Data Assisted Compressed Sensing (PDACS) has previously been proposed as an acceleration method that combines the advantages of 2D compressed sensing and the KEYHOLE view-sharing technique. However, as PDACS relies on prior data acquired at the beginning of a dynamic imaging sequence, decline in image quality occurs for longer duration scans due to drifts in MR signal. Novel sliding windowbased techniques for refreshing prior data are proposed as a solution to this problem. Methods: MR acceleration is performed by retrospective removal of data from the fully sampled sets. Six patients with lung tumors are scanned with a clinical 3 T MRI using a balanced steady-state free precession (bssfp) sequence for 3 min at approximately 4 frames per second, for a total of 650 dynamics. A series of distinct pseudo-random patterns of partial k-space acquisition is generated such that, when combined with other dynamics within a sliding window of 100 dynamics, covers the entire k-space. The prior data in the sliding window are continuously refreshed to reduce the impact of MR signal drifts. We intended to demonstrate two different ways to utilize the sliding window data: a simple averaging method and a navigatorbased method. These two sliding window methods are quantitatively compared against the original PDACS method using three metrics: artifact power, centroid displacement error, and Dice s coefficient. The study is repeated with pseudo 0.5 T images by adding complex, normally distributed noise with a standard deviation that reduces image SNR, relative to original 3 T images, by a factor of 6. Results: Without sliding window implemented, PDACS-reconstructed dynamic datasets showed progressive increases in image artifact power as the 3 min scan progresses. With sliding windows implemented, this increase in artifact power is eliminated. Near the end of a 3 min scan at 3 T SNR and 59 acceleration, implementation of an averaging (navigator) sliding window method improves our metrics by the following ways: artifact power decreases from without sliding window to (0.031), centroid error decreases from 2.64 to 1.41 mm (1.28 mm), and Dice coefficient 84 Med. Phys. 44 (1), January /2017/44(1)/84/ American Association of Physicists in Medicine 84

3 85 Yip et al.: Sliding Window PDACS for Tumor Tracking 85 agreement increases from to (0.915). At pseudo 0.5 T SNR, the improvements in metrics are as follows: artifact power decreases from without sliding window to (0.0985), centroid error decreases from 2.92 mm to 1.36 mm (1.32 mm), and Dice coefficient agreements increases from to (0.896). Conclusions: In this work we demonstrated the negative impact of slow changes in MR signal for longer duration PDACS dynamic scans, namely increases in image artifact power and reductions of tumor tracking accuracy. We have also demonstrated sliding window implementations (i.e., refreshing of prior data) of PDACS are effective solutions to this problem at both 3 T and simulated 0.5 T bssfp images American Association of Physicists in Medicine [ Key words: compressed sensing, dynamic MRI, linac-mr, MRI acceleration, tumor tracking 1. INTRODUCTION Respiratory motion is a considerable challenge for lung radiation therapy. 1 Recent developments of hybrid linac MRI systems 2 4 hold the promise for the real-time tracking of lung tumors using fast MR imaging during the beam on time of radiation. In a proposed real-time tumor tracking scheme, 5 sequential 2D MR images of patient are acquired, reconstructed, and auto-contoured in real time, determining the tumor s position and shape; the radiation beam tracks the moving tumor by shifting the multi leaf collimator (MLC). However, all the required steps in this process sequentially add to time delay in the system. AAPM s task group for respiratory management (TG-76) recommends 1 less than 0.5 s for system delay. Since every task in the tumor tracking (imaging, reconstruction, contouring, and MLC motion) must be performed within this time frame, fast MR imaging method with a fast image reconstruction time is critical for the tumor tracking to be effective. A great deal of effort has been spent in increasing image acquisition speed of MRI. For example, steady-state image sequences such as the balanced steady-state free precession 6 (bssfp) is a fast imaging method that requires a short repetition time (TR) to cover k-space efficiently. Imaging speed can be further improved by using MR acceleration methods that reconstruct images with only partial k-space data. MR acceleration can provide other benefits for tracking tumors in additional to improved frame rates and reduced system delay times. Improving image spatial resolution requires additional phase encodes, decreasing the frame rate. Accelerated MR acquisition could allow for image resolution to be improved while maintaining a frame rate capable of lung tumor tracking (i.e., 4 fps). Furthermore, if an acceleration strategy is sufficiently powerful, multiple imaging slices, in either parallel or orthogonal directions, may be acquired in real time, which may more accurately capture the overall trajectory of tumor motion. In dynamic MRI where the same image volume is imaged repeatedly to capture temporal changes such as contrast uptake or motion, temporal redundancy can be exploited for acceleration. Partial k-space patterns can be designed to capture different parts of the k-space in different dynamics, with the missing k-space filled by sharing of k-space data that was captured at a different time point. These methods can broadly be categorized as viewsharing, with KEYHOLE 7 being a well-known example, in which only the central region of k- space is acquired dynamically, with the peripheral k-space acquired before and after the dynamic scans. More advanced implementation of viewsharing includes Time Resolved Imaging of Contrast Kinetics 8 (TRICKS) in which different regions of k-space are acquired at different frequency, with the periphery of k-space acquired with reduced frequency. In nondynamic MR acquisitions, viewsharing of k-space is not possible and the image must be reconstructed with only partial data. Reconstruction from partial k-space violates the Nyquist criterion, and results in aliasing artifacts. Accelerated MRI methods have been devised to removing these aliasing artifacts with various strategies. Parallel MRI, such as SENSE 9 relies on coil sensitivity information to essentially unwrap fold-over artifacts. Compressed Sensing 10,11 (CS) methods, on the other hand, achieve image acceleration by employing incoherent under-sampling of the k-space sampling pattern as well as model-based iterative techniques to reconstruct images from under-sampled k-space. Typically, CS reconstruction is a constrained optimization of the image in some sparse domain (i.e., Total Variations, 11 Wavelet, 11 Coutourlet, 12 Shearlet 13 Transforms, etc.) that also satisfies the partially acquired k-space data. The use of a prior, lower resolution signal estimate 14 has shown to improve CS reconstruction, while the idea of using a similar, prior image as constraint to improve CS reconstruction has been successful in Computed Tomography. 