Continuous monitoring of prostate position using stereoscopic and ...

Continuous monitoring of prostate position using stereoscopic and monoscopic kV image guidance M. Tynan R. Stevens, Dave D. Parsons, and James L. Robar Citation: Medical Physics 43, 2558 (2016); doi: 10.1118/1.4947295 View online: http://dx.doi.org/10.1118/1.4947295 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/43/5?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in The first clinical treatment with kilovoltage intrafraction monitoring (KIM): A real-time image guidance method Med. Phys. 42, 354 (2015); 10.1118/1.4904023 Evaluation of the geometric accuracy of surrogate-based gated VMAT using intrafraction kilovoltage x-ray images Med. Phys. 39, 2686 (2012); 10.1118/1.4704729 Clinical development of a failure detection-based online repositioning strategy for prostate IMRT—Experiments, simulation, and dosimetry study Med. Phys. 37, 5287 (2010); 10.1118/1.3488887 Dosimetric consequences of misalignment and realignment in prostate 3DCRT using intramodality ultrasound image guidance Med. Phys. 37, 2787 (2010); 10.1118/1.3429127 Prostate intrafraction motion evaluation using kV fluoroscopy during treatment delivery: A feasibility and accuracy study Med. Phys. 35, 1793 (2008); 10.1118/1.2899998

Continuous monitoring of prostate position using stereoscopic and monoscopic kV image guidance M. Tynan R. Stevens, Dave D. Parsons, and James L. Robar Department of Medical Physics, Dalhousie University, Halifax, Nova Scotia B3H 4R2, Canada and Nova Scotia Cancer Centre, QEII Health Science Centre, Halifax, Nova Scotia B3H 2Y9, Canada

(Received 18 November 2015; revised 29 March 2016; accepted for publication 9 April 2016; published 27 April 2016) Purpose: To demonstrate continuous kV x-ray monitoring of prostate motion using both stereoscopic and monoscopic localizations, assess the spatial accuracy of these techniques, and evaluate the dose delivered from the added image guidance. Methods: The authors implemented both stereoscopic and monoscopic fiducial localizations using a room-mounted dual oblique x-ray system. Recently developed monoscopic 3D position estimation techniques potentially overcome the issue of treatment head interference with stereoscopic imaging at certain gantry angles. To demonstrate continuous position monitoring, a gold fiducial marker was placed in an anthropomorphic phantom and placed on the Linac couch. The couch was used as a programmable translation stage. The couch was programmed with a series of patient prostate motion trajectories exemplifying five distinct categories: stable prostate, slow drift, persistent excursion, transient excursion, and high frequency excursions. The phantom and fiducial were imaged using 140 kVp, 0.63 mAs per image at 1 Hz for a 60 s monitoring period. Both stereoscopic and monoscopic 3D localization accuracies were assessed by comparison to the ground-truth obtained from the Linac log file. Imaging dose was also assessed, using optically stimulated luminescence dosimeter inserts in the phantom. Results: Stereoscopic localization accuracy varied between 0.13 ± 0.05 and 0.33 ± 0.30 mm, depending on the motion trajectory. Monoscopic localization accuracy varied from 0.2 ± 0.1 to 1.1 ± 0.7 mm. The largest localization errors were typically observed in the left–right direction. There were significant differences in accuracy between the two monoscopic views, but which view was better varied from trajectory to trajectory. The imaging dose was measured to be between 2 and 15 µGy/mAs, depending on location in the phantom. Conclusions: The authors have demonstrated the first use of monoscopic localization for a roommounted dual x-ray system. Three-dimensional position estimation from monoscopic imaging permits continuous, uninterrupted intrafraction motion monitoring even in the presence of gantry rotation, which may block kV sources or imagers. This potentially allows for more accurate treatment delivery, by ensuring that the prostate does not deviate substantially from the initial setup position. C 2016 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4947295] Key words: stereoscopic, monoscopic, intrafraction motion, prostate cancer, x-ray imaging

1. INTRODUCTION The accurate delivery of external beam radiation therapy depends on precise localization of the anatomy to be irradiated. While planning CT and pretreatment imaging are routinely used for patient setup, this cannot account for intrafraction motion observed for many internal organs like the prostate. Indeed, prostate motion of more than 1 cm is not uncommon, and for most patients, the prostate will spend at least 5% of the treatment fraction more than 4 mm from the expected location.1 These deviations from the setup position can affect the dosimetric outcomes of treatment, as it has been shown that motion of 5 mm can result in a 10% reduction of the 100% dose coverage.2 Although prostate motion is not always large enough to produce serious dosimetric impact, intrafraction motion monitoring can help avoid this possibility altogether. An additional consideration regarding intrafraction motion is the impact of this positional uncertainty on planning target 2558

