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First published online April 26, 2006
British Journal of Radiology (2006) 79, 745-755
© 2006 British Institute of Radiology
doi: 10.1259/bjr/63249054
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Full paper

Improved motion compensation in 3D-CT using respiratory-correlated segment reconstruction: diagnostic and radiotherapy applications

S Mori, PhD, M Endo, PhD, R Kohno, PhD and S Minohara, PhD

National Institute of Radiological Sciences, Inage-ku, Chiba 263-8555, Japan


   Abstract
Top
 Abstract
Introduction
 Materials and methods
 Results
 Discussion
 Appendix 1
 References
 
Conventional respiratory-gated CT and four-dimensional CT (4DCT) are disadvantaged by their low temporal resolution, which results in the inclusion of anatomic motion-induced artefacts. These represent a significant source of error both in radiotherapy treatment planning for the thorax and upper abdomen and in diagnostic procedures. In particular, temporal resolution and image quality are vitally important to accurate diagnosis and the minimization of planning target volume margin due to respiratory motion. To improve both temporal resolution and signal-to-noise ratio (SNR), we developed a respiratory-correlated segment reconstruction method (RS) and adapted it to the Feldkamp-Davis-Kress algorithm (FDK) with a 256 multidetector row CT (256MDCT). The 256MDCT scans approximately 100 mm in the craniocaudal direction with a 0.5 mm slice thickness in one rotation. Data acquisition for the RS-FDK relies on the assistance of a respiratory sensing system operating in cine scan mode (continuous axial scan with the table stationary). We evaluated the RS-FDK for volume accuracy and image noise in a phantom study with the 256MDCT and compared results with those for a full scan (FS-FDK), which is usually employed in conventional 4DCT and in half scan (HS-FDK). Results showed that the RS-FDK gave a more accurate volume than the others and had the same SNR as the FS-FDK. In a subsequent animal study, we demonstrated a practical sorting process for projection data which was unaffected by variations in respiratory period, and found that the RS-FDK gave the clearest visualization among the three algorithms of the margins of the liver and pulmonary vessels. In summary, the RS-FDK algorithm provides multi-phase images with higher temporal resolution and better SNR. This method should prove useful when combined with new radiotherapeutic and diagnostic techniques.


   Introduction
Top
 Abstract
 Introduction
Materials and methods
 Results
 Discussion
 Appendix 1
 References
 
Continuing rapid progress in computer hardware and software has led to better radiation therapy planning and dramatic improvements in delivery. New types of conformal planning and delivery technology, of which intensity-modulated radiation therapy (IMRT) is a prominent example [1, 2], have the potential to achieve a much higher degree of target conformity and normal tissue sparing than existing treatment techniques. Since higher target conformity generally requires more accurate definition of the target, the new radiation therapy requires a reduction in the target volume error arising from the respiratory motion of organs such as the lung and liver. Moreover, the human respiratory cycle is not strictly regular, but varies in amplitude and period from one cycle to the next [3–5], and greater time is spent in exhalation than in inhalation [6, 7]. These complexities hamper the accuracy of radiotherapy, for example in the determination of peak-to-peak amplitude of external chest motion. Voluntary or imposed breath-hold techniques have been proposed to reduce or eliminate these effects of breathing during both imaging and radiotherapy treatment [8–11], but these prolong treatment and in any case cannot be tolerated by many patients. Respiratory motion during CT acquisition may produce artefacts that resemble disease symptoms [12], and these remain a significant source of error in radiotherapy treatment planning for the thorax and upper abdomen [12–14].

Many investigators have introduced automatic respiratory-gated CT [15, 16] or four-dimensional CT (4DCT) [17, 18] acquisition techniques which provide wide craniocaudal (CC) coverage beyond the CT detector width without image gaps during free breathing, and have adapted them to radiation therapy [19–21]. In the respiratory-gated CT technique, CT images are taken by an axial scan gated to respiratory signals from a respiratory motion detection system. In contrast, the 4DCT technique obtains CT images by cine scan and sorts the CT images obtained in the same respiratory phase. The temporal resolution, therefore, is determined by the gantry rotation time. Due to their relatively low temporal resolution, however, these techniques do not remove motion artefacts completely.

