Ryu Kawamorita^{1,2*}, Hajime Monzen^{1}, Wataru Okada^{2}, Ryuta Nakahara^{2}, Shun Kishimoto^{2}, Kentaro Ishii^{2}, Toshifumi Nakajima^{2} and Yasumasa Nishimura^{1}  
^{1}Department of Radiation Oncology, Kinki University, Faculty of Medicine, OsakaSayama, Osaka, Japan  
^{2}Department of Radiation Oncology, Tane General Hospital, OsakaNishiku, Osaka, Japan.  
Corresponding Author :  Ryu Kawamorita Department of Radiation Oncology Tane General Hospital, 11221 KujoMinami, Nishiku Osaka city, Osaka 5500025, Japan Tel: +81665811071 Fax: +81665852772 Email: [email protected] 
Received: July 18, 2015 Accepted: August 11, 2015 Published: August 14, 2015  
Citation:Kawamorita R, Monzen H, Okada W, Nakahara R, Kishimoto S, et al. (2015) Novel Anisotropic Margin Calculation Based On the Cumulative Frequency Distribution of Uncertainties in the Clinical Target Volume. OMICS J Radiol 4:202. doi:10.4172/21677964.1000202  
Copyright: © 2015 Kawamorita R et al. This is an openaccess article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. 
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Objective: The purpose of this study was to determine the PTV margins from the cumulative frequency of uncertainties of the clinical target volume (CTV) position obtained using hybridimage guided radiotherapy (HIGRT) with volumetricmodulated arc therapy (VMAT).
Materials and Methods: Study participants were 22 patients with intermediaterisk prostate cancer who underwent VMAT. All patients were treated using the following imageguided (IG) procedure: 1) nocorrection skin mark setup (no IG); 2) bony anatomy registration with 2Dimaging (2DIG); and 3) organ registration using CBCT images (3DIG). The systematic (Σtot) and random (σtot) errors were obtained from the noIG, 2DIG, and 3DIG registration images of 198 fractions. The PTV margin was computed using the cumulative frequency distribution of the actual position errors of the CTV, and which was compared with the formulation by MPTV = 2.5 Σtot + 0.7 σtot.
Results: The margin size of 3D IG procedure was as follows: 3DIG: 7.6, 5.4, and 3.5 mm for the AP, SI, and LR axes, respectively. Using MPTV = 2.5 Σtot + 0.7 σtot: 3DIG: 4.2, 3.7, and 1.3 mm for the AP, SI, and LR axes, respectively. In MPTV: = α Σtot + β σtot, the coefficients α and β were α = 3.4, 2.3, and 4.6 and β = 2.9, 3.0, and 3.0 for AP, SI, and LR, respectively.
Conclusion: The margin size (MPTV) calculated by our modified formulation based on the margin direction satisfied 99% of the prescription dose coverage in each direction and a minimum of 95% of the dose coverage to the CTV for all patients using HIGRT
Keywords 
Hybrid imageguided radiotherapy; Planning target volume margin; Prostate cancer; CTV position uncertainty 
Introduction 
Online image guided radiotherapy (IGRT) is used for prostate registration for prostate cancer patients [15]. At our hospital, online correction via a threestep setup protocol with hybridimage guided radiotherapy (HIGRT) is conducted, i.e., twodimensional (2D)/ threedimensional (3D) and 3D/3D registrations are performed using HIGRT. Our IGRT protocol preferentially uses organ registration relative to the anterior rectal wall, which corrects for almost all systematic errors; however, several random errors remain. Setup correction protocols may reduce geometric treatment uncertainties and the clinical target volume (CTV)toplanning target volume (PTV) margins. Therefore, a novel approach is required for PTV margin calculations (M_{PTV}) in HIGRT that accounts for small systematic uncertainty, random uncertainty and target registration residual error (TRE) depend on HIGRT system, in contrast to the more general formulation by van Herk et al., i.e., M_{PTV} = 2.5 Σ + 0.7 σ, which accounts for the population systematic uncertainty Σ and random uncertainty σ. This formula (M_{PTV} = 2.5 Σ + 0.7 σ) was computed with statistical procedure using systematic and random uncertainties of CTV position [6]. Furthermore, the coefficients of the model parameters were numerically calculated under a spherically symmetric condition thereby leading to an isotropic margin perpendicular to a spherical tumor surface. However, did not consider about residual error to be TRE in case of using IGRT. For example, as TRE arise due to deformation of prostate and/or seminal vesicles even if the registration at CTV using image guidance with CBCT. The purpose of this study was to determine the_{PTV} margins from the cumulative frequency of CTV uncertainties include TRE obtained by an HIGRT system. 