15 For dynamic MRI, spatial-temporal CS techniques, such as k-t SLR, 16 or blind compressed sensing with rank penalty, 17 exploit dynamic redundancy in the spatial temporal domain by using low-rank recovery techniques. These methods are powerful tools for non-real-time applications such as pre-treatment motion assessment. Currently, these methods require a longer reconstruction time, from several hours for an entire dynamic dataset 17 to 14 s for each new 2D image, 18 making them unsuitable for real-time tumor tracking. PDACS is developed specifically for the real-time applications (i.e., tumor tracking), as it takes advantage of temporal redundancy in a highly efficient manner for near real-time reconstruction (0.1 s/image). The original PDACS method pre-acquires a pool of preparatory data that represents a motion averaged image at the beginning of the dynamic sequence. All subsequent acquisitions use a partial, randomly sampled k-space pattern, and 2D images are reconstructed in

4 86 Yip et al.: Sliding Window PDACS for Tumor Tracking 86 sequence using a modified CS method that constrains nonsampled k-space locations to an averaged prior data pool. In a sense, this original PDACS implementation represents some combination of compressed sensing and the KEYHOLE method. While this approach is simple to implement and improves CS reconstruction for dynamic images, 19 there are large regions of unsampled k-space in the dynamic images that may become progressively more mismatched from the prior data as the scan series progresses. Slow changes in the MR signal, possibly due to magnetic field instability arising from hardware heating, 20 or shifts in a patient s position during scans could lead to the prior data and the current data to be severely mismatched in longer duration scans, leading to image artifacts. In the original PDACS paper, it was suggested 19 that fully sampled prior data should be periodically re-acquired during the dynamic scan for best results. In practice, this will be inconvenient to perform as tumor tracking with prediction algorithm is best performed with images with a consistent frame rate, and hence re-acquiring slower, fully sampled data may require the tracking dynamic images to be periodically stopped, interrupting treatment. In this work we aim to 1) evaluate the negative impact on image quality of PDACS accelerated image reconstruction due to slow signal changes; and 2) propose two sliding window strategies for PDACS reconstruction that allows for continuously updated prior data as the dynamic scan progresses, without requiring for separate acquisition of prior data. 2. MATERIALS AND METHODS 2.A. Compressed sensing In Compressed Sensing, MR images are reconstructed from a subset of k-space sampling points. CS theory 10 states that such an under-sampled image can be reconstructed accurately if 1) the k-space is sampled in a pseudo-random manner which leads to incoherent aliasing artifacts; and 2) the image solution is itself sparse or has a known sparse transform. The original CS method proposed by Lustig et al. 11 involves solving the following unconstrained penalized objective function: arg min F 2D f~qðx; yþgj ks Dðk s Þ 2 þk ~q 2 1kW 2D ~qðx; yþk 1 where eq ðx; yþ is the solution matrix in image space, k s are the pre-defined incoherent sampling k-space locations, F 2D fg is the 2D Fourier Transform operator, Dðk s Þ represents acquired data in k space k x ; k y. The minimization of L 2 norm enforces fidelity of the solution s k-space representation to the originally acquired k-space data. In the L 1 regularization term, Ψ 2D represents a sparsifying transform (e.g., wavelet, discrete cosine or finite difference). In the original implementation of CS on nondynamic images, CS can be categorized as a method that exploits spatial redundancy in MR images. (1) 2.B. Acceleration methods for dynamic MR imaging MR-based tracking of lung tumor motion requires a dynamic time series of MR images. Acceleration in dynamic imaging can be often performed by exploiting temporal redundancies, such as the use of k-space viewsharing methods (i.e., KEYHOLE, 7 TRICKS 8 ) where acceleration is achieved by acquiring only a subset of the k-space data normally needed, with the missing k-space points shared from data acquired at different time points. The simplest on the fly reconstruction of individual images select data using zeroth order hold, 21 which selects the most recently acquired data available for missing k-space points. The KEYHOLE method pre-acquires a fully sampled image, followed by only capturing the central regions of k-space for the dynamic series, with the missing k-space substituted from the fully sampled image at the beginning of the series. In this method, the peripheral k-space points will not be updated throughout the duration of the dynamic scan. The mismatching of k-space data in the peripheral zone is known to create some ringing artifacts. 22 For nonreal-time studies, these artifacts can be reduced by acquiring peripheral data both before and after the scan, and substituting a weighted sum of the two data sets. This strategy is, however, not suitable for real-time studies. On the other hand, in more sophisticated viewsharing strategies (i.e., TRICKS 8 ), all the k-space locations are updated at certain time points in the series, with the update frequency in the peripheral k-space being slower than in the central k-space. 2.C. Prior data assisted compressed sensing In nondynamic MRI, the used of a low resolution image estimate PDACS 19 is a spatial temporal method that improves image quality of highly accelerated images by using additional data to the aid the reconstruction algorithm. PDACS imposes an additional constraint into the penalty function. For the unsampled k-space locations, the penalized function constraints these points to some averaged prior data D ðk us Þ: 2 kf 2D feqðx; yþgj ks Dðk s Þk 2 arg min eq þ k 1 kw 2D eqðx; yþ k 1 þ k 2 kf 2D feqðx; yþgj kus Dðk us Þk 2 2 The two fidelity terms apply separately to sampled and unsampled regions of k-space, namely k s and k us. The reconstructed image is dominated mostly by current data, Dðk s Þ since it samples most of the central region of k-space. As such, there may be differences between current and prior datasets, causing discontinuities in k-space that will give rise to artifacts. These artifact will be made incoherent by the sampling pattern and suppressed by the k 1 kw 2D eq ðx; yþk 1 term. To avoid large discrepancies between prior data D and current data D due to breathing phase, D was averaged over breathing phases as an average of twenty fully sampled images which were acquired at the start of the dynamic (2)

