

ORIGINAL ARTICLE 

Year : 2017  Volume
: 3
 Issue : 6  Page : 185193 

Markerless fourdimensionalcone beam computed tomography projectionphase sorting using prior knowledge and patient motion modeling: A feasibility study
Lei Zhang^{1}, Yawei Zhang^{2}, You Zhang^{3}, Wendy B Harris^{4}, FangFang Yin^{5}, Jing Cai^{6}, Lei Ren^{4}
^{1} Medical Physics Graduate Program, Duke University, Durham, NC; Department of Radiation Oncology, Duke University Medical Center, Durham, NC, USA ^{2} Department of Radiation Oncology, Duke University Medical Center, Durham, NC, USA ^{3} Medical Physics Graduate Program, Duke University, Durham, NC; Department of Radiation Oncology, Duke University Medical Center, Durham, NC; Department of Radiation Oncology, UT Southwestern Cancer Center, TX, USA ^{4} Medical Physics Graduate Program, Duke University; Department of Radiation Oncology, Duke University Medical Center, Durham, NC, USA ^{5} Medical Physics Graduate Program, Duke University; Department of Radiation Oncology, Duke University Medical Center, Durham, NC, USA; Medical Physics Graduate Program, Duke Kunshan University, Kunshan, Jiangsu, China ^{6} Medical Physics Graduate Program, Duke University, Durham, NC, USA; Medical Physics Graduate Program, Duke Kunshan University, Kunshan, Jiangsu; Department of Health Technology and Informatics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China
Date of Web Publication  29Dec2017 
Correspondence Address: Lei Ren Department of Radiation Oncology, Duke University Medical Center, PO Box. 3295, Durham, NC 27710 USA
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/ctm.ctm_38_17
Aim: During cancer radiotherapy treatment, onboard fourdimensionalcone beam computed tomography (4DCBCT) provides important patient 4D volumetric information for tumor target verification. Reconstruction of 4DCBCT images requires sorting of acquired projections into different respiratory phases. Traditional phase sorting methods are either based on external surrogates, which might miscorrelate with internal structures; or on 2D internal structures, which require specific organ presence or slow gantry rotations. The aim of this study is to investigate the feasibility of a 3D motion modelingbased method for markerless 4DCBCT projectionphase sorting. Methods: Patient 4DCT images acquired during simulation are used as prior images. Principal component analysis (PCA) is used to extract three major respiratory deformation patterns. Onboard patient image volume is considered as a deformation of the prior CT at the endexpiration phase. Coefficients of the principal deformation patterns are solved for each onboard projection by matching it with the digitally reconstructed radiograph (DRR) of the deformed prior CT. The primary PCA coefficients are used for the projectionphase sorting. Results: PCA coefficients solved in nine digital phantoms (XCATs) showed the same pattern as the breathing motions in both the anteroposterior and superoinferior directions. The mean phase sorting differences were below 2% and percentages of phase difference < 10% were 100% for all the nine XCAT phantoms. Five lung cancer patient results showed mean phase difference ranging from 1.62% to 2.23%. The percentage of projections within 10% phase difference ranged from 98.4% to 100% and those within 5% phase difference ranged from 88.9% to 99.8%. Conclusion: The study demonstrated the feasibility of using PCA coefficients for 4DCBCT projectionphase sorting. High sorting accuracy in both digital phantoms and patient cases was achieved. This method provides an accurate and robust tool for automatic 4DCBCT projection sorting using 3D motion modeling without the need of external surrogate or internal markers.
Keywords: Fourdimensionalcone beam computed tomography, markerless, motion modeling, phase sorting, prior knowledge
How to cite this article: Zhang L, Zhang Y, Zhang Y, Harris WB, Yin FF, Cai J, Ren L. Markerless fourdimensionalcone beam computed tomography projectionphase sorting using prior knowledge and patient motion modeling: A feasibility study. Cancer Transl Med 2017;3:18593 
How to cite this URL: Zhang L, Zhang Y, Zhang Y, Harris WB, Yin FF, Cai J, Ren L. Markerless fourdimensionalcone beam computed tomography projectionphase sorting using prior knowledge and patient motion modeling: A feasibility study. Cancer Transl Med [serial online] 2017 [cited 2018 Oct 17];3:18593. Available from: http://www.cancertm.com/text.asp?2017/3/6/185/221915 
Introduction   
Target control and normal tissue complication probabilities are highly correlated to the target localization accuracy in radiation therapy.^{[1],[2]} Accurate localization of moving targets is challenging due to the respiratory motion of the normal tissue and target.^{[3]} Conventionally, threedimensionalconebeam computed tomography (3DCBCT) has been used for target localization before the treatment. However, 3DCBCT does not capture the motion information and only provides an average location of the moving target, which may not be sufficient for highprecision radiotherapy treatments. More recently, 4DCBCT has been developed for 4D localization of moving targets. 4DCBCT reconstructs patient onboard 4D images by first sorting the acquired cone beam projections into different respiratory phases.^{[4],[5],[6],[7],[8],[9]} The accuracy of the projection sorting determines the accuracy of the reconstructed 4DCBCT images, which in turn affects the tumor localization accuracy using 4DCBCT.
