|Year : 2017 | Volume
| Issue : 5 | Page : 153-158
Motion estimation of the liver based on deformable image registration: a comparison between four-dimensional-computed tomography and four-dimensional-magnetic resonance imaging
Xiao Liang1, Fang-Fang Yin2, Yilin Liu1, Brian Czito3, Manisha Palta3, Mustafa Bashir4, Jing Cai2
1 Medical Physics Graduate Program, Duke University, Durham, NC, USA
2 Medical Physics Graduate Program, Duke University; Department of Radiation Oncology, Duke University Medical Center, Durham, NC, USA
3 Department of Radiation Oncology, Duke University Medical Center, Durham, NC, USA
4 Department of Radiology, Duke University Medical Center, Durham, NC, USA
|Date of Submission||28-Jun-2017|
|Date of Acceptance||17-Sep-2017|
|Date of Web Publication||26-Oct-2017|
Department of Radiation Oncology, Duke University Medical Center, Box 3295, Durham, NC 27710
Source of Support: None, Conflict of Interest: None
Aim: The aim of this study was to evaluate deformable image registration (DIR)-based motion estimation of the liver for four-dimensional-computed tomography (4D-CT) and 4D-magnetic resonance imaging (MRI).
Methods: Five liver cancer patients were included. Each patient was imaged with 4D-CT and 4D-MRI under an Institutional Review Board-approved protocol. Motion estimation of the liver was obtained by performing DIR on 4D-CT and 4D-MRI. A region of interest (ROI) encompassing the expert-determined gross tumor volume was used as surrogate to evaluate the accuracy of the motion estimation. ROI motion trajectories were estimated by averaging the displacement vector fields (DVFs) within the ROI during the breathing cycles for 4D-CT and 4D-MRI and were compared to those extracted from cine MR. Target registration error (TRE), correlation coefficient (CC) for phase agreement, difference in phase at maximum displacement (ΔPmax), and Dice's Similarity Coefficient (DSC) for overall motion agreement were determined.
Results: As compared to 4D-CT, 4D-MRI resulted in smaller TRE in DVFs (anterior-posterior [AP]: 1.0 ± 0.4 mm vs. 1.5 ± 0.5 mm, superior-inferior [SI]: 1.9 ± 0.7 mm vs. 2.2 ± 0.8 mm), greater CC (AP: 0.67 ± 0.32 vs. 0.49 ± 0.26, SI: 0.84 ± 0.15 vs. 0.58 ± 0.28), smaller ΔPmax (AP: 1.4 ± 1.7 vs. 2.0 ± 1.0, SI: 0.4 ± 0.9 vs. 1.2 ± 0.8), and greater DSC (AP: 0.67 ± 0.08 vs. 0.61 ± 0.11, SI: 0.73 ± 0.12 vs. 0.67 ± 0.10).
Conclusion: 4D-MRI can potentially provide more realistic respiratory DVFs of the liver than 4D-CT.
Keywords: Deformable image registration, four-dimensional-computed tomography, four-dimensional-magnetic resonance imaging, liver cancer, respiratory motion
|How to cite this article:|
Liang X, Yin FF, Liu Y, Czito B, Palta M, Bashir M, Cai J. Motion estimation of the liver based on deformable image registration: a comparison between four-dimensional-computed tomography and four-dimensional-magnetic resonance imaging. Cancer Transl Med 2017;3:153-8
|How to cite this URL:|
Liang X, Yin FF, Liu Y, Czito B, Palta M, Bashir M, Cai J. Motion estimation of the liver based on deformable image registration: a comparison between four-dimensional-computed tomography and four-dimensional-magnetic resonance imaging. Cancer Transl Med [serial online] 2017 [cited 2018 Feb 18];3:153-8. Available from: http://www.cancertm.com/text.asp?2017/3/5/153/217260
| Introduction|| |
Respiratory motion has been of clinical and research interest in radiation therapy. On the one hand, respiratory motion complicates radiation therapy treatment and may compromise treatment outcome of radiation therapy. On the other hand, respiratory motion provides biomechanical information that can be used to predict physiological changes before anatomical changes can be observed. A common approach to quantitatively estimate respiratory motion is to perform deformable image registration (DIR) on images at different respiratory phases. Under the assumption that a displacement vector field (DVF) generated from DIR is a good approximation to real tissue motion, DIR has been used for motion modeling,, contour propagation,, dose warping,,, and biomechanical metric calculation.,
