Three-dimensional liver motion tracking using real-time two-dimensional MRI Lau Brix, Steffen Ringgaard, Thomas Sangild Sørensen, and Per Rugaard Poulsen Citation: Medical Physics 41, 042302 (2014); doi: 10.1118/1.4867859 View online: http://dx.doi.org/10.1118/1.4867859 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/41/4?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in A new method for tracking organ motion on diagnostic ultrasound images Med. Phys. 41, 092901 (2014); 10.1118/1.4892065 4D tumor centroid tracking using orthogonal 2D dynamic MRI: Implications for radiotherapy planning Med. Phys. 40, 091712 (2013); 10.1118/1.4818656 Real-time automatic fiducial marker tracking in low contrast cine-MV images Med. Phys. 40, 011715 (2013); 10.1118/1.4771931 Four-dimensional dose distributions of step-and-shoot IMRT delivered with real-time tumor tracking for patients with irregular breathing: Constant dose rate vs dose rate regulation Med. Phys. 39, 5557 (2012); 10.1118/1.4745562 Adapting liver motion models using a navigator channel technique Med. Phys. 36, 1061 (2009); 10.1118/1.3077923
Three-dimensional liver motion tracking using real-time two-dimensional MRI Lau Brixa) Department of Procurement and Clinical Engineering, Region Midt, Olof Palmes Allé 15, 8200 Aarhus N, Denmark and MR Research Centre, Aarhus University Hospital, Skejby, Brendstrupgaardsvej 100, 8200 Aarhus N, Denmark
Steffen Ringgaard MR Research Centre, Aarhus University Hospital, Skejby, Brendstrupgaardsvej 100, 8200 Aarhus N, Denmark
Thomas Sangild Sørensen Department of Computer Science, Aarhus University, Aabogade 34, 8200 Aarhus N, Denmark and Department of Clinical Medicine, Aarhus University, Brendstrupgaardsvej 100, 8200 Aarhus N, Denmark
Per Rugaard Poulsen Department of Clinical Medicine, Aarhus University, Brendstrupgaardsvej 100, 8200 Aarhus N, Denmark and Department of Oncology, Aarhus University Hospital, Nørrebrogade 44, 8000 Aarhus C, Denmark
(Received 11 October 2013; revised 17 February 2014; accepted for publication 20 February 2014; published 14 March 2014) Purpose: Combined magnetic resonance imaging (MRI) systems and linear accelerators for radiotherapy (MR-Linacs) are currently under development. MRI is noninvasive and nonionizing and can produce images with high soft tissue contrast. However, new tracking methods are required to obtain fast real-time spatial target localization. This study develops and evaluates a method for tracking three-dimensional (3D) respiratory liver motion in two-dimensional (2D) real-time MRI image series with high temporal and spatial resolution. Methods: The proposed method for 3D tracking in 2D real-time MRI series has three steps: (1) Recording of a 3D MRI scan and selection of a blood vessel (or tumor) structure to be tracked in subsequent 2D MRI series. (2) Generation of a library of 2D image templates oriented parallel to the 2D MRI image series by reslicing and resampling the 3D MRI scan. (3) 3D tracking of the selected structure in each real-time 2D image by finding the template and template position that yield the highest normalized cross correlation coefficient with the image. Since the tracked structure has a known 3D position relative to each template, the selection and 2D localization of a specific template translates into quantification of both the through-plane and in-plane position of the structure. As a proof of principle, 3D tracking of liver blood vessel structures was performed in five healthy volunteers in two 5.4 Hz axial, sagittal, and coronal real-time 2D MRI series of 30 s duration. In each 2D MRI series, the 3D localization was carried out twice, using nonoverlapping template libraries, which resulted in a total of 12 estimated 3D trajectories per volunteer. Validation tests carried out to support the tracking algorithm included quantification of the breathing induced 3D liver motion and liver motion directionality for the volunteers, and comparison of 2D MRI estimated positions of a structure in a watermelon with the actual positions. Results: Axial, sagittal, and coronal 2D MRI series yielded 3D respiratory motion curves for all volunteers. The motion directionality and amplitude were very similar when measured directly as in-plane motion or estimated indirectly as through-plane motion. The mean peak-to-peak breathing amplitude was 1.6 mm (left-right), 11.0 mm (craniocaudal), and 2.5 mm (anterior-posterior). The position of the watermelon structure was estimated in 2D MRI images with a root-mean-square error of 0.52 mm (in-plane) and 0.87 mm (through-plane). Conclusions: A method for 3D tracking in 2D MRI series was developed and demonstrated for liver tracking in volunteers. The method would allow real-time 3D localization with integrated MR-Linac systems. © 2014 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4867859] Key words: MR-Linac, real-time MRI, organ motion, vessel tracking, MRI 1. INTRODUCTION Precise treatment delivery is crucial in radiotherapy in order to maximize the therapeutic ratio between tumor dose and 042302-1
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normal tissue dose. Optimally, a mobile tumor and the surrounding normal tissue should be imaged during treatment delivery to ensure correct treatment delivery. This has motivated substantial research activities in developing methods
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© 2014 Am. Assoc. Phys. Med.
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for tumor motion monitoring and compensation during radiotherapy delivery.1–3 Several research groups are integrating radiotherapy treatment units with magnetic resonance imaging (MRI),4–6 and these efforts have recently lead to the first phantom studies demonstrating MRI-guided real-time motion adaptation during treatment delivery.7, 8 MRI is attractive for tumor and organ motion monitoring as it gives high contrast volumetric imaging of soft tissue without the use of ionizing radiation. However, current MRI technology does not allow real-time acquisition and reconstruction of three-dimensional (3D) volumes at sufficiently high spatial and temporal resolution for monitoring respiratory motion. Proposed techniques to overcome this include one-dimensional (1D) imaging by means of a pencil-beam navigator, which can be placed either directly on the tracked target7, 9 or on the diaphragm to function as a target position surrogate.10 It gives very fast imaging, but only in 1D, and the observed 1D motion may not represent the actual organ motion component in the navigator direction, as the apparent motion could be a result of organ motion perpendicular to the navigator. More spatial information is obtained by two-dimensional (2D) MRI (Refs. 8 and 11–13) where current clinical MRI systems allow for real-time image acquisition and reconstruction with frame rates of up to 10 Hz.14–16 Similar to 1D MRI, full 3D motion information is missing and cautious interpretation of observed motion in 2D MRI is needed since through-plane motion perpendicular to the image plane may result in apparent in-plane motion. Nevertheless, previous 2D MRI motion studies have often neglected the through-plane motion,17–23 which may be justified if the through-plane motion is expected to be small such as in sagittal 2D MRI of the liver. Cervino et al. suggested to address through-plane motion in 2D MRI of the lung by using the diaphragm as a surrogate for the (in-plane) position of a target when it moves outside the imaged 2D plane.11 Ries et al. demonstrated 3D tracking in 2D MRI by continuous shifts of the 2D image plane to follow the through-plane target motion, which was estimated by a perpendicular pencil beam navigator.24 3D tracking may also be obtained by alternating between sagittal and coronal 2D imaging combined with template based segmentation of anatomical structures in both 2D image sets.12, 13 This strategy has been demonstrated for retrospective tracking of lung structures using 2D templates cropped from arbitrarily selected sagittal and coronal 2D reference images13 as well as kidney tracking using 3D templates obtained from a breath-hold 3D MRI scan.12 These studies had relatively low frame rates of 2 Hz and the use of alternating orthogonal image planes results in dark saturation stripes at the intersection between the image planes. In this study, we develop and evaluate a new method for 3D motion tracking in 2D real-time MRI series. The method estimates the 3D position of a tracked anatomical structure for each 2D MRI image. As a first application we demonstrate the method for 3D tracking of blood vessel structures in axial, sagittal, and coronal 2D MRI images of the liver. The blood vessels could function as reliable landmarks or surrogates to determine the position of MR invisible tumors in cancer patients. Medical Physics, Vol. 41, No. 4, April 2014
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2. METHODS AND MATERIALS 2.A. Data dimensions
Throughout this paper, 2D and 3D refer to the number of spatial dimensions. All 2D images were acquired and reconstructed continuously and a temporal dimension is therefore present as well. While the 3D volume scans do not have a temporal dimension, 3D tracking implicitly denotes tracking of 3D motion over time.