Previous projection sorting algorithms can be classified into the following categories: (1) External surrogatebased sorting. This method uses the motion of external surrogates such as abdominal displacement or lung air volume to determine the respiratory phase. Commercially available products include the Varian realtime position management (RPM) system (Varian Medical Systems, Palo Alto, CA, USA)^{[10],[11]} and straingauged Anzai belt (Anzai Medical Systems, Tokyo, Japan).^{[12],[13]} Spirometry was also implemented to detect changes in lung air volume.^{[14]} All of these external surrogates were assumed to correlate with the displacement of internal anatomy, but studies have demonstrated that uncertainties exist in this relationship,^{[15],[16],[17],[18]} which can potentially lead to sorting errors. (2) Internal surrogatebased sorting. To mitigate the limitations of external surrogates, several internal “markerless” techniques were proposed. One example is known as the Amsterdam shroud (AS) technique,^{[19]} in which the diaphragm motion is enhanced by converting 2D projections into the socalled AS image and then breathing signal is extracted by temporal derivative. However, this technique requires a visible oscillating structure present across all projection angles, which may not always be available. Berbeco et al.^{[20]} proposed a technique based on the radiological pathlength change with lung volume expansion/retraction. The breathingphase information is extracted by analyzing the image intensity fluctuation of fluoroscopic images in the middle of lung ^{[20]} or region of interest in CBCT projections.^{[21]} However, the angular dependence of image intensities may affect the accuracy of the sorting. Siochi ^{[22]} developed a motion tracking method by converting the megavoltage CBCT rotating coordinate system into a patient coordinate system. The method requires the diaphragm to be present in the projections images, which may not always be available for upper lobe lesions. Lewis et al.^{[23]} proposed a templatebased tumor tracking algorithm that registers each phase of 4DCT to CBCT and generates digitally reconstructed radiographs (DRRs) to match with the projections. This method could be affected by the “out of range” problem when the onboard motion range exceeds that of the template. Vergalasova et al.^{[24]} proposed a Fourier domainbased method to extract breathing signal from CBCT projections. The accuracy of this method is degraded for 4DCBCT scans with faster gantry rotation speeds due to the angular dependence of the image intensities.
The aforementioned internal markerless phase sorting techniques either require specific anatomical features,^{[19],[22],[23]} or are affected by gantry rotation angle or speed.^{[20],[21],[24]} Recently, our group and others have proposed using prior information and motion modeling for CBCT volume reconstruction with limited angle cone beam projections.^{[9],[25]} The CBCT volume can be estimated by iteratively matching DRRs of deformed prior CT to onboard projection images. Our previous results demonstrated that a single projection is not adequate for CBCT reconstruction when there is substantial breathing pattern change from simulation to onboard treatment.^{[8],[9]} However, we hypothesized in this study that the motion model coefficients solved from a single projection are adequate for projectionphase sorting for 4DCBCT reconstruction.^{[26]} Since the motion model coefficients are correlated with the overall 3D motion information of the patient, they can potentially provide more robust information for projection sorting without the need of specific anatomical features or gantry rotation speeds. In our study, the method was developed and evaluated using XCAT simulation with different scenarios and lung cancer patient CBCT data with different gantry rotation speeds and scanning modes.