Segment reconstruction correlated to a physiological signal was first developed using electrocardiograms (ECG), and ECG-correlated reconstruction has been widely used to delineate coronary arteries with intravenous injection of contrast agent [22–26]. To our knowledge, however, few papers have appeared on respiratory-correlated segment reconstruction. Koenig et al [27] introduced data acquisition processing on several half-turns in order to reduce the dose delivered per rotation with the same signal-to-noise ratio (SNR). Sonke et al [28] reported the use of respiratory-correlated cone beam CT integrated with a linear accelerator, but their rotation speed of approximately 4 min is considerably longer than that with our 256 multidetector row CT (256MDCT), rendering their experience not directly applicable to the present study.

To improve temporal resolution and image quality, and thereby minimize planning target volume (PTV) margin due to respiratory motion, we developed a respiratory-correlated segment reconstruction method (RS) and adapted it to the Feldkamp-Davis-Kress algorithm (FDK) [29] with a 256MDCT [30]. The RS-FDK algorithm provides multiphase images with higher temporal resolution and a better SNR than the conventional respiratory-gated CT and 4DCT techniques, and should therefore prove useful when combined with new radiotherapy techniques such as four-dimensional (4D) radiation therapy [31–34]. Here, with a view to clinical utilization, we evaluated the use of RS-FDK with the 256MDCT in phantom and animal studies.


   Materials and methods
Top
 Abstract
 Introduction
 Materials and methods
Results
 Discussion
 Appendix 1
 References
 
Prototype 256 multidetector row CT-scanner (256MDCT)
The 256MDCT was developed at the National Institute of Radiological Sciences (NIRS) [30, 35]. A wide-area two-dimensional (2D) detector was designed on the basis of existing CT technology [36] and mounted on the gantry frame of an advanced MDCT. The number of elements was 912 (transverse)x256 (craniocaudal), each of approximately 0.5 mmx0.5 mm at the centre of rotation. Rotation time was 1.0 s. Owing to disk storage limitations, continuous scan time was limited to 15 s for acquisition at 256 mmx0.5 mm, 30 s at 128 mmx1.0 mm, and 60 s at 64 mmx2.0 mm. The scanner could scan approximately 100 mm in the craniocaudal direction in one rotation. Data sampling rate was 900 views/s, and dynamic range of the A–D converter was 16 bits. The detector element consisted of a scintillator and photodiode, the former being the same as that used in the MDCT (Toshiba Aquilion; Toshiba Medical Systems, Japan). A FDK algorithm was used for reconstruction. Reconstruction of volume data of 512x512x128 voxels with a high-speed image processor in a field-programmable gate array (FPGA)-based architecture took less than 1 s.

External respiratory signal tracking system and signal processing
Generally, two kinds of external respiratory signal tracking system are used. These have tagging points with artificial markers that reflect or emit light, termed "passive" and "active". The latter type is routinely used for gated irradiation and CT acquisition during heavy ion radiotherapy at our institution [20]. A number of problems with these markers have been reported, such as a residual error between the marker position and surface point of interest, patient setup, and a reduction in resolution in orthogonal directions [37–39]. Here, however, the passive marker was used to obtain respiratory phase alone, and not absolute distance of motion.

The respiratory sensing system consisted of a workstation (Dell, Roundrock, TX) equipped with a real-time digital video analyser, in-house gating software and user interface within the PV-WAVE programming package (Visual Numerics, San Ramon, CA), and a charged-coupled-device (CCD) camera (XC-EI50; Sony Corp., Tokyo, Japan) with an attached infrared illuminator (OTR, Tokyo, Japan) (Figure 1aGo). SNR of the camera signal was 60 dB and vibration tolerance was 10 G (20–200 Hz). Since the reflected marker was captured around the centre of view, distortion was negligible. The respiratory sensing system was affixed to the patient table in this study. To perform an RS scan using conventional CT, movement of the couch to the adjacent position is necessary to obtain the next respiratory cycle. Because this process is repeated until the entire scan range is completed, the respiratory sensing system may induce significant mechanical disturbances that would be amplified by zoom optics. In contrast, couch movement is not necessary for RS-FDK using the 256MDCT, and the vibration induced by rotation of the gantry does not significantly disturb the couch. Mechanical disturbance with this equipment is therefore negligible.