2.B. Method for 3D motion tracking in 2D MRI images
Assume that a 2D MRI series is acquired in the fixed spatial position denoted Location 0 in Fig. 1. An observed motion of the left-most blood vessel in the MRI series could either be due to pure in-plane motion in the XY-plane, pure throughplane motion in the Z direction, or a combination of these motions. There is no way to discriminate between these options by monitoring a single traversing blood vessel alone. However, since the relative positions of several nonparallel blood vessels change with through-plane motion (Fig. 1, right), the observed pattern of blood vessels can be used as a fingerprint to determine the through-plane position, thereby discriminating between in-plane and through-plane motion. The proposed 3D tracking method has three steps as illustrated in Fig. 2. First, a 3D volumetric scan of the liver is obtained, and the blood vessel structure (or tumor) to be tracked is determined [dot in Fig. 2(a)]. Second, the 3D volume is resliced and resampled to generate a series of 2D slices with the same orientation, slice thickness and pixel size as in the later acquired real-time 2D MRI image series. A library of 2D templates [black rectangles in Fig. 2(b)] with well-defined 3D positions relative to the tracked structure is formed by cutting segments of identical sizes and in-plane locations from each of the 2D slices. Third, the templates of the library are used for template-based segmentation in the real-time 2D MRI series. In each 2D real-time MRI image, the normalized cross correlation between the image and a suitable range of templates in the library is calculated for a range of 2D positions in the
F IG . 1. Schematic 3D view of liver blood vessels (left) and their appearance in four parallel 2D MRI planes (right).
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F IG . 2. Flowchart for 3D tracking of a liver blood vessel structure (dot) in 2D MRI series, illustrating tracking in axial slices. A 3D scan (a) is used to create a library of templates [black rectangles in (b)] for template based segmentation in real-time 2D images (c).
image. The template and 2D position that yield the highest cross correlation coefficient are selected. Since each template has a known 3D position relative to the tracked structure, the selection and 2D localization of a specific template translates into quantification of both the through-plane and in-plane position of the structure. 2.C. Volunteers and MR image acquisition
Five healthy volunteers with a mean age of 42.6 years (range: 26–64 years) were included in the study. The experiments were carried out on a Siemens Avanto 1.5 T MRI scanner (Siemens, Erlangen, Germany, software release VB17a) using a 32 channel cardiac receiver coil. First, a 3D volumetric MRI scan (3D prescan) was obtained during free breathing using a navigator situated on the left diaphragm dome for respiratory motion compensation. Data were sampled during expiration with an 8 mm navigator window. The protocol was set up to exhibit the same type of contrast as in subsequent 2D real-time image series. The 3D sequence was a True Fast Imaging with Steady State Precession (TrueFISP) 3D single-shot sequence (TR = 3.52 ms, TE = 1.54 ms, field of view = 300 mm, matrix size = 192 × 192, image resolution = 1.56 × 1.56 × 1.60 mm3 , flip angle = 80◦ , 80 sagittal slices, total scan time ≈4 min including the navigator). To speed up the data acquisition, parallel imaging was applied using the GRAPPA reconstruction technique25 at an undersampling factor of 2. The 3D images were reconstructed using the reconstruction system provided by Siemens. Next, a real-time 2D protocol was used to acquire and reconstruct data during free breathing in the axial, coronal, and sagittal planes. To cover approximately the same volume as the 3D volume scan, the liver was imaged sequentially using 7 mm gaps between consecutive 2D series. Each slice location was imaged for 30 s to capture several respiratory cycles. The real-time 2D scan was a dynamic TrueFISP 2D single-shot Medical Physics, Vol. 41, No. 4, April 2014
sequence (TR = 2.82–2.88 ms, TE = 1.41–1.44 ms, field of view = 300–319 mm, matrix size = 192 × 192, in-plane resolution = (1.56 × 1.56)–(1.67 × 1.67) mm2 , slice thickness = 8 mm, flip angle = 45◦ , GRAPPA factor = 3, scan time = 184 ms per image [5.4 images per second]). All 2D images were reconstructed using the Gadgetron software package, which is an open source framework for medical imaging reconstruction.26 The reconstruction was carried out in realR FX8120 8time on an external workstation with an AMD R core processor and a NVIDIA GTX-580 Graphics Processing Unit. The Interactive Front End provided by Siemens was used for interactive real-time control of the image planes during scanning. Whenever the position or orientation of the 2D slices were altered, the first few images appeared aliased until enough data were buffered to calculate the parallel imaging coefficients needed for the GRAPPA reconstruction. These distorted images were removed before further analysis. After acquisition of the 2D real-time image series a second 3D volumetric MRI scan (3D postscan) was acquired with the same settings as the 3D prescan, with the purpose of detecting possible liver deformations and shifts during the time course of the examination. 2.D. Demonstration of the 3D tracking method
As a proof of principle, the proposed tracking method was demonstrated off-line after image acquisition using in-house built software (Matlab, R2012b, Mathworks, Natick, MA). For each of the five volunteers, characteristic liver blood vessel structures were first selected in the 3D prescan MR volume and then tracked in subsequent real-time 2D image series by the proposed method. The tracking was performed in two different axial, sagittal, and coronal 2D MRI series located reasonably close to the selected structures. In each of the six 2D series, 3D tracking was performed with two different, nonoverlapping template libraries, resulting in 12 respiratory
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3D motion trajectories of 30 s per volunteer. For each trajectory, the maximum and mean breathing peak-to-peak amplitude was calculated using six consecutive breathing cycles. The tracking resolution was one 2D pixel length for the inplane localization (1.56–1.67 mm) and one 3D voxel length for the through-plane localization (1.56 mm for axial and coronal 2D series, 1.6 mm for sagittal series). 2.E. In vitro validation of the 3D tracking method
To investigate the accuracy of the 3D tracking method for a rigid system without deformations, a 3D prescan and subsequent real-time 2D MRI scans were acquired in a watermelon using the same scanning parameters and off-line analysis as for the liver scans. The watermelon was placed on a platform that was manually moved stepwise in the craniocaudal (CC) direction by adding plastic spacers of known thickness between the platform side and a fixed support. The 2D MRI series were acquired with axial, coronal, and sagittal orientations for nine CC positions of the watermelon spanning a range of 17 mm. The MRI contrast between heterogeneously distributed air cavities and the pulp of the watermelon was used for 3D tracking in the same way as the blood vessels in the liver parenchyma. Since the watermelon air cavities were less unique than liver blood vessels as fingerprints for the through-plane position, approximated 50% larger templates were used for the watermelon than for the liver to ensure robust tracking. The CC positions estimated by 2D MRI were compared with the actual CC positions. 2.F. Liver deformations
The through-plane localization of the tracked liver vessel structure assumes that the structure remains at the same distance from the currently imaged 2D liver slice as it had during the 3D prescan. Thus, liver deformations were assumed to be neglectable on a length scale of up to a few cm. This assumption was tested in the current MRI data sets in two ways. First, possible liver deformations and shifts between the 3D preand postscans were investigated. In each volunteer, a square region of 40 × 40 pixels was selected in 40 consecutive sagittal slices of the 3D prescan, covering a total liver volume of 62 × 62 × 64 mm3 . Each of the 40 squares were subdivided into four adjacent 20 × 20 pixel templates, yielding a total of 160 subvolumes of size 31 × 31 × 1.6 mm3 that were all located completely within the liver and contained characteristic blood vessel structures. Each subvolume was then used as the template in a template based search in the 3D postscan performed with the same computer program as used for 3D tracking in the 2D image series. This analysis yielded the 3D shifts of each of the 160 subvolumes between the 3D prescan and postscan. The mean and standard deviations of the subvolume shifts were calculated as measures of the shift and deformation of the liver, respectively. The assumption of rigidity was further investigated in relation to possible breathing induced deformations in a sagittal real-time 2D image series in each of the five volunteers. In the first frame of the series, four regions of 15 × 15 pixel (23 × 23 Medical Physics, Vol. 41, No. 4, April 2014
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mm2 ) with recognizable blood vessel structures were selected such that they constituted two pairs with at least 40 pixel (62 mm) separations in the CC direction and in the anterioposterior (AP) direction, respectively. The four regions in the first frame were used as templates for segmentation of the structures in all frames of the 2D series. The breathing motion and mean breathing amplitudes were compared between the four regions as a measure of the breathing induced deformations across a length scale of approximately 6 cm.