Materials and Methods 
Patients and treatment plan 
Twentytwo intermediaterisk prostate cancer patients who were treated using VMAT between 2012 and 2013 were included in this study. All patients were immobilized in a position using a vacuum cushion (VacLok; MedTech, Orange City, IA, USA). Computed tomography (CT) scans were acquired with 2.5 mm slice thicknesses using a 16–detector row CT scanner (Optima CT580W; GE Medical Systems, Waukesha, WI, USA) from the lower abdomen to 50.0 mm below the ischial tuberosity. The initial reference markers and associated skin marks were placed at the time of CT simulation. 
CTV was defined as the entire prostate and the proximal 15.0 mm of the seminal vesicles. PTV was generated by adding an 8.0 mm margin to CTV in all dimensions except posteriorly, where a 5.0 mm margin was used. Contouring of the organ at risk (OAR) included the rectum, bladder, femoral heads, penile bulb, and small bowel, defined according to the Radiation Therapy Oncology Group (RTOG) pelvic normal tissue contouring guidelines [7]. The total prescription dose was 78.0 Gy to the_{PTV} at 2.0 Gy per fraction. Dose normalization was set to the_{PTV} mean dose. The treatment plans were generated using singlearc VMAT (358 degree; 74 sec per rotation). All treatment plans were developed using Eclipse^{TM} ver.10.0 planning software (Varian Medical Systems, Palo Alto, CA, USA) for 10 MV photon irradiation. The dose was calculated using the Analytical Anisotropic Algorithm in Eclipse^{TM}. 
To verify leaf motion of each beam or specific patient’s plans, various quality assurance tests were conducted [8,9]. Once the VMAT plan was developed and approved, CT simulation datasets were imported into the ExacTrac^{®} Xray 6D system (BrainLab AG, Feldkirchen, Germany) for 2D/3D registration using digital reconstructed radiographs (DRRs) of 2D oblique images to the planning CT images [10]. The CT simulation datasets were also imported into the ARIA record and verification system (Varian Medical Systems, Palo Alto, CA, USA) for 3D/3D registration using CBCT images and planning CT images [11,12]. VMAT was delivered using linear accelerators equipped with a highdefinition multileaf collimator (HDMLC; spatial resolution: 2.5 mm at the isocenter; Novalis TX; BrainLab AG, Feldkirchen, Germany). The daily treatment time, including image registration from the final image acquisition until the end of irradiation, was 4 to 6 min. Before each fractionation, the bladder and rectum volume were prepared in the same way as at the time of CT simulation. 
IGRT strategy for prostate cancer at our hospital 
Figure 1 shows a diagram of the IGRT procedure used in this study. The HIGRT system consisted of an ExacTrac^{®}Xray 6D system and linear accelerator equipped with CBCT. All patients were treated using the stepbystep IG procedures involving nocorrection skin mark setup (no image guidance; noIG), bony anatomy 3D registration using 2D images from ExacTrac^{®} Xray 6D system (2D image guidance; 2DIG), and 3D organ registration using CBCT images (3D image guidance; 3DIG). 
Firstly, the noIG procedure was used to align the skin mark with the lasers. However, setup residual error of the CTV arose due to geometrical constraints associated with the bony anatomy [11,13]. Also, a systematic pitching error (maximum: 2.0 mm) was present due to the difference between the flexibility of the CT couch and that of the linear accelerator treatment couch. Therefore, as a next step, the 2DIG procedure using the ExacTrac^{®} Xray 6D system was used to correct for the setup residual error of the bony anatomy and systematic pitching error of the linear accelerator treatment couch. At the same time, the interfractional setup error was calculated by the BrainLab iterative rigid registration process, which uses mutual information as a similarity measure for its calculation [10,11]. Subsequently, interfractional organ motion error was corrected using 3DIG, with priority given to the anterior rectal wall while simultaneously ensuring that the portion of the rectum overlapping the_{PTV} is excluded. 