Figure 1
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  		Figure 1. Sorting process in the respiratory-correlated segment reconstruction method (RS). (a) A respiratory signal is obtained from the infrared video camera. (b) Projection data with projection angle are obtained from the 256MDCT. (c) Relationship between projection angle and moving object position. (d) Projection data for the same respiratory phase are sorted to obtain four data sections (sections A–D). (e) The four projection-quadrant sections – each section corresponds to {pi}/2 of projections. (f) RS-FDK images are obtained after generating cone-beam back projection (FDK).

 
The cycle of respiratory phase was monitored with a CCD camera focused on a reflective marker seal on the patient's chest or abdominal area. Video signals from the camera were transferred to the workstation and software routines were run to determine respiratory function from the detected marker position. Tracking of the marker was facilitated by observation of the seal at very high contrast. A spline curve was fitted to the respiratory function to reduce noise in the detected signal and to correlate the sampling rate of 30 frame/s for respiratory function with the 900 frames/s for the projection data [40].

Reconstruction algorithms
Three types of reconstruction algorithm based on the FDK were used, namely full scan (FS-FDK), half scan (HS-FDK) and respiratory-correlated segment FDK (RS-FDK). The usual reconstruction algorithm, FS-FDK, uses a uniform weight over the 2{pi} of the projections, and is usually employed in conventional respiratory-gated CT. To increase temporal resolution, we employed the HS-FDK, which uses only {pi} plus the fan angle of the projections with a Parker weighting function applied prior to the filtered back projection operation [41]. Results showed an effective scan time of 500 ms (central ray) when a 1.0 s rotation mode was used. Details of the HS-FDK have been described elsewhere [42].

With regard to the RS-FDK, its essential concept is to sort projection data in the same respiratory phase, rather than reconstructing CT images as in the conventional respiratory-gated CT technique. Data acquisition for anatomical sites subject to breathing motion such as the lung and abdomen relies on the assistance of the respiratory sensing system to reduce the impact of respiratory motion. The 256MDCT uses a cine scan mode (continuous axial scanning with the table stationary) to acquire all respiratory phase projection data (Figure 1aGo). The respiratory phase is determined from the respiratory signal collected by the respiratory sensing system (see below) during the cine scan (Figure 1b,cGo).

Projection angle shift per respiratory period, PS, between rotation time Trot and respiratory period Tres is defined as:


Formula 001

where PS is normalized by Trot, and is given by a fraction of rotation. The number of sections, Ns, is then obtained as:


Formula 002

[ ] denotes floor function, which yields the greatest integer lower or equal. Projection data for the same respiratory phase are sorted to obtain RS-FDK projection data PRS(beta) as follows:


Formula 003

where p(beta) is the projection datum obtained from the cine scan at projection angle beta, and n is an integer between 0 and Ns–1.

The 2{pi} projection data set thereby acquired is used for FDK reconstruction. For RS-FDK, the total scan time TS and temporal resolution TR are given as follows:


Formula 004



Formula 005

We noted that it was necessary to desynchronize the respiratory period from the gantry rotation time, because if the respiratory period is a harmonic (PS = 0) or subharmonic (PS = 0.5) of this time, the restricted temporal resolution Trot or Trot/2 is obtained, respectively.

In this study, the data set was divided into four projection-quadrant sections (Ns = 4), with each section therefore corresponding to {pi}/2 of the projections (sections A–D) (Figure 1dGo), covering 2{pi} (Figure 1eGo). Since temporal resolution was increased in proportion to the number of sections (Equation 5), temporal resolution of the RS-FDK was four and two times as high as those of the FS-FDK and HS-FDK, respectively. However, total scan time was also increased in proportion to the number of sections (Equation 5). To avoid high patient doses, total scan time was conservatively limited to 17 s, less than that proposed by the Institutional Review Board (IRB) of the National Institute of Radiological Sciences (NIRS).