5 87 Yip et al.: Sliding Window PDACS for Tumor Tracking 87 imaging sequence prior to tumor tracking. Compared to the undersampled frames, these 20 fully sampled images are expected to be acquired at a slower frame rate, and over several breathing cycles. Averaging them results in a time and motion blurred 2D k-space. Only one random sampling pattern was generated. In this sense, the PDACS method represents a combination of CS and KEYHOLE methods. The penalty function is solved using the Split Bregman method proposed by Goldstein et al, 23 with a reconstruction time of 100 ms per image. 2.D. Sampling pattern generation Coherent undersampling of k-space violates the Nyquist criterion, leading to coherent aliasing artifact (i.e., copies of the imaged object) that is difficult to eliminate. However, Lustig et al., have shown 11 that incoherent sampling pattern leads to aliasing artifacts which appears as incoherent, noise like structures with much lower signals compared to imaged object, which can then be removed by the iterative reconstruction algorithm. Random sampling patterns are generated using the Monte Carlo process described by Lustig et al. 11 For our study, we restricted the k-space undersampling so that only the phase encode direction is randomized; as it is only practical to undersample along the phase encode direction in a Cartesian 2D bssfp imaging sequence. A probability density function (PDF) is defined, with the total area under the curve proportional to the degree of undersampling (i.e., 40%). For our original PDACS study, 19 the PDF is separated into two zones: a central region where it is sampled with 100% probability and a peripheral region governed by a decreasing function (i.e., p(k) = (1 k/k max ) 2 where k/k max is the normalized distance from the k-space center). Once p(k)is defined, sampling patterns are generated in the manner described by Lustig et al. 11 : A uniformly distributed random number (0 < n(k) <1) is generated for each k space line location, and the line locations where n(k) < p(k) are sampled. If n(k) results in a sampling pattern that violates the degree of undersampling, the pattern is rejected and a new pattern is created by generating new random numbers. The algorithm then generates 1000 patterns with the correct number of sampling lines, and selects the optimal pattern using a criterion suggested by Lustig et al, 11 as follows: an image consisting of a single signal peak is Fourier transformed into k-space, undersampled with every test pattern, and transformed back to the image domain. This resulting image is the point spread function (PSF) of an undersampling pattern; containing the original signal peak with many additional smaller side peaks due to incoherent aliasing. The sampling pattern whose PSF contains the lowest secondary side lobe is chosen as the optimal pattern. 11 This single optimal pattern was used for the entire dynamic sequence in the original implementation of PDACS. (Fig. 1, left). FIG. 1. Left the original PDACS sampling pattern (25%) which uses identical sampling patterns for all image dynamic in which the nonsampled k-space locations are not updated, and the sliding window pattern in which all k-space locations are updated.

6 88 Yip et al.: Sliding Window PDACS for Tumor Tracking 88 2.D.1. Sliding window sampling patterns The crucial difference for sliding window reconstruction is that, instead of repetitively using a single sampling pattern for all dynamic images, a series of different random patterns is used. These patterns cover different k-space sampling locations, such that whenever a k-space point is acquired, it will be used to update the pool of prior data, allowing it to be partially updated continuously. Unfortunately, the shape of the probability function often drops to near zero in the most peripheral regions, often results in a long time between updates of peripheral k- space points. In our sampling strategy, k-space is separated into three regions. The very center of k-space (5 lines) is sampled with 100% probability. Next, the middle region is governed by the same polynomial function as suggested by Lustig et al. In the most peripheral region, arbitrarily defined as the region where P < 0.25, we devised an iterative process to ensures the limited sampling points here are well spaced out in the temporal domain, as shown in Fig. 2. In the first iteration of this process, a uniform probability, p peripheral is chosen such that, p central + p middle + p peripheral is equal to the constant total probability required for a particular degree of acceleration (i.e., for the fully sampled 128 k-lines, the total probability will ensure 64 and 32 k-space lines for 29 and 49 accelerations, respectively). A sampling pattern is generated resulting in sampled locations, k s,1 and unsampled location k us,1. For the next pattern, in the peripheral region, the probability for the previously sampled location is reduced to zero to prevent those locations from being immediately resampled again, such that, p 2 (k s,1 ) = 0. However, this will result into decreased p periheral by a certain amount. To maintain the constant total probability p periheral, the probability of the unsampled locations is increased uniformly, i.e., p 2 (k us,1 ) = p 1 (k us,1 ) + c 2, where c 2 represents the lost probability equally redistributed to all unsampled locations of the first iteration. Generally, p n+1 (k s,n ) = 0, and p n+1 (k us,n ) = p 1 (k us,n ) + c n+1. Note that any previously sampled location with lost probability will eventually become un-sampled and will have probability transferred back via the c n+1 term, this iterative sampling method eventually reaches a steady state that yields well-distributed patterns (shown in Fig. 1, right). PDACS and SWPDACS patterns are generated for a wide range of MR undersampling/acceleration factors, 50%, 40%, 30%, 25%, 20% sampling which is equivalent to image acceleration of 29, 2.59, 