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volume (PTV) margins. PTV margins must be made large enough to ensure that the prescribed dose to the clinical target volume (CTV) is maintained despite systematic and random variations in treatment delivery.3 However, smaller PTV margins are desirable in order to reduce the dose delivered to healthy tissue, particularly for nearby organs-at-risk (OARs). The widely used formula of van Herk et al.3 for calculating PTV margins contains terms for both systematic preparation errors and random variations throughout treatment. Thus, knowledge of intrafraction motion can be used to reduce PTV margins by accounting for a substantial component of random variance,4 for example, by gating treatment or dynamically updating couch5,6 or MLC positions.7–9 The impact of intrafraction motion is especially important to consider given the recent interest in hypofractionated radiotherapy of prostate tumors.10,11 Hypofractionation is an attractive option for prostate tumors because the generally accepted α/ β ratio of prostate tumors is low compared to

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the surrounding organs-at-risk,12 which allows for improved tumor cell kill with potentially fewer adverse effects. Whereas it is typically assumed that position deviations average out across fractions (i.e., contribute to random variation only),3 this assumption is invalid in hypofractionated treatment due to the small number of fractions. It is thus especially important to employ motion monitoring in hypofractionated treatment, in order to achieve the desired tumor control and OAR sparing. There are several techniques available for intrafraction motion monitoring, including implanted RF transponders,7,13,14 stereoscopic x-ray imaging,15–17 or monoscopic imaging.18–22 Stereoscopic techniques include kV/MV imaging using the on-board imager (OBI) and MV beam’s eye view,17 and roommounted dual16 or quad23,24 kV imaging. These techniques usually rely on implanted gold fiducial markers as prostate surrogates. Stereoscopic kV/MV imaging has the advantage of widespread availability; however, the fiducial markers can be obstructed in the MV images by movements of the MLC leaves, and the changing view-angle can result in variable fiducial overlap with other fiducials or bony anatomy. Room-mounted kV systems are not affected by MLC positions and provide a constant view angle, which makes it easier to ensure no overlap of fiducials. However, dual kV room-mounted systems frequently have one of their tube/detector pairs blocked by the gantry at certain angles as it rotates around the patient (Fig. 1). While this shortcoming is addressed by quad kV systems like that used by Shimizu et al.,23 these systems have not been widely adopted. The intermittent blocking of one x-ray tube/detector by the treatment head has presented a substantial challenge in the implementation of intrafraction motion monitoring with roommounted systems, as 3D location cannot be exactly determined from a single 2D image perspective. However, techniques for monoscopic localization of fiducial markers have recently been developed for OBI systems.19,22 While monoscopic imaging only provides absolute localization in two dimensions,

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correlations between prostate motion in the anterior–posterior and inferior–superior directions can be used in order to perform an informed estimate of the unresolved dimension. Although 3D position estimation from monoscopic imaging is naturally less accurate than stereoscopic localization, it can achieve submm accuracy,19 and therefore is a substantial improvement on no intrafraction monitoring. While monoscopic localization has been demonstrated for OBI systems, to our knowledge no studies have investigated the use of monoscopic localization for room-mounted kV systems. We therefore aim to demonstrate monoscopic localization using a room-mounted kV system. This technique alleviates the issue of restricted gantry angles, enabling uninterrupted intrafraction motion monitoring for room-mounted systems. In this work, we demonstrate the accuracy of the monoscopic and stereoscopic localization technique in phantom by comparison with a ground-truth trajectory and assess the extra dose delivered by the added kV imaging.