Multiphase images were obtained by shifting the start projection angle for FS-FDK and HS-FDK. Both algorithms provide volumetric multiphase images over the total acquisition period. In contrast, RS-FDK provided multiphase images by sorting projection data for each respiratory phase, and thereby produced images for only one respiratory cycle.

Image noise ratios for FS-FDK, HS-FDK and RS-FDK are given in Appendix 1.

Phantom study
Volume accuracy results for RS-FDK were compared with those for FS-FDK and HS-FDK following evaluation with a moving phantom designed for the 256MDCT (Figure 2Go). The phantom contained a 30 mm diameter acrylic ball as the target volume placed on a moving table connected to a mechanically driven motor with speed adjustment. To simulate human respiratory motion, sinusoidal movement was employed in an oblique direction by setting the moving phantom at 45° to the CC direction. Motion distance and time period of the moving phantom were 40 mm and 3.74 s, respectively. The phantom position was denoted using a motion function f(t) as follows:


Formula 006



Formula 007

where t denotes time [s], and (LR(t), AP(t), CC(t)) are relative coordinates of the ball's position where LR, AP and CC denote the left–right, anterior–posterior and craniocaudal directions, respectively. A slow-motion phase was defined as the ball positioned at f(t1) = ±20 [mm] and having a displacement in 1 s of 6.8 mm. A fast-motion phase was defined as the ball positioned at f(t2) = 0 [mm] and having a displacement in 1 s of 30.0 mm.


Figure 2
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  		Figure 2. Photographs of the moving phantom.(a) The phantom was set 45° to the caudocranial direction and connected to a mechanically driven motor with speed adjustment. (b) The phantom contained a 30 mm diameter acrylic ball as the target volume placed on a moving table.

 
The ball volume was obtained by applying a threshold to images, where the actual volume of the ball was 14 137 mm3 ( = 4/3x{pi}x153). Volume error in the moving phantom was assessed as the percent ratio (%) of volume from images of the moving phantom to the actual volume.

Scan conditions were 120 kV, 150 mA using a 0.5 mm 256 row detector and 15 s acquisition time. Reconstruction parameters were a voxel size of 0.35 mmx0.35 mmx0.35 mm, matrix size of 512x512x256 and 0.35 mm reconstruction increment. The convolution kernel was a standard body kernel (FC10).

Animal study
Image quality of RS-FDK was evaluated in an animal study in comparison with those for FS-FDK and HS-FDK. Four domestic pigs were used to simulate a human model. The animals were aged 21–23 weeks, weighed 20–25 kg and had a diameter and circumference of 130 mm and 590 mm, respectively. Although diameter and circumference were smaller than those of adult humans, pigs were selected owing to their ease of handling, and well-developed interlobular septa and anatomic structures that are similar to those of the human lung [43]. All animal procedures were approved by the IRB of the NIRS. The pigs were given an intramuscular injection of a mixture of 10 mg kg–1 of ketamine hydrochloride (Sankyo Yell, Tokyo, Japan) and 7 mg kg–1 of xylazine 2% (Bayer, Tokyo, Japan) and sedated and ventilated with a respiratory pump with isoflurane 2–2.5%. The breathing cycle was adjusted to 4.2–4.3 s. A video camera was focused on a reflective marker seal set on the interseptum to track respiratory motion and obtain the respiratory signal.

Scan conditions were 120 kV, 200 mA using a 1.0 mm 128 row detector and 17 s acquisition time, and cine scan mode. Reconstruction parameters were a voxel size of 0.47 mmx0.47 mmx0.47 mm, matrix size of 512x512x216 and 0.47 mm reconstruction increment. The convolution kernel was FC10. Effective dose was estimated as 38.6 mSv ( = 2.27 mSv s–1x17 s).