3.39, 49, D.2. Sliding window strategies 1 sliding window averaging We propose two different schemes in selecting prior data D from the window to improve reconstruction. The first method is a simple sliding average method where a sliding window of data is simply averaged as prior data (Fig. 3, left). The window is first pre filled with the same 20 fully sampled images as it is in the PDACS method. As the scan progresses, additional data is added to the window until image 80, after the window begins to slide, removing the oldest prior data from the window. From images 101 on, the window of 100 undersampled images immediately prior to a particular dynamic is averaged as D in Eq. (2). Note that with a sliding window implementation the pre-filling of the window with initial fully sampled prior data is not a necessity, as one can simply acquire 100 under-sampled frames to serve as prior data instead. Nevertheless, it is applied in this study to give the most straight forward comparison to the nonsliding method. FIG. 2. The probability redistribution process, applied in a simple case of 5 k-space locations, the algorithm starts with equal probability in all locations at p 1 (0.2), the Monte Carlo process determines a sampling pattern from it, after which the probability from the sampled location is redistributed to the nonsampled location, resulting in probability distribution p 2. This process ensures good temporal spacing between sampling points while maintaining incoherent sampling required for Compressed Sensing. [Color figure can be viewed at wileyonlinelibrary.com] 2.D.3. Sliding window strategies 2 sliding window with navigator guidance The second proposed scheme is a navigator guided approach (Fig. 3, right). It uses the same sliding window as described previously, but instead of averaging all the data in the window, it uses data most closely matched to the current diaphragm position, which can be quickly approximated by acquiring a navigator. To test this approach with the patient data that has been acquired previously, the central, superior-inferior k-space line is used as an intrinsic navigator. No additional navigator pulses are used. The 1D Fourier transform of the central k-space line is an anterior-posterior projection of the 2D sagittal image as shown in Fig. 4. As the diaphragm and other structures move throughout the breathing cycle, the navigator profile will shift accordingly; for every navigator profile after the first one, a 1D cross-correlation operation is performed against first profile and the location of maximum correlation is determined. The

7 89 Yip et al.: Sliding Window PDACS for Tumor Tracking 89 FIG. 3. Left sliding window averaging method, each circle represents a k-space line. All data that corresponds to an unsampled location of current data (filled circle) is averaged and applied in reconstruction. Right sliding window with navigator, the data within the sliding window is ranked based on navigator similarity with the closest available match in each location used as prior data. [Color figure can be viewed at wileyonlinelibrary.com] FIG. 4. Left a 2D Fourier transform of the full k-space, Right the equivalent profile resulted from a 1D FT of the central K-space line. [Color figure can be viewed at wileyonlinelibrary.com] location of maximum correlation will change during the breathing period. The maximum correlation location of the navigator profile is highly influenced by the diaphragm position in the breathing cycle, and is shown with the corresponding tumor position in Fig. 5. The prior data, D; is chosen from within the sliding window based on the closest available match to the current navigator position, such that reconstruction artifacts will be minimized. The additional computation of a 1D FFT for the navigator, a 1D cross correlation and data selection adds 10 ms of reconstruction time before 2D image reconstruction, but may reduce motion blurring 24 of the tumor associated with time averaged data. 2.D.4. Determination of reconstruction weights, k 1, k 2 The reconstruction weights in Eq. (2), k 1, k 2 are optimized in the same manner as in the original PDACS method. 19 For this retrospective study, we used the first 20 images for weight optimization, and it is assumed that these images can be acquired before the dynamic imaging begins. From these 20 images, the first 19 images are treated as prior data to reconstruct image #20. Optimal weights are determined in a two-step, (i.e., rough and fine tuning) process Fig. 6. In the first step, a wide range of possible k 1, k 2 values are used to reconstructs image #20. From Eq. (2), one could surmise that k 2 < 1, as the weight given to prior data should be less than that of current data. In practice, we have found that for images acquired with our protocol, our reconstruction algorithm will generate an acceptable solution using weights in the range of 10 4 < k 1 < 10 1 and 0.02 < k 2 < 0.1. While our optimization method doesn t guarantee a global minimum, the values of weights searched Fig. 6 were generally adequate for a near optimal solution for images encountered in our MRI protocol, though this may require modification for images acquired with a different protocol. The algorithm selects the weights that which reconstruct the image with the minimal artifact power, defined as 25,26 AP ¼ P i 2 eq US eq Full Pi eq Full 2

8 90 Yip et al.: Sliding Window PDACS for Tumor Tracking 90 FIG. 5. Actual tumor superior-inferior centroid position(top, blue) for a single patient as determined by contouring vs. approximate diaphragm position (bottom, green) as determined by the maximum correlation calculations of the navigator profiles. [Color figure can be viewed at wileyonlinelibrary.com] FIG. 6. A plot describing the search fork 1, k 2 values. Dots represent a tested pair ofk 1, k 2, with the color and size of the dots representing the artifact power. Once the minimum is found in the rough search (left), a finer search (right) is done in the neighboring regions. [Color figure can be viewed at wileyonlinelibrary.com] where eq US and eq Full represents the signal intensity for the reconstructed image from the undersampled and fully acquired k-space. The summations are both over all pixels, i. In the second step, a finer search is performed near around the optimal k 1, k 2 from the first step. The acquisition of the required 20 fully sampled dynamic images and the weight optimization process takes <1 min. It is therefore feasible to determine suitable k 1, k 2 values immediately before a longer duration dynamic scan required for tumor tracking.