Methods   
Motion modeling from prior fourdimensionalcomputed tomography
As illustrated in [Figure 1], patient motion model is generated from 10phase planning 4DCT images. One phase of the planning 4DCT (e.g., end of exhalation phase) is defined as the “prior.” The other nine phases are deformed to the prior using Velocity AI (Varian Medical Systems, Palo Alto, USA) to generate nine 3D deformation vector fields (DVFs) which describe patient respiratory deformations. Principal component analysis (PCA) is then used to extract the principal components {PC_{i}} of the deformation fields, which represent the major deformation patterns of the patient. Patient respiratory deformation at any instant can be represented as a linear combination of the principal components. In this study, we used the first three principal components corresponding to the three largest eigenvalues as they were proven to be sufficient in depicting lung motion:^{[27],[28],[29]}  Figure 1: Flowchart of patient motion modeling and onboard principal component analysis coefficient calculation
Click here to view 
Where, D is the deformation field vector at any instant, D_{avg} is the average of the nine deformation fields initially extracted from 4DCT, PC_{i} is the i^{th} principal component, and w_{i} represents the corresponding coefficients for the principal components.
Solving the principal component analysis coefficients for each single cone beam computed tomography projection
The onboard CBCT volume at any instant is approximately considered as a deformation from the CT “prior.” The deformation field map D is represented as a weighted linear combination of the principal motion modes {PCi} as shown in Eq (1).
The weighting coefficients {w_{i}} are solved by minimizing the objective function f (w), which is defined based on the data fidelity constraint:
Where, NCC is normalized cross correlation between two 2D images, M is projection operator calculating DRR from new CBCT volume, CBCT_{new} is the new volume after applying estimated deformation map onto prior volume I_{prior}, and OBI is the single CBCT onboard projection image.
The PCA coefficients {w_{i}} are solved iteratively using the gradient descent method with a maximum of ten iterations and ten backtracking line searches for each iteration. The PCA coefficients describe the degree of 3D patient deformation caused by the respiratory motion, and therefore can be used as surrogates for 4D projection sorting. In our study, the primary PCA coefficients along the superoinferior (SI) and/or anteroposterior (AP) directions were used for CBCT projectionphase sorting due to the more substantial respiratory motions along these two directions.
Phase sorting based on principal component analysis coefficients
The PCA coefficients {w_{i}} are solved for all projections and the primary coefficient w_{1} in the SI or AP direction was used for phase sorting. The coefficients are plotted for all projections and the valley projections are defined as the peakinspiration phase (0% or 100%). The phase for each projection is defined as the percentage of the respiratory cycle that has passed since peak inspiration.
XCAT digital phantom study
The 4D digital extendedcardiactorso (XCAT) phantom ^{[30]} was used to test the algorithm. Based on the human anatomical database from the National Library of Medicine, XCAT uses nonuniform rational Bspline surfaces to model highly realistic and detailed human anatomical structures and images. It can be utilized to generate 4D images according to respiratory profiles and anatomical parameters specified by the user. XCAT has been widely used in multiple studies as an algorithm and as an evaluation and verification tool.^{[9],[24],[27],[31],[32],[33]}
The respiratory motion of the body volume is controlled by two breathing curves: diaphragm and chest wall curves. The diaphragm curve controls both diaphragm motion and motions of the lung, liver, stomach, and other downstream organs. It generally determines motion in the SI direction. The chest wall curve controls AP expansions of the body, the ribcage, and lungs. In this study, both curves were simplified as sinusoidal curves with 5 s respiratory period. The peaktopeak amplitude of the two curves was set to 3 and 2 cm, respectively. A spherical lesion of 30 mm diameter was inserted in the middle of the lung.
A tenphase 4DCT was then simulated as the prior knowledge. We used 40 keV monochromatic CT source to approach the effective energy of 120 kVp polychromatic spectrum used in clinical CT scanners. CT volume of each phase was composed of 256 × 256 × 150 voxels, with 1.67 mm isotropic resolution. The endexpiration phase was selected as the prior volume as the body structure is most stable in this phase.
As shown in [Table 1], nine XCAT scenarios were generated to simulate 4DCBCT volumes. Scenario 0 represents no breathing pattern or anatomical changes from prior 4DCT, while scenarios 1–8 include changes in tumor motion amplitude (S1: 3 cm to 2 cm), tumor diameter (S2: 30 mm to 20 mm, S3: 30 mm to 40 mm), tumor spatial shifts (S4: 8 mm SI, S5: 8 mm AP, and S6: 5 mm in SI, AP, and LR), and motion removal in SI or both SI and AP directions (S7, S8).  Table 1: Fourdimensional digital extendedcardiactorso scenarios simulating changes in respiratory motion amplitude, tumor dimension and position, and respiratory motion directions
Click here to view 
These 4DCBCT volumes were set as “ground truth” onboard images to simulate onboard projections to be sorted by the proposed method. Totally around 200 projections within 20 respiratory cycles were simulated over the 200° scan angle. The source to isocenter distance was set to 100 cm, and isocenter of detector distance was set to 50 cm. Each projection contains 512 × 384 pixels with each pixel of 0.78 mm in both dimensions.