2. METHODS We evaluated monoscopic localization accuracy using a room-mounted dual kV imaging system. We identified three motion monitoring schemes: (1) full stereoscopic localization, (2) monoscopic localization (using either x-ray sources, see Fig. 1), and (3) no imaging. In all cases, the gantry was parked at zero degrees to prevent image obstruction, and monoscopic image series were created retrospectively. The no imaging scenario represents a worst case, as only the initial setup position is known. For each scheme, we evaluated the accuracy by comparison with prescribed phantom motion and determined the extra imaging dose delivered for the purpose of motion monitoring. 2.A. Motion phantom

A cylindrical gold fiducial marker (1 × 5 mm) was fixed between two layers of an anthropomorphic phantom (ATOM Dosimetry Phantoms, Norfolk, VA) at the approximate location of the prostate gland (Fig. 2). The phantom was placed on the treatment couch of the linear accelerator (Varian STx, Varian Medical Systems, Inc.), and the alignment lasers were used to place the fiducial marker initially at isocenter. The Linac couch was utilized as a programmable translation stage using Developer Mode, with real prostate motion trajectories implemented from published Calypso-based patient data.21 Five unique trajectories of approximately 1 min duration were implemented, including stable prostate position, slow drift, transient excursion, persistent excursion, and frequent excursions.21,22 For each motion trajectory, a log file of the couch positions produced by the Linac was collected as the ground-truth locations. F. 1. Gantry angle restrictions for our room-mounted stereoscopic imaging system. When the gantry angle is in the red-shaded zones, the treatment head blocks one of the two stereo x-ray panels (1 and 2) or sources (3 and 4). For the green-shaded angles, both panels have unobstructed views of isocenter. The exact angles available for stereo imaging will vary from setup to setup. Medical Physics, Vol. 43, No. 5, May 2016

2.B. Image acquisition and analysis

Monoscopic and stereoscopic x-ray imaging was performed using a room-mounted dual kV system (ExacTrac, Brainlab

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F. 2. Experimental setup: (a) A fiducial marker (x) was fixed between two slabs of the anthropomorphic phantom. The phantom also contained several inserts for optically stimulated luminescent dosimeters. (b) The phantom was placed on the Linac couch, which was used as a programmable translation stage, and the fiducial motion was imaged using the room-mounted x-ray system. The couch motion and image data were temporally coregistered using a microcomputer equipped with an accelerometer and two field diodes.

AG, Feldkirchen, Germany). This system consists of two xray sources embedded in the floor of the treatment room, and two ceiling mounted flat panel detectors, providing orthogonal oblique image projections with approximately 13.5 cm field of view at isocenter (Fig. 3). Continuous images were acquired at a rate of 1 Hz throughout each motion trajectory, resulting in 60 images per experiment. The xray tubes were set to deliver 0.63 mAs per acquisition at a tube potential of 140 kVp, to provide adequate fiducial contrast. The fiducial markers were automatically detected from the x-ray images using a maximum convolution approach.25,26 For this purpose, a 64 × 64 pixel convolution kernel was created with the central pixels set to 1, surrounded by a 1 pixel border with a negative value, determined such that the summed pixel value of the entire kernel is zero. When convolved with an image, this kernel thus produces zero for features much larger than the central kernel area, and maximal values for features the same size and orientation as this central region. To optimize the detection process, the angle and size of the fiducial marker in the two projections were determined from an initial image acquisition pair. As the acquisition geometry is constant for room-mounted systems, this projected shape is consistent from image to image. For each image projection, the Medical Physics, Vol. 43, No. 5, May 2016

point of maximum convolution was taken as the image location of the fiducial marker (i.e., [i 1, j1] and [i 2, j2] in Fig. 3). From the detected image locations of the fiducials, patient coordinates for the fiducial markers were computed via both stereoscopic and monoscopic approaches (see the Appendix for detailed calculations). In order to relate the fiducial locations determined by imaging to the known couch positions obtained from the Linac log file, a common temporal frame of reference is required. A custom microcomputer was built for this purpose (Fig. 2), which included an accelerometer to detect the couch motion, and two field diode inputs to monitor the x-ray output. Continuous recording from each of these three devices was performed throughout each motion monitoring experiment. With this system, the exact timing of image acquisition with respect to the motion trajectories was determined by coregistering the onset of movement in the accelerometer data to the Linac log file. The localization accuracy was assessed by the root-mean-square (RMS) localization error (averaged across all imaging time-points), using the Linac log file positions as ground-truth. Significance of accuracy differences was assessed using a paired t-test of the accuracy versus time for each localization method and trajectory.

