A modified McKinnon-Bates (MKB) algorithm for improved 4D cone-beam computed tomography (CBCT) of the lung

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1 A modified McKinnon-Bates (MKB) algorithm for improved 4D cone-beam computed tomography (CBCT) of the lung Josh Star-Lack* and Mingshan Sun Applied Research Laboratory, Varian Medical Systems, 3120 Hansen Way, Palo Alto, CA 94304, USA Markus Oelhafen and Timo Berkus Imaging Laboratory, Varian Medical Systems, Tafernstrasse 7, CH-5405 Baden-Dattwil, Switzerland John Pavkovich Applied Research Laboratory, Varian Medical Systems, 3120 Hansen Way, Palo Alto, CA 94304, USA Marcus Brehm, Marcel Arheit, and Pascal Paysan Imaging Laboratory, Varian Medical Systems, Tafernstrasse 7, CH-5405 Baden-Dattwil, Switzerland Adam Wang Applied Research Laboratory, Varian Medical Systems, 3120 Hansen Way, Palo Alto, CA 94304, USA Peter Munro, a) Dieter Seghers, and Luis Melo Carvalho Imaging Laboratory, Varian Medical Systems, Tafernstrasse 7, CH-5405 Baden-Dattwil, Switzerland W.F.A.R. Verbakel Department of Radiation Oncology, VU University Medical Center, Cancer Center Amsterdam, Amsterdam, The Netherlands (Received 18 January 2018; revised 23 April 2018; accepted for publication 24 May 2018; published 4 July 2018) Purpose: Four-dimensional (4D) cone-beam computed tomography (CBCT) of the lung is an effective tool for motion management in radiotherapy but presents a challenge because of slow gantry rotation times. Sorting the individual projections by breathing phase and using an established technique such as Feldkamp Davis Kress (FDK) to generate corresponding phase-correlated (PC) three-dimensional (3D) images results in reconstructions (FDK-PC) that often contain severe streaking artifacts due to the sparse angular sampling distributions. These can be reduced by further slowing down the gantry at the expense of incurring unwanted increases in scan times and dose. A computationally efficient alternative is the McKinnon-Bates (MKB) reconstruction algorithm that has shown promise in reducing view aliasing-induced streaking but can produce ghosting artifacts that reduce contrast and impede the determination of motion trajectories. The purpose of this work was to identify and correct shortcomings in the MKB algorithm. Methods: In the general MKB approach, a time-averaged 3D prior image is first reconstructed. The prior is then forward-projected at the same angles as the original projection data creating time-averaged reprojections. These reprojections are subsequently subtracted from the original (unblurred) projections to create motion-encoded difference projections. The difference projections are reconstructed into PC difference images that are added to the well-sampled 3D prior to create the higher quality 4D image. The cause of the ghosting in the traditional 4D MKB images was studied and traced to motion-induced streaking in the prior that, when reprojected, has the undesirable effect of re-encoding for motion in what should be a purely time-averaged reprojection. A new method, designated as the modified McKinnon-Bates (mmkb) algorithm, was developed based on destreaking the prior. This was coupled with a postprocessing 4D bilateral filter for noise suppression and edge preservation (mmkb bf ). The algorithms were tested with the 4D XCAT phantom using four simulated scan times (57, 60, 120, 180 s) and with two in vivo thorax studies (acquisition time of 60 and 90 s). Contrast-to-noise ratios (CNRs) of the target lesions and overall visual quality of the images were assessed. Results: Prior destreaking (mmkb algorithm) reduced ghosting artifacts and increased CNRs for all cases, with the biggest impacts seen in the end inhale (EI) and end exhale (EE) phases of the respiratory cycle. For the XCAT phantom, mmkb lesion CNR was 44% higher than the MKB lesion CNR and was 81% higher than the FDK-PC lesion CNR (EI and EE phases). The bilateral filter provided a further average CNR improvement of 87% with the highest increases associated with longer scan times. Across all phases and scan times, the maximum mmkb bf -to-fdk-pc CNR improvement was over 300%. In vivo results agreed with XCAT results. Significantly less ghosting was observed throughout the mmkb images including near the lesions-of-interest and the diaphragm allowing for, in one case, visualization of a small tumor with nearly 30 mm of motion. The maximum FDK-PCto-MKB bf CNR improvement for Patient 1 s lesion was 261% and for Patient 2 s lesion was 318% Med. Phys. 45 (8), August /2018/45(8)/3783/ Varian Medical Systems. Medical Physics published by Wiley Periodicals, Inc. on behalf of American Association of Physicists in Medicine. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes. 3783