Patient study
In addition to the XCAT digital phantom studies, the proposed method was evaluated on five sets of patient data that were previously acquired under an investigational 4DCBCT study.^{[34],[35]} The 4DCBCT projections were acquired with an Xray flat panel detector mounted orthogonally to the MV treatment gantry on the Varian Trilogy system (Varian Medical Systems, Palo Alto, CA, USA). Two of the patients were scanned with fullfan projections over a 200° arc at slowgantry speeds of 0.71 and 0.6°/s, with total scan lengths of 4.5 and 5.7 min and frame rates of 7 and 5 fps, respectively. Three of the patients were scanned with halffan projections over 360° arc at normal gantry speed of 6°/s, with total scan length of 1 min and frame rate of 10, 15, and 15 fps, respectively.
Phase sorting evaluation
In order to evaluate the phase sorting accuracy of the proposed technique, respiratory phases were derived from the ground truth respiratory signal in the digital phantom study and visual inspection of the onboard projections in patient study. Projections that correspond to peak inspiration were identified and recorded as 0% or 100%. The projection phases inbetween peak inspirations were linearly interpolated as before. This “manual phase sorting” served as the gold standard for comparison.
The projectionphase sorting accuracy was evaluated by three parameters. One is the average difference in phases across the entire dataset, which is defined as:
Where, n is the total number of projections, i is the index of projection, phase (i_{manual}) is the phase value sorted by manual method for the i^{th} projection, and phase (i_{pca}) is the phase value sorted by PCA coefficient based method for the i^{th} projection.
The other two parameters are the percentage of projections with a phase difference within 10% or 5%:
Where, n, phase (i_{manual}), and phase (i_{pca}) had the same definition.
The three quantitative evaluations were performed on all the XCAT simulation scenarios and five patient data sets. All image processing and data analyses were performed with inhouse developed MATLAB programs (The Mathworks Inc., Natick, MA, USA).
Results   
XCAT study
To verify the effectiveness of the PCA coefficients in representing the respiratory motion in the original prior 4DCT images, we calculated the coefficients along all the three directions for the nine DVFs extracted from the 4DCT, as shown in [Figure 2]. Sinusoidal respiration motion patterns are manifested in the coefficients of the first principal component along all directions. Second and third PCA coefficients (w2, w3) did not show clear sinusoidal pattern since the 2^{nd} and 3^{rd} principal components capture much smaller portion of the variances of the respiratory deformations. The coefficients for the SI and AP directions showed clearer breathing patterns than those for the lateral direction, due to the more substantial respiratory motions along SI and AP directions in the XCAT phantom. In the following studies, we will use the PCA coefficient of the first principal component (w1) for projection sorting.  Figure 2: Principal component analysis coefficients of nine deformation vector fields of prior fourdimensionalcomputed tomography. From top to bottom, the principal component analysis coefficients (w1, w2, and w3) correspond to deformable field vectors along different directions (superoinferior, anteroposterior, and lateral). From left to right, the principal component analysis coefficients correspond to the first three primary principal components. The Xaxis represents the phase number of the nine deformation vector fields used to calculate principal component analysis coefficients
Click here to view 
[Figure 3] shows the calculated primary PCA coefficients (w1) for each CBCT projection in XCAT scenario 0 in three orthogonal directions. Fullfan scanning with 200° rotation was simulated, with a rotation speed of 3.3°/s and 0.9° projection interval. The PCA coefficients calculated for all projections formed a sinusoidal cycle pattern, which was most clear in SI and AP directions and less apparent in lateral direction.  Figure 3: Primary principal component analysis coefficient (w1) for three orthogonal motion directions for XCAT scenario 0. Each dot represents principal component analysis coefficient calculated for one onboard projection. From top to bottom: superoinferior, anteroposterior, and lateral directions, respectively
Click here to view 