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settings (0.63, 1.0, 1.2, and 1.6 mAs). The variance in the detected fiducial location across the 20 images was assessed for each mAs and gantry angle pairing. 3. RESULTS 3.A. Localization accuracy

F. 3. The x-ray imaging geometry is specified by the spherical coordinates of the image sources and detectors, parameterized by the polar angle “Θ,” azimuthal angle “Φ,” source to axis (isocenter) distance (SAD), and axis to detector distance (ADD). The image coordinate systems can be specified in terms of pixel locations ([i 1, j 1] and [i 2, j 2]) or mm relative to the projection of isocenter ([x im1, yim1] and [x im2, yim2], respectively). The above geometry is then used to convert image locations to patient or room coordinates ([x p , y p , z p ]).

2.C. Measurement of imaging dose

We assessed the dose associated with the additional kV images required for motion monitoring, as any additional patient dose represents an important consideration when adopting this technique. For this purpose, optically stimulated luminescent dosimeters (OSLDs, Landauer Nanodots, Chicago, IL) were placed in prefabricated inserts at various locations in the phantom slabs immediately above and below the fiducial marker [Fig. 2(a)]. The OSLDs were cross-calibrated against an ion chamber (Exradin A12, Standard Imaging, Middleton, WI) calibrated for the same kVp and half-value layer following TG-61. To achieve sufficient signal on the OSLDs, the phantom was exposed to 50 acquisitions from a single x-ray tube operating at 140 kVp and 40 mAs. The dose from the other tube and from stereoscopic acquisitions was then inferred by symmetry. 2.D. MV scatter

The experiments described above were performed with the MV treatment beam off, in order to exclude the influence of MV scatter on accuracy of fiducial detection in the images, and subsequently 3D localization. To ensure that the methods used are viable in situ, we evaluated reproducibility of the fiducial detection with the treatment beam on, using a 5 × 5 cm2 field and a dose rate of 500 MU/min. We tested the two worst-casescenarios for MV scatter: gantry at 180◦ (when the beam is most pointed toward the detectors) and 90◦ (where the lateral dimension of the patient creates the most scatter). For each gantry angle, we collected 20 images at four different kV mAs Medical Physics, Vol. 43, No. 5, May 2016

The results of motion monitoring using stereoscopic or monoscopic imaging are shown in Fig. 4 for the various classes of prostate motion. Stereoscopic imaging produced very accurate localization, with less than 0.4 mm RMS error for all five trajectories (Fig. 5). The highest RMS error for the stereoscopic localization was for the “persistent excursion” trajectory (0.34 ± 0.30 mm), for which there was a brief localization error around the time of the excursion. This error was the largest in the left–right direction, with a peak 3D mislocalization of 1.8 mm. In the trajectories with rapid prostate motion (e.g., frequent excursions), the imaging rate of 1 Hz can be insufficient to sample the full dynamics. While this typically only results in small interpolation errors, higher imaging frequency may be desirable. Monoscopic localization also produced sub-mm accuracy on average in 3D, in all but one case (tube 1, transient excursion trajectory). In this case, the RMS error was only marginally larger than 1 mm (1.1 ± 0.7 mm), largely due to an underestimation of the excursion amplitude around t = 41 s [Fig. 4(d)], and an overestimation of motion in the left–right direction at the same time. A similar underestimation of motion in the ant/post and sup/inf directions, accompanied by a mislocalization in the left/right direction was observed using tube 2 in the slow drift trajectory [Fig. 4(b)]. The largest error in monoscopic localization was approximately 4 mm (tube 1, transient excursion at 41 s), but still accounted for the majority of the relatively large (∼12 mm) and rapid (∼5 s) excursion at that point in the trajectory. In general, monoscopic imaging accurately detected most of the motion in all trajectories. For all trajectories, stereoscopic imaging produced significantly better localization accuracy than no imaging (p < 0.001). For monoscopic imaging, all but the stable prostate trajectory produced significantly better localization than no imaging (p < 0.001), with no difference in the case of the stable prostate. Stereoscopic localization was significantly more accurate than monoscopic at the p < 0.001 level except for the persistent excursion trajectory, which was only significant at p < 0.05 for monoscopic tube 2. While there were significant differences in the accuracy of the two views for monoscopic localization, the superior view varied between trajectories. 3.B. Imaging dose

The imaging dose per mAs delivered by a single xray tube is shown in Fig. 6 for a number of locations in the slab above and below the fiducial marker. The peak dose (15.3 ± 0.1 µGy/mAs) was observed at the posterior of the phantom, nearest to the beam entry point. Dose was significantly higher (p < 0.001) in the slab below the fiducial

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F. 4. Actual and reconstructed fiducial marker trajectories for a variety of prostate trajectories. Examples of (top to bottom) stable prostate, slow drift, persistent excursions, transient excursions, and high frequency excursions are shown.