2 3784 Star-Lack et al.: Modified McKinnon-Bates algorithm for 4D CBCT 3784 Conclusions: The 4D mmkb algorithm yields good quality coronal and sagittal images in the thorax that may provide sufficient information for patient verification Varian Medical Systems. Medical Physics published by Wiley Periodicals, Inc. on behalf of American Association of Physicists in Medicine. [ Key words: four-dimensional cone-beam computed tomography (4D CBCT), image-guided radiotherapy (IGRT), modified McKinnon-Bates (mmkb) algorithm 1. INTRODUCTION On-board cone-beam computed tomography (CBCT) has become a critical technology for image-guided radiotherapy (IGRT). 1,2 For stationary targets, conventional three-dimensional (3D) acquisition and reconstruction protocols are generally suitable. However, for moving targets such as lung tumors, four-dimensional (4D) techniques may be required to improve patient setup for treatment of an internal target volume (ITV). 3 It also may be possible to use 4D CBCT to determine a tumor s trajectory-of-the-day that, when correlated with an external surrogate, can be used with real-time beam gating or dynamic multileaf collimator (MLC) tracking to improve targeting capabilities. 4 CBCT acquisition times in a radiotherapy environment are typically on the order of 1 min due to slow gantry rotation times and the relatively low frame rates of amorphous silicon flat panel imagers. This creates a challenge for lung tumor imaging where subsecond temporal resolution is required to characterize respiratory-related motion patterns. If periodicity is assumed, the projections can be sorted and grouped according to their respective phases in the breathing cycle and each projection group can be reconstructed using the FDK algorithm and combined to create a 4D image. 5 7 However, since only a limited number of breathing cycles occur during a typical acquisition, sparse angular sampling distributions are created that can cause severe view aliasing-induced streaking artifacts. These artifacts can be mitigated by increasing the total number of breathing cycles in a scan, 8 which has the undesired effect of further elevating scan times and radiation dose. To maintain shorter scan times, advanced processing techniques have been proposed involving iterative reconstruction and/or deformable registration techniques As these processes can be computationally expensive, we have chosen to investigate the more efficient McKinnon-Bates algorithm (MKB) which was originally developed for cardiac applications at a time when diagnostic CT gantry rotation times were too slow to freeze heart motion. 15,16 The MKB approach was first applied to 4D CBCT of the lung by Leng et al. 17 who showed that streaking is significantly reduced, but that temporal resolution can also be compromised. 18 To overcome this limitation, we identify in this work the inherent shortcomings in the original MKB algorithm that leads to the loss of temporal information and propose a solution designated as the modified McKinnon-Bates (mmkb) algorithm. 19,20 The core of the mmkb algorithm, excluding the bilateral filter, has been introduced into the Varian TrueBeam TM software (Varian, Palo Alto, CA). 2. METHODS AND MATERIALS 2.A. Original MKB algorithm The quasi-iterative MKB algorithm involves two full back projection operations and one full forward projection operation. Briefly, assume we acquire Np raw data projections, P. Next, using either an external surrogate such as the optically based real-time position management (RPM) system, 21 aspirometer, 22 or an internal marker such as the diaphragm, 23 each projection is assigned to a single respiratory phase bin b for 1 <= b <= N b, where N b is the total number of breathing phases to be resolved. Then, using appropriate projection weighting, phase-correlated images FDK-PC(b) are reconstructed. Due to view aliasing, they will generally contain severe streaking artifacts. The phase-correlated images can be summed to create a well-sampled time-averaged prior image with reduced artifacts: Prior ¼ X N b FDK-PCðbÞ (1) b¼1 Alternatively, and more commonly, the prior is obtained by simply performing an FDK reconstruction using all projections belonging to all phases. Once created, the prior is reprojected at the same angles as the original projections. These reprojections rp are binned into phases using one of the same approaches described above, and reprojected phase-correlated images FDK-RC(b) are then reconstructed. While these images will have very similar view aliasing artifacts caused by stationary objects as their corresponding phase-correlated images FDK-PC(b), motion should not be resolved from phase-to-phase because the reprojections are generated from the time-averaged prior image. Thus, to encode for motion and to remove streaks, each reprojected image can be subtracted from its phase-correlated counterpart to create a difference image Diff(b). Diff ðbþ ¼a b ðfdk-pcðbþ FDK-RCðbÞÞ (2) where, based on the number of projections contributing to phase b, a b normalizes the difference images so that they have the same intensities as the prior. As the difference images are nominally devoid of view aliasing artifacts emanating from areas where there was no motion, they contain signal only where motion is present. They are then added to the original prior image to create the final phase-correlated MKB images, MKB(b) MKBðbÞ ¼Prior þ Diff ðbþ (3)

3 3785 Star-Lack et al.: Modified McKinnon-Bates algorithm for 4D CBCT 3785 In areas where no motion exists, the final phase-correlated MKB images differ little from the (higher quality) prior. In areas where motion is present, the final images more closely resemble the conventional 4D phase-correlated reconstructions FDK-PC based on limited projection data. In a lung scan, streaks in the FDK-PC reconstruction mainly arise from the largely stationary (high contrast) ribs and thus are mostly removed from the difference images that are added to the prior. Note that, due to the linearity of the reconstruction process, the difference images also can be obtained by subtracting the reprojections rp from the original projections P, binning the results according to phase, and reconstructing each binned projection set using the FDK algorithm. The original MKB algorithm is illustrated as part of the Fig. 3 flowchart. 2.A.1. MKB challenges A weakness of the basic MKB algorithm lies in the fact that it may produce ghosting artifacts. This is illustrated in Fig. 1 using the 2D digital lung phantom introduced by Leng et al. 17 that contains a 1 cm diameter circular object oscillating horizontally 1 cm peak to peak. The effects of using two different priors are shown: (a) a conventional prior computed using Eq. (1) and (b) an ideal prior which is the actual time average of all phases. The simulated imaging time was 1 min and breathing period was 4 s. In total, 600 projections were computed and 12 phases were reconstructed. Shown are the FDK-PC, FDK-RC, and MKB images associated with two breathing phases, b = 1 and b = 7, representing the minima and maxima of the extent of travel. As seen in Fig. 1(d), when using the conventional prior, the MKB images exhibit ghosting artifacts near the moving object (arrows). This ghosting can be traced to errors in the reprojected images FDK-RC that incorrectly exhibit residual motion [in Fig. 1(c), it can be seen that the 1 cm object is displaced between phases b = 1 and b = 7 when, in fact, it should be stationary]. This false motion can be traced to motion-induced streaks in the conventional prior [Fig. 1(a)] that erroneously encode for motion in the reprojection operation. As a result, subtraction of FDK-RC(p) from FDK-PC (p) [Eq. (2)] creates ghosting artifacts that are carried through to the MKB image after the difference image is added to the prior [Eq. (3)]. In comparison, when an ideal streak-free prior is used, the moving object in FDK-RC is stationary [Fig. 1(g)] and the resulting moving object is well defined [Fig. 1(h)]. 2.B. Prior image destreaking The above analysis suggests that the key to removing ghosting is to remove motion-induced streaks from the prior image. Our proposed destreaking algorithm employs a combination of segmentation and boundary erosion operations and is designed to eliminate streaks while minimizing discontinuities. The four-step procedure, termed Threshold-Erosion (Fig. 2), is performed on sequential 2D axial slices as outlined below: 1. Select a set of CT number (HU) thresholds that best separate key tissue segments air, lung, soft tissue, and bone. An adaptive method for automatic threshold selection is described in the next Section 2.B Segment the corresponding structures accordingly using these thresholds. 3. Assign the pixels in each segment to the mean HU value for that segment. 4. Smooth the transition regions between adjacent segments [Fig. 2(d)]. This can be achieved by eroding the boundaries by a fixed distance (we use 5 mm) and replacing the eroded pixel values with their original intensities. 5. Replace tissue segmented as bone with its original pixel values. 2.B.1. Adaptive thresholding For thoracic applications, we have found it suitable to segment k = 4 tissue types: air, lung, soft tissue (e.g., adipose, muscle, etc.), and bone. Normally, when using a stable, wellcalibrated CBCT system, air has an intensity of 1000 HU, tissue in the lung can range between 900 and 200 HU with other soft tissues ranging between 150 and 100 HU, and bone generally being above 700 HU. Therefore, for Step 1 of the Threshold-Erosion algorithm described above, one could logically set thresholds as follows: air < 900 HU < lung < 175 HU <soft tissue < 400 HU < bone. However, due to patient-to-patient variations in anatomy and the existence of artifacts from motion, data truncation, scatter, and other sources, it is impractical to use the same thresholds for all cases. For this reason, we developed an automatic approach based on the k-means algorithm to more robustly determine optimal segmentation thresholds. First, an initial guess is made. Then, the thresholds are evolved iteratively by calculating the mean HU value of each segment and setting new thresholds that are halfway between the mean HU values of the adjacent tissue types. This process is repeated until convergence is reached. There are several important aspects of segmentation that are unique to thoracic applications that require special consideration. Firstly, of the four segments, bone occupies only a small fraction of the total voxels. Thus, its presence in the intensity histogram may be too small to provide an accurate measure of its mean value. To overcome this limitation, the soft tissue-to-bone threshold was set to be a fixed offset relative to the mean soft-tissue intensity. We have also observed that the air lung threshold should be set closer to the air intensity value than the lung intensity value to ensure that, after thresholding, the lung voxels do not contain abnormal amounts of air. In this way, the destreaked lung is more uniform. Taking the above considerations into account, the proposed adaptive k-means algorithm for thoracic applications executes as follows:

4 3786 Star-Lack et al.: Modified McKinnon-Bates algorithm for 4D CBCT 3786 (b) FDK-PC(b) (c) FDK-RC(b) (d) MKB(b) (a) Conventional Prior (has streaks) b=1 (f) FDK-PC(b) (g) FDK-RC(b) (h) MKB(b) (e) Ideal Prior b=7 b=1 b=7 FIG. 1. Comparison of the performance of the MKB algorithm if using either a conventional prior (a) containing motion-induced streaks or a streak-free ideal prior (e) to compute the reprojections. Two phases are shown, b = 1, b = 7, representing the extent of travel. As expected, view aliasing is significant in the FDK-PC phase-correlated reconstructions (b, f) but the extent of motion (0.5 cm) still can be seen in reference to the vertical dotted line. Using a conventional prior, the moving object in the FDK-RC reprojected reconstructions (c) should be stationary but exhibits erroneous motion. This false motion, in turn, causes ghosts (solid line with arrows) to be formed in the resulting MKB images (d). The FDK-RC reprojected reconstructions (g) computed from an ideal prior exhibit no false motion, and thus, no ghosting is evident in the resulting MKB image (h). [Color figure can be viewed at wileyonlinelibrary.com] Adaptive k-means Algorithm 1. Initialize the thresholds based on standard tissue intensity (HU) values. 2. Segment the image and calculate the mean HU values for the air, lung, soft tissue, and bone regions. 3. Set the new thresholds midway between the mean HU value of each of the adjacent pairs. 4. Adjust the soft tissue-to-bone threshold to be equal to the soft tissue mean HU. 5. Check for convergence by calculating the maximum difference between a threshold from this iteration and the previous iteration. If it is greater than 1 HU, go back to Step Reset the air-to-lung threshold so that it is three times further from the lung HU mean than to the air HU mean [i.e., equal to a value of 0.75 mean(air) mean(lung)]. To increase the computational efficiency of the segmentation process, we have found it is acceptable to apply the computed thresholds from just the central slice to the entire volume. 2.B.2. Full Implementation The mmkb algorithm (except Step 12) was integrated into the Varian TrueBeam reconstructor 24 and implemented as shown in Fig. 3. For computational efficiency, operations were performed in projection space as opposed to in image space. Of note, the prior should be reconstructed using as large a transaxial field of view (FOV) as possible to minimize truncation artifacts so that the forward projection operation will produce reprojections that are as consistent as possible with the original projections. 25 In a radiotherapy environment, this step is important for minimizing streaking from the patient table edges. Once reprojected, the prior can be cropped before addition (Step 10) to the difference images that are generally reconstructed with a smaller FOV to minimize reconstruction times and volumes (Step 8). The preprocessing operations of Step 2 include scatter, beam hardening,

5 3787 Star-Lack et al.: Modified McKinnon-Bates algorithm for 4D CBCT 3787 (a) (b) Pixel Count Air Lung 1500 Soft Tissue Bone HU (c) (d) FIG. 2. Threshold-erosion method for destreaking the prior image. (a) Original prior computed using Eq. (1). (b) Histogram of the number of pixels per intensity bin. The green lines demark the bin boundaries after adaptive threshing while the red lines demark the starting (default) bin boundaries. (c) Destreaked prior after segmentation and assignment of a single HU value to each tissue type. (d) Final destreaked prior including boundary erosion and bone pixel restoration operations (highlighted by solid white arrows). One residual streak remains (horizontal, yellow-dashed arrow). Window width = 2000 HU. [Color figure can be viewed at wileyonlinelibrary.com] log normalization, and filtering operations as previously described. 26,27 Ring correction 28 is performed on each of the final phase-correlated mmkb images (Step 11). 2.B.3. Noise Reduction Garden and Robb 16 described the application of an edgepreserving nonlinear filter to the difference projections in order to improve the SNR of the original MKB algorithm. Our experience indicates that filtering both the difference images and the mmkb images themselves is more robust and effective. For difference image filtration, we implemented a two-dimensional median filter (Fig. 5, Step 9) of size 3 9 3pixels. The filter applied to the mmkb images I was a multidimensional edge-preserving bilateral Gaussian operator 25,29 defined as follows: mmkb bf ðrþ ¼ P s2wðrþ G r x ðr x ; s x ÞG ry ðr y ; s y ÞG rz ðr z ; s z ÞG rb ðr b ; s b ÞG ri ði r ; I s ÞI s P s2wðrþ G r x ðr x ; s x ÞG ry ðr y ; s y ÞG rz ðr z ; s z ÞG rb ðr b ; s b ÞG ri ði r ; I s Þ (4) where the superscript bf indicates bilateral filtration, W(r) isa fixed-sized 4D window region surrounding the point-ofinterest r=(r x, r y, r z, r b ), and G r (r, s) is the Gaussian kernel given by G r ðr; sþ ¼e ðr sþ2 2r 2 : (5) In total, five Gaussian weights, r x, r y, r z, r b, and r I are used. The first three weights r x, r y, and r z define the smoothing parameters along the x, y, and z axes, respectively, r b defines the smoothing parameter in time (phase), and r I is an intensity-determined filtering parameter that preserves edges. For our implementation, the filtering parameter values were r x = r y = 2.0 mm, r z = 1.2 mm (r z was reduced compared to r x and r y since motion predominates in the SI direction), r b = 3 breathing phases, r I = 120 HU. The size of the window region W was 5 pixels in the spatial (x, y, z) dimensions and was of length 9 (out of 10) phase bins b. For these studies, the filter was implemented in MATLAB (MathWorks, Natick, MA) and exhibited quite long execution times. However, we have shown previously that the same filter implemented on a GTX480 GPU (Nvidia Inc, Santa Clara, CA) executes in less than 7 s for a 4D matrix of size