However, it has been widely recognized that DIR is subject to registration errors. Although certain restraints are used in DIR algorithms to ensure smoothness and avoid unrealistic changes of DVF, no consideration of physiological motion of real anatomy is integrated in the DVF optimizing process. Consequently, a DVF may be a mathematical solution to the optimization problem but makes no sense physiologically. Therefore, DIR must be carefully examined and valuated against known truth, which is not always readily available. In recognition of the importance of DIR accuracy, performance of DIR on 4D-CT of the lung has been extensively examined using phantoms and patients' data. In a multi-institutional study, post-registration mean absolute errors in lung 4D-computed tomography (CT) were 0.5–1.2 mm left-right (LR), 0.4–1.9 mm anterior-posterior (AP), and 0.7–1.9 mm superior-inferior (SI), all of which are less than the slice thickness, 2.5 mm. As respiration also induces considerable motion in the liver, post-registration mean absolute errors in liver were found in the same study to be 0.9–1.9 mm LR, 1.2–3.3 mm AP, and 1.2–7.4 mm SI. This increased registration error may be attributed to poor soft tissue contrast in liver 4D-CT images.
It is worth noting that since DIR is usually evaluated through matching landmarks which in fact enhance local contrast, results of these studies indicate DIR accuracy in high contrast region. For applications where accurate displacement vectors throughout the region of interest (ROI) (including low-contrast region) are required, DIR accuracy remains in question. Recent studies that specifically investigated DIR accuracy in low-contrast regions concluded that DIR algorithms can yield satisfactory matching of the contour but the internal displacement vectors may be subject to large errors due to the lack of contrast.,
Primary liver cancer is the third leading cause of cancer deaths worldwide. Liver metastases from solid malignancies are a large source of morbidity and mortality. Radiotherapy is used alone or in combination with surgery/chemotherapy to control liver cancer. As the liver is affected by respiratory motion, it is of clinical importance to estimate the intrafractional liver motion as accurately as possible for the purpose of escalating dose to tumors and sparing normal liver tissues., 4D-CT is among the clinically standard procedure for radiation therapy in liver but has been known to have suboptimal soft tissue contrast, which, in turn, based on the studies mentioned above,, may induce large errors in motion estimation using DIR. In contrast, liver 4D-MRI , can provide better soft tissue contrast, which may improve DIR accuracy. Therefore, this study aims to evaluate and compare the accuracy of DIR-based motion estimation of the liver between clinical 4D-CT and 4D-magnetic resonance imaging (MRI).
| Methods|| |
This research was performed under an institutionally approved Institutional Review Board (IRB) protocol for human data.
In this study, DVFs from 10-phase 4D-CT and 10-phase 4D-MRI were evaluated by comparing motion represented by the displacement vectors against motion extracted from cine MRI in the tumor region. The overall study design and data process are illustrated in [Figure 1]. 4D-CT images were acquired as part of routine clinical procedure for treatment simulation, and 4D-MRI and cine MRI images were collected under IRB-approved protocol. Each phase of the 10-phase 4D images was registered to the eosinophilic esophagitis (EOE) phase, resulting in a total of 9 DVFs for each set of 4D images. An ROI was identified as a cube encompassing expert-determined gross tumor volume (GTV) in 4D-CT and 4D-MRI images for each patient. In each DVF, displacement vectors within the ROI were averaged to represent the bulk motion of the ROI. At last, a motion trajectory of the ROI was generated by plotting the ROI motion as a function of respiratory phase. For cine MRI images, respiratory motion of the ROI was extracted using an in-house developed motion tracking program based on cross-correlation maximization., The resulted multicycle motion curve was then converted to a 10-phase single cycle motion trajectory, used as the reference trajectory, for evaluating the ROI motion trajectories determined from 4D-CT or 4D-MRI.
