Radiation Environment and Medicine 2017 Vol.6, No.1 6–12

Regular Article

*Yoichirou Hosokawa: Department of Radiological Technology, Hirosaki University School of Health Sciences, 66-1 Hon-cho, Hirosaki, Aomori, JapanE-mail: hosokawa@ hirosaki-u.ac.jp

Copyright © 2017 by Hirosaki University. All rights reserved.

This study aimed to prove the theoretical possibility of planning intensity modulated radiation therapy (IMRT) using filtered back projection (FBP). To this end, we created an image reconstruction algorithm on a personal computer using FBP and then reconstructed a tumour planning target volume (PTV) image. From this, tumours FBP data was acquired. This projection was then input into a radiotherapy planning system (RTPS) as beam intensities of IMRT plan. We then acquired the dose distribution within the tumours image from this system. We acquired the dose distribution in the film by irradiating the area according to the treatment plan and then compared the two dose distributions. The dose distribution in tumours image from the RTPS was almost identical to that in the PTV showed by one CT image. IMRT is currently planned using an optimization algorithm, but the current findings show that beam intensities of IMRT can also theoretically be determined by only the processing of image reconstruction by using FBP without dose calculation by using iterative methods.

Key words: intensity modulated radiation therapy (IMRT), optimization, filtered back projection (FBP), inverse planning, reconstruction algorithm

Implementation of Filtered back Projection (FBP) Theory for Intensity Modulated Radiation Therapy (IMRT) Planning

Kouichi Shioya1, Kazuki Nomura2, Fumio Komai3, Shingo Terashima2, Masahiko Aoki4 and Yoichirou Hosokawa2*

1Department of Radiological Technology, Odate Municipal General Hospital,3-1 Toyomachi, Odate, Akita, Japan 2Department of Radiological Technology, Hirosaki University Graduate School of Health Sciences, 66-1 Hon-cho, Hirosaki, Aomori, Japan

3Department of Radiological Technology, Hirosaki University Hospital, 53 Hon-cho, Hirosaki, Aomori, Japan 4Department of Radiology and Radiation Oncology, Hirosaki University Graduate School of Medicine, 5 Zaifu-cho, Hirosaki, Aomori, Japan

Received 23 August 2016; revised 14 November 2016; accepted 6 December 2016

1. Introduction

Intensity modulated radiation therapy (IMR T) has increased in popularity as an advanced radiotherapy technique in recent years. To date, various IMR T devices have been developed in the USA, and IMR T is performed in more than half of the treatment facilities1). The concept of inverse planning was first repor ted by Brahme et al. in 1988, which paved the way for the

clinical application of IMR T2). Most software programs for IMR T are made in the USA, and the detailed optimization calculations performed within them are unclear. Furthermore, dose calculations used in the present inverse planning methods require a lot of time to formulate an ideal treatment plan3, 4). We suggested that alternative method of beam intensity could be determined by using filtered back projection (FBP) which is used for single photon emission computed tomography (SPECT).

Figure 1-I shows the image reconstruction process5) used in SPECT. A phantom has two radiation sources therein (Fig. 1-I-a), and projection data were obtained by 360° photographing with a γ camera. Subsequently, this projected image was subjected to filter correction in

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an image processing apparatus (Fig. 1-I-b) and was then back-projected onto Cartesian coordinates to reconstruct an original image. Finally, after the noise was processed, a reconstructed image was displayed on a monitor (Fig. 1-I-c). What is notable here is that the back projection (Fig. 1-I-b) during the image reconstruction and the IMR T (Fig. 1-II-b) during rotational irradiation in the inverse planning process (Fig. 1-II-a) look similar. In other words, we believed that if slit irradiation was performed using a back-projected image as intensity modulation to reconstruct an image, target dose distribution could be achieved.

A calculation method using FBP for radiation therapy equipment has been developed in the past6). However, when using the original FBP method, it is dif ficult to directly calculate doses because of the negative intensity produced by the filter correction. Iterative filtered back projection (IFP) is required in order to avoid getting beam intensity under zero. Therefore, the FBP dose calculation has been used to develop an inverse treatment planning algorithm to use IFP 6). We devised a method to directly determine the beam intensities of slit beam radiation exposed by rotational IMR T without iterative dose calculation used by the original IFP method. In optimization algorithm nowadays, it takes a long time for calculation time in order to reiterate calculations to determine proper beam intensity. We suggest that the time taken by our method theoretically is almost as much as the time taken by CT reconstruction because the beam intensity is determined by using image processing without the dose calculated by FBP. We expect that radiation planning time is getting shorter and we think this point is the advantage of this method compared to other algorithms. We report here that an appropriate dose distribution can be obtained by our calculation method in this study.

2. Material and methods

2.1. Creation of image reconstruction programA program for image reconstruction of an original CT-image showing PTV input into 64×64 cells on a

Fig. 1. Schematic of the basic theory of this study. I: Image reconstruction algorithm; I-a: Projection data obtained from two radiation sources in a phantom; I-b: Back-projected image after filter correction; I-c: Reconstructed image on a monitor after noise processing; II: Intensity modulated radiation therapy (IMRT); II-a: Concept of inverse planning; II-b: IMRT during rotational irradiation.

Fig. 3. The prostate image and planning target volume (PTV) image obtained by inputting the prostate PTV into Excel. A negative value was written in red letters.