6 3788 Star-Lack et al.: Modified McKinnon-Bates algorithm for 4D CBCT Phase Bin Difference Projections 8. Reconstruct N b Difference Images 9. Median Filter Difference Images Acquire Projections 2. Pre-Process Projections 5. Forward Project 3. Reconstruct Prior 4. Destreak Prior 2.C. Experimental studies 2.C.1. 4D XCAT phantom Algorithm performance was first assessed using the 4D XCAT digital phantom. 30 Breathing motion was programmed to have a cycle time of 4 s and movement of the diaphragm was set to be 1 cm peak to peak. Cardiac motion was also enabled. Projections were calculated using the Varian CBCT half-fan geometry (Varian Medical Systems, Palo Alto CA) with the cm imager ( pixels, mm pitch) offset by 16 cm. The source-to-imager (SID) distance was 150 cm and the source-to-axis (SAD) distance was 100 cm. Four different acquisition times (57, 90, 120, and 180 s) were simulated which produced, due to the half-fan geometry, respectively 7, 11, 14, and 22 effective projection angles per phase. For each experiment, a total of N p = 650 projections were computed using a 125 kvp polychromatic beam. The resulting simulated frame rates were 11.5, 7.2, 5.4, and 3.6 Hz. Poisson noise was added to each projection in an amount equivalent to that produced by 0.8 mas acquisition resulting in a weighted computed tomography dose index (CTDIw) value of 0.7 cgy for a full 650 projection thorax Ring Correct N b Phase- Correlated 3DImages amkb 12. Bilaterally Filter amkb images amkb bf FIG. 3. Implementation of the mmkb algorithm to reconstruct N b phase-correlated images. The original MKB algorithm does not include Step 4 (prior destreaking), Step 9 (median filtering), and Step 12 (bilateral filtering). [Color figure can be viewed at wileyonlinelibrary.com] scan. Each of the simulations was acquired with the same total dose and the same total number of projections allowing for fair comparisons of the algorithms effects on Poisson and view aliasing noise as a function of scan time. In total, N b = 10 phases, each having a temporal resolution of 0.4 s, were reconstructed using (a) the standard FDK- PC approach, (b) the original MKB algorithm, (c) the mmkb algorithm, and (d) the mmkb bf algorithm. The isotropically reconstructed voxel size was 1 mm and the final reconstruction matrix size was 512(x) 9 512(y) 9 174(z) 9 10(b). The prior was reconstructed onto a pixel matrix with isotropic 1 mm resolution. The preprocessing and ring correction operations (Fig. 3, Steps 2 and 11) did not have to be applied to the simulated data. Two regions-of-interest were studied (Fig. 4) ina1mm thick coronal slice: (a) R1, a59 25 mm 2 size area containing a 8 mm diameter moving lesion-of-interest L, (b) R2, a larger mm 2 uniform area in the heart. For each phase b, the contrast of the lesion L, Contrast(L b ) was computed as ContrastðL b Þ¼meanðL b Þ meanðb b Þ (6) where B is an annular-shaped background surrounding the lesion L with an inner diameter of 8 mm and an outer diameter of 16 mm. The measurement of the mean(l) was performed across a 5 9 5mm 2 area centered in its known location. For each phase b, the contrast-to-noise ratio of the lesion L, CNR(L b ), was computed by dividing the Contrast(L b )by the root-mean-squared error (RMS) of the background region B (i.e., the background noise) CNRðL b Þ¼ContrastðL b Þ=RMSðB b Þ (7) where sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 X j¼npixb RMSðB; bþ ¼ ðbðj; bþ XC Npix j¼1 B ðj; bþþ 2 B (8) XC B (j) is the ground truth XCAT phantom intensity (HU) value for the pixels j in the background region B, each with index j = 1,2,... N pixb. The signal-to-noise SNR of the uniform region R2 was computed as the mean(r2)/standard deviation(r2). 2.C.2. In vivo studies CBCT scans of two lung tumor patients (Patients 1 and 2) were acquired using the TrueBeam kv imaging system. Patient 1 had a small approximately 8 mm diameter tumor situated near the diaphragm with a large 28 mm range of motion peak to peak in the SI direction and a 6 mm range in the AP direction. Acquisition time for the 4D sequence was 60 s. Because of the large range of motion, the images were reconstructed into 20 breathing phase bins. Patient 2 had an approximate 20 mm diameter tumor located more superiorly with ranges of motion of 8 mm and 4 mm in the SI and AP