(i.e., closer to the gantry), as the beams enter from this direction (see Fig. 3). The oblique orientation of the x-ray sources also causes the strong dose gradient in the anterior/posterior direction shown in Fig. 6. The protocol in this study used 0.63 mAs per image, resulting in 37% lower dose per image than what is shown in Fig. 6. This was the lowest mAs setting available on our x-ray system and produced sufficient image quality to identify the fiducial markers. During stereoscopic imaging, when both x-ray tubes are firing, the dose will be equivalent to about 1.26 mAs per image pair. The total dose delivered is proportional to the number of images acquired, which itself is the product of imaging frequency and fraction duration. Using 1 Hz imaging as in this study, a 3 min VMAT plan would result in a peak dose of 5.4 ± 0.1 mGy in the case of stereoscopic imaging (worst-case-scenario). Medical Physics, Vol. 43, No. 5, May 2016

3.C. MV scatter

With the MV beam on, it was necessary to increase the kV tube current in order to clearly resolve the fiducial in the images (Fig. 7). For kV tube current of 1.2 mAs or greater, the fiducial was detected in the images with perfect reproducibility. Although difficult to see in the raw images, scatter was more problematic with the gantry at 90◦ than 180◦, due to the thicker lateral dimension of the phantom. 4. DISCUSSION To our knowledge, this is the first report of monoscopic motion monitoring, with estimate of 3D position, using a room-mounted kV x-ray system. This avoids the most serious

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F. 5. Accuracy of the motion monitoring techniques. The 25th to 75th percentiles are indicated by the boxes, with the median error shown by the white lines. The whiskers end at the 5th and 95th percentiles, with outliers shown with circles. For the slowly moving prostates (stable, drift, and persistent excursions), the no imaging case results in large median errors, whereas for the prostates with rapid dynamics (transient and frequent excursions), the largest deviations appear as outliers. All three motion monitoring techniques accurately account for the majority of the prostate motion.

pitfall of motion monitoring using room-mounted systems, i.e., blocking of the x-ray tubes by the Linac treatment head. Both stereoscopic motion and monoscopic motion monitoring successfully reduced the intrafraction positional uncertainty for this simulated prostate treatment. Although by definition stereoscopic localization is capable of producing more accurate results, monoscopic localization was able to account for the majority of prostate motion, significantly reducing position uncertainty. The knowledge of actual prostate position throughout treatment can be used as feed-forward to dynamic MLC (Refs. 7–9) or couch position updates5,6 in order to increase the accuracy and conformality of dose delivery. Our monoscopic error localization errors ranged from 0.2 to 1.1 mm RMS, with a maximum of 3.8 mm. For comparison, stereoscopic localization errors ranged from 0.1 to 0.3 mm RMS, with a maximum of 1.8 mm. Previous studies using the same monoscopic localization algorithm for OBI imaging systems found approximately 0.35 mm RMS error, with a 3.6 mm maximum error.20 Using a dynamically updated probability density function (PDF), slightly smaller RMS error was Medical Physics, Vol. 43, No. 5, May 2016