[Figure 4] shows the effect of changes in motion amplitude and tumor anatomy from prior 4DCT to onboard 4DCBCT scans on the calculated PCA coefficients. [Figure 4]a shows that, with lower motion amplitude, the oscillation pattern of PCA coefficient stayed the same, while the amplitude decreased (red dotted line). [Figure 4]b illustrates the sensitivity of PCA coefficient in detecting the changes in respiratory motion directions. The PCA coefficients showed no cyclic pattern in the AP direction when the respiratory motion in AP direction was removed (red), and there was no cyclic pattern in both AP and SI directions when the respiratory motions in both AP and SI directions were removed (green). [Figure 4]c demonstrates that changes of tumor diameter from 30 mm to 20 mm or 40 mm did not change the cyclic patterns or amplitudes of the PCA coefficients (green and red). [Figure 4]d shows that shifts of tumor central location in three orthogonal directions (blue, green, and red) did not change the cyclic pattern or amplitudes of the PCA coefficients.  Figure 4: Primary principal component analysis coefficients (w1) of XCAT scenarios 0–8 in superoinferior and anteroposterior directions. (a) Change in motion amplitude; (b) changes in motion directions (superoinferior and anteroposterior, superoinferior only, and no motion); (c) changes in tumor size (20 mm, 30 mm, and 40 mm); and (d) shifts in tumor central location in superoinferior, anteroposterior, and diagonal directions
Click here to view 
[Table 2] shows the phase sorting accuracy of the nine XCAT scenarios. For all the eight quantifiable scenarios, the average phase difference was 2% or less. All of the projections in the eight scenarios showed a < 10% phase difference from the ground truth. Similar accuracies were observed using PCA coefficients in SI and AP directions.  Table 2: Principal component analysis coefficientbased phase sorting accuracy for nine fourdimensional digital extendedcardiactorso scenarios
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Patient study
[Figure 5] shows a representative OBI and final DRR of the deformed prior CT images in a patient case with halffan mode and fast gantry rotation (~1 min). The anatomy showed in the final estimated DRR [Figure 5]b agrees well with the OBI [Figure 5]a. The normalized cross correlation between OBI and final DRRs optimized in Equation 2 was above 0.9 for most of the projections, as shown in [Figure 5]c.  Figure 5: Patient cone beam computed tomography onboard projection and final digitally reconstructed radiograph after optimization. (a) Onboard projection; (b) final digitally reconstructed radiograph after optimization; and (c) normalized cross correlation between onboard projection and digitally reconstructed radiographs for all 885 projections
Click here to view 
[Figure 6] displays the solved PCA coefficients (SI direction, primary) for all the five CBCT patients. Respiratory motion patterns were clearly manifested by the changes in the coefficients in both fullfan slow gantry rotation cases (patients 1 and 2) and halffan fast gantry rotation cases (patients 3–5). As expected, only the SI direction coefficients showed clear breathing patterns, possibly because SI is perpendicular to the OBI projection direction and is the major breathing motion direction.  Figure 6: Principal component analysis coefficients in the SI direction for all the five cone beam computed tomography patients. Patients 1–2, fullfan cone beam computed tomography slow gantry rotation (~5 min); patients 3–5, halffan cone beam computed tomography fast gantry rotation (~1 min). The temporal resolution in the Xaxis is not to the same scale because of different gantry rotation speeds and frame rate settings for each patient
Click here to view 
[Figure 7] shows the evaluation process for the PCA coefficientbased sorting for patient 1. The sorting result based on PCA coefficients is shown in blue, with 0/100% phases corresponding to the valleys in the coefficient plot in [Figure 6]. Manual phase sorting result is shown in red, with 0/100% phases corresponding to visually identified peak inspiration projections. The phase differences were < 10% for most of the projections.  Figure 7: Comparison of principal component analysis coefficientbased sorting with manual phase sorting. Top, phase sorting result using principal component analysis coefficient; middle, phase sorting result by visual inspection; and bottom, phase difference between the two methods
Click here to view 
[Table 3] shows the accuracy of PCA coefficientbased phase sorting for the five lung cancer patient 4DCBCT datasets. The average phase differences ranged from 1.62% to 2.23%. The percentage of projections with phase sorting difference < 10% ranged from 98.4% to 100% and ranged from 88.9% to 99.8% when the sorting difference threshold reduced to 5%.  Table 3: Principal component analysis coefficientbased phase sorting accuracy for five lung cancer patients
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Discussion   
The results presented in this article have demonstrated the feasibility of using patient motion modelingbased PCA coefficients as an internal markerless surrogate for 4DCBCT phase sorting. High phase sorting accuracy was achieved in both XCAT digital phantoms and real 4DCBCT lung cancer patient data sets. The method avoids using any internal marker or external surrogates which may cause complications such as pneumothorax or errors due to potential mismatch between external surrogates and internal organ motions.