7 3789 Star-Lack et al.: Modified McKinnon-Bates algorithm for 4D CBCT 3789 End Exhale (EE) Mid End Inhale (EI) Ground Truth (XC) L R1 R2 Zoomed Region FDK-PC MKB mmkb mmkb BF FIG. 4. Coronal FDK-PC, (conventional) MKB, mmkb, and mmkb bf slices of the XCAT phantom (57 s acquisition) for three breathing phases. Two regionsof-interest R1 and R2 are delineated for later analysis. The arrow points to the moving lesion L in R1 which is seen to be blurred in the EI and EE phases of the MKB images. Window width = 2000 HU. directions, respectively. For this patient, the acquisition time was 90 s and reconstruction was into ten breathing phase bins. A summary of the acquisition and reconstruction parameters is given in Table I. Concurrent with the scans, breathing traces were acquired using the Varian respiratory breathing monitoring system. The difference projections were sorted by phase (Fig. 3, Step 7) using a retrospective analysis of the respiratory signal with a projection s phase given by its position in time relative its nearest neighboring end inhale times (zero phase) as determined by peak amplitudes. Contrasts and CNRs of the lesions were calculated using Eqs. (6), (7), and (8). Since a ground truth did not exist for the in vivo data, the mean(b) was used instead of XC b for the RMS noise calculation in Eq. (8). Thus, the CNR just equaled the lesion contrast divided by the standard deviation of its background region. For Patient 1, similar to what was used in the XCAT studies, the background region was a 14 pixel-wide annulus that tracked and surrounded the lesion. For Patient 2, a fixed background location was used. TABLE I. Acquisition and reconstruction parameters for in vivo datasets. Patient 1 Patient 2 Approximate tumor diameter 8 mm 20 mm Range of motion (SI/AP) 28/6 mm 8/4 mm Acquisition time 60 s 90 s Number of projections Beam energy 125 kvp 125 kvp mas CTDI dose 9 mgy 7 mgy Reconstruction matrix (x, y, z) Voxel Size (x, y, z) mm mm Number of reconstructed breathing phases (N b ) Total mmkb reconstruction time Dell TM T5600 workstation (Dell Computers, Round Rock Texas) 205 s 123 s

8 3790 Star-Lack et al.: Modified McKinnon-Bates algorithm for 4D CBCT RESULTS 3.A. 4D-XCAT phantom Figure 4 shows reconstructed FDK-PC, MKB, mmkb, and mmkb bf coronal XCAT images for three breathing phases (b): (a) end exhale (EE), (b) a midrange position (MID), and (c) end inhale (EI). Acquisition time was 57 s. The arrow points to the moving lesion-of-interest L in R1. As expected, the FDK- PC images possess significant amounts of view aliasing noise. Lesion blurring is seen in the EE and EI MKB images which can be better appreciated in Fig. 5 which contains a montage of a Zoomed Region of the reconstructed right lobe (EI phase). The two mmkb images show increased sharpness and contrast compared to the MKB images. The application of the bilateral filter (mmkb bf ) to the mmkb images provides a further reduction in background noise and muddle. In general, the quality of the images improves from the top left to the lower right of the montage corresponding to increased scan times (less intrinsic view aliasing) and more advanced processing (prior destreaking and bilateral filtering). Aside from the lesion blurring, ghosting is also exhibited near the diaphragm edge (horizontal yellow arrows) in the conventional MKB images. Figure 6 shows snapshots of vertical (superior inferior) intensity profiles through the lesion obtained by averaging R1 across its five columns. Each row corresponds to one of three breathing phases (EE, MID, and EI) with each column corresponding to a scan time. The humps in the curves adjacent to the main peaks are the ghosting signals. Consistent with Fig. 5, the largest amount of ghosting is seen in the MKB EE and EI phases, with the artifact being reduced in the mmkb and mmkb bf profiles. The figure legends contain the ratios of the measured lesion contrast computed using Eq. (6) to the ground truth lesion contrast for each reconstruction method. The MKB reconstructions have the lowest contrasts. As shown in Fig. 7(a), for the EI and EE phases, the mmkb algorithm improves contrast relative to the conventional MKB algorithm by average factors of 1.7, 1.5, 1.7, 1.7, respectively, for the four scan times (57, 90, 120, 180 s). Due to less ghosting in the MID phases, mmkb contrast improvements are smaller (1.1, 1.3, 1.1, 1.1). For all phases and all scan times, mmkb bf contrast is within 4% of mmkb contrast indicating that the bilateral filter preserved the vast majority of relevant structural information. Note that FDK-PC contrast is highly variable due to considerable view aliasing noise. CNRs calculated using Eq. (7) are plotted in Fig. 7(b). On average, mmkb EE and EI phase CNRs are increased by factors of 1.4, 1.4, 1.4, and 1.6 relative to MKB CNR for each 57 sec 90 sec 120 sec 180 sec FDK-PC MKB mmkb mmkb BF FIG. 5. Montage of end inhale (EI) XCAT phantom coronal images of the Zoomed Region of the right lung that is outlined in Fig. 4. Images with acquisition times of 57, 90, 120, and 180 s were reconstructed using the FDK-PC, MKB, mmkb, and mmkb bf algorithms. The simulated lesion L (white arrow) is blurred to varying degrees in all conventional MKB reconstructions. Ghosting is also evident near the diaphragm (horizontal yellow arrows). Overall, the quality of the images improves from the top left to the lower right of the montage corresponding to increased scan times (less intrinsic view aliasing) and more advanced processing (prior destreaking and bilateral filtering). Window width = 2000 HU. [Color figure can be viewed at wileyonlinelibrary.com]

9 3791 Star-Lack et al.: Modified McKinnon-Bates algorithm for 4D CBCT 3791 FIG. 6. Vertical (superior inferior) intensity profiles through the XCAT phantom lesion obtained by averaging the region R1 across its five columns. Each row corresponds to one of three breathing phases (EE, MID, and EI). Each column corresponds to a scan time (57, 90, 120, 180 s). The figure legends contain the ratios of the measured lesion contrast to the ground truth lesion contrast (solid gray line) for the FDK-PC, MKB, mmkb, and mmkb bf reconstructions. The humps in the curves adjacent to the main peaks are the ghosting signals. The ghost-to-peak signal is highest for the MKB EE and EI phases while the mmkb and mmkb BF profiles have significantly reduced artifact. [Color figure can be viewed at wileyonlinelibrary.com]

10 3792 Star-Lack et al.: Modified McKinnon-Bates algorithm for 4D CBCT 3792 FIG. 7. XCAT phantom lesion contrast and CNR for region R = 1 for the EE, MID, EI phases and average of all phases. (a) For the EI and EE phases, the mmkb algorithm improves contrast relative to the MKB algorithm by average factors of 1.7, 1.5, 1.5, and 1.4, respectively, for the four scan times (57, 90, 120, 180 s). (b) For the EI and EE phases, the mmkb bf algorithm increases image CNR by factors of 1.5, 3.6, 2.7, and 3.1 relative to basic FDK-PC reconstruction. Averaged across all ten phases, the increase was by factors of 2.0, 3.0, 3.1, and 3.3. [Color figure can be viewed at wileyonlinelibrary.com] the four scan times. It is interesting that for most scan times, EE and EI phase MKB CNRs are generally equivalent to FDK-PC CNRs. For the MID phases, MKB and mmkb CNRs are largely equivalent and are approximately 29 higher than FDK-PC CNRs. Averaged across all phases, the bilateral filter (mmkb bf ) increased CNR by additional factors of 1.3, 1.4, 1.7, and 1.7 relative to mmkb CNR as function of scan time. Notably, the improved performance of the bilateral filter for increased scan times indicates that the reduction of view aliasing noise associated with longer scan times affords more fidelity to the edge detection component of the filter thus increasing its effectiveness. In total for the EI and EE phases,