2.G. Validity of the 3D liver tracking
Since the true motion of the tracked vessel structure is unknown, a series of analyses were performed to indirectly assess the validity of the 3D tracking method. Liver motion is normally largest in the CC direction with a smaller motion component in the AP direction and even less motion in the left-right (LR) direction.27, 28 Typically, there is a strong correlation between CC and AP motion such that the caudal motion seen during inspiration is associated with a simultaneous anterior motion. As a result, there is a preferred motion directionality in the sagittal plane, which has been shown to be relatively stable over time for a given point in a given individual.29 To determine this directionality for each volunteer the motion of the four 15 × 15 pixels regions tracked in the sagittal plane (see Sec. 2.F) was analyzed by principal component analysis. The first principal component (1st PC) of the combined motion of the four regions was calculated and assumed to represent the overall sagittal plane liver motion directionality of the volunteer. In order to investigate how well the 3D motion estimated from 2D image series agreed with the directionality obtained in a single sagittal slice plane, the angular deviation between the overall liver motion directionality and the 1st PC of the estimated 3D motion in the 2D data sets was determined for each 2D image orientation for each volunteer. The through-plane motion was expected to be largest in the axial 2D image series, where it corresponded to CC motion. For each volunteer, the agreement between the estimated through-plane motion at the two nonoverlapping template locations in the axial plane (anterior and posterior locations) was quantified as the root-mean-square (RMS) difference and as the difference in mean peak-to-peak breathing motion amplitude for six subsequent breathing cycles. These differences should be zero if the liver moved as a rigid body. However, if the anterior part of the liver moved differently from the posterior part the estimated through-plane motions of the two template locations should also be different. Therefore, the difference in estimated through-plane motion amplitude was compared with the amplitude difference measured between the anterior and the posterior 15 × 15 pixels regions in the sagittal plane (See Sec. 2.F).
3. RESULTS The CC position of the watermelon structure was estimated with root-mean-square errors of 0.86 mm (axial MRI),
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F IG . 3. Scatter plots of the actual CC position of a watermelon structure versus the CC position estimated in 2D MRI images with axial (diamonds), coronal (circles), and sagittal (crosses) slice orientations. The unity line illustrates perfect position estimation.
0.44 mm (coronal MRI), and 0.59 mm (sagittal MRI) in 2D MRI series by the 3D tracking method (Fig. 3). For all five volunteers, the 3D prescan and postscan MRI volumes and 2D real-time MRI series were successfully acquired, reconstructed, and visualized. The axial and sagittal 2D images had similar image quality and contrast as the 3D scans, while the coronal images had a lower signal-to-noise ratio (SNR). Nevertheless, all three slice orientations exhibited image qualities sufficient for 3D motion tracking. For each volunteer and slice orientation, two 2D MRI series were selected for 3D tracking. The mean width and height of the templates used for tracking were 45 mm (range: 30–61 mm) and 41 mm (range: 31–53 mm), respectively, while the mean area was 1854 mm2 (range: 872–3008 mm2 ). Figure 4 shows examples of 2D liver MRI images, with matching templates and resulting 3D position estimations of the tracked structure in extreme breathing phases for the subject exhibiting the largest breathing motion (Volunteer 2). Figure 5 presents 3D motion curves of a blood vessel structure in axial, coronal, and sagittal image series for Volunteers 1 and 2. In general, the estimated 3D motion was largest in the CC direction, and it was of similar magnitude independent of the 2D image orientation (Fig. 5 and Table I). For Volunteer 1, the exhale position of the tracked structure stayed close to its position in the 3D prescan [(0,0,0) in Fig. 5], whereas Volunteer 2 had a large baseline shift of 13.4 mm (LR), −12.6 mm (CC), and 0.5 mm (AP) [Fig. 5(b)]. The comparison with the 3D postscan [Fig. 5(b), right] showed that this was a true systematic shift of the volunteer, which was thus detected correctly by the 3D tracking method in all three 2D image orientations. Volunteer 2 was the only subject with a substantial shift between the two 3D scans: The mean shifts of the other four volunteers between the 3D prescan and postscan was below 2 pixels in all directions with absolute mean shift averages of 1.9 mm (CC), Medical Physics, Vol. 41, No. 4, April 2014
F IG . 4. Examples of (a) axial, (b) coronal, and (c) sagittal 2D MRI images in maximum expiration (left) and inspiration (right) for Volunteer 2. Each figure shows the template selected from the library (inset), the segmented position of this template (white rectangle), and the resulting absolute 3D position estimation of the tracked structure in millimeter.
1.7 mm (AP), and 0.5 mm (LR). Volunteer 2 was also the only subject with a tendency of deformations between the two (exhale) 3D scans, i.e., systematic differential shifts of the 160 subvolumes, between the two volume scans. Here, the CC shift depended on the lateral position and was on average 2.1 mm larger for the 40 most right-lateral subvolumes compared to the 40 most medial subvolumes. The average standard deviation of the subvolume shifts for all five volunteers was 1.0 mm (CC), 0.6 mm (AP), and 0.8 mm (LR). Regarding breathing induced deformations, segmentation of the four 15 × 15 pixels regions in sagittal real-time 2D image series showed that the mean CC breathing motion amplitude was invariably larger (2.3–3.3 mm) for the cranial region than for the caudal region. There was no systematic trend for the AP region pair as the mean CC motion amplitude was largest for the anterior region for some volunteers (up to 2.3 mm) and largest for the posterior region for others (up to 2.0 mm) (mean difference = 0.3 mm). These results show that breathing induced CC liver deformations of up to 3.3 mm over distances of approximately 6 cm in the included group of volunteers. For all volunteers, the 1st PC of the four regions tracked in the sagittal plane was in the cranial direction with inclinations between 8.9◦ and 21.1◦ towards the posterior direction (black arrows in Fig. 6). The mean absolute deviation between this direction and the 1st PC of the 3D motion as estimated from the 2D data sets (remaining arrows in Fig. 6) was
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F IG . 5. Time resolved position of tracked blood vessel structure in LR, CC, and AP directions estimated for Volunteers 1 and 2 in axial, coronal and sagittal 2D image series. The positions are shown relative to the structure location in the 3D prescan MRI volume. The horizontal lines to the right depict the structure location in the 3D postscan MRI volume. The time stamps indicate the time since the 3D prescan. In-plane and through-plane motion are shown with dotted and solid curves, respectively.
3.0◦ (±2.0◦ , 1 standard deviation) (axial series), 1.5◦ (±1.6◦ ) (sagittal slices), and 2.9◦ (±2.0◦ ) (coronal slices). The RMS difference between the CC through-plane motion estimated from two nonoverlapping templates in the same 2D axial series had a mean value of 2.0 mm (range: 1.3–3.2 mm) and it exceeded 2 mm only for Volunteer 2. Figure 7 shows the estimated through-plane motion and template locations for a case with RMS difference close to the mean value and for the case with highest RMS difference. Figure 8 compares the CC breathing amplitude difference between the posterior and anterior template locations in the axial series with the CC amplitude difference between posterior and anterior liver parts as measured directly in-plane by
region tracking in sagittal slices. Although not significantly correlated (p = 0.08, Spearman’s rank test), the through-plane measured breathing amplitude difference corresponded reasonably to the in-plane measured amplitude difference between posterior and anterior parts of the liver (mean absolute difference of 1.4 mm between through-plane and in-plane amplitude differences). The cross correlation calculation time for a 2D MRI image is roughly proportional to the length and width of the template, the length and width of the search area, and the searched number of planes in the template library. The calculation time for the average template size (29 × 27 pixels) in a 3D search volume of 25 × 25 × 25 voxels was 90 ms
TABLE I. Mean [and range] of peak-to-peak liver motion measured in 2D real-time MRI series for five volunteers. Bold font indicates through-plane motion. 2D slice orientation
LR motion (mm)
CC motion (mm)
AP motion (mm)
Maximum for entire series
Axial Coronal Sagittal
2.5[1.6–3.3] 2.5[1.6–6.3] 3.8[3.2–4.8]
15.3[10.9–18.8] 14.6[10.9–20.0] 13.0[9.4–15.6]
3.5[1.6–4.7] 4.1[3.1–6.3] 3.8[3.1–4.7]
Mean of six consecutive breathing cycles
Axial Coronal Sagittal
1.8[0–3.1] 1.2[0–3.1] 1.9[0–4.8]
12.1[4.7–18.8] 10.0[4.7–20.0] 11.0[7.8–15.6]
2.5[1.6–4.7] 2.4[0–4.7] 2.7[0–4.7]
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F IG . 6. Direction of 1st principal component for Volunteers 1–5 in the sagittal plane for four in-plane tracked regions in the sagittal plane (black) and for 3D tracking in 2D MRI series.
in the current Matlab implementation. It would be considerably faster in a clinical implementation, using C++ or an equivalent programming language, indicating that the 3D tracking can be carried out in real-time.