|Figure 1: Flow chart of data processing. Raw data are in ellipses, processed data in rounded rectangles|
Click here to view
Image acquisition and reconstruction
Five patients (mean age: 61; two females, three males) were included in this study. 4D-CT images were acquired on a General Electric Medical Systems Light Speed RT ® CT scanner and a Siemens Biograph™ 40 positron emission tomography/CT scanner in cine mode, using a phase gating protocol with following parameters: KVp: 120 kVp; tube current: 40–344 mA; matrix: 512 × 512; in-plane resolution: 1.27–1.37 mm; slice thickness: 2.5–3.0 mm. The 4D-CT images were generated using phase sorting by matching the time stamp of each image with the synchronized respiratory curve recorded by a Varian ® Real-time Position Management™ RPM system.
4D-MRI images were acquired on a 1.5T MR scanner (Signa, GE Medical Systems). A fast imaging employing steady-state acquisition (FIESTA) sequence was adapted to acquire 2D axial images in the cine mode, with following parameters: Repetition time/echo time: 2.7–3.0 ms/1.0–1.1 ms; flip angle: 50°; matrix: 256 × 256; in-plane resolution: 1.41–1.88 mm; and slice thickness: 5 mm. This sequence uses the T2 steady-state contrast mechanism to provide high signal-to-noise ratio images with strong signal from fluid tissues while suppressing background tissue for contrast and anatomic detail of small structures. In addition, the ultra-short TR and TE enable extremely short acquisition times, which satisfy the requirement for temporal resolution of 4D-MRI. In 4D reconstruction, the body area, defined as the number of voxels inside the skin, was used as the internal surrogate of respiration. The phase of each image was determined by the body area in the image. The validity of using the body area as an internal surrogate to extract breathing signal has been affirmed by the previous studies. All 4D-CT and MRI images were interpolated to the same resolution, 1.27 mm in-plane, 2.5 mm through-plane, for the purpose of eliminating possible effects image resolution may have on DIR process.
Cine MRI images were acquired using the FIESTA sequence, with following parameters: repetition time/echo time: 2.7-3.1 ms/1.0–1.1 ms; flip angle: 50°; matrix: 256 × 256; in-plane resolution: 1.41–1.88 mm; and slice thickness: 5 mm. Cine MRI images were acquired in both the coronal and sagittal planes passing through the center of the tumor with a frame ware of 3–5 frames/s. The cine images were acquired because they contain motion information in the SI direction, which has the largest magnitude and is thus of most clinical relevance as compared with motion in the ML and the AP direction. The motion trajectories of the tumor were determined by tracking the position of the tumor in cine MRI images using a template matching method based on maximum similarity. [Figure 2] shows the cine MRI, 4D-CT, and 4D-MRI images of a representative subject.
|Figure 2: (a) 10-phase coronal view of cine magnetic resonance imaging, (b) four-dimensional-computed tomography, and (c) four-dimensional-magnetic resonance imaging of a representative subject|
Click here to view
Deformable image registration
In this study, a B-spline DIR algorithm, implemented in Velocity AI software (Varian Medical Systems, Palo Alto, CA), was applied on the 4D-CT and 4D-MRI images to generate 4D-CT DVF and 4D-MRI DVF. The Velocity's B-spline model was based on Mattes formulation of mutual information. The B-spline model defines the deformation only on a sparse lattice of nodes overlaid on the image, and the displacement at any voxel is obtained by interpolation from the closet lattice nodes. Information on the parameter setting in the current version of this software was not disclosed by the vendor and not able to be changed by the user. Two DIR strategies (Deformable and Deformable multipass) were implemented in Velocity AI. Deformable is an approach to deform one image in a single stage, the resolution of which is determined by the user. Deformable multipass is an approach to perform DIR sequentially from low resolution to high resolution. After registration has been completed in one image-resolution stage, the result is used as the initial condition for the next image registration stage. These resolutions for each stage are automatically determined. Since deformable multipass is recommended by the vendor for use in a clinical, this approach was used in this study.
Among all phases of the 4D images, the EOE phase was the most stable one and was thus selected as the reference phase,, to which volumes of other phases were registered. Through the registration, for each patient, 9 sets of DVF were generated, with each set representing correspondence between the volume at a phase and the reference volume, and containing displacement vectors along the three orthogonal directions. Since these DVFs share the same reference volume, they are all in the same coordinates as the reference volume. DIR was repeated three times on 4D-CT and 4D-MRI images, respectively, for each patient to reduce uncertainty.