9 91 Yip et al.: Sliding Window PDACS for Tumor Tracking 91 For sliding window PDACS, the sampling pattern for each individual image dynamic (Fig. 1, right) will be different, but we have found that optimal weights do not have large variations between different patterns with a similar degree of undersampling, it is therefore applied to the entire 650 image dataset. 2.E. Retrospective study evaluating the sliding window reconstruction method 2.E.1. Acquisition of MR Data With ethics approval from the Alberta Cancer Research Ethics Committee, we have recruited a total of six non-smallcell lung cancer patients who are candidates for lung radiotherapy/radiosurgery to undergo dynamic MRI in a clinical 3 T MR system (Philips Medical Systems) under free breathing for 3 min using a balanced steady-state free precession (bssfp) sequence (TE/TR = 1.1/2.2 ms), FOV = , Voxel size: = mm). A total of 650 full sampled images are acquired at a rate of 270 ms/image. It must be noted that these parameters are designed to acquire images at a frame rate capable of capturing lung tumor motion (i.e., 4fps) without the application of any other acceleration scheme, such that this particular acceleration strategy can be validated. Since speed is inversely related to pixel resolution, this results in a very modest resolution of 3 mm. If an acceleration strategy (i.e., PDACS) is successfully validated and implemented, image resolution can be substantially improved while maintaining this frame rate. As bssfp is particularly susceptible to off resonance induced banding artifacts at 3 T, localized shimming around the tumor is performed to avoid banding artifacts in those regions. A single, thick (20 mm) imaging slab was chosen to ensure the lung tumor does not move out of the stationary imaging volume due to any through-plane tumor motion. The extent of captured tumor motion from these patients is measured on these fully sampled images using our tumor tracking algorithm E.2. Evaluating the image reconstruction quality The performance of the two sliding window algorithms (sliding average and navigator guided) is to be compared with the original PDACS method. For the purpose of comparison, complex valued, fully sampled images, reconstructed by the scanner, are retrospectively under sampled (2 59) by Fourier transformation and selective removal of k-space data based on the pre-defined sampling patterns. Reconstruction then follows using each of these three methods. Reconstruction weights k 1, k 2 are optimized for each patient for each individual degree of acceleration, with the results shown in Table I. The reconstructed images are then compared against the fully sampled images in terms of their overall reconstruction errors, which is represented by the artifact power, as defined in 2.D.4. As we are primarily interested in this method as a means of performing real-time tumor tracking, we also investigated how these image reconstruction errors affect our tracking algorithm. 27 We run the auto contouring algorithm using the previously published parameters 27 on the fully sampled images to generate a set of standard tumor contours, we then run the same algorithm using the undersampled images to see how the segmented tumor contours change with respect to the standard contours. We measure the agreement between the contours using the Dice Coefficient metric, defined as 28 T AreaðROI Full ROIUS Þ DC ¼ 2 AreaðROI Full ÞþAreaðROI US Þ The ROI here represents the automatically contoured tumor shape in a given image. We also evaluated the accuracy of tumor position by the centroid displacement, pwhich is simply the displacement in mm, i.e., Md ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Mx 2 þmy 2, between contours from the standard and test sets. 2.E.3. Evaluating decline in image quality due to outdated prior data One of the main benefits of a sliding window reconstruction is that the prior data will be drawn from relatively TABLE I. Optimal weights determined by the 2-step algorithm for this study. Patient Acceleration 3 T 0.5 T log 10 (k 1 ) k 2 log 10 (k 1 ) k

10 92 Yip et al.: Sliding Window PDACS for Tumor Tracking 92 recent acquisitions, which would reduce the impact of gradual changes in MR signal unrelated to breathing motion (i.e., due to MR signal drift or patient shifting position). For the PDACS reconstruction that uses the prior data acquired at the beginning of the scan series, the slow signal drift could lead to artifacts. In our analysis, the average of first 20 acquisitions is used as prior data, and the remaining 630 images are separated into three groups of 210 images (each representing 1 min of breathing data). The three groups of data will be averaged separately for all the patients, to observe possible decline in image quality from the 1 st to the 3 rd group. 2.F. Image reconstruction with reduced SNR As the integrated MRI and linac systems (Linac-MR) operate at a lower field strength (0.35 T to 1.5 T) 2 4 compared to the 3 T system used in this study, the signal noise ratio (SNR) of the images acquired by the Linac-MR system will be lower compared to the images acquired for this experiment. SNR changes in the MR images can be roughly estimated using the relationship of SNR / B 0, which can be used to simulate 0.5 T images that can be expected from the Linac-MR system. 2 Noise is measured as the combined standard deviation, r meas in a region of no signal in the real and imaginary images. The signal to noise ratio in the 3 T images is degraded to 0.5 T levels by adding Gaussian noise maps, which consist of complex valued, normally distributed, random numbers with zero mean and standard deviation r added, determined by the following expression, with N = 3 T/0.5 T = 6. ðnr meas Þ 2 ¼ r 2 meas þ r2 added pffiffiffiffiffiffiffiffiffiffiffiffiffiffi r added ¼ N 2 1 r meas We performed the PDACS and SW-PDACS reconstruction using these pseudo 0.5 T images to test these methods in lower SNR situations. It should be noted that this is a simplistic approach that likely underestimates the quality of 0.5 T images, due to the following reasons: Firstly, at 0.5 T, reduced specific absorption ratio (SAR) allows for larger flip angles, compensating for lost SNR. 29 Secondly, imaging at 0.5 T is less sensitive to off resonance effects, reducing bssfp banding artifacts. 29 Finally, tissue contrast for bssfp is determined by tissue relaxation properties (the ratio T2/T1) are often improved at lower fields. 29 These effects are not accounted for in our pseudo 0.5 T images, which only serve as an indicator of how the algorithm performs in a worst case scenario for 0.5 T. The tumor SNR for all patients in the fully sampled scans, for 3 T and pseudo 0.5 T images are measured and reported. 3. RESULTS 3.A. Fully sampled images The first fully sampled image in the dynamic series for our six patients is shown in Fig. 7. The extent of tumor motion, as determined by our tracking algorithm, 27 is shown in Fig. 8. In our patient group, the tumor size ranges from 2.35 to 7.97 cm 2 in the images, and the tumor SNR ranges from in 3 T images while it ranges from in the pseudo 0.5 T images. The maximum motion observed from FIG. 7. Fully sampled images of our six patients. Red arrows indicated tumor target. [Color figure can be viewed at wileyonlinelibrary.com]