4. DISCUSSION A method for 3D tracking in 2D MRI images was developed and successfully used to obtain the 3D respiratory motion of liver blood vessel structures from real-time axial, sagittal, and coronal 2D MRI image series in five volunteers. Although the slice thickness in the 2D image series was 8 mm the through-plane motion was found with a resolution of 1.6
mm. The method provided the absolute 3D position of the tracked structures in the coordinate system of the MRI scanner. The demonstrated workflow would be directly applicable for a MR-Linac, where either a liver tumor or a nearby surrogate blood vessel structure is first identified in the 3D prescan MRI and then tracked in subsequent 2D MRI images at a frequency that can be used for real-time beam adaptation to respiratory motion.30 In agreement with previous studies, we found that liver motion was largest in the CC direction and smallest in the LR direction,17, 20, 27–29, 31–34 that AP and CC motion were correlated such that inspiration caused simultaneous caudal and anterior motion18, 27–29 and that the respiratory motion was larger in cranial than in caudal parts of the liver.28
F IG . 7. Craniocaudal through-plane motion estimated using nonoverlapping posterior and anterior template library locations in axial 2D MRI series for (a) Volunteer 1 and (b) Volunteer 2. The inserted images show the template positions. The RMS difference between the motion curves estimated by the two template locations is indicated. Medical Physics, Vol. 41, No. 4, April 2014
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F IG . 8. Difference in craniocaudal mean peak-to-peak motion amplitude between posterior and anterior liver regions as measured in-plane in sagittal slices and through-plane in axial slices for the five volunteers. The straight line illustrates unity correlation.
The true 3D motion of the tracked liver vessel structures was unknown in this study, but several observations on the motion patterns lend credibility to the estimated 3D motion. First, the method was shown to have submillimeter accuracy for the rigid motion of a watermelon. Second, the motion in the LR, CC, and AP directions was of similar magnitude whether estimated in-plane or through-plane (Table I and Fig. 4). Third, the preferred motion directionality, which is expected to be relatively stable over time,29 was similar for all 2D slice orientations (Fig. 6). Finally, through-plane respiratory motion estimated in two different areas of axial 2D series in most cases agreed well [Fig. 7(a)], while the occasionally observed amplitude differences [Fig. 7(b)] are likely to reflect true physiological differences between motion of the anterior and posterior parts of the liver since they were similar to directly in-plane measured amplitude differences (Fig. 8). In the 3D tracking method, a fixed 2D slice within the MRI scanner is imaged continuously, and the part of the liver that appears inside the template region of the current 2D image is identified by comparison with the 3D prescan. The position of the tracked structure is then determined assuming that it maintains the same distance to the imaged liver part as in the 3D prescan MRI. This strategy will fail if either (1) the identification of the imaged liver part is wrong (i.e., a wrong template or template location is selected) or (2) the distance to the tracked structure has changed due to liver deformations. To ensure correct identification of the imaged liver part, the vessel to parenchyma contrast must be high and the templates must be large enough to contain unique characteristics, yet small enough to allow robust segmentation in case of in-plane liver deformations. We found that template sizes of 3–6 cm in each direction in general fulfilled these requirements when located completely inside the liver. On the other hand, in sagittal or coronal image series, the templates were often not sufficiently unique for robust through-plane localization if located Medical Physics, Vol. 41, No. 4, April 2014
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in the most cranial part of the liver at the diaphragm. Here, the blood vessel contrast was poor [Figs. 4(b) and 4(c)] and the diaphragm dome appeared very similarly in several templates in the library hindering unambiguous anatomy identification. In these cases it would be more robust to track only in-plane motion based on the diaphragm position in the 2D series, i.e., assuming that through-plane motion is absent. Deformation induced localization errors caused by distance changes between the tracked blood vessel structure and the template, relative to the 3D prescan anatomy, may be minimized by selecting a 2D image position close to the tracked structure. The 2D image plane can typically be selected such that the distance to the tracked structure remains smaller than 2 cm throughout the breathing cycle. The maximum localization errors caused by liver deformation would then be on the order of 1 mm since the largest observed breathing induced deformation over distances of 6 cm was 3.3 mm. Use of liver surrogate landmarks for accurate localization of targets over distances of a few cm is in accordance with Seppenwoolde et al.35 who found that implanted gold markers in the liver functioned as accurate surrogates for the position of nearby tumors (closer than a few cm). The localization uncertainties caused by liver deformations may be overcome by using breathing phase dependent template libraries based on 3D prescans recorded in different phases.31 Note that the localization with two different template libraries in the same axial series generally agreed much better in the exhale phase than in the inhale phase [Fig. 7(b)], reflecting that the template libraries were generated from an exhale 3D scan. Furthermore, the maximum cross correlation between the template and the 2D images in a MRI series changed with respiration yielding higher normalized cross correlation coefficients in exhale than in inhale. This is also a result of the template libraries being generated from a 3D scan of the exhale anatomy, and it may result in less robust localization in exhale. While phase dependent templates libraries would increase the complexity (and the computation time), they would also increase the 3D localization robustness (because they yield higher cross correlation coefficients throughout the breathing cycle) and the localization accuracy (because exhale templates would more accurately estimate the through-plane distance between the image 2D MRI slice and the tracked structure throughout the breathing cycle). Although the 3D tracking method was demonstrated with axial, sagittal, and coronal 2D MRI image series in this study, the most obvious image orientation with least anticipated through-plane motion would be in the sagittal plane or, alternatively, in the plane defined by the 1st and the 2nd principal components of the respiratory motion, e.g., determined from a planning 4DCT scan.29 However, even these image orientations may experience large through-plane motion due to patient shifts [Fig. 5(b)]. As demonstrated, such motion can be detected by the proposed method. As the primary goal of the applied MRI sequence was to achieve the highest possible frame rate, the TrueFISP sequence was chosen because it provides high temporal resolution with high contrast between blood vessels and the surrounding liver parenchyma.36 The temporal resolution was
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increased by undersampling and GRAPPA reconstruction, which reduces the SNR depending on the degree of k-space undersampling and the geometric arrangement of the receiver coils. A good compromise between SNR and temporal resolution was found to be at an undersampling factor of 3 yielding a frame rate of 5.4 Hz. In this study, 3D tracking of selected blood vessel structures was demonstrated in healthy volunteers. For patients with liver tumors, either the tumor itself or nearby blood vessels serving as surrogates could be tracked in future MRLinacs. The blood vessels can be used as tumor position surrogates in much the same way as gold markers in x-ray based localization, thus allowing tumor motion tracking even if the chosen MRI sequence cannot reliably image the liver tumor due to the applied real-time sequence. The method may also be used to track organ or tumor motion at other anatomical locations such as lung, pancreas, or kidney. 5. CONCLUSION In conclusion, a method for 3D tracking in 2D MRI images that explicitly accounts for through-plane motion was developed and demonstrated for axial, coronal, and sagittal image series in the liver. The applied workflow could be directly used in a MR-Linac for 3D real-time localization in 2D MRI images at a frequency that can be used for real-time beam adaptation to respiratory motion. ACKNOWLEDGMENTS This work was supported by The Danish Cancer Society and CIRRO—The Lundbeck Foundation Center for Interventional Research in Radiation Oncology and The Danish Council for Strategic Research. The authors have no conflicts of interest to declare.
a) Author
to whom correspondence should be addressed. Electronic mail: [email protected]; Fax: +45 7841 4580. 1 P. J. Keall, G. S. Mageras, J. M. Balter, R. S. Emery, K. M. Forster, S. B. Jiang, J. M. Kapatoes, D. A. Low, M. J. Murphy, B. R. Murray, C. R. Ramsey, M. B. Van Herk, S. S. Vedam, J. W. Wong, and E. Yorke, “The management of respiratory motion in radiation oncology report of AAPM Task Group 76,” Med. Phys. 33, 3874–3900 (2006). 2 D. A. Jaffray, “Image-guided radiotherapy: From current concept to future perspectives,” Nat. Rev. Clin. Oncol. 9, 688–699 (2012). 3 M. Guckenberger, A. Richter, J. Boda-Heggemann, and F. Lohr, “Motion compensation in radiotherapy,” Crit. Rev. Biomed. Eng. 40, 187–197 (2012). 4 B. W. Raaymakers, J. J. Lagendijk, J. Overweg, J. G. Kok, A. J. Raaijmakers, E. M. Kerkhof, R. W. van der Put, I. Meijsing, S. P. Crijns, F. Benedosso, V. M. van, C. H. de Graaff, J. Allen, and K. J. Brown, “Integrating a 1.5 T MRI scanner with a 6 MV accelerator: Proof of concept,” Phys. Med. Biol. 54, N229–N237 (2009). 5 B. G. Fallone, B. Murray, S. Rathee, T. Stanescu, S. Steciw, S. Vidakovic, E. Blosser, and D. Tymofichuk, “First MR images obtained during megavoltage photon irradiation from a prototype integrated linac-MR system,” Med. Phys. 36, 2084–2088 (2009). 6 J. F. Dempsey, D. Benoit, J. R. Fitzsimmons, A. Haghighat, J. G. Li, D. A. Low, S. Mutic, J. R. Palta, H. E. Romeijn, and G. E. Sjoden, “A device for realtime 3D image-guided IMRT,” Int. J. Radiat. Oncol., Biol., Phys. 63, S202 (2005).