Motion estimation based on displacement vector field
In both 4D-CT and 4D-MRI DVFs, the ROI was selected in the plane where the cine images were acquired. Since cine MRI images were acquired at a plane across the center of the GTV, the ROI was selected as a minimum rectangular area encompassing the gross tumor area in the plane [Figure 3]. Displacement vectors originating within the ROI were averaged, and the averaged vector was used as an approximation of motion of the ROI. By repeating the process for the 9 DVFs, for 4D-CT and 4D-MRI, respectively, 9 sets of vectors were obtained, serving as approximated ROI displacement between the reference phase and the other phases. Connecting the endpoints of these vectors plus the common start point in a loop resulted in a DVF-derived trajectory. Of the three orthogonal of the displacement vectors, the two in-plane axes of motion are of our interest because the through-plane motion cannot be obtained from cine MR images and therefore, the through-plane trajectory cannot be verified. A time point with zero amplitude was added to each curve to represent the EOE phase.
|Figure 3: Region of interest selection in coronal and sagittal slices of (a) cine magnetic resonance imaging, (b) four-dimensional-computed tomography, and (c) four-dimensional-magnetic resonance imaging at the eosinophilic esophagitis phase|
Click here to view
Motion extraction from cine magnetic resonance imaging images
Motion extraction from cine MRI images was facilitated by an in-house developed graphical user interface with the functions of ROI selection and ROI tracking. A rectangular area encompassing visible tumor area [Figure 3] was manually selected in the first frame of the cine MRI images as the ROI, which would be used as a template in the subsequent tracking process. The tracking algorithm was based on cross-correlation maximization. The template was shifted to each position in a user-defined searching scope and the shift that maximized the cross-correlation was recorded as the displacement of ROI for that frame. This process was automatically implemented for every frame and the displacement of each frame was combined in temporal order to form a motion curve. Breathing cycles of the motion curve were averaged and resampled to a 10-phase motion trajectory, which is referred to as the reference trajectory. Since the EOE phase was chosen as the reference phase, the entire curve was shifted so that the amplitude of the first bin equals zero. Cine MRI images of each patient were tracked 5 times to ensure the reproducibility. The average reference trajectory was used in the subsequent analysis.
Four metrics were used to describe how different they are: 4D target registration error (TRE) (Eq. 1), which measures the deviation of the DVF-derived trajectory from the reference trajectory in terms of absolute distance; correlation coefficient (CC) (Eq. 2), which reflects the agreement of curve shape between the DVF-derived and the reference trajectories regardless of the distance between the DVF trajectory and the reference trajectory; the difference of phase at maximum displacement (Δpmax), which is a straightforward indicator of the curve's shape; Dice's Similarity Coefficient (DSC) (Eq. 3), which serves as a metric that is sensitive to both the distance and the agreement of curve shape between the DVF-derived and the reference trajectories (see [Figure 4] for illustration of ai, ri, and pmax).
|Figure 4: Four-dimensional-computed tomography and four-dimensional-magnetic resonance imaging displacement vector field trajectories for the SI direction are shown along with the reference trajectory|
Click here to view
Where A is the area encompassed by the DVF trajectory and the X-axis, B is the area encompassed by the reference trajectory and the X-axis.
| Results|| |
Among the 5 patients analyzed in this study, the median respiratory amplitude of the reference trajectories in the ML, AP, and SI direction is 1.71 mm, 3.21 mm, and 7.75 mm, respectively. Since the median respiratory amplitude of the reference trajectories in the ML direction is smaller than the inplane resolution of the cine images, and the accuracy of the tracking program is one pixel, the tracking result may be heavily interfered with random errors and thus considered not reliable. Therefore, the motion in the ML direction is excluded from the following analysis.