11 3793 Star-Lack et al.: Modified McKinnon-Bates algorithm for 4D CBCT 3793 R2 SNR End Exhale (EE) Mid End Inhale (EI) All FIG. 8. SNR of uniform XCAT phantom region R2. The MKB and amkb reconstructions offer approximately a 29 SNR improvement of over FDK-PC SNR with a substantial further improvement provided by the bilateral filter depending on scan time. On average, for all scan times and phases, the ratios of FDK: MKB:mMKB:mMKB bf SNR were 1.0:3.1:2.5:4.9. [Color figure can be viewed at wileyonlinelibrary.com] FIG. 9. (a) Respiratory breathing trace from Patient 1, (b) breathing period duration as a function of time. Excluding the outlier (#12), the standard deviation of the breathing periods was 0.12 s. Including the outlier, the standard deviation was 0.67 s. [Color figure can be viewed at wileyonlinelibrary.com] the mmkb bf algorithm increased image CNR by factors of (1.5, 3.6, 2.7, 3.1) relative to basic FDK-PC CNR. Averaged across all ten phases, the increase was by factors of 2.0, 3.0, 3.1, and 3.3. Figure 8 shows that, for the spatially uniform heart region R2, the MKB approach in general provides a large benefit in reducing image noise for all phases. On average, for all scan times and phases, the ratios of FDK:MKB:mMKB:mMKB bf SNR were 1.0:3.1:2.5:4.9. Although conventional MKB SNRs were 21% higher than mmkb SNRs, this benefit is due to unwanted smoothing that leads to ghosting. A better approach to noise reduction is provided by the bilateral filter which reduces noise and still maintains motion conspicuity. 3.B. In vivo studies 3.B.1. Patient 1: 60 s scan. Small tumor (8 mm diameter) with a large amount of motion (SI peak to peak = 28 mm, AP peak to peak = 6 mm) The patient s breathing period averaged 4.1 s and was very regular with the exception of one outlier breath. For the half-

12 3794 Star-Lack et al.: Modified McKinnon-Bates algorithm for 4D CBCT 3794 EI EE Phase 1/20 Phase 3/20 Phase 6/20 Phase 12/20 FDK-PC MKB mmkb mmkb BF FIG. 10. Sagittal FDK-PC, MKB, mmkb, and mmkb bf reconstructions of EI, MID, and EE phases for Patient 1. MKB ghosting (vertically-oriented, yellowdashed arrows) is reduced in the mmkb reconstructions with further noise suppression and subsequent image quality improvements seen in the mmkb bf images. As a result, it becomes possible to visually track the tumor from frame-to-frame (white vertical arrows). The mmkb algorithm also lessens ghosting near the diaphragm (white horizontal-dashed arrows). Note also that the significant reduction in background noise provided by the bilateral filter (mmkb bf ) greatly improves visibility in the diaphragm and chest wall regions. Window width = 1900 HU. [Color figure can be viewed at wileyonlinelibrary.com]

13 3795 Star-Lack et al.: Modified McKinnon-Bates algorithm for 4D CBCT 3795 fan geometry, a 60 s scan time equates to roughly 7.5 effective projection angles per phase across the vast majority of the FOV with the exception being in the overlap region. The respiratory gating signal used to bin the projections is shown in Fig. 9(a) with the computed breathing periods stem plotted in Fig. 9(b). Excluding the outlier (#12), the standard deviation of the breathing periods was 0.12 s. Including the outlier, the standard deviation was 0.67 s. Sagittal FDK-PC, MKB, mmkb, and mmkb bf reconstructions of EI, MID, and EE phases are shown in Fig. 10 with the range of motion outlined by a dashed line rectangle. As expected, the FDK-PC images demonstrate high amounts of view aliasing-induced streaking and noise which obscure critical features and render the images functionally unusable. Similar to the XCAT results, the conventional MKB reconstructions are much less noisy but exhibit ghosting which in some cases makes it extremely difficult to discern the location of the lesion (see regions indicated by verticallyoriented, yellow-dashed arrows in the MKB EE and EI images). This ghosting is reduced, although not completely eliminated in the mmkb reconstructions, with further noise suppression and subsequent image quality improvements seen in the mmkb bf images. As a result, it becomes possible to visually track the tumor from frame-to-frame (white vertical arrows), especially when played in a video loop. The utility of 4D-CBCT for patient setup can be appreciated by viewing the 3-D FDK image in Fig. 11 which is the average of all 20 phases. Due to low SNR and overlap of the exhale diaphragm position with the inhale tumor position, it is very difficult to estimate an ITV position from this image. Figure 10 shows that, in addition to reducing lesion ghosting, the mmkb algorithm also lessens ghosting near the diaphragm (white horizontal-dashed arrows) in a manner similar to that seen in the XCAT studies. Note also the significant reduction in background noise provided by the bilateral filter which greatly improves visibility in more uniform regions including those near the chest wall and inferior to the diaphragm. Here, the measured mmkb bf SNR was over 39 that of FDK-PC SNR. Figure 12 shows lesion CNR as a function of breathing phase and reconstruction method. Averaged across all phases, tumor CNRs for each reconstruction method, FDK-PC, MKB, mmkb, and mmkb bf, were 1.8, 1.8, 2.5, and 2.7, which were approximately half the 60 s XCAT CNRs (3.4, 4.8, 5.1, 6.7). This is likely due a combination of factors stemming from the large range of motion necessitating the need to reconstruct 20 (instead of 10) respiratory phase bins; as well as intrabin motion blurring. The lower CNRs associated with the inspiration portion of the breathing cycle are due to higher velocities during those phases compared to the longer expiration portion. Nevertheless, in line with the XCAT results, the mmkb algorithm provided on average a 1.49 CNR increase over FDK-PC CNR (XCAT average increase was 1.59) with the traditional MKB algorithm providing no significant benefit. A further CNR improvement of 1.19 was provided by the bilateral filter. This improvement was not as high for the XCAT phantom (1.39) most likely FIG. 11. Patient 1 3D image. It is difficult to estimate an ITV position and extent of travel due to low SNR and overlap of the exhale diaphragm position with the inhale tumor position. Window width = 1900 HU EI Phase Expiration EE Phases Inspiration EI Phase FIG. 12. Patient 1 lesion CNR as a function of breathing phase and reconstruction method. In accordance with the XCAT results, FDK-PC and MKB CNRs are similar to each other with the mmkb algorithm providing, on average, a 1.49 CNR increase over MKB CNR. A further 1.19 CNR improvement is provided by the bilateral filter. The duration of inspiration is half that of expiration. The higher inspiration velocities increased motion blurring and decreased CNR during that portion of the breathing cycle. [Color figure can be viewed at wileyonlinelibrary.com] due to the reduced absolute lesion contrast which rendered the bilateral filter less able to preserve contrast. Note also that, unlike for the XCAT simulation, mmkb CNRs were higher than MKB CNRs for some MID phases which may be due to high lesion velocities and complicating influences of