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S. Hansen and T. S. Sorensen, “Gadgetron: An open source framework for medical image reconstruction,” Magn. Reson. Med. 69, 1768– 1776 (2013). 27 J. C. Park, S. H. Park, J. H. Kim, S. M. Yoon, S. Y. Song, Z. Liu, B. Song, K. Kauweloa, M. J. Webster, A. Sandhu, L. K. Mell, S. B. Jiang, A. J. Mundt, and W. Y. Song, “Liver motion during cone beam computed tomography guided stereotactic body radiation therapy,” Med. Phys. 39, 6431–6442 (2012). 28 M. von Siebenthal, G. Szekely, U. Gamper, P. Boesiger, A. Lomax, and P. Cattin, “4D MR imaging of respiratory organ motion and its variability,” Phys. Med. Biol. 52, 1547–1564 (2007). 29 E. S. Worm, M. Hoyer, W. Fledelius, A. T. Hansen, and P. R. Poulsen, “Variations in magnitude and directionality of respiratory target motion throughout full treatment courses of stereotactic body radiotherapy for tumors in the liver,” Acta Oncol. 52, 1437–1444 (2013). 30 P. R. Poulsen, W. Fledelius, B. Cho, and P. Keall, “Image-based dynamic multileaf collimator tracking of moving targets during intensity-modulated arc therapy,” Int. J. Radiat. Oncol., Biol., Phys. 83, e265–e271 (2012). 31 T. Rohlfing, C. R. Maurer, Jr., W. G. O’Dell, and J. Zhong, “Modeling liver motion and deformation during the respiratory cycle using intensity-
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Three-dimensional liver motion tracking using real-time two-dimensional MRI Lau Brixa) Department of Procurement and Clinical Engineering, Region Midt, Olof Palmes Allé 15, 8200 Aarhus N, Denmark and MR Research Centre, Aarhus University Hospital, Skejby, Brendstrupgaardsvej 100, 8200 Aarhus N, Denmark
Steffen Ringgaard MR Research Centre, Aarhus University Hospital, Skejby, Brendstrupgaardsvej 100, 8200 Aarhus N, Denmark
Thomas Sangild Sørensen Department of Computer Science, Aarhus University, Aabogade 34, 8200 Aarhus N, Denmark and Department of Clinical Medicine, Aarhus University, Brendstrupgaardsvej 100, 8200 Aarhus N, Denmark
Per Rugaard Poulsen Department of Clinical Medicine, Aarhus University, Brendstrupgaardsvej 100, 8200 Aarhus N, Denmark and Department of Oncology, Aarhus University Hospital, Nørrebrogade 44, 8000 Aarhus C, Denmark
(Received 11 October 2013; revised 17 February 2014; accepted for publication 20 February 2014; published 14 March 2014) Purpose: Combined magnetic resonance imaging (MRI) systems and linear accelerators for radiotherapy (MR-Linacs) are currently under development. MRI is noninvasive and nonionizing and can produce images with high soft tissue contrast. However, new tracking methods are required to obtain fast real-time spatial target localization. This study develops and evaluates a method for tracking three-dimensional (3D) respiratory liver motion in two-dimensional (2D) real-time MRI image series with high temporal and spatial resolution. Methods: The proposed method for 3D tracking in 2D real-time MRI series has three steps: (1) Recording of a 3D MRI scan and selection of a blood vessel (or tumor) structure to be tracked in subsequent 2D MRI series. (2) Generation of a library of 2D image templates oriented parallel to the 2D MRI image series by reslicing and resampling the 3D MRI scan. (3) 3D tracking of the selected structure in each real-time 2D image by finding the template and template position that yield the highest normalized cross correlation coefficient with the image. Since the tracked structure has a known 3D position relative to each template, the selection and 2D localization of a specific template translates into quantification of both the through-plane and in-plane position of the structure. As a proof of principle, 3D tracking of liver blood vessel structures was performed in five healthy volunteers in two 5.4 Hz axial, sagittal, and coronal real-time 2D MRI series of 30 s duration. In each 2D MRI series, the 3D localization was carried out twice, using nonoverlapping template libraries, which resulted in a total of 12 estimated 3D trajectories per volunteer. Validation tests carried out to support the tracking algorithm included quantification of the breathing induced 3D liver motion and liver motion directionality for the volunteers, and comparison of 2D MRI estimated positions of a structure in a watermelon with the actual positions. Results: Axial, sagittal, and coronal 2D MRI series yielded 3D respiratory motion curves for all volunteers. The motion directionality and amplitude were very similar when measured directly as in-plane motion or estimated indirectly as through-plane motion. The mean peak-to-peak breathing amplitude was 1.6 mm (left-right), 11.0 mm (craniocaudal), and 2.5 mm (anterior-posterior). The position of the watermelon structure was estimated in 2D MRI images with a root-mean-square error of 0.52 mm (in-plane) and 0.87 mm (through-plane). Conclusions: A method for 3D tracking in 2D MRI series was developed and demonstrated for liver tracking in volunteers. The method would allow real-time 3D localization with integrated MR-Linac systems. © 2014 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4867859] Key words: MR-Linac, real-time MRI, organ motion, vessel tracking, MRI 1. INTRODUCTION Precise treatment delivery is crucial in radiotherapy in order to maximize the therapeutic ratio between tumor dose and 042302-1
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normal tissue dose. Optimally, a mobile tumor and the surrounding normal tissue should be imaged during treatment delivery to ensure correct treatment delivery. This has motivated substantial research activities in developing methods
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© 2014 Am. Assoc. Phys. Med.
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for tumor motion monitoring and compensation during radiotherapy delivery.1–3 Several research groups are integrating radiotherapy treatment units with magnetic resonance imaging (MRI),4–6 and these efforts have recently lead to the first phantom studies demonstrating MRI-guided real-time motion adaptation during treatment delivery.7, 8 MRI is attractive for tumor and organ motion monitoring as it gives high contrast volumetric imaging of soft tissue without the use of ionizing radiation. However, current MRI technology does not allow real-time acquisition and reconstruction of three-dimensional (3D) volumes at sufficiently high spatial and temporal resolution for monitoring respiratory motion. Proposed techniques to overcome this include one-dimensional (1D) imaging by means of a pencil-beam navigator, which can be placed either directly on the tracked target7, 9 or on the diaphragm to function as a target position surrogate.10 It gives very fast imaging, but only in 1D, and the observed 1D motion may not represent the actual organ motion component in the navigator direction, as the apparent motion could be a result of organ motion perpendicular to the navigator. More spatial information is obtained by two-dimensional (2D) MRI (Refs. 8 and 11–13) where current clinical MRI systems allow for real-time image acquisition and reconstruction with frame rates of up to 10 Hz.14–16 Similar to 1D MRI, full 3D motion information is missing and cautious interpretation of observed motion in 2D MRI is needed since through-plane motion perpendicular to the image plane may result in apparent in-plane motion. Nevertheless, previous 2D MRI motion studies have often neglected the through-plane motion,17–23 which may be justified if the through-plane motion is expected to be small such as in sagittal 2D MRI of the liver. Cervino et al. suggested to address through-plane motion in 2D MRI of the lung by using the diaphragm as a surrogate for the (in-plane) position of a target when it moves outside the imaged 2D plane.11 Ries et al. demonstrated 3D tracking in 2D MRI by continuous shifts of the 2D image plane to follow the through-plane target motion, which was estimated by a perpendicular pencil beam navigator.24 3D tracking may also be obtained by alternating between sagittal and coronal 2D imaging combined with template based segmentation of anatomical structures in both 2D image sets.12, 13 This strategy has been demonstrated for retrospective tracking of lung structures using 2D templates cropped from arbitrarily selected sagittal and coronal 2D reference images13 as well as kidney tracking using 3D templates obtained from a breath-hold 3D MRI scan.12 These studies had relatively low frame rates of 2 Hz and the use of alternating orthogonal image planes results in dark saturation stripes at the intersection between the image planes. In this study, we develop and evaluate a new method for 3D motion tracking in 2D real-time MRI series. The method estimates the 3D position of a tracked anatomical structure for each 2D MRI image. As a first application we demonstrate the method for 3D tracking of blood vessel structures in axial, sagittal, and coronal 2D MRI images of the liver. The blood vessels could function as reliable landmarks or surrogates to determine the position of MR invisible tumors in cancer patients. Medical Physics, Vol. 41, No. 4, April 2014
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2. METHODS AND MATERIALS 2.A. Data dimensions
Throughout this paper, 2D and 3D refer to the number of spatial dimensions. All 2D images were acquired and reconstructed continuously and a temporal dimension is therefore present as well. While the 3D volume scans do not have a temporal dimension, 3D tracking implicitly denotes tracking of 3D motion over time.