As shown in [Table 1], 4D-MRI DVF-derived trajectories show better agreement with reference trajectories in terms of 4D TRE in both motion directions. A considerable variation of the CC exists, with the smallest being 0.17 (AP CT-reference) and the largest being 0.96 (SI MRI-reference). On average, the 4D-MRI DVF-derived trajectories show better correlation with reference trajectories. The DSC result shows that in both motion directions, 4D-MRI DVF-derived trajectories show better agreement than 4D-CT DVF-derived trajectories, in agreement with results of 4D TRE and CC. Except for patient 2, 4D-MRI DVF-derived trajectories reach maximum displacement concurrently with reference trajectories whereas 4D-CT DVF-derived trajectories show delayed maximum displacement. As shown in the table, 4D-MRI DVF-derived trajectories show better agreement with reference trajectories in terms of the phase of maximum displacement than 4D-CT DVF-derived trajectories in both the AP and the SI directions. A trend between the AP and the SI directions is also observed that the discrepancies of the maximum displacement for CT-reference and MRI-reference in the AP direction are both larger than in the SI direction. It should be noted that the absolute average, which is the average of 4D TRE between the phases of maximum displacement, is used here.
|Table 1: Four-dimensional target registration error, correlation coefficient, dice similarity coefficient and difference in the phase of maximum displacement between the four-dimensional computed tomography or four-dimensional-magnetic resonance image displacement vector field trajectory and the reference trajectory|
Click here to view
| Discussion|| |
In this study, performance of DIR on 4D-CT and 4D-MRI of the liver was evaluated by comparing respiratory motion determined from DVFs against respiratory motion extracted from cine MRI. Our preliminary results indicated that motion estimation based on 4D-MRI, on average, matched better with ground truth motion as compared to that based on 4D-CT (AP: 1.0 ± 0.4 mm vs. 1.5 ± 0.5 mm; SI: 1.9 ± 0.7 mm vs. 2.2 ± 0.8 mm). The 4D TRE of our study is overall in agreement with post-registration mean absolute errors in the liver in 4D-CT reported by Brock et al. In our study, the errors in the AP direction in 4D-MRI are found to be smaller than those previously reported (0.3–1.3 mm vs. 1.2–3.3 mm). The errors in the AP direction in 4D-CT (1.1–2.0 mm vs. 1.2–3.3 mm) and in the SI direction in both 4D-CT (1.2–3.0 mm vs. 1.2–7.4 mm) and 4D-MRI (1.0–2.8 mm vs. 1.2–7.4 mm) are comparable to results reported in the previous study. It is expected that the location, size, and contrast of the tumor in CT may have an effect on the results, which is of interest to determine in a later study with more patients. However, the major source of uncertainty in 4D-CT is the low soft-tissue contrast (low tumor contrast), which we believe, leads to the underperformance in DIR as compared to 4D-MRI. The clinical significance of these findings is application dependent. Small differences between 4D-MRI and 4D-CT may not affect certain applications such as contouring but may lead to meaningful impact to other applications such as dose mapping and function estimation (e.g. liver elasticity). Considering that the target investigated in this study in an ROI with a similar size of a tumor rather than points used in previous studies, these findings again emphasizes that DIR must be used with caution as registration errors are still present even after averaging over an ROI. It is apparent that 4D TREs in the SI direction is in general greater than those in the AP direction, confirming that DVF errors are correlated with the motion magnitude as demonstrated in the study by Yeo et al.
In contrast, the CC was observed to be more consistent than TRE between patients. Since the phases of 4D images represent the relative temporal position in a cycle, the period is not reflected in 4D images. Moreover, although a DVF-derived motion trajectory reflects the amplitude of breathing cycles, the CC only depends on curve shapes and ignores difference in amplitude. As shown in our results, MR-cine CCs in the SI direction are close to 1 except for patient 2. This discrepancy can be explained by the large Δpmax, indicating large phase shifts between respiratory motion extracted from 4D-CT and 4D-MRI and that extracted from cine MRI.
Although MRI has been long known to be able to provide better soft tissue contrast, low temporal resolution of 3D MRI resulted from long acquisition time hinders the applicability for motion evaluation. Recently developed 4D-MRI techniques can resolve the motion within a breathing cycle, enabling the trajectory-based evaluation used in this study. This approach provides more insight into DIR accuracy within a breathing cycle. Although 10-phase 4D-CT has been long used as a standard procedure in the course of radiation treatment, most previous studies have focused on the DIR accuracy between two static volumes, typically the EOE and the EOI phases. The two-phase approach provides a rough approximation to the respiratory motion, whereas the trajectory approach is able to provide more perspectives to evaluate the DIR accuracy than displacement between two images.