14 3796 Star-Lack et al.: Modified McKinnon-Bates algorithm for 4D CBCT 3796 (a) RPM Trace (b) Breathing Period (sec) FIG. 13. (a) Respiratory breathing trace from Patient 2, (b) breathing period duration as a function of time. The breathing period standard deviation was 0.88 s. [Color figure can be viewed at wileyonlinelibrary.com] the diaphragm. Across all phases, the mmkb bf algorithm produced a maximum 2.69 CNR increase compared to FDK- PC CNR and an average increase of B.2. Patient 2: 90 s scan, medium size tumor (20 mm diameter) with a smaller amount of motion (SI peak to peak = 8 mm, AP peak to peak = 4 mm) The patient s breathing period averaged 4.5 s which, for the 90 s scan time, equates to roughly 10 effective projection angles per phase across the vast majority of the FOV. The respiratory gating trace is shown in Fig. 13(a) and the breathing periods in Fig. 13(b). Breathing was less regular than for Patient 1 becoming gradually become more frequent as the scan progressed. The breathing period standard deviation was 0.88 s. Coronal FDK-PC, MKB, mmkb, and mmkb bf reconstructions of the EE, MID, and EI phases are shown in Fig. 14. Similar to the previous cases, the FDK-PC images demonstrate high amounts of view aliasing-induced noise. The conventional MKB reconstructions are much less noisy, but ghosting is evident particularly in the right side of the lung near the diaphragm (downward-pointing, solid yellow arrows). This ghosting is significantly less pronounced in the mmkb reconstructions resulting in sharper features and more clearly defined boundaries. Improvements in lesion CNR are measurable (see Fig. 15) but not particularly visible except in the EI phase (horizontal white arrow). The unwanted vertical stripes (horizontal, yellow-dashed arrows) seen in the MKB images are significantly reduced in the mmkb images, an improvement that was traced to mmkb s median-filtering operation (the source of the stripes in the original MKB reconstruction was not explored). Figure 15 shows lesion CNR values which, averaged across all phases, were 4.5, 6.7, 7.4, and 10.3 for each of the four respective reconstruction algorithms (FDK-PC, MKB, mmkb, and mmkb bf ). These values are in accordance with the 90 s XCAT phantom results (3.1, 5.7, 6.7, 9.3). For the EE And EI phases, the mmkb algorithm improves lesion by 1.39 CNR compared to the original MKB algorithm (XCAT improvement = 1.49) with the bilateral filter providing another 1.39 CNR improvement (XCAT = 1.49). On average, across all phases, the mmkb bf algorithm produced a 2.49 improvement in lesion CNR compared to FDK-PC CNR (XCAT improvement = 3.09) with a maximum improvement of An approximate 49 SNR improvement is seen the liver region which is also in accordance with the XCAT results for uniform Region 2 (XCAT improvement = 4.49). 4. DISCUSSION The aim of performing 4D CBCT in a radiotherapy environment is to quantify the amount and nature of motion for the purposes of improving patient setup or calibrating an external surrogate or both. The results show that the mmkb algorithm, which eliminates some of the deficiencies of the original MKB approach, may aid considerably in performing these tasks. In the XCAT phantom studies, due to reduced ghosting, average EI and EE phase MKB CNRs were increased by over 44% compared to MKB CNRs and by over 81% compared to FDK-PC CNRs. On average across all phases, an additional 87% CNR improvement was provided by the multidimensional bilateral filter. This resulted in some mmkb bf CNRs being over 300% higher than the corresponding FDK-PC CNRs. The in vivo mmkb results matched the XCAT results showing significant improvements in CNR and reduction of ghosting. For Patient 1, a maximum 2.69 CNR improvement was realized and, despite the lower absolute CNR level due to the short scan time and large amount of motion, it

15 3797 Star-Lack et al.: Modified McKinnon-Bates algorithm for 4D CBCT 3797 EE MID EI Phase 6/10 Phase 3/20 Phase 1/10 FDK-PC MKB mmkb mmkb BF FIG. 14. Patient 2 coronal images with the range of motion outlined by a white-dashed box. Ghosting is evident MKB reconstructions particularly in the right side of the lung near the diaphragm (downward-pointing, solid yellow arrows). An improvement in lesion CNR in the mmkb and mmkb bf images can be seen in the EI phase (horizontal white arrow) with the unwanted vertical stripes (horizontal, yellow-dashed arrows) in the MKB images also significantly reduced. On average, across all phases, the mmkb bf algorithm produces a 2.49 improvement in lesion CNR compared to FDK-PC CNR. In the more uniform liver region, the mmkb bf algorithm provides an approximate 49 SNR improvement over FDK-PC SNR. Window width = 1900 HU. [Color figure can be viewed at wileyonlinelibrary.com] was still possible to identify the motion pattern and determine the extent of travel. With a tumor size of only 8 mm and almost 3 cm of motion, the tumor became clearly visible using the mmkb approach while it was not possible to visualize the tumor in the 4D FDK-PC and 3D reconstructions. Nevertheless, for robustness, longer scan times are advised to increase the number of distinct source angles per phase and, hence, overall CNR. It is for this and other reasons that the default scan time for the TrueBeam 4D CBCT protocol is set to 120 s. The two main modifications to the MKB algorithm described in this work include (a) prior destreaking and (b) bilateral filtering. The prior destreaking component was shown to reduce ghosting from the diaphragm and improve lesion CNR mainly in the EI and EE phases, although for Patient 1, significant improvements were also seen in MID phases perhaps due to high velocities and complicating influences of the diaphragm. Bilateral filtering improved the CNR for all breathing phases but, as shown for Patient 1 and can be inferred from the XCAT data, may not be as effective if the intrinsic CNR is too low to begin with. The goal of the threshold-erosion technique that was developed for prior destreaking is to strike a balance between EI Phase EE Phases EI Phase FIG. 15. Patient 2 lesion CNR. For the EE and EI phases, mmkb CNR is increased by relative to MKB CNR with the bilateral filter providing another improvement. On average across all phases, the mmkb bf algorithm produces a 2.49 improvement in lesion CNR compared to FDK- PC CNR. [Color figure can be viewed at wileyonlinelibrary.com] removing as many motion-induced streaks as possible while preserving the maximum amount of useful content. As there still was residual streaking in the prior which produces