Uncertainty component of the CTV for each image guidance procedure 
Inter and intrafractional variations in the CTV positions relative to the treatment beam were represented as systematic (Σ) or random (σ) uncertainties which were calculated based on components of each CTV in the Table 1, respectively. Σ is the standard deviation of the overall means per patient (M), σ is the overall standard deviation of the population, and Σ and σ uncertainties were calculated from 2D and 3DIG image set data. The authors evaluated a total of 396 image sets for interfractional variation (198 fractions) and a total of 288 image sets for intrafractional variation (144 fractions) in the CTV position for the 22 patients. 
Interfractional systematic (Σ_{intersetup}) and random (σ_{intersetup}) setup uncertainties of the bony anatomy were calculated from bony anatomy registration data obtained from 2DIG images (Figure 1). 
The CTV position error associated with our setup was categorized into inter and intrafractional bony anatomy error (CTV_{intersetup} and CTV_{intratreat} [14]. Interfractional organ motion systematic (Σ_{interorg} ) and random (σ_{interorg}) uncertainties of the CTV were calculated between the planning CTV position and the CTV position after 2DIG bony anatomy registration, which was obtained by preregistration of the 3DIG images; these CTV uncertainty components were defined as CTV_{interorgan} (Figure 1). Note that Σ_{interorg} and σ_{interorg} include the position error due to deformation [1517]. Although Σ_{interorg} and σ_{interorg} were corrected using 3DIG, interfractional residual systematic (Σintertreat ) and random (σ_{intertreat}) uncertainties of the CTV remained due to the anterior rectal wall reference with 3DIG. Consequently, Σ_{intertreat} and σ_{intertreat} were calculated using the difference between the planning CTV position and the final CTV position used for treatment in the hybrid image guidance (CTV_{intertreat}), i.e., the final CTV position after the noIG, 2DIG, and 3DIG procedures. As described above, 3DIG was performed with preferential registration given to the anterior rectal wall in this study. Therefore, CTV_{intratreat} was included in the deformation error of the CTV due to rectal deformation and/or filling as well as interfractional prostate motion error (Figure 2). 
The intrafractional setup random uncertainty (σ_{intrasetup}) was calculated from the pre and posttreatment position error of the bony anatomy. Systematic (Σ_{intratreat}) and random (σ_{intratreat}) uncertainties for intrafractional organ motion were calculated from the position error during the CTV_{intratreat} fraction (CTV_{intratreat}). σ_{intrasetup}, Σ_{intratreat}, and σ_{intratreat} were calculated using image sets of pre and posttreatment registration of 16 of 22 patients. These intrafractional uncertainties were obtained using 2D and 3DIG images immediately after irradiation. 
CTV_{intersetup}, CTV_{intratreat}, CTV_{interorgan}, CTV_{intratreat}, and CTV_{intratreat} (CTV_{all}) included only translational motion errors related to displacement; rotational angle errors were excluded from evaluation in this study. These five uncertainty components (referred to as CTV_{all}) were included in the residual uncertainty from 3DIG in addition to the CTV uncertainty reported in the International Committee on Radiation Units (ICRU) Report62 [18]. The coordinates of CTV_{all} centre were obtained using the isocenter automatic setting function for the_{PTV}. To minimize interobserver variation, the contouring of organs for definition of the centroid coordinates was performed by a single physicist. 
Overall systematic (Σ_{tot}) and random (σ_{tot}) uncertainties 
The noIG, 2DIG, and 3DIG procedures all had different overall systematic (Σ_{tot}) and random (σ_{tot}) uncertainty components for the CTV, as shown in Table 1. Σ_{tot} and σ_{tot} of each IGRT were calculated using the rootsumsquare (RSS) of the components of CTV_{all}, as shown in Table 1. Σ, σ, and the mean of these uncertainty components are listed in Table 2; the values for Σ and σ are represented as Gaussian distributions. 
Equations (1)–(3) were used to calculate Σ_{tot} and σ_{tot} for the_{PTV} margin size for noIG, 2DIG, and 3DIG (noPTV margin, 2DPTV margin, and 3DPTV margin, respectively) [6]. 
NoPTV margin: skin mark setup correction. 
(1) 
2DPTV margin: NoIG and bone corrections using 2DIG. 