We acknowledge that there are a few limitations in this study. First, the number of DIR algorithms studied is limited. The B-spline DIR algorithm used in this study is one of the most commonly used method in clinic and research, the results of this study are therefore considered representative and clinically relevant. Second, the number of patient included in this study is limited. Despite the small number of subjects, our study clearly showed the trend that 4D-MRI enhances the DIR performance in the liver region as compared to 4D-CT. Considering that 4D-MRI is still a developing technology, it can be expected that future 4D-MRI techniques with improved image quality can further improve the DIR performance in the liver. Studies with a larger sample size and more DIR algorithms are warranted in the future to demonstrate the clinical and statistical significance of 4D-MRI over 4D-CT in liver motion estimation. Third, it is worth noting that original 4D-CT and 4D-MRI images do not have the same resolution, which may result in certain error in DIR. To minimize the potential effect, all images are interpolated to the same resolution for DIR. It was found in our study (data not shown) that DVFs remain nearly the same for the interpolated images and the original images. Forth, the comparing image datasets (4D-CT, 4D-MRI, cine MRI) were not acquired at exactly the same condition, for example, breathing and positioning could be different. Nevertheless, it was assumed the patient's breathing pattern retains the same despite small variations. The motion trajectories obtained from these datasets should represent the major motion pattern of the patient. It is challenging to perfectly reproduce the same scanning condition between the CT and MRI scans in practice in real patients. It might be helpful in the future to perform a deformable physical phantom for a better-controlled evaluation.
Our preliminary results in this pilot study demonstrated that DIR in the liver varies between patients and image modalities. Despite individual variations, there is a clear trend that DVFs derived from 4D-MRI generally matched better with the physiological ground truth than those from 4D-CT, indicating that 4D-MRI can potentially provide more accurate motion estimation of the liver than 4D-CT. It can be expected that many DIR-based radiation therapy applications, such as 4D dose accumulation and contour propagation, can benefit from 4D-MRI which provides super soft-tissue contrast and subsequently more physiologically accurate DVFs as compared to 4D-CT.
The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.
Financial support and sponsorship
This research was supported by the National Cancer Institute (1R21CA165384) of the National Institutes of Health.
Conflicts of interest
There are no conflicts of interest.
| References|| |
Boldea V, Sharp GC, Jiang SB, Sarrut D. 4D-CT lung motion estimation with deformable registration: Quantification of motion nonlinearity and hysteresis. Med Phys
2008; 35 (3): 1008–18.
Yang D, Lu W, Low DA, Deasy JO, Hope AJ, El Naqa I. 4D-CT motion estimation using deformable image registration and 5D respiratory motion modeling. Med Phys
2008; 35 (10): 4577–90.
Speight R, Sykes J, Lindsay R, Franks K, Thwaites D. The evaluation of a deformable image registration segmentation technique for semi-automating internal target volume (ITV) production from 4DCT images of lung stereotactic body radiotherapy (SBRT) patients. Radiother Oncol
2011; 98 (2): 277–83.
Wijesooriya K, Weiss E, Dill V, Dong L, Mohan R, Joshi S, Keall PJ. Quantifying the accuracy of automated structure segmentation in 4D CT images using a deformable image registration algorithm. Med Phys
2008; 35 (4): 1251–60.
Birkner M, Yan D, Alber M, Liang J, Nusslin F. Adapting inverse planning to patient and organ geometrical variation: Algorithm and implementation. Med Phys
2003; 30 (10): 2822–31.
Velec M, Moseley JL, Eccles CL, Craig T, Sharpe MB, Dawson LA, Brock KK. Effect of breathing motion on radiotherapy dose accumulation in the abdomen using deformable registration. Int J Radiat Oncol Biol Phys
2011; 80 (1): 265–72.
Zhang P, Hugo GD, Yan D. Planning study comparison of real-time target tracking and four-dimensional inverse planning for managing patient respiratory motion. Int J Radiat Oncol Biol Phys
2008; 72 (4): 1221–7.