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achievable (0.22 mm),20 depending on the prostate trajectory. A study by Poulsen et al.21 using the same prostate trajectories as in our study found a mean RMS error of 0.3–1.0 mm, with a maximum localization error of 2 mm. The main competitive technique is implanted electromagnetic transponders, with reported localization accuracy of 0.4–1.5 mm.1,7,13 Overall, the monoscopic localization accuracy of this study compares favorably with those reported previously in the literature, and the stereoscopic accuracy exceeds other available methods. The potential impact of the intrafraction monitoring on PTV margins (MPTV) can be estimated using the formula of van Herk et al.:3 MPTV = 2.5Σ + 0.7σ, where Σ and σ are the systematic and random setup variances respectively, including both inter√ fraction and intrafraction errors (e.g., σ = (σ2inter + σ2intra)). The potential margin reductions (∆M) afforded by resolving intrafraction motion are thus ∆M = 0.7(σ − σmonitored), where σmonitored includes interfraction random error, as well as the residual variance unaccounted √ for by intrafraction motion monitoring (i.e., σmonitored = (σ2inter + σ2residual)). Taking the value of σinter = (1.4 mm LR, 1.6 mm AP, 1.4 mm SI) for initial setup using fiducial marker surrogates from Tanyi et al.,4 the PTV margin reduction made possible by accounting for intrafraction motion ranges from negligible in the stable prostate case to (0, 1.5, 0.6 mm) in the case of the persistent excursion. For the four relatively dynamic prostate trajectories investigated, there was no difference between the margin reduction for monoscopic (0, 1.1, 0.5 mm) and stereoscopic (0, 1.2, 0.5 mm) motion monitoring on average. Importantly, the largest margin reduction was observed in the AP direction, which is the direction of one of the principal OARs for prostate treatment—the rectal wall. These margin reductions would need to be facilitated by either restrictive motion gating tolerances or (preferably) highly accurate tracking mechanisms, such as the dynamic MLC system proposed by Poulsen et al.8 There are several inherent advantages of the room-mounted x-ray system compared to the OBI. With the room-mounted system, a pretreatment imaging period (i.e., with the gantry parked at vertical) can be used to build a patient-specific PDF under the same geometry as will be used for monitoring. This direct measurement of motion variance/covariance is more efficient than the alternative probabilistic techniques needed in the OBI case.20 Furthermore, there is also no sag or flex corrections needed to compensate for the change in isocenter/imager relationships as the gantry rotates. Finally, the constant view angle simplifies the problem of detecting the fiducial markers in the images, as there is no change in the projection geometry, and likewise no substantial changes in fiducial overlap with other fiducials or with background anatomy. While both of these fiducial detection issues can be overcome via sophisticated detection strategies [e.g., see the work of Feldelius et al. 2011 (Ref. 27) and 2014 (Ref. 28)], the added complexities will reduce overall sensitivity/specificity of detection. An additional consideration regarding imaging geometry is that not all motions are equally important from a dosimetric perspective. Due to the rapid fall off of typical beam profiles,

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F. 6. Dose per mAs at the locations of the OSLD dosimeters in the phantom slabs above (a) and below (b) the fiducial marker. Peak dose was observed at the posterior aspect of the phantom in the slice below the fiducial marker (i.e., closer to the gantry), due to the beam entry angle.

motion perpendicular to the beam’s-eye-view (BEV) is more detrimental to target coverage than motion along the BEV.29,30 In the case of OBI imaging, motion along the BEV is always resolved directly, whereas one of the axes perpendicular to BEV is not directly observable. In the case of the roommounted geometry, the monoscopic image plane is at an angle to the BEV, such that both perpendicular axes are partially resolved. Alternatively, in-line or BEV imaging in theory is capable of resolving all off-axis motion directly, but suffers from MLC blockage and poor MV image contrast. A potentially useful development is in-line kilovoltage imaging;31,32 however, in order to achieve the desired energy spectrum, special Linac targets must be used, preventing this technique from being employed during treatment. We are currently investigating a rapidly switching target system to overcome this issue,33 with one of the potential applications being intrafraction imaging. It is worth pointing out that for each trajectory, the localization method with the highest error represents a worst-case-scenario. In practice, gantry rotation during the treatment fraction would necessitate toggling the tube used for monoscopic imaging as the treatment head rotates (i.e., quadrants 1 and 3 versus 2 and 4 in Fig. 1), and indeed would allow for periods of stereoscopic monitoring around each of the cardinal angles. Thus the accuracy obtained in a realistic implementation would be somewhere in the middle of the range shown in Fig. 6. The added information afforded by the intermittent stereoscopic imaging opportunities could potentially be used to improve the monoscopic localization model and should be investigated in future studies. Medical Physics, Vol. 43, No. 5, May 2016