11 93 Yip et al.: Sliding Window PDACS for Tumor Tracking 93 the group is 34.9 mm in the SI direction and 9.9 mm in the AP direction. These key metrics about our patient group are summarized in Table II. 3.B. Image reconstruction error 3 T SNR The average artifact power for the three image groups (images 1 210, , and ) for MR acceleration factors from 2-59, averaged across six patients, for three different image reconstruction methods is shown in the first row of Fig. 9. For all methods, the image artifact power increases with the increasing acceleration factor. Please note that the ordinate scale is different for different acceleration factors in Fig. 9. At each acceleration factor, without sliding window, the image artifact power shows a clear increasing trend as the dynamic scan progresses, as indicated by the TABLE II. Tumor SNR, size, and motion metrics of lung tumor images. Patient # 3 T SNR 0.5 T SNR Area (cm 2 ) Mean (SD) Mean (SD) Mean (SD) Max. Extent SI Motion (mm) Max. Extent AP Motion (mm) (1.9) 6.7 (0.5) 4.76 (0.19) (1.0) 3.1 (0.5) 6.81 (0.37) (1.8) 4.2 (0.4) 2.35 (0.31) (1.5) 5.4 (0.4) 6.41 (0.68) (1.0) 4.3 (0.5) 3.10 (0.35) (1.2) 4.6 (0.3) 7.97 (0.29) increasing white bar from image group 1 to 3 in the first row of Fig. 9. This trend is not observed for both the average or navigator-based sliding window methods, which have very similar performances between three image groups. The two sliding window techniques yield similar artifact power to each other. The nonsliding window performs similarly well to the sliding window methods in the first image group; however, in image groups 2 and 3, the two sliding window methods consistently yields lower artifact power compared to the nonsliding window technique. Image group 3 and 59 acceleration presents the most challenging scenario for the original nonsliding method, resulting in an artifact power of 0.065; however, the averaging and navigator sliding window approach reduce the artifact power to and 0.031, respectively. 3.C. Tumour tracking error 3TSNR The centroid displacement error and Dice coefficient are shown in rows 2 and 3 of Fig. 9, respectively. For 2.59 and 59 acceleration factors without using a sliding window, the centroid displacement error increases and Dice coefficient decreases from image groups 1 to 3, indicating a loss in tracking accuracy. The navigator sliding window generally yields lower centroid displacement errors and higher Dice coefficients compared averaged sliding method. At accelerations >29, the sliding window methods show improved performance and this is particular evident in the at 2.59 and 59 accelerations. In the most challenging scenario for the original nonsliding method, (i.e., image group 3 and 59 acceleration factor), the centroid displacement error reduces from FIG. 8. Degree of Superior Inferior (Green, Solid) and Anterior Posterior (Blue, Dashed) tumor motion of six patients scanned. [Color figure can be viewed at wileyonlinelibrary.com]

12 94 Yip et al.: Sliding Window PDACS for Tumor Tracking 94 FIG. 9. Quantitative comparison of the 3 acceleration method for 3 T images. First row, Artifact power for 2 59 acceleration are shown. Second Row: Centroid Displacement Error (in mm) is shown. Third row, Dice s Coefficients are shown. Image groups 1, 2, 3 represent a binned average of image 1 210, , Error bars indicate 95% confidence intervals mm, without sliding window, to 1.41 mm (1.28 mm) with the averaging (navigator) sliding window implemented, while the Dice coefficient increases from 0.860, without sliding window to (0.915). 3.D. Image reconstruction error Pseudo 0.5 T SNR The results from the pseudo 0.5 T images are shown in the first row of Fig. 10. The image reconstruction error is generally higher compared to the 3 T images due to the higher noise present in the data. There are several trends in the 0.5 T data that are similar to the 3 T data. Larger acceleration factors lead to larger image artifact powers for all methods. For a particular acceleration factor, without sliding window, there is a clear trend of increase in image artifact power as the dynamic scan progresses, i.e., from image group 1 to image group 3 as indicating in the first row of Fig. 10. This trend is not observed for both the sliding average and navigator guided sliding window methods, which have very similar performances between groups, as indicated in the first row of Fig. 10. Unlike the original 3 T data, the navigator sliding window method (black bars) yields higher artifact powers compared to the sliding averaging method (gray bars), as shown in Fig. 10. The averaging sliding window method results in lower artifact power compared to the nonsliding window method, particularly in image groups 2 and 3. Again the case of group 3 with 59 acceleration presents most challenging scenario for the original nonsliding method, resulting in an artifact power of 0.110; however, the averaging and navigator sliding window approach reduce the artifact power to and , respectively. 3.E. Tumour tracking error Pseudo 0.5 T SNR For the pseudo 0.5 T images, despite having a higher artifact power in the navigator-based sliding window, the two sliding methods actually yield similar Dice coefficient and centroid displacement error with each other. Like the 3 T data, the trends of reduced accuracy (increase in centroid error and decline in Dice coefficient) for outdated data of image groups 2 and 3 is observed in the 2.59 and 59 acceleration in Fig. 10 (rows 2 and 3). The advantage of the sliding window methods is most pronounced in these cases. In the most challenging scenario for the original nonsliding method, (i.e., image group 3 with 59 acceleration factor), the centroid displacement error reduces from 2.92 mm, without sliding window, to 1.36 mm (1.32 mm) with the averaging (navigator sliding) window methods implemented, whereas the Dice coefficient increases from 0.851, without sliding window, to (0.896). 3.F. Qualitative example The qualitative demonstration of the impact of outdated prior data, as well as the benefits of the sliding window methods are shown in Fig. 11. Without a sliding window (Row 2), minimal artifacts are observed in group 1, but a progressive increase in artifact structures is observed in groups 2 and 3.