16 3798 Star-Lack et al.: Modified McKinnon-Bates algorithm for 4D CBCT 3798 residual ghosting in the mmkb reconstructions, further refinements may be required. For example, comprehensive optimization of the thresholding and erosion parameters along with improved methods for blending the adjacent segmented regions together may lead to further streak removal. Alternatively, as suggested by one reviewer, advanced segmentation techniques based on connection analysis could prove valuable. In another vein, more effort in optimizing the bilateral filtration parameters may improve the balance between noise reduction, edge preservation, and temporal resolution in the final reconstructions particularly for such cases as presented by Patient 1. This includes comprehensive spatial resolution analysis to ensure that small structures are not suppressed. There is one limitation we have observed with the mmkb algorithm and that is in the presence of metal fiducial markers. The current destreaking algorithm does not handle metal fiducial markers well and, rather than appearing as moving objects, reconstructed metal fiducial markers can appear as elongated structures covering the range of motion. This may then lead to erroneous impressions of fiducial motion. Until further improvements are made, it is not recommended that 4D CBCT images produced by the mmkb algorithm described here be used to estimate the motion of metal fiducial markers. It is important to note that, even under the best of circumstances, the MKB algorithm will not be able to remove all view aliasing noise from the final reconstructions since any objects that are in motion will still be subsampled in the difference images. Fortunately, lung tumors tend to be of relatively low contrast (at least as compared to bone-tissue contrast) and are thus more immune to the worst complications from view aliasing. Another reason the MKB approach appears to be effective in the thorax region is that the most severe view aliasing-induced artifacts tend to emanate from the lateral portions of the ribs, which are comparatively motionless. The residual streak artifacts that do remain are seen mainly in axial slices and may not be a significant clinical encumbrance as sagittal and coronal slices are sufficient to provide all the information required for image guidance. In fact, they may be preferred given that respiratory motion predominates in the superior inferior direction. The main advantage of a quasi-iterative approach such as the mmkb algorithm is its computational efficiency. Starting with 990 projections, the total reconstruction time was 123 s for a matrix size of 512(x) 9 512(y) 9 174(z) 9 10 (b) using a quad-core Dell T5600 Workstation (not including bilateral filtering and disk I/O). Since the preprocessing operations along with the bulk of the prior reconstruction operation can be performed simultaneously with data acquisition, the time to completion after the end-of-acquisition is predicted to be 82 s. For a more typical matrix size of 426(x) 9 426(y) 9 116(z) 9 10(b), this time is reduced to 41 s. The bilateral filter was not included in the first software release due to long CPU processing times. However, use of a GPU is expected to reduce all reconstruction times to less than 20 s even when bilateral filtering is included. 25 It should be noted that the advent of powerful GPU-based computing platforms may allow for clinical implementation of more advanced 4D reconstruction algorithms that utilize iterative reconstruction and/or deformable registration techniques and which promise to produce accurate results completely devoid of streak artifacts Some of these approaches (e.g., Prior Image Constrained Compressive Sensing PICCS 9 and Motion Compensated Image Reconstruction MOCO 13 ) also rely on the computation of prior images. Possibly, the development of these methods could benefit from relevant insights gained from this study. Independent of the reconstruction method employed, the surrogate signal required for phase binning must be of high quality. If an external surrogate is used, good internal external motion correlation is more likely to be achieved if respiratory motion is regular and periodic. This can be encouraged by using audio visual feedback to help guide the patient s breathing 31 although such coaching may lead to deeper breathing and thus a larger tumor motion amplitude. While the XCAT simulation study had a ground truth from which to calculate absolute errors, such a ground truth did not exist for the in vivo study, and thus, the images could only be assessed qualitatively. Moreover, the impacts of the breathing rate increase in Patient 2 during the scan or the outlier breath in Patient 1 are unknown. As such, comprehensive studies of the effects of irregular breathing on the algorithm in general would be valuable. Using an internal marker such as the diaphragm edge may offer improved reliability but presents other challenges; for example, the marker potentially could be difficult to identify in all projections when employing the offset-detector geometry. It is interesting to note that some of the deficiencies of an ITV or the challenges in gating or tracking during free breathing may be eliminated entirely with the implementation of breath-hold treatments. 32 This may also obviate the need for onboard 4D-CBCT altogether. Finally, identification of the need to destreak the prior image to remove unwanted motion-related information was largely a phenomenological observation and many questions remain unanswered. For example, it is unclear why the biggest impact occurred for breathing phases at the extrema of travel (EE and EI). As such, it would be valuable to perform a detailed theoretical and experimental analysis of the links between the motion-induced prior imaging streaking and ghosting artifacts. Conversely, it might be interesting to investigate if there is potentially useful motion-related information to be gleaned from the nature and extent of streaking in a given prior. 5. CONCLUSION The mmkb reconstruction algorithm improves soft tissue motion conspicuity and reduces noise in 4D-CBCT images by destreaking the prior and employing other nonlinear filtration techniques. Acquisition times as low as s may be accommodated even when using the more challenging offsetdetector geometry to maximize the FOV. As with the original MKB algorithm, sagittal and coronal perspectives are