In general, the monoscopic localization technique was highly accurate in the sup/inf and ant/post directions, with the largest errors occurring in the lateral direction. This result is likely due to a combination of two factors: (1) motion in the left/right directions is much less correlated with the other two dimensions and is thus less certain to infer from the 2D measurement, and (2) the geometry of the room-mounted imaging system is such that (unlike the lab-frame covariance matrix), the rotated covariance matrix has no near-zero entries. Because of this latter point, variance in the sup/inf and ant/post directions tends to get projected somewhat into the lateral dimension. The added dose to patients of approximately 5 mGy per fraction is low in the context of a typical 2 Gy fraction. Over the course of a typically fractionated treatment, this could add up to as much as 20 cGy, or 10% of a single fraction dose, assuming conventional fractionation. This result is comparable to previous estimates of 10–15 cGy from 1 Hz imaging over the course of a VMAT treatment using OBI imaging.34 The only published data on ExacTrac imaging dose available estimate 0.551 mGy entrance dose per image at 140 kVp and 15 mAs,35 or equivalently 37 µGy/mAs. This is about 2.5 times our observed dose at the depth of the rectum, which is consistent with the PDD at this depth and energy.36 Any increase in the image rate or treatment time changes to the imaging technique (kVp or mAs), or added pretreatment imaging can increase the imaging dose. However, in hypofractionated treatment, the total treatment time is typically reduced, which lowers the relative contribution of imaging dose for a fixed image frequency.34 Thus hypofractionated regimens are not only the best candidate for prostate motion

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F. 7. Reproducibility of fiducial detection in the presence of MV scatter, for gantry angles of (a) 90◦ and (b) 180◦. A small ROI of representative raw images around the fiducial marker is shown in the top rows of (a) and (b). The mean ± standard deviation of the detected fiducial location (x i , yi ) was determined from 20 replications of the images at each of four tube current levels (bottom rows). At 0.63 mAs, the fiducials are obscured by the MV scatter contribution, resulting in unreliable fiducial detection. For 1.2 mAs or higher, the fiducial is reliably detected at both gantry angles.

monitoring, but benefit the most from the added localization certainty. In this study, we initially ignored the influence of MV scatter on image quality, and subsequently on the accuracy of fiducial detection and localization. It has previously been shown for OBI imaging that accurate fiducial detection is achievable even at high MV dose rates,27,28 and the increased isocenter-to-detector distance of the ceiling mounted panels should further reduce the added scatter noise. Nonetheless, the presence of MV scatter noise necessitated increased mAs to maintain adequate image quality. Our results suggest that tube current of approximately 1.2 mAs would produce sufficient image quality for typical MV dose rates and field Medical Physics, Vol. 43, No. 5, May 2016

sizes. While this would approximately double the imaging dose, the result would still only represent 0.5% of a typical treatment fraction and could in principle be accounted for during treatment planning. Additionally, the dose estimates above were produced using the conservative assumption of constant stereoscopic imaging, which in practice would be reduced by almost half given the large range of gantry angles for which monoscopic imaging would be used. A more sophisticated approach would be to modulate the kV imaging technique as a function of gantry angle and (MLC-modulated) field size in order to provide constant image quality while minimizing accumulated dose, but this is outside the scope of this paper.

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and d2 = [x d2, y d 2,z d2] respectively). For example, for the first detector,  x  im1 d1 = R · [(p1 − po1) ◦ dp] + do1 = R ·  yim1  0 

F. 8. Illustration of (a) stereoscopic and (b) monoscopic localization schemes employed (shown in 2D for simplicity of illustration). Stereoscopic localization finds the intersection point (black circle) of the ray lines connecting the detected image locations (i 1,i 2) of the fiducials (grey filled circles) with the corresponding source locations (s1 and s2, respectively). Monoscopic localization finds the maximum likelihood position (black circle) along the single ray line connecting the detected image location and source point using a PDF derived from the motion covariances (P x, y ). Monolocalization and stereolocalization modes can be toggled in real time depending on which imaging panels have an unobstructed view of the fiducial markers.

5. CONCLUSION We have implemented both stereoscopic and monoscopic motion monitorings using a room-mounted kV imaging system. The availability of both localization modes allows continuous 3D localization despite the wide range of angles over which the treatment head may obstruct one of the xray tubes and detectors. The motion monitoring accuracy rivals that available with other published methods and is superior when stereoscopic views are available. Accurate intrafraction prostate localization is especially beneficial for hypofractionated treatment where movement of the target volume can have critical dosimetric impact.

ACKNOWLEDGMENTS The authors would like to acknowledge financial support from Varian Medical Systems and technical support from Brainlab AG. Lee MacDonald provided guidance on using developer mode for driving motion trajectories and Dr. Mike Sattarivand who contributed details on the geometry of their specific ExacTrac system setup. The authors also recognize valuable contribution from machinist John Noddin for creating the custom OSLD inserts for their phantom experiments.