13 95 Yip et al.: Sliding Window PDACS for Tumor Tracking 95 FIG. 10. Quantitative comparison of the 3 acceleration method for pseudo 0.5 T images. First row, Artifact power for 2 59 acceleration are shown. Second Row: Centroid Displacement Error (in mm) is shown. Third row, Dice s Coefficients are shown. Image groups 1, 2, 3 represent a binned average of image 1 210, , Error bars indicate 95% confidence intervals. These artifacts are not observed in the sliding window reconstructed images. 4. DISCUSSION One of the objectives of this work is to evaluate the impact on PDACS reconstruction quality if prior data is not continuously updated. By separating our dynamic data into three groups, one can observe a clear trend of increased image artifact power (Figs. 9 and 10, first row, white bars). This trend is also clearly observed, in two of the five cases (2.59 and 59 acceleration), leading to poorer tumor tracking performance as the dynamic scan progresses (i.e., image groups 2 and 3) in the PDACS images (Figs. 9 and 10, second and third row), as the prior data gets progressively more outdated, this can also be observed qualitatively in Fig. 11. The presence of these artifacts (Fig. 11, row 2, column 2 and 3) indicate a limitation of the original PDACS implementation for longer duration (3 min) dynamic scans. The original PDACS strategy of incorporating of prior data in CS (i.e., Eq. (2)) has been shown to substantially improve standard CS (i.e., Eq. (1)) reconstruction in our previous study, 19 where prior data supports 1 min of dynamic images. However, the results for this study, where prior data supports 3 min of dynamic images, have revealed that incorporations of outdated prior data introduced additional artifacts to the images. The development of sliding window approach is therefore essential for implementation of PDACS in longer duration scans. This trend of increasing artifact is greatly reduced by the two sliding window methods, at 3 T images in Fig. 9 and by the sliding averaging method, in pseudo 0.5 T images, as shown in Fig. 10. Some possible culprits include shifting of patient position throughout the scan, slow drift in MR signal that gradually builds up over time, possibly due to change in hardware temperature, (i.e., heating due rapid switching gradients), 20 or any other form of slowly varying instability. While the exact cause remains unknown, its effect can clearly be observed in the form of large incremental increases in artifact power of measured in the images of groups 2 and 3 in the nonsliding window results Fig. 9. The increase in disparity between the current data and prior data leads to a gradual increase in image artifact power that is reduced by a constantly updated pool of prior data in sliding window schemes. Increased artifact power does not always correspond to reduced tumor tracking accuracy Figs. 9 and 10; this may be due to the fact that some artifacts appear close to the tumor (Fig. 11, row 2, right) and have a much greater impact on tracking metrics compared to artifacts that appear farther away from the tumor, such as the ones observed in the diaphragm area in the other accelerated images in Fig. 11. To the best of author s knowledge (i.e., cited by list), this is the first time the negative impact of outdated prior data have been quantitatively demonstrated specifically to the PDACS method in MRI, since it was introduced in However, the pitfalls of using outdated prior data for reconstructing dynamic image series have been demonstrated in related techniques such as PICCS in CT imaging, and KEY- HOLE in MRI. In CT imaging, PICCS 15 is a CS technique that relies on prior image and it also suffers from increased artifacts when the prior image is mis-registered with the

14 96 Yip et al.: Sliding Window PDACS for Tumor Tracking 96 FIG. 11. Qualitative comparisons of representative images (chosen similar phase) from groups 1 in 3 (left to right). Fully sampled images (row 1), 2.59 accelerated images from nonsliding window (row 2), sliding window with navigator (row 3) and sliding window with averaging (row 4) are shown. Progressive increase in artifacts is easily observed in row 2, which are not observed in the sliding window methods. under-sampled image, 30 and requires image registration to improve image quality. In MRI, analogous effects are observed in prospective KEYHOLE imaging, 31 in which changes in image contrast lead to ringing artifacts due to discontinuous k-space between current and prior, reference data acquired at the beginning of a sequence. Similarly, we speculate that signal shifts may have occurred during our dynamic scans, leading to artifacts that are too coherent for the CS algorithm to remove Fig. 11, row 2). It should be noted that the degree of signal drift over time may be dependent on the MR scanner and may not be the same for other MR systems (i.e., 0.5 T linac-mr). However, since the sliding window methods are relatively simple to implement, they provide a solution that continuously update the prior data without stoppage or a change in frame rate. This would be particularly useful if the tracking scan has a long duration (>1 min). In the context of radiation therapy, this could potentially include MR guided Stereotactic Body