2.B. Method for 3D motion tracking in 2D MRI images
Assume that a 2D MRI series is acquired in the fixed spatial position denoted Location 0 in Fig. 1. An observed motion of the left-most blood vessel in the MRI series could either be due to pure in-plane motion in the XY-plane, pure throughplane motion in the Z direction, or a combination of these motions. There is no way to discriminate between these options by monitoring a single traversing blood vessel alone. However, since the relative positions of several nonparallel blood vessels change with through-plane motion (Fig. 1, right), the observed pattern of blood vessels can be used as a fingerprint to determine the through-plane position, thereby discriminating between in-plane and through-plane motion. The proposed 3D tracking method has three steps as illustrated in Fig. 2. First, a 3D volumetric scan of the liver is obtained, and the blood vessel structure (or tumor) to be tracked is determined [dot in Fig. 2(a)]. Second, the 3D volume is resliced and resampled to generate a series of 2D slices with the same orientation, slice thickness and pixel size as in the later acquired real-time 2D MRI image series. A library of 2D templates [black rectangles in Fig. 2(b)] with well-defined 3D positions relative to the tracked structure is formed by cutting segments of identical sizes and in-plane locations from each of the 2D slices. Third, the templates of the library are used for template-based segmentation in the real-time 2D MRI series. In each 2D real-time MRI image, the normalized cross correlation between the image and a suitable range of templates in the library is calculated for a range of 2D positions in the
F IG . 1. Schematic 3D view of liver blood vessels (left) and their appearance in four parallel 2D MRI planes (right).
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F IG . 2. Flowchart for 3D tracking of a liver blood vessel structure (dot) in 2D MRI series, illustrating tracking in axial slices. A 3D scan (a) is used to create a library of templates [black rectangles in (b)] for template based segmentation in real-time 2D images (c).
image. The template and 2D position that yield the highest cross correlation coefficient are selected. Since each template has a known 3D position relative to the tracked structure, the selection and 2D localization of a specific template translates into quantification of both the through-plane and in-plane position of the structure. 2.C. Volunteers and MR image acquisition
Five healthy volunteers with a mean age of 42.6 years (range: 26–64 years) were included in the study. The experiments were carried out on a Siemens Avanto 1.5 T MRI scanner (Siemens, Erlangen, Germany, software release VB17a) using a 32 channel cardiac receiver coil. First, a 3D volumetric MRI scan (3D prescan) was obtained during free breathing using a navigator situated on the left diaphragm dome for respiratory motion compensation. Data were sampled during expiration with an 8 mm navigator window. The protocol was set up to exhibit the same type of contrast as in subsequent 2D real-time image series. The 3D sequence was a True Fast Imaging with Steady State Precession (TrueFISP) 3D single-shot sequence (TR = 3.52 ms, TE = 1.54 ms, field of view = 300 mm, matrix size = 192 × 192, image resolution = 1.56 × 1.56 × 1.60 mm3 , flip angle = 80◦ , 80 sagittal slices, total scan time ≈4 min including the navigator). To speed up the data acquisition, parallel imaging was applied using the GRAPPA reconstruction technique25 at an undersampling factor of 2. The 3D images were reconstructed using the reconstruction system provided by Siemens. Next, a real-time 2D protocol was used to acquire and reconstruct data during free breathing in the axial, coronal, and sagittal planes. To cover approximately the same volume as the 3D volume scan, the liver was imaged sequentially using 7 mm gaps between consecutive 2D series. Each slice location was imaged for 30 s to capture several respiratory cycles. The real-time 2D scan was a dynamic TrueFISP 2D single-shot Medical Physics, Vol. 41, No. 4, April 2014
sequence (TR = 2.82–2.88 ms, TE = 1.41–1.44 ms, field of view = 300–319 mm, matrix size = 192 × 192, in-plane resolution = (1.56 × 1.56)–(1.67 × 1.67) mm2 , slice thickness = 8 mm, flip angle = 45◦ , GRAPPA factor = 3, scan time = 184 ms per image [5.4 images per second]). All 2D images were reconstructed using the Gadgetron software package, which is an open source framework for medical imaging reconstruction.26 The reconstruction was carried out in realR FX8120 8time on an external workstation with an AMD R core processor and a NVIDIA GTX-580 Graphics Processing Unit. The Interactive Front End provided by Siemens was used for interactive real-time control of the image planes during scanning. Whenever the position or orientation of the 2D slices were altered, the first few images appeared aliased until enough data were buffered to calculate the parallel imaging coefficients needed for the GRAPPA reconstruction. These distorted images were removed before further analysis. After acquisition of the 2D real-time image series a second 3D volumetric MRI scan (3D postscan) was acquired with the same settings as the 3D prescan, with the purpose of detecting possible liver deformations and shifts during the time course of the examination. 2.D. Demonstration of the 3D tracking method
As a proof of principle, the proposed tracking method was demonstrated off-line after image acquisition using in-house built software (Matlab, R2012b, Mathworks, Natick, MA). For each of the five volunteers, characteristic liver blood vessel structures were first selected in the 3D prescan MR volume and then tracked in subsequent real-time 2D image series by the proposed method. The tracking was performed in two different axial, sagittal, and coronal 2D MRI series located reasonably close to the selected structures. In each of the six 2D series, 3D tracking was performed with two different, nonoverlapping template libraries, resulting in 12 respiratory
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3D motion trajectories of 30 s per volunteer. For each trajectory, the maximum and mean breathing peak-to-peak amplitude was calculated using six consecutive breathing cycles. The tracking resolution was one 2D pixel length for the inplane localization (1.56–1.67 mm) and one 3D voxel length for the through-plane localization (1.56 mm for axial and coronal 2D series, 1.6 mm for sagittal series). 2.E. In vitro validation of the 3D tracking method
To investigate the accuracy of the 3D tracking method for a rigid system without deformations, a 3D prescan and subsequent real-time 2D MRI scans were acquired in a watermelon using the same scanning parameters and off-line analysis as for the liver scans. The watermelon was placed on a platform that was manually moved stepwise in the craniocaudal (CC) direction by adding plastic spacers of known thickness between the platform side and a fixed support. The 2D MRI series were acquired with axial, coronal, and sagittal orientations for nine CC positions of the watermelon spanning a range of 17 mm. The MRI contrast between heterogeneously distributed air cavities and the pulp of the watermelon was used for 3D tracking in the same way as the blood vessels in the liver parenchyma. Since the watermelon air cavities were less unique than liver blood vessels as fingerprints for the through-plane position, approximated 50% larger templates were used for the watermelon than for the liver to ensure robust tracking. The CC positions estimated by 2D MRI were compared with the actual CC positions. 2.F. Liver deformations
The through-plane localization of the tracked liver vessel structure assumes that the structure remains at the same distance from the currently imaged 2D liver slice as it had during the 3D prescan. Thus, liver deformations were assumed to be neglectable on a length scale of up to a few cm. This assumption was tested in the current MRI data sets in two ways. First, possible liver deformations and shifts between the 3D preand postscans were investigated. In each volunteer, a square region of 40 × 40 pixels was selected in 40 consecutive sagittal slices of the 3D prescan, covering a total liver volume of 62 × 62 × 64 mm3 . Each of the 40 squares were subdivided into four adjacent 20 × 20 pixel templates, yielding a total of 160 subvolumes of size 31 × 31 × 1.6 mm3 that were all located completely within the liver and contained characteristic blood vessel structures. Each subvolume was then used as the template in a template based search in the 3D postscan performed with the same computer program as used for 3D tracking in the 2D image series. This analysis yielded the 3D shifts of each of the 160 subvolumes between the 3D prescan and postscan. The mean and standard deviations of the subvolume shifts were calculated as measures of the shift and deformation of the liver, respectively. The assumption of rigidity was further investigated in relation to possible breathing induced deformations in a sagittal real-time 2D image series in each of the five volunteers. In the first frame of the series, four regions of 15 × 15 pixel (23 × 23 Medical Physics, Vol. 41, No. 4, April 2014
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mm2 ) with recognizable blood vessel structures were selected such that they constituted two pairs with at least 40 pixel (62 mm) separations in the CC direction and in the anterioposterior (AP) direction, respectively. The four regions in the first frame were used as templates for segmentation of the structures in all frames of the 2D series. The breathing motion and mean breathing amplitudes were compared between the four regions as a measure of the breathing induced deformations across a length scale of approximately 6 cm.