(2) 
3DPTV margin: No, 2DIG and organ registration using 3DIG 
(3) 
Cumulative frequency distribution of CTV_{all} and PTV margins calculation 
As described above, the uncertainties associated with CTV_{all} were calculated using the standard deviation of CTV_{all}. van Herk et al. described a PTV margin formula for minimal dose to 95% of the CTV in 90% of the patient population [6], in contrast, the cumulative frequency distributions of the actual CTV_{all} position were obtained to investigate the frequency tolerance level within 80,90,95 and 99% of CTV_{all}. The cumulative frequency distribution was approximated using polynomial regression (R^{2} > 0.99) fitting. 
For PTV generation, the CTV is generally expanded with a socalled “rolling ball” algorithm as a spherically symmetric condition [19]. As such, the prostate cancer CTV was considered an organ in the shape of an ellipsoid. Hence, to properly represent the 3D anisotropy of the CTV for a minimal dose prescription of 95% using the cumulative frequency distribution, the tolerance level must be more than 98.5% ; (i.e., the tolerance level was calculated using the formula (95% ≤ (x y z)), where x, y, and z, which correspond to LR, AP, and SI directions, respectively, were 98.5%. From this, the authors used a 99% tolerance level to compute the margin size in each direction for CTV_{all}. 
To prescribe the minimum dose of the 95% the CTV for each vector of the_{PTV} margin size (M_{PTV}: vector) for each IG procedure (noIG, 2DIG, and 3DIG) was calculated using the RSS of Eq. (4) and the uncertainty components for each IG, shown in Table 1. 
(4) 
where m_{1}–m_{5} were required to describe the margin size of the CTV position uncertainty, computed using cumulative frequency distributions of m1: CTV_{intersetup}; m2: CTV_{interorgan}; m3: CTV_{intratreat}; m4: CTV_{intratreat}, and m5: CTV_{intratreat} (Figure 1). The uncertainties with respect to the_{PTV} margin for each IG procedure are listed in Table 1. To compare the margin size with our results, the noIG, 2DIG, and 3DIG PTV margins were calculated using the margin formula of van Herk et al. (M = 2.5 Σ_{tot}+0.7 σ_{tot}) [6]. 
Design of the equation to calculate the anisotropic PTV margins for HIGRT 
The anisotropic PTV margins can be calculated using the formula M_{PTV}: vector = α Σ_{tot}+β σ_{tot}. M_{PTV}: vector was calculated at a 99% confidence level based on the cumulative frequency distribution of CTV position error covering more than 95% of the dose distribution for the 3D margin (AP, SI, and LR). Σ_{tot} and σ_{tot}, the percentage of the CTV_{all} error, and the anisotropy of the_{PTV} margin are given in Tables 35, respectively. The formula coefficients α and β for the_{PTV} margin calculation (M_{PTV}:vector = α Σ_{tot}+β σ_{tot}) were estimated using a leastsquares matrix operation. 
IRB 
The study design was approved by our institutional review board. 
Results 
Systematic (Σ) and random (σ) uncertainties of CTV_{all} 
The systematic (Σ) and random (σ) uncertainties of CTV for each IG condition are shown in Figure 1. The uncertainty components of the CTV position error with respect to the_{PTV} margin are shown in Table 1. Σ, σ, and the mean of these uncertainty components are listed in Table 2; the values for Σ and σ are represented as Gaussian distributions. The uncertainty of the CTV position for each IG procedure increased in the order AP, SI, and LR for both Σ and σ. According to van Herk et al., Σ for each dimension was larger than σ [6], similar to our results, with Σ having a greater value than σ overall (Table 2). 
Σ_{tot} and σ_{tot} values for each IG were computed using Eqs. (1) – (3). For the HIGRT strategy proposed in this study, systematic and random errors were revised progressively over the IG procedure (no IG, 2DIG, and 3DIG); hence, Σ_{tot} and σ_{tot} were relatively small after the completion of 3DIG (Table 3). 
Although Σ_{tot} and σ_{tot} for the SI and LR directions for 2DIG and 3DIG showed the same results, the individual uncertainty components differed, as shown in Table 1. As described above, the authors adopted the anterior rectal wall registration for the 3DIG procedure. Therefore, despite prior rectal preparation, rectal filling had an impact on CTV position in 3DIG; specifically, the LR value was greater than that for 2DIG. 
Comparison of the_{PTV} margin sizes using the theoretical formula and actual distributions of the variations in CTV position in our HIGRT strategy 
The cumulative dose frequency distributions of CTV position errors were obtained using inter and intrafractional error for CTV_{all}. The curves of the cumulative dose frequency distributions were computed using polynomial regression (R^{2} > 0.99) fitting (Figure 3). 