15 97 Yip et al.: Sliding Window PDACS for Tumor Tracking 97 Radiation Therapy (SBRT), for which a much larger dose is applied per fraction, requiring longer treatment times. Another example is the case MR guided gated treatment with a lower duty cycle. In these situations where longer scans are required, sliding window PDACS should be implemented to avoid unnecessary stoppages during treatment. One interesting observation from our study is that the two proposed sliding window methods perform differently at different SNR levels. At 3 T SNR, the navigator guided method provides similar artifact power to average-based method, but performs better in terms of the tracking metrics in all scenarios Fig. 9, rows 2 and 3). Since the navigator chooses the prior data with the closest matched to the current dynamic image data, it may reduce the effect of motion blurring 24 in the prior data obtained with time averaging. This effect is not visible in terms of global image artifact power, but leads to improved tracking accuracy (i.e., reduced centroid displacement error and increased Dice coefficient) as shown in our results. With a dedicated navigator pulse, or an external navigator signal (i.e., respiratory belt) the benefits of the navigator could be further enhanced. At the pseudo 0.5 T, however, the navigator-based approach leads to higher global artifacts, but similar tracking accuracy is achieved compared to the averaged sliding window method. Fig. 10. The ability of the CS algorithm to suppress artifacts is dependent on its ability to distinguish signal (high intensity) from incoherent artifacts/noise (low intensity). 11 The presence of higher intensity noise therefore makes it more difficult for the algorithm to distinguish artifacts from signal. Unlike the navigator process which only uses one sample from the window (Fig. 1, right), the averaging of many samples (Fig. 3, left), has the effect p ffiffiffiffi of reducing the added noise, as noise is proportional to 1/ N, where N is the number of samples averaged. The increase in global artifacts may have counteracted any benefit in tracking accuracy from reduced motion blurring. One must be cautious in interpreting the results of the pseudo 0.5 T data, which is meant to serve as a worst case scenario for 0.5 T performance, due to all the un-accounted factors mentioned in section 2.F. The use of a dedicated navigator pulse, or an external navigator independent of SNR (i.e., respiratory belt) may improve performance for the navigator method at lower fields. With all these caveats, it may be premature to rule out the use of navigators at 0.5 T. Nevertheless, despite being a worst case scenario, we have presented a workable solution (sliding window with averaging) for PDACS acceleration at lower fields. One of the motivations for developing a CS-based strategy such as PDACS is the ability to accelerated k-space acquisition without specialized hardware (i.e., phase array coil and multiple receive channels), which may not be available or practical in some MRI systems. The algorithm is therefore designed to operate on either single coil data or combined coil data from a phase array coil. In our study, the data from individual coils is combined by the manufacturer s software to serve as the starting point of our study, essentially mimicking a single channel volume coil. The methods of combining data from individual coils, as implemented in the MRI system software, may affect the image SNR. To demonstrate our algorithm s validity with raw coil data, we performed an additional scan with a healthy volunteer. In additional to the scanner reconstructed data, PDACS was performed on raw coil data from individual coils after a simple k-space phase normalization and summation. Please note this rudimentary coil combination strategy represents a nonoptimal, worst case scenario in terms of SNR. 32 Using raw coil data from the individual channels as the starting point, rather than the scanner combined data, resulted in the SW-PDACS reconstructed images with marginally higher artifact power. Using raw coil data as a starting point, the artifact power values with 29, 2.59, 3.39, 49, 59 accelerations are 0.023, 0.035, 0.059, 0.061, and 0.074, respectively. The identical experiment performed using the scanner combined data as a starting point yielded artifact power values of 0.018, 0.028, 0.048, 0.048, and 0.062, respectively. The reduced SNR in the raw coil case may be recovered using more sophisticated coil combination strategies, 32 which is beyond the scope of our work. Nevertheless, this does not alter the utility of our algorithm as it has been demonstrated to work for a range of SNR values in this study. If multiple coils are available, numerous studies 14,33,34 have indicated that coil sensitivity information and multiple coil data may be incorporated into CS reconstruction to improve image reconstruction and/or acceleration. The feasibility of incorporating parallel acquisition into PDACS warrants further investigation, with the potential benefits of enhanced acceleration/image quality to be weighed against potential increased reconstruction time, which makes the technique less suitable for real-time tracking. Finally, translating the PDACS method from an off-line, retrospective study to an on line, prospective approach, that is useful for tracking tumors on the Linac-MR, is a subject of future research. Some of the technical challenges include the implementation and integration of software required for the acquisition of pseudo-random k-space lines, PDACS reconstruction, autocontouring, and MLC adjustment. Overcoming these challenges in the on-line implementation of this approach will allow the ultimate validation of our technique. 5. CONCLUSIONS Prior data assisted compressed sensing (PDACS) can improve compressed sensing reconstruction of dynamic scans by adding in prior data acquired at beginning of the dynamic scan, but the quality of the prior data can have a considerable impact on the reconstructed image quality. In this work we have, for the first time, demonstrated the negative impact of slow changes in MR signal in longer duration PDACS dynamic scans, which consists of increases in image artifact power and reductions in tumor tracking accuracy. A sliding window approach, using either sliding averaging at 0.5 T or preferably a navigator guided approach at 3.0 T, are solutions that allow prior data to be continuously updated. These schemes are preferred in dynamic MR tracking with

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