   Results
Top
 Abstract
 Introduction
 Materials and methods
 Results
Discussion
 Appendix 1
 References
 
Phantom study
Motion functions (a) and reconstructed images for (b) slow- and (c) fast-motion phases are shown in Figure 3Go. With regard to the slow-motion phase, FS-FDK images were severely degraded and distorted while those with HS-FDK did not seem spherical. In contrast, the RS-FDK images visualized the ball as spherical and were of better quality than the HS-FDK images due to their better temporal resolution. Furthermore, image quality with RS-FDK was the same for three different cross-sections. For the fast-motion phase, although the reconstructed images showed greater degradation than those of the slow-motion phase for all algorithms, image quality with RS-FDK was nevertheless better than with the others. In particular, the RS-FDK images show the ball as round in both coronal and sagittal sections. The magnitude of artefacts differed between the transverse and longitudinal sections.


Figure 3
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  		Figure 3. Motion functions for oblique motion(a). CT images of the 30 mm diameter acrylic ball in oblique motion in (b) the slow- and (c) fast-motion phases. Images in each of the vertical frames from top to bottom were reconstructed with FS-FDK, HS-FDK and RS-FDK. The left–right, anterior–posterior and caudocranial directions are denoted as LR, AP and CC, respectively. Window level is –373 HU and window width is 1190 HU for all images.

 
Volume using the threshold of 50% of CT number in the static image was 14 123 mm3, which nearly equals the actual value of 14 137 mm3. The volume ratios decreased as threshold CT number increased. The threshold was fixed at 50% of the difference between the CT number of the ball and the background CT number, because this gives the approximate actual volume of the ball.

Figure 4Go shows the volume percentage of the ball obtained from images of oblique motion. The volume percentage decreased from unity for all cases, with that by RS-FDK larger than with the other two, and that by FS-FDK being the smallest. For the fast phase, the volume ratio by RS-FDK was 5% larger than that for HS-FDK and more than 40% larger than that by FS-FDK.


Figure 4
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  		Figure 4. Volume percentage obtained from the axial image where the ball motion is in the oblique direction.

 
Animal study
The phase of respiratory signals for all animals as sensed by the respiratory sensing system is shown in GoFigures 5 and 6Go, and respiratory periods for all animals are summarized in Table 1Go. Animal respiration was controlled with almost complete regularity by the ventilator, with only a few irregular periodic motions due to voluntary breathing. Breathing motion at peak inhalation was slightly faster than that at peak exhalation. This is similar to the behaviour seen for human respiratory signals, which are not sinusoidal; dwell time at peak exhalation is often longer than is shown by a sinusoidal signal.


Figure 5
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  		Figure 5. Respiratory signal obtained from the external respiratory signal tracking system(pig 1). The solid line shows raw respiratory data and the broken one shows a spline fitting to the raw data.

 

Figure 6
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  		Figure 6. Respiratory signal for four pigs; (a) pig 1, (b) pig 2, (c) pig 3 and (d) pig 4. Four respiratory cycles are overlapped to show reproducibility of each cycle.

 

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  		Table 1. Respiratory cycle for four pigs

 
Figure 7Go shows projection data of the pig in the AP direction at peak exhalation, mid inhalation and peak inhalation phases. The length of respiratory motion was approximately 17 mm in the CC direction.


Figure 7
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  		Figure 7. Images of projection data in the anterior–posterior direction. (a) Peak exhalation, (b) mid inhalation and (c) peak inhalation. Window level is –373 HU and window width is 1190 HU for all images.

 
Coronal and sagittal images for each respiratory phase (pig 1) are shown in GoFigures 8 and 9Go, respectively. These images captured each respiratory phase exactly. The margins of the liver and the pulmonary vessels were sharper in the RS-FDK than in the FS-FDK and HS-FDK images. FS-FDK gave the worst image quality due to its low temporal resolution. For mid-exhalation and mid-inhalation, geometrical distortion of the pulmonary vessels and interlobular septa became visible in FS-FDK and HS-FDK images, and the latter exhibited a streak artefact on the ribs in spite of their good temporal resolution.