The approximate expressions shown in Figure 3 were then used to compute the_{PTV} margin size within tolerance levels of 80, 90, 95 and 99% for the five components (Table 5). Among the individual components, CTV_{intersetup} had the greatest influence on PTV margin size, followed by CTV_{interorgan}, CTV_{intratreat}, CTV_{intratreat}, and CTV_{intratreat} (Table 4). Intrafractional organ motion and intrafractional setup uncertainty values (CTV_{intratreat} and CTV_{intratreat}) were similar to others> in the literature [20,21]. The maximum position error of the CTV was in the AP direction of CTV_{intersetup} (>9.0 mm, 99% confidence level). 
The PTV margins (NoPTV margin, 2DPTV margin and 3DPTV margin) were computed using the RSS of the uncertainties of CTV under each IG condition (Tables 1 and 5). The margin sizes corresponding to a 99% tolerance level for a prescription dose of 95% for the anisotropic margin size of CTV are listed in Table 5. 
The 3DPTV margin size required for the HIGRT was 7.6, 5.4, and 3.5 mm in the AP, SI, and LR directions, respectively. Comparing our results for the_{PTV} margin size with those obtained using van Herk’s formulation (M_{PTV} = 2.5 Σ_{tot} + 0.7 σ_{tot}), our PTV margin was larger in all three directions (Table 6). The maximum difference observed for each IG was as follows: noIG: 4.3 mm (AP); 2DIG: 3.0 mm (SI); and 3DIG: 3.3 mm (AP). Using van Herk’s formula, both the 2D and 3DPTV margins in the LR direction were 1.3 mm; these sizes are not suitable for clinical use. 
Design of an anisotropic PTV margin for HIGRT 
In this study, α and β in the equation (M_{PTV} = α Σ_{tot} + β σ_{tot}) were derived for the calculation of the anisotropic PTV margin via HIGRT. Σ_{tot} and σ_{tot} were obtained from the uncertainties for CTV_{all}, shown in Table 3. M_{PTV} for a prescription dose of 95% to the CTV was determined using the cumulative frequency distributions of CTV_{all} shown in Table 6. Accordingly, α and β in this equation were computed using a least squares matrix operations (Table 7). Σ_{tot} and σ_{tot} were reduced during the HIGRT procedure (Figure 1) due to the progressive corrections that occurred for each process (noIG, 2DIG, and 3DIG). Consequently, for adequate anisotropic PTV margin size calculations, α ranged from 2.3–5.5 and β was 2.8–3.0 (Table 7). 
Discussion 
The authors performed online correction using HIGRT to all fractions for prostate cancer patients undergoing VMAT. The HIGRT strategy corrected for the systematic and random errors of CTV. The systematic (Σ_{tot}) and random uncertainties (σ_{tot}), according to the each IG correction protocol were computed with image data sets acquired for inter and intrafractional errors of CTV (Tables 1 and 2). Additionally, the proposed PTV margin calculation considered not only interfractional prostate movement which was acquired from each IGRT procedure but also a TRE that arise with No, 2D and 3DIG. 
CTV position exhibits anisotropic variation; thus, the_{PTV} margin size calculation must consider all three dimensions for a minimum dose of more than 95% to the CTV. The CTV is generally expanded with a “rolling ball” algorithm [19] as a spherically symmetric condition in treatment planning for prostate cancer. In this instance, each PTV margin direction should be kept within 98.5% tolerance for a minimum dose of >95% to the CTV. Using the proposed HIGRT strategy, the 3DPTV margin size was 7.6, 5.4, and 3.5 mm in the AP, SI, and LR directions, respectively (Table 5), whereas the current PTV margin in the current study (8.0 mm in all dimensions, except posteriorly, where it was 5.0 mm ) were barely reduced. Since the authors are adopting anterior rectal wall registration, rectal side margin will be enough at 5.0 mm. 
With regard to daily variations in prostate position, several authors described prostate movement of 6.0–20.0 mm in each direction by interfractional organ motion or deformation [2224]; interfractional organ motions are larger than intrafractional motions [25]. Thus, without online IGRT procedures, safety margins of 10.0 mm for the AP and SI directions and 8.0 mm in the LR direction around the prostate have been recommended [1,2]. Hurkmans et al. and Rudat et al. [1,2] computed the_{PTV} margin from actual interfractional setup uncertainty; safety margins of 8.0 mm (LR) and 10.0 mm (AP and SI) were reported for prostate cancer patients. Smitsman et al. and Meijer et al. [17,26] considered interfractional organ motion uncertainty and residual error of the seminal vesicles in their margin design. 