Reinhardt JM, Ding K, Cao K, Christensen GE, Hoffman EA, Bodas SV. Registration-based estimates of local lung tissue expansion compared to xenon CT measures of specific ventilation. Med Image Anal
2008; 12 (6): 752–63.
Zhong H, Jin JY, Ajlouni M, Movsas B, Chetty IJ. Measurement of regional compliance using 4DCT images for assessment of radiation treatment. Med Phys
2011; 38 (3): 1567–78.
Brock KK. Results of a multi-institution deformable registration accuracy study (MIDRAS). Int J Radiat Oncol Biol Phys
2010; 76 (2): 583–96.
Liu F, Hu Y, Zhang Q, Kincaid R, Goodman KA, Mageras GS. Evaluation of deformable image registration and a motion model in CT images with limited features. Phys Med Biol
2012; 57 (9): 2539–54.
Yeo UJ, Supple JR, Taylor ML, Smith R, Kron T, Franich RD. Performance of 12 DIR algorithms in low-contrast regions for mass and density conserving deformation. Med Phys
2013; 40 (10): 101701.
Stewart BW, Wild CP, editors. World cancer report 2014. Lyon: International Agency for Research on Cancer; 2014.
Ruers T, Bleichrodt RP. Treatment of liver metastases, an update on the possibilities and results. Eur J Cancer
2002; 38 (7): 1023–33.
Rohlfing T, Maurer CR Jr., O'Dell WG, Zhong J. Modeling liver motion and deformation during the respiratory cycle using intensity-based nonrigid registration of gated MR images. Med Phys
2004; 31 (3): 427–32.
Kirilova A, Lockwood G, Choi P, Bana N, Haider MA, Brock KK, Eccles C, Dawson LA. Three-dimensional motion of liver tumors using cine-magnetic resonance imaging. Int J Radiat Oncol Biol Phys
2008; 71 (4): 1189–95.
Kirilova A, Lockwood G, Choi P, Bana N, Haider MA, Brock KK, Eccles C, Dawson LA. Evaluation of lobar biomechanics during respiration using image registration. Med Image Comput Comput Assist Interv
2009; 12 (Pt 1): 739–46.
Li HS, Zhong H, Kim J, Glide-Hurst C, Gulam M, Nurushev TS, Chetty IJ. Direct dose mapping versus energy/mass transfer mapping for 4D dose accumulation: fundamental differences and dosimetric consequences. Phys Med Biol
2014; 59 (1): 173.
Cai J, Read PW, Altes TA, Molloy JA, Brookeman JR, Sheng K. Evaluation of the reproducibility of lung motion probability distribution function (PDF) using dynamic MRI. Phys Med Biol
2007; 52 (2): 365–73.
Cai J, Sheng K, Sheehan JP, Benedict SH, Larner JM, Read PW. Evaluation of thoracic spinal cord motion using dynamic MRI. Radiother Oncol
2007; 84 (3): 279–82.
Cai J, Chang Z, Wang Z, Paul Segars W, Yin FF. Four-dimensional magnetic resonance imaging (4D-MRI) using image-based respiratory surrogate: A feasibility study. Med Phys
2011; 38 (12): 6384–94.
Nie K, Chuang C, Kirby N, Braunstein S, Pouliot J. Site-specific deformable imaging registration algorithm selection using patient-based simulated deformations. Med Phys
2013; 40 (4): 041911.
Kadoya N, Fujita Y, Katsuta Y, Dobashi S, Takeda K, Kishi K, Kubozono M, Umezawa R, Sugawara T, Matsushita H, Jingu K. Evaluation of various deformable image registration algorithms for thoracic images. J Radiat Res
2014; 55 (1): 175–82.
Mageras GS, Yorke E. Deep inspiration breath hold and respiratory gating strategies for reducing organ motion in radiation treatment. Semin Radiat Oncol
2004; 14 (1): 65–75.
Rietzel E, Pan T, Chen GT. Four-dimensional computed tomography: Image formation and clinical protocol. Med Phys
2005; 32 (4): 874–89.
[Figure 1], [Figure 2], [Figure 3], [Figure 4]