2.G. Validity of the 3D liver tracking
Since the true motion of the tracked vessel structure is unknown, a series of analyses were performed to indirectly assess the validity of the 3D tracking method. Liver motion is normally largest in the CC direction with a smaller motion component in the AP direction and even less motion in the left-right (LR) direction.27, 28 Typically, there is a strong correlation between CC and AP motion such that the caudal motion seen during inspiration is associated with a simultaneous anterior motion. As a result, there is a preferred motion directionality in the sagittal plane, which has been shown to be relatively stable over time for a given point in a given individual.29 To determine this directionality for each volunteer the motion of the four 15 × 15 pixels regions tracked in the sagittal plane (see Sec. 2.F) was analyzed by principal component analysis. The first principal component (1st PC) of the combined motion of the four regions was calculated and assumed to represent the overall sagittal plane liver motion directionality of the volunteer. In order to investigate how well the 3D motion estimated from 2D image series agreed with the directionality obtained in a single sagittal slice plane, the angular deviation between the overall liver motion directionality and the 1st PC of the estimated 3D motion in the 2D data sets was determined for each 2D image orientation for each volunteer. The through-plane motion was expected to be largest in the axial 2D image series, where it corresponded to CC motion. For each volunteer, the agreement between the estimated through-plane motion at the two nonoverlapping template locations in the axial plane (anterior and posterior locations) was quantified as the root-mean-square (RMS) difference and as the difference in mean peak-to-peak breathing motion amplitude for six subsequent breathing cycles. These differences should be zero if the liver moved as a rigid body. However, if the anterior part of the liver moved differently from the posterior part the estimated through-plane motions of the two template locations should also be different. Therefore, the difference in estimated through-plane motion amplitude was compared with the amplitude difference measured between the anterior and the posterior 15 × 15 pixels regions in the sagittal plane (See Sec. 2.F).
3. RESULTS The CC position of the watermelon structure was estimated with root-mean-square errors of 0.86 mm (axial MRI),
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F IG . 3. Scatter plots of the actual CC position of a watermelon structure versus the CC position estimated in 2D MRI images with axial (diamonds), coronal (circles), and sagittal (crosses) slice orientations. The unity line illustrates perfect position estimation.
0.44 mm (coronal MRI), and 0.59 mm (sagittal MRI) in 2D MRI series by the 3D tracking method (Fig. 3). For all five volunteers, the 3D prescan and postscan MRI volumes and 2D real-time MRI series were successfully acquired, reconstructed, and visualized. The axial and sagittal 2D images had similar image quality and contrast as the 3D scans, while the coronal images had a lower signal-to-noise ratio (SNR). Nevertheless, all three slice orientations exhibited image qualities sufficient for 3D motion tracking. For each volunteer and slice orientation, two 2D MRI series were selected for 3D tracking. The mean width and height of the templates used for tracking were 45 mm (range: 30–61 mm) and 41 mm (range: 31–53 mm), respectively, while the mean area was 1854 mm2 (range: 872–3008 mm2 ). Figure 4 shows examples of 2D liver MRI images, with matching templates and resulting 3D position estimations of the tracked structure in extreme breathing phases for the subject exhibiting the largest breathing motion (Volunteer 2). Figure 5 presents 3D motion curves of a blood vessel structure in axial, coronal, and sagittal image series for Volunteers 1 and 2. In general, the estimated 3D motion was largest in the CC direction, and it was of similar magnitude independent of the 2D image orientation (Fig. 5 and Table I). For Volunteer 1, the exhale position of the tracked structure stayed close to its position in the 3D prescan [(0,0,0) in Fig. 5], whereas Volunteer 2 had a large baseline shift of 13.4 mm (LR), −12.6 mm (CC), and 0.5 mm (AP) [Fig. 5(b)]. The comparison with the 3D postscan [Fig. 5(b), right] showed that this was a true systematic shift of the volunteer, which was thus detected correctly by the 3D tracking method in all three 2D image orientations. Volunteer 2 was the only subject with a substantial shift between the two 3D scans: The mean shifts of the other four volunteers between the 3D prescan and postscan was below 2 pixels in all directions with absolute mean shift averages of 1.9 mm (CC), Medical Physics, Vol. 41, No. 4, April 2014
F IG . 4. Examples of (a) axial, (b) coronal, and (c) sagittal 2D MRI images in maximum expiration (left) and inspiration (right) for Volunteer 2. Each figure shows the template selected from the library (inset), the segmented position of this template (white rectangle), and the resulting absolute 3D position estimation of the tracked structure in millimeter.
1.7 mm (AP), and 0.5 mm (LR). Volunteer 2 was also the only subject with a tendency of deformations between the two (exhale) 3D scans, i.e., systematic differential shifts of the 160 subvolumes, between the two volume scans. Here, the CC shift depended on the lateral position and was on average 2.1 mm larger for the 40 most right-lateral subvolumes compared to the 40 most medial subvolumes. The average standard deviation of the subvolume shifts for all five volunteers was 1.0 mm (CC), 0.6 mm (AP), and 0.8 mm (LR). Regarding breathing induced deformations, segmentation of the four 15 × 15 pixels regions in sagittal real-time 2D image series showed that the mean CC breathing motion amplitude was invariably larger (2.3–3.3 mm) for the cranial region than for the caudal region. There was no systematic trend for the AP region pair as the mean CC motion amplitude was largest for the anterior region for some volunteers (up to 2.3 mm) and largest for the posterior region for others (up to 2.0 mm) (mean difference = 0.3 mm). These results show that breathing induced CC liver deformations of up to 3.3 mm over distances of approximately 6 cm in the included group of volunteers. For all volunteers, the 1st PC of the four regions tracked in the sagittal plane was in the cranial direction with inclinations between 8.9◦ and 21.1◦ towards the posterior direction (black arrows in Fig. 6). The mean absolute deviation between this direction and the 1st PC of the 3D motion as estimated from the 2D data sets (remaining arrows in Fig. 6) was
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F IG . 5. Time resolved position of tracked blood vessel structure in LR, CC, and AP directions estimated for Volunteers 1 and 2 in axial, coronal and sagittal 2D image series. The positions are shown relative to the structure location in the 3D prescan MRI volume. The horizontal lines to the right depict the structure location in the 3D postscan MRI volume. The time stamps indicate the time since the 3D prescan. In-plane and through-plane motion are shown with dotted and solid curves, respectively.
3.0◦ (±2.0◦ , 1 standard deviation) (axial series), 1.5◦ (±1.6◦ ) (sagittal slices), and 2.9◦ (±2.0◦ ) (coronal slices). The RMS difference between the CC through-plane motion estimated from two nonoverlapping templates in the same 2D axial series had a mean value of 2.0 mm (range: 1.3–3.2 mm) and it exceeded 2 mm only for Volunteer 2. Figure 7 shows the estimated through-plane motion and template locations for a case with RMS difference close to the mean value and for the case with highest RMS difference. Figure 8 compares the CC breathing amplitude difference between the posterior and anterior template locations in the axial series with the CC amplitude difference between posterior and anterior liver parts as measured directly in-plane by
region tracking in sagittal slices. Although not significantly correlated (p = 0.08, Spearman’s rank test), the through-plane measured breathing amplitude difference corresponded reasonably to the in-plane measured amplitude difference between posterior and anterior parts of the liver (mean absolute difference of 1.4 mm between through-plane and in-plane amplitude differences). The cross correlation calculation time for a 2D MRI image is roughly proportional to the length and width of the template, the length and width of the search area, and the searched number of planes in the template library. The calculation time for the average template size (29 × 27 pixels) in a 3D search volume of 25 × 25 × 25 voxels was 90 ms
TABLE I. Mean [and range] of peak-to-peak liver motion measured in 2D real-time MRI series for five volunteers. Bold font indicates through-plane motion. 2D slice orientation
LR motion (mm)
CC motion (mm)
AP motion (mm)
Maximum for entire series
Axial Coronal Sagittal
2.5[1.6–3.3] 2.5[1.6–6.3] 3.8[3.2–4.8]
15.3[10.9–18.8] 14.6[10.9–20.0] 13.0[9.4–15.6]
3.5[1.6–4.7] 4.1[3.1–6.3] 3.8[3.1–4.7]
Mean of six consecutive breathing cycles
Axial Coronal Sagittal
1.8[0–3.1] 1.2[0–3.1] 1.9[0–4.8]
12.1[4.7–18.8] 10.0[4.7–20.0] 11.0[7.8–15.6]
2.5[1.6–4.7] 2.4[0–4.7] 2.7[0–4.7]
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F IG . 6. Direction of 1st principal component for Volunteers 1–5 in the sagittal plane for four in-plane tracked regions in the sagittal plane (black) and for 3D tracking in 2D MRI series.
in the current Matlab implementation. It would be considerably faster in a clinical implementation, using C++ or an equivalent programming language, indicating that the 3D tracking can be carried out in real-time.