Figure 8
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  		Figure 8. Coronal images obtained at four respiratory phases(peak inhalation, mid exhalation, peak exhalation and mid inhalation). Reconstruction increment is 0.4 mm and slice thickness is 0.4 mm. (a) FS-FDK, (b) HS-FDK and (c) RS-FDK. Window level is –373 HU and window width is 1190 HU for all images.

 

Figure 9
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  		Figure 9. Sagittal images obtained at four respiratory phases(peak inhalation, mid exhalation, peak exhalation and mid inhalation). Reconstruction increment is 0.4 mm and slice thickness is 0.4 mm. (a) FS-FDK, (b) HS-FDK and (c) RS-FDK. Window level is –373 HU and window width is 1190 HU for all images.

 
These results indicate that the RS-FDK algorithm provides the best image quality for all respiratory phases due to its good temporal resolution.


   Discussion
Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
Appendix 1
 References
 
In the present study, we developed the RS-FDK algorithm to allow the precise capture of anatomical structures under free breathing conditions, and compared results with those for two other reconstruction algorithms, FS-FDK and HS-FDK, in experiments using a moving phantom and in animal studies. Results showed that RS-FDK gives better temporal resolution than HS-FDK and FS-FDK and the equivalent SNR as FS-FDK (Appendix 1).

Although conventional respiratory-gated CT and 4DCT techniques provide wide CC coverage beyond the detector width for the same respiratory phase, the inclusion of motion artefact is not completely mitigated due to the relatively low temporal resolution. This disadvantage means that the actual position of a moving object in radiotherapy treatment planning CT is uncertain, as is the volume of a moving object relative to its actual volume. These uncertainties result in planning errors. Furthermore, respiratory motion during irradiation can cause the radiation beam to miss part of the target itself. To avoid these errors, PTV is defined with a margin of several centimetres added to the clinical target volume (CTV); but this in turn carries the risk that an excessively wide margin will unnecessarily irradiate normal tissue. It is therefore necessary to minimize the PTV margin. As seen in the phantom study, the reconstructed images did not visualize the actual shape due to distortion or motion artefacts. These errors may result in the delivery of an insufficient dose to the target volume or an excess dose to normal tissue.

HS and RS allow the precise imaging of a periodically moving object. The shorter acquisition time with HS, however, may lead to a lower SNR than that provided by a conventional acquisition time [44], necessitating careful analysis of the trade-off between temporal resolution and image quality (e.g. artefact and image noise). In contrast, RS provides multiphase images with better temporal resolution than HS and the same SNR as FS, and may supply useful information for 4D radiation therapy planning. With the multiphase images we may make a dynamic treatment plan that enables irradiation with continually adjusted beam shape to match the respiratory phase. If such a dynamic treatment could be realised, it brings greater accuracy in radiation therapy than respiratory-gated radiation therapy, which irradiates at the most stable point, such as peak exhalation [45].

The limitation of RS is its higher patient dose. This occurs because the CT scans the same position continuously, and because the effective dose increases in proportion to acquisition time. Acquisition time should be minimized even for patients receiving radiation therapy. Because the respiratory period at small PS values such as 0.1 requires a longer scan time, rotation time should be adjusted so that total scan time is decreased. If this is difficult, an alternative is to scan in one or two respiratory cycles, and thereafter to scan in appropriate respiratory phases only. Devices providing such functionality are essential to avoiding excessive patient dose. In the present study, scan time was minimized by adjusting respiratory period to 3.74 s for the phantom study and to 4.2–4.3 s for the animal study.

Many authors have reported the limitations of the abdomen as an external surrogate for the respiratory phase, namely that longer CT scanning time under free breathing and the placement of the marker result in inconsistency between the position of the marker and internal anatomy motion [16, 18, 46]. Lujan et al [6] have reported that the motion of the diaphragm due to respiration is predominantly in the CC direction and is periodic but asymmetric, with more time spent at the end of expiration than at the end of inspiration. This may lead to erroneous prediction of the dose delivered to the patient, and when examination time is prolonged, may result in the degradation of RS-FDK image quality. However, examination time in the present study was only 17 s, and the pigs were sedated and ventilated with a respiratory pump with an almost constant respiratory cycle. The relationship between the respiratory signal and target motion is therefore better correlated using the amplitude and cycle of the respiratory cycle. Since the breathing characteristics of patients are not always as reproducible as those of sedated pigs, the respiratory control discussed below is necessary when the RS-FDK is used in free-breathing patients.