APPENDIX: LOCALIZATION CALCULATIONS 1. Stereoscopic localization

To find patient coordinates (r = [x p , y p ,z p ]) of the fiducial marker using stereoscopic localization (rstereo), the method of Brost et al.15 is followed. Using the geometry shown in Fig. 3, the image locations (p1 = [i 1, j1,0] and p2 = [i 2, j2,0], in pixels) are first converted to room coordinates (d1 = [x d1, y d 1,z d1] Medical Physics, Vol. 43, No. 5, May 2016

   + do1,  

(A1)

where R is the rotation matrix that aligns unit vectors in the detector plane with the room coordinate system (see Fig. 3), po1 = [i o1, j o1,0] is the pixel coordinates of the projected isocenter, dp = [dx,d y,0] is the vector of pixel dimensions, and do1 = [x o1, y o1,z o1] are the room coordinate for the projected isocenter (i.e., ADD∗[cos Θ cos Φ, cos Θ sin Φ, cos Θ]). Points (r1 = [x p 1, y p 1,z p 1]) on the line connecting the detected point with the source location (s1 = [x s1, y s 1,z s1] = SAD∗[−cos Θ cos Φ, −cos Θ sin Φ, −cos Θ]) can then be parameterized as r1 = d1 + m1 (s1 − d1) = d1 + m1a1,

(A2)

where m1 governs the distance along the ray line from the detector. Likewise for the line connecting the second detector and source, r2 = d2 + m2a2.

(A3)

The location of the fiducial marker is the point at which these two lines intersect (Fig. 8), and thus d1 + m1a1 = d2 + m2a2

(A4)

or equivalently  m  1  d = A ·  , −m2

(A5)

where d = d2 − d1 and A = [a1,a2]. In practice the two ray lines will not intersect perfectly due to finite measurement precision; however, an approximate solution to
this equation is given by finding the pseudo-inverse for A A† , A† = AT · A


−1

· AT,

(A6)

yielding  m   1  = A†d. −m2

(A7)

The values of m1 and m2 are then used to estimate the two (ideally equivalent) world points (r1 and r2), and the mean of these is used as the final stereoscopic localization rstereo. 2. Monoscopic localization

The algorithm employed for 3D localization from monoscopic imaging relies on a priori information in the form of motion covariances “C” (Fig. 8), which can be obtained directly from stereoscopic localization pretreatment, or from

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published population averages,19  var cov x y cov x z  x  C = cov x y var y cov y z   cov cov y z varz  xz   0.3163 −0.0775 0.0114   = −0.0775 2.4733 1.5051 mm2.  0.0114 1.5051 1.8820 

(A8)

This covariance matrix can be used to determine a Gaussian PDF for the fiducial locations (P(x, y,z)),  det(C−1) −rTC−1r/2 e (A9) P(x, y,z) = 8π 3 or in the coordinate system rotated to be parallel to the image plane,  det(C−1) −rT R−1C−1Rrrot/2 Prot(x rot, yrot,zrot) = e rot . (A10) 8π 3 Identifying the matrix elements of the rotated covariance as  A  rot R−1C−1R =  Drot/2  E /2  rot

Drot/2 Brot Frot/2

Erot/2 Frot/2  . Crot 

(A11)

Poulsen et al.19 showed that the expectation value for the position along the axis perpendicular to the imaging plane (⟨zrot⟩) is  ( y )2 ( x )2 x im yim im im ⟨zrot⟩ = SAD Arot + Brot + Drot SDD SDD SDD2  x im yim − Erot − Frot σ 2, (A12) 2 · SDD 2 · SDD where SDD is the source-to-detector distance (i.e., SDD = SAD + ADD) and σ is the standard deviation,  ( x )2 ( y )2 im im σ = Arot + Brot +Crot SDD SDD  −1/2 x im x im yim yim + Drot − E − F . (A13) rot rot SDD SDD SDD2 By appropriately scaling the image coordinates ([x im, yim]) according to zrot, we obtain the (rotated) 3D location of the fiducial marker (rrot = [x rot, yrot,zrot]), x rot = x im (SAD − zrot)/(SAD + ADD), yrot = yim (SAD − zrot)/(SAD + ADD).

(A14) (A15)

Finally, the monoscopic localization coordinates (rmono) are obtained by applying the rotation matrix (i.e., rmono = R · rrot).

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