As demonstrated in the XCAT digital phantoms, this method showed robustness against patient breathing or anatomical changes from prior to onboard imaging, including changes in tumor size, location, and breathing motion amplitudes. By controlling the motion directions and changing the breathing amplitudes in the digital phantom, we further demonstrated that the primary PCA coefficient can also be indicative of the major motion directions and amplitudes.
The proposed motion modeling and PCA coefficientbased method utilizes prior 4DCT, 3D deformation maps, dimensional reduction, onboard CBCT projection matching, and iterative optimization for phase sorting. Instead of using 1D or 2Dbased information as in previous methods,^{[31],[32],[14],[20],[21],[24]} 3D motion information is used in searching for the correct breathing phase. Using information in this higher dimension may have led to several advantages of this method.
First, different from the Fourier transformbased phase sorting method ^{[24]} or image intensity based methods,^{[21]} this method does not have gantry rotation speed dependence. This advantage has been demonstrated in our 4DCBCT patient datasets, in which a high accuracy was achieved with both fast and slow rotation speeds. This feature allows us to increase the gantry rotation speed to substantially reduce the scanning time and imaging dose of 4DCBCT.^{[36]}
Second, no postfiltering of the surrogate is required because, rather than using the summation of Xray attenuation information in intensitybased methods, the PCA coefficient represents the overall 3D deformation based on motion modeling. Therefore, no correction for the slow changing signal due to projection pathlength angular change is needed, which is sensitive to variations in external structure or internal structure deformations.^{[21],[24]}
Finally, for halffan CBCT patient cases, lateral projections may have very limited 2D information. Using 3D motion modeling and matching, this method have achieved decent sorting results in these areas, which could be one of the contributing factors for its overall high accuracy.
This method was inspired by our earlier work in CBCT image reconstruction using the motion modeling method. Due to the suboptimal accuracy of reconstruction using motion modeling alone, Zhang et al.^{[9]} used freeform deformation to further improve the reconstruction accuracy after motion modeling. While 3D motion modeling itself may not be sufficient for 3D volumetric reconstruction, our study demonstrated that 3D motion modeling is accurate for 1D breathing signal extraction and thereafter used for projectionphase sorting. The method can be used for 4DCBCT reconstruction using either fullscan angles or limited scan angles.^{[7],[37],[38]}
XCAT results for scenarios S0, S1, S7, and S8 showed potential correlation between the values of PCA coefficients and breathing motion amplitudes, which suggests the potential to use the PCA coefficient as surrogates for amplitudebased sorting.^{[13],[39]}
The limitation of this method may be the calculation speed. On a Dell Optiplex 7010 PC with 3.4 GHz CPU and 8 GB RAM, 3–6 min is required for each projectionphase calculation. However, the PCA coefficient calculation for the projections is completely independent and thus can be paralleled. In addition, graphics processing unit acceleration can potentially accelerate the calculation speed substantially (< 1 s).^{[32]}
In conclusion, the feasibility of using the PCA coefficient of a patient respiratory motion model as an internal markerless surrogate for phase sorting of 4DCBCT projections has been demonstrated through both simulation and patient studies. The percentages of projections sorted within 10% phase difference were 100% and 98% for XCAT and patient data, respectively. The average phase differences between sorted phases and the gold standard were below 3% for both XCAT and patient data. Overall, the proposed method is promising in providing robust markerless automatic projection sorting for 4DCBCT scans.
Financial support and sponsorship
This study was financially supported by the National Institutes of Health under Grant No. R01CA184173; research grant from Varian Medical Systems.
Conflicts of interest
There are no conflicts of interest.
References   
1.  Soike M, Kilburn JM, Lucas JT, AyalaPeacock D, Blackstock AW, Kearns WT, Hinson WH, Miller AT, Petty WJ, Urbanic JJ. Image guided radiation therapy results in improved local control in lung cancer patients treated with fractionated radiation therapy for stage IIBIIIB disease. Int J Radiat Oncol Biol Phys 2013; 87 (2): S547–8. 
2.  Zelefsky MJ, Kollmeier M, Cox B, Fidaleo A, Sperling D, Pei X, Carver B, Coleman J, Lovelock M, Hunt M. Improved clinical outcomes with highdose image guided radiotherapy compared with nonIGRT for the treatment of clinically localized prostate cancer. Int J Radiat Oncol Biol Phys 2012; 84 (1): 125–9. 