4. DISCUSSION A method for 3D tracking in 2D MRI images was developed and successfully used to obtain the 3D respiratory motion of liver blood vessel structures from real-time axial, sagittal, and coronal 2D MRI image series in five volunteers. Although the slice thickness in the 2D image series was 8 mm the through-plane motion was found with a resolution of 1.6
mm. The method provided the absolute 3D position of the tracked structures in the coordinate system of the MRI scanner. The demonstrated workflow would be directly applicable for a MR-Linac, where either a liver tumor or a nearby surrogate blood vessel structure is first identified in the 3D prescan MRI and then tracked in subsequent 2D MRI images at a frequency that can be used for real-time beam adaptation to respiratory motion.30 In agreement with previous studies, we found that liver motion was largest in the CC direction and smallest in the LR direction,17, 20, 27–29, 31–34 that AP and CC motion were correlated such that inspiration caused simultaneous caudal and anterior motion18, 27–29 and that the respiratory motion was larger in cranial than in caudal parts of the liver.28
F IG . 7. Craniocaudal through-plane motion estimated using nonoverlapping posterior and anterior template library locations in axial 2D MRI series for (a) Volunteer 1 and (b) Volunteer 2. The inserted images show the template positions. The RMS difference between the motion curves estimated by the two template locations is indicated. Medical Physics, Vol. 41, No. 4, April 2014
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F IG . 8. Difference in craniocaudal mean peak-to-peak motion amplitude between posterior and anterior liver regions as measured in-plane in sagittal slices and through-plane in axial slices for the five volunteers. The straight line illustrates unity correlation.
The true 3D motion of the tracked liver vessel structures was unknown in this study, but several observations on the motion patterns lend credibility to the estimated 3D motion. First, the method was shown to have submillimeter accuracy for the rigid motion of a watermelon. Second, the motion in the LR, CC, and AP directions was of similar magnitude whether estimated in-plane or through-plane (Table I and Fig. 4). Third, the preferred motion directionality, which is expected to be relatively stable over time,29 was similar for all 2D slice orientations (Fig. 6). Finally, through-plane respiratory motion estimated in two different areas of axial 2D series in most cases agreed well [Fig. 7(a)], while the occasionally observed amplitude differences [Fig. 7(b)] are likely to reflect true physiological differences between motion of the anterior and posterior parts of the liver since they were similar to directly in-plane measured amplitude differences (Fig. 8). In the 3D tracking method, a fixed 2D slice within the MRI scanner is imaged continuously, and the part of the liver that appears inside the template region of the current 2D image is identified by comparison with the 3D prescan. The position of the tracked structure is then determined assuming that it maintains the same distance to the imaged liver part as in the 3D prescan MRI. This strategy will fail if either (1) the identification of the imaged liver part is wrong (i.e., a wrong template or template location is selected) or (2) the distance to the tracked structure has changed due to liver deformations. To ensure correct identification of the imaged liver part, the vessel to parenchyma contrast must be high and the templates must be large enough to contain unique characteristics, yet small enough to allow robust segmentation in case of in-plane liver deformations. We found that template sizes of 3–6 cm in each direction in general fulfilled these requirements when located completely inside the liver. On the other hand, in sagittal or coronal image series, the templates were often not sufficiently unique for robust through-plane localization if located Medical Physics, Vol. 41, No. 4, April 2014
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in the most cranial part of the liver at the diaphragm. Here, the blood vessel contrast was poor [Figs. 4(b) and 4(c)] and the diaphragm dome appeared very similarly in several templates in the library hindering unambiguous anatomy identification. In these cases it would be more robust to track only in-plane motion based on the diaphragm position in the 2D series, i.e., assuming that through-plane motion is absent. Deformation induced localization errors caused by distance changes between the tracked blood vessel structure and the template, relative to the 3D prescan anatomy, may be minimized by selecting a 2D image position close to the tracked structure. The 2D image plane can typically be selected such that the distance to the tracked structure remains smaller than 2 cm throughout the breathing cycle. The maximum localization errors caused by liver deformation would then be on the order of 1 mm since the largest observed breathing induced deformation over distances of 6 cm was 3.3 mm. Use of liver surrogate landmarks for accurate localization of targets over distances of a few cm is in accordance with Seppenwoolde et al.35 who found that implanted gold markers in the liver functioned as accurate surrogates for the position of nearby tumors (closer than a few cm). The localization uncertainties caused by liver deformations may be overcome by using breathing phase dependent template libraries based on 3D prescans recorded in different phases.31 Note that the localization with two different template libraries in the same axial series generally agreed much better in the exhale phase than in the inhale phase [Fig. 7(b)], reflecting that the template libraries were generated from an exhale 3D scan. Furthermore, the maximum cross correlation between the template and the 2D images in a MRI series changed with respiration yielding higher normalized cross correlation coefficients in exhale than in inhale. This is also a result of the template libraries being generated from a 3D scan of the exhale anatomy, and it may result in less robust localization in exhale. While phase dependent templates libraries would increase the complexity (and the computation time), they would also increase the 3D localization robustness (because they yield higher cross correlation coefficients throughout the breathing cycle) and the localization accuracy (because exhale templates would more accurately estimate the through-plane distance between the image 2D MRI slice and the tracked structure throughout the breathing cycle). Although the 3D tracking method was demonstrated with axial, sagittal, and coronal 2D MRI image series in this study, the most obvious image orientation with least anticipated through-plane motion would be in the sagittal plane or, alternatively, in the plane defined by the 1st and the 2nd principal components of the respiratory motion, e.g., determined from a planning 4DCT scan.29 However, even these image orientations may experience large through-plane motion due to patient shifts [Fig. 5(b)]. As demonstrated, such motion can be detected by the proposed method. As the primary goal of the applied MRI sequence was to achieve the highest possible frame rate, the TrueFISP sequence was chosen because it provides high temporal resolution with high contrast between blood vessels and the surrounding liver parenchyma.36 The temporal resolution was
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increased by undersampling and GRAPPA reconstruction, which reduces the SNR depending on the degree of k-space undersampling and the geometric arrangement of the receiver coils. A good compromise between SNR and temporal resolution was found to be at an undersampling factor of 3 yielding a frame rate of 5.4 Hz. In this study, 3D tracking of selected blood vessel structures was demonstrated in healthy volunteers. For patients with liver tumors, either the tumor itself or nearby blood vessels serving as surrogates could be tracked in future MRLinacs. The blood vessels can be used as tumor position surrogates in much the same way as gold markers in x-ray based localization, thus allowing tumor motion tracking even if the chosen MRI sequence cannot reliably image the liver tumor due to the applied real-time sequence. The method may also be used to track organ or tumor motion at other anatomical locations such as lung, pancreas, or kidney. 5. CONCLUSION In conclusion, a method for 3D tracking in 2D MRI images that explicitly accounts for through-plane motion was developed and demonstrated for axial, coronal, and sagittal image series in the liver. The applied workflow could be directly used in a MR-Linac for 3D real-time localization in 2D MRI images at a frequency that can be used for real-time beam adaptation to respiratory motion. ACKNOWLEDGMENTS This work was supported by The Danish Cancer Society and CIRRO—The Lundbeck Foundation Center for Interventional Research in Radiation Oncology and The Danish Council for Strategic Research. The authors have no conflicts of interest to declare.
a) Author
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