Moreover, it should be remembered that a tumour located in a lower lobe of the lung has a larger range of tumour motion than one in an upper lobe due to proximity to the diaphragm [47]. This may also impact RS-FDK in clinical use, which requires correction of the correlation between respiration and target motion, such as by control of the patient's breathing by operator guidance [8–10, 16, 48, 49] or by means of an occlusion valve [11, 50, 51]. It will be necessary to control for this time dependency of respiratory asymmetry through suitable correction methods.

With regard to the projection data sorting process, adaptation of spline curve fitting may induce overlapping or a lack of projection data at adjacent quadrant sections (A–D in Figure 1Go). However, the spline curve of respiratory function showed good regulation (Table 1Go).

In this study, respiratory period for all animals was controlled with a ventilator to between 4.2 s to 4.3 s. Generally, if the period shifts between respirations, errors in the sorting process may lead to incorrect classification of the projection data into the wrong projection data section, and thereby result in image artefacts in the resultant RS-FDK. The same problem is seen in cardiac imaging with ECG gating [52, 53]. In this case, compensation of the projection data must be done by extending or shortening the range of the quadrant in both quadrant sections. Here, however, thanks to the use of the ventilator, the respiratory period was controlled and these errors were minimized, resulting in acceptable image quality.

We have carried out clinical trials at NIRS using carbon-ion beams [54]. Gated irradiation is a useful method and several findings have been reported [20, 21]. Depth dose distributions of charged particles exhibit a strong Bragg peak at the very end of the maximum distance that a charged particle travels in a tissue (range), beyond which the dose very rapidly falls to zero [55]. Charged particle beam radiotherapy may therefore be valuable when the organs at risk are closely proximal to the target volume. However, the presence of a range-shortening tissue inhomogeneity such as the soft tissue moving into the lung would not only reduce the target dose from the value in the stretched Bragg peak to essentially zero, but the dose would also put nearby organs at risk. Range is therefore an important factor in charged particle radiation therapy, even more so than in photon beam therapy. The use of RS-FDK in charged particle therapy as well as 4D radiation therapy should allow a significant increase in dose distribution accuracy and provide sufficient information to allow the minimization of the PTV margin in radiation therapy planning. We are now investigating these points.


   Appendix 1
Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Appendix 1
References
 
The image noise ratios for FS-FDK, HS-FDK and RS-FDK were calculated as follows. If {sigma}P is the noise magnitude (the standard deviation) of the measured projection data, noise magnitude of FS-FDK {sigma}FS, HS-FDK {sigma}HS and RS-FDK {sigma}RS can be calculated by noise propagation analysis by integrating the squared weights over the range of 2{pi}:


Formula 008



Formula 009

where {omega}HS({gamma}, beta) is the Parker weighting, {gamma}m is the fan angle, beta denotes the range of the projection angle and {gamma} denotes the ray-sum angle within a projection. RS also uses a uniform weight over the 2{pi} of projections, as for FS. Figure A1Go shows 3D images of weighting functions of FS-FDK, HS-FDK and RS-FDK. From the above analysis, the magnitude of the image noise for HS-FDK is 1.36 times larger than that for FS-FDK, whereas RS-FDK gives the same magnitude of image noise as FS-FDK.


Figure 10
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  		Figure A1. 3D images of the weighting functions of(a) FS-FDK and RS-FDK, and (b) HS-FDK. beta denotes the projection angle and {gamma} denotes the ray-sum angle within a projection.

 

Received for publication August 16, 2005. Revision received January 6, 2006. Accepted for publication January 24, 2006.


   References
Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Appendix 1
 References
 

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