3.  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 fourdimensionalcomputed tomography and fourdimensionalmagnetic resonance imaging. Cancer Transl Med 2017; 3 (5): 153–8. 
4.  Chang J, Sillanpaa J, Ling CC, Seppi E, Yorke E, Mageras G, Amols H. Integrating respiratory gating into a megavoltage conebeam CT system. Med Phys 2006; 33 (7): 2354–61. 
5.  Dietrich L, Jetter S, Tucking T, Nill S, Oelfke U. Linacintegrated 4D cone beam CT: first experimental results. Phys Med Biol 2006; 51 (11): 2939–52. 
6.  Purdie TG, Moseley DJ, Bissonnette JP, Sharpe MB, Franks K, Bezjak A, Jaffray DA. Respiration correlated conebeam computed tomography and 4DCT for evaluating target motion in Stereotactic Lung Radiation Therapy. Acta Oncol 2006; 45 (7): 915–22. 
7.  Sonke JJ, Zijp L, Remeijer P, van Herk M. Respiratory correlated cone beam CT. Med Phys 2005; 32 (4): 1176–86. 
8.  Zhang Y, Yin FF, Pan T, Vergalasova I, Ren L. Preliminary clinical evaluation of a 4DCBCT estimation technique using prior information and limitedangle projections. Radiother Oncol 2015; 115 (1): 22–9. 
9.  Zhang Y, Yin FF, Segars WP, Ren L. A technique for estimating 4DCBCT using prior knowledge and limitedangle projections. Med Phys 2013; 40 (12): 121701. 
10.  Keall PJ, Starkschall G, Shukla H, Forster KM, Ortiz V, Stevens CW, Vedam SS, George R, Guerrero T, Mohan R. Acquiring 4D thoracic CT scans using a multislice helical method. Phys Med Biol 2004; 49 (10): 2053–67. 
11.  Pan T, Lee TY, Rietzel E, Chen GT. 4DCT imaging of a volume influenced by respiratory motion on multislice CT. Med Phys 2004; 31 (2): 333–40. 
12.  Kleshneva T, Muzik J, Alber M. An algorithm for automatic determination of the respiratory phases in fourdimensional computed tomography. Phys Med Biol 2006; 51 (16): N269–76. 
13.  Wink NM, Panknin C, Solberg TD. Phase versus amplitude sorting of 4DCT data. J Appl Clin Med Phys 2006; 7 (1): 77–85. 
14.  Low DA, Nystrom M, Kalinin E, Parikh P, Dempsey JF, Bradley JD, Mutic S, Wahab SH, Islam T, Christensen G, Politte DG, Whiting BR. A method for the reconstruction of fourdimensional synchronized CT scans acquired during free breathing. Med Phys 2003; 30 (6): 1254–63. 
15.  Gierga DP, Brewer J, Sharp GC, Betke M, Willett CG, Chen GT. The correlation between internal and external markers for abdominal tumors: implications for respiratory gating. Int J Radiat Oncol 2005; 61 (5): 1551–8. 
16.  Hoisak JD, Sixel KE, Tirona R, Cheung PC, Pignol JP. Correlation of lung tumor motion with external surrogate indicators of respiration. Int J Radiat Oncol 2004; 60 (4): 1298–306. 
17.  Koch N, Liu HH, Starkschall G, Jacobson M, Forster K, Liao Z, Komaki R, Stevens CW. Evaluation of internal lung motion for respiratorygated radiotherapy using MRI: part I – Correlating internal lung motion with skin fiducial motion. Int J Radiat Oncol 2004; 60 (5): 1459–72. 
18.  Yan H, Yin FF, Zhu GP, Ajlouni M, Kim JH. The correlation evaluation of a tumor tracking system using multiple external markers. Med Phys 2006; 33 (11): 4073–84. 
19.  Zijp L, Sonke JJ, van Herk M. Extraction of the Respiratory Signal from Sequential Thorax ConeBeam Xray Images. In: Proceedings of the 14th International Conference on the Use of Computers in Radiation Therapy; 2004 May 914; Seoul, Korea. 
20.  Berbeco RI, Mostafavi H, Sharp GC, Jiang SB. Towards fluoroscopic respiratory gating for lung tumours without radiopaque markers. Phys Med Biol 2005; 50 (19): 4481–90. 