In the present study, the_{PTV} margin size was calculated using the cumulative frequency distributions of inter and intrafractional variations and TRE, which included the seminal vesicles in the CTV. The margin of the noIG (only skin mark setup) were 12.6, 7.3, and 5.9 mm for the AP, SI, and LR directions, respectively, calculated using the cumulative frequency distribution of CTV_{all}. Σ_{tot} and σ_{tot} were substituted into van Herk’s et al. formula (M = 2.5 Σ_{tot}+0.7 σ_{tot}), and the_{PTV} margin was calculated again, revealing margins of 8.3, 5.0, and 4.4 mm for the AP, SI, and LR directions, respectively. The maximum difference between those results and ours was observed in the AP direction. Also, the 2D and 3DPTV margins using van Herk et al. were 1.7–3.4 mm smaller than our results (Table 6). Meijer et al. [26] computed the_{PTV} margin size using a modelbased deformable image registration and online IGRT, and compared their results with van Herk et al. [6], whose values were reportedly smaller by a maximum of 3.0, 2.0, and 2.0 mm in the AP, SI, and LR directions, respectively. Coverage in each direction of the CTV computed using the margin size formula proposed by van Herk et al. was no more than 80–95%, with 3D coverage limited to 51–86% (Tables 5 and 6). 
Engels et al. [27] analysed the correlation of the_{PTV} margin size and impact on the fiveyear freedom from biochemical failure (FFBF) in IGRT for prostate cancer. The PTV margins of 5.0, 4.0, and 3.0 mm (AP, SI, and LR, respectively) were compared with an isotropic PTV margin of 6.0 mm in all directions; PTV margins of 6.0 mm in all directions indicated a fiveyear FFBF percentage of 96%, compared with 74% for the tighter PTV margin group. In our results, the_{PTV} margin sizes with M_{PTV}=2.5 Σ_{tot}+0.7 σ_{tot} were 4.2, 3.7 and 1.3 mm (in the AP, SI, and LR directions, respectively); thus, the_{PTV} margin may be inadequate if van Herk et al.’s formula is used for HIGRT. Given this margin size, the coverage would range from 51 to 86% for the 3D CTV. Hence, the authors concluded that the use of the M_{PTV}=2.5 Σ_{tot}+0.7 σ_{tot} formula for prostate cancer may be inadequate. 
Van Herk et al. assumed that organ movement could be represented by a normal probability distribution; the margin recipe was represented with one formula for all directions for the_{PTV} calculation. In contrast, our recipe offers greater flexibility in that it can accommodate random variation using a cumulative distribution function, because uncertainty of CTV position of the respective direction has a certain variance and distribution. Additionally, HIGRT can cover variations in the CTV position for each vector, using our recipe, by correcting for nearly all associated systematic errors. More specifically, assuming that Σ is zero by use of the HIGRT system, and then the calculation for the_{PTV} margin size considers only the random uncertainty (σ), which is simply multiplied by a coefficient value, ranges from 2.8–3.0 to the σ. In this study, the proposed method considers equations for the_{PTV} margin calculation for No, 2D and 3DIGRT in three axes, AP, SI, and LR. 
Conclusion 
HIGRT was corrected for systematic and random errors of the CTV for almost all fractions. The margin size (M_{PTV}) was calculated using a novel formula that accounted for the anisotropy of the organ considered (the prostate); the recipe satisfied a 99% prescription dose in three directions (AP, SI, and LR). Moreover, using the HIGRT procedure, the minimum dose to the CTV was 95% of the prescribed dose over three dimensions for all prostate cancer patients. 
Acknowledgment 
The authors would like to thank their colleagues for their support in the data analysis. 
Funding 
This study was supported in part by a GrantinAid for Cancer Research (H26 090) from the Ministry of Health, Labour and Welfare of Japan, and by the National Cancer Centre Research and Development Fund (26A4). 
References 

Table 1  Table 2  Table 3  Table 4 
Table 5  Table 6  Table 7 
Figure 1  Figure 2  Figure 3 
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