21.  Kavanagh A, Evans PM, Hansen VN, Webb S. Obtaining breathing patterns from any sequential thoracic Xray image set. Phys Med Biol 2009; 54 (16): 4879–88. 
22.  Siochi RA. Deriving motion from megavoltage localization cone beam computed tomography scans. Phys Med Biol 2009; 54 (13): 4195–212. 
23.  Lewis JH, Li R, Watkins WT, Lawson JD, Segars WP, Cerviño LI, Song WY, Jiang SB. Markerless lung tumor tracking and trajectory reconstruction using rotational conebeam projections: a feasibility study. Phys Med Biol 2010; 55 (9): 2505–22. 
24.  Vergalasova I, Cai J, Yin FF. A novel technique for markerless, selfsorted 4DCBCT: feasibility study. Med Phys 2012; 39 (3): 1442–51. 
25.  Mishra P, Li R, Mak RH, Rottmann J, Bryant JH, Williams CL, Berbeco RI, Lewis JH. An initial study on the estimation of timevarying volumetric treatment images and 3D tumor localization from single MV cine EPID images. Med Phys 2014; 41 (8): 171–8. 
26.  Harris W, Zhang Y, Yin FF, Ren L. Estimating 4DCBCT from prior information and extremely limited angle projections using structural PCA and weighted freeform deformation for lung radiotherapy. Med Phys 2017; 44 (3): 1089–104. 
27.  Li R, Lewis JH, Jia X, Gu X, Folkerts M, Men C, Song WY, Jiang SB. 3D tumor localization through realtime volumetric Xray imaging for lung cancer radiotherapy. Med Phys 2011; 38 (5): 2783–94. 
28.  Ruan D, Keall P. Online prediction of respiratory motion: multidimensional processing with lowdimensional feature learning. Phys Med Biol 2010; 55 (11): 3011–25. 
29.  Vaman C, Staub D, Williamson J, Murphy MJ. A method to map errors in the deformable registration of 4DCT images. Med Phys 2010; 37 (11): 5765–76. 
30.  Segars WP, Mahesh M, Beck TJ, Frey EC, Tsui BM. Realistic CT simulation using the 4D XCAT phantom. Med Phys 2008; 35 (8): 3800–8. 
31.  Cai J, Chang Z, Wang ZH, Segars WP, Yin FF. Fourdimensional magnetic resonance imaging (4DMRI) using imagebased respiratory surrogate: a feasibility study. Med Phys 2011; 38 (12): 6384–94. 
32.  Li R, Jia X, Lewis JH, Gu X, Folkerts M, Men C, Jiang SB. Realtime volumetric image reconstruction and 3D tumor localization based on a single Xray projection image for lung cancer radiotherapy. Med Phys 2010; 37 (6): 2822–6. 
33.  Panta RK, Segars P, Yin FF, Cai J. Establishing a framework to implement 4D XCAT Phantom for 4D radiotherapy research. J Cancer Res Ther 2012; 8 (4): 565–70. 
34.  Ren L, Zhang J, Thongphiew D, Godfrey DJ, Wu QJ, Zhou SM, Yin FF. A novel digital tomosynthesis (DTS) reconstruction method using a deformation field map. Med Phys 2008; 35 (7): 3110–5. 
35.  Lu J, Guerrero TM, Munro P, Jeung A, Chi PC, Balter P, Zhu XR, Mohan R, Pan T. Fourdimensional cone beam CT with adaptive gantry rotation and adaptive data sampling. Med Phys 2007; 34 (9): 3520–9. 
36.  Maurer J, Pan T, Yin FF. Slow gantry rotation acquisition technique for onboard fourdimensional digital tomosynthesis. Med Phys 2010; 37 (2): 921–33. 
37.  Ren L, Zhang Y, Yin FF. A limitedangle intrafraction verification (LIVE) system for radiation therapy. Med Phys 2014; 41 (2): 020701. 
38.  Zhang Y, Yin FF, Zhang Y, Ren L. Reducing scan angle using adaptive prior knowledge for a limitedangle intrafraction verification (LIVE) system for conformal arc radiotherapy. Phys Med Biol 2017; 62 (9): 3859–82. 
39.  Lu W, Parikh PJ, Hubenschmidt JP, Bradley JD, Low DA. A comparison between amplitude sorting and phaseangle sorting using external respiratory measurement for 4D CT. Med Phys 2006; 33 (8): 2964–74. 
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7]
[Table 1], [Table 2], [Table 3]