Ⅰ-a. Scanning Ⅰ-b. Back projection Ⅰ- c. Reconstruction Ⅱ-a. Inverse planning Ⅱ-b. IMRT

Fig. 2. Flow chart of the image reconstruction and intensity modulated radiation therapy used in our method.

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Fig.3. (a)

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sheet in Microsoft Excel 2010 (Microsoft Corporation, Redmond, WA, USA) in accordance with FBP, an image reconstruction theory of SPECT, was created (Figs. 2a, 2b). The program was created by combining an Excel function and Visual Basic for Application. Next, shapes of prostate, pharyngeal, and postoperative breast and lung cancers were inputted as PTV into cells created in Excel. A multileaf collimator (MLC) of a linear accelerator (CLINAC iX; Varian Medical Systems, Palo Alto, CA, USA) has a width of 5 mm. Accordingly, on the assumption that the cell size was also 5 mm on all sides, the PTV shape was manually inputted as density 1 with reference to a CT image, which was used as the original image (Fig. 3).

2.2. Transplantation of a back-projected image to a treatment planning system (TPS) To implement a back-projected image in the linear accelerator, a filter-corrected sinogram obtained in the middle of the image reconstruction program of the PTV was transplanted to a TPS (Pinnacle3, version 8.0m; Hitachi Medical Corporation, Tokyo, Japan). T he 10 MV X-ray beam was used in this experiment. Because of capacity restriction of the TPS, the transplantation of a back-projected image was carried out with ≤ 120 ports for one treatment plan. Therefore, the plan was created by a field-in-field technique in which one port is expressed of three-stage intensity together with 36-port rotatory irradiation (Fig. 4).

2.3. Creation and verification of a dose distributionA dose distribution was created by the TPS by calculating a transplanted treatment plan as multiple-port rotational irradiation. Superposition method was used as calculation algorithm. Dose calculations were per formed by superposition algorithm with grid size of 4 mm. We

Fig. 4. Rotational intensity modulated radiation therapy concept transplanted by the field-in-field technique and dividing X-ray intensity into three stages using a multileaf collimator.

Fig. 5. Reproducibility with changing collection directions. The figure shows the projections obtained in 24, 36, or 72 collection directions during the reconstruction of an original image. Reproducibility was improved by increasing the number of collection directions. A similar tendency was confirmed in a single photon emission computed tomography test.

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needed to confirm that the use of the linear accelerator with the dose distribution calculated by this method is deliverable. In order to confirm that, the beam used in our method to obtain appropriate dose distribution is deliverable. Verification was performed by a DD-System verification system (R-tech, Tokyo, Japan) by irradiating R T-3000-New, a phantom exclusive for IMR T (R-tech) that actually sandwiches an EDR2 film (Eastman Kodak Company, Rochester, NY, USA) for verification. In the irradiation method, when the collimator of the linear accelerator is rotated by 90 degrees, beam intensity is realized due to the slit of MLC. With one port having 3 stage intensity, we irradiated 2 monitor unit（MU）per segment. We irradiated 3 times from one port and irradiated from 36 ports in all.”

3. Results

3.1. Creation and reproducibility of an image reconstruction programThe image reproduction program had specifications that allowed a projected image to be acquired by arbitrarily changing a starting and ending angle as well as an angle interval. It was thereby known that, as the number of collection directions was increased to 24, 36, and 72, for example, even in the same 360°collection, noise was reduced and reproducibility was increased (Fig. 5). This tendency was similar to that of a SPECT test.

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3.2. Reconstruction of PTV showed by CT-imageProjection data were obtained by radon transform as an alternative to 360°photographing in a SPECT test. Starting at the lowest position as 0°, projection data were superimposed for ever y 10° clockwise to complete the 360°sinogram (Fig. 6a). For the sinogram, Fourier transform was performed for one line at a time, correction was applied by a ramp filter, and then inverse fast Fourier transform was performed to complete a filtered sinogram (Fig. 6b). A reconstructed image was created by back-projecting the filtered sinogram (Fig. 7). The reconstruction was performed and the density was reduced in half and became non-uniform when the reconstruction was performed. Meanwhile, values ≤ 0.2 were eliminated as noise. The tumours PTV shape was thereby reconstructed by this method.

3.3. Transport methods of beam intensities to treatment planning systemFigure 8a shows a back-projected image obtained by graphing data of the uppermost stage (θ= 0) of the filtered sinogram (Fig. 6b). Back-projected data as beam intensities are too large to be transplanted into the TPS. Therefore, negative values in the data were cut of f and the intensity was consolidated into three stages (Fig. 8b). Accordingly, programs shown under the filtered sonogram in Figure 2b were added. With one direction having three-stage intensity, an MLC was operated and a plan was created (Fig. 8c). The back-projected image was transplanted to the TPS by fixed multiportal irradiation. For the image reconstruction, the calculation was performed from the back projection in 36 directions. As for the IMRT, irradiation from 36 ports and slit irradiation

Fig. 6. Prostate sonograms before the back projection step. (a) Prostate sonogram. A 360° sinogram completed by superimposing projection data for each 10° with the lowest position set as 0° after the projection data were obtained by radon conversion. (b) Prostate filtered sonogram obtained by filter correction processing of 360° sinogram completed by superimposing projection data for each 10° with the lowest position set as 0° after the projection data were obtained by radon conversion. A negative value was written in red letters.

Fig. 6.

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12 13 12 13 10 9 7 3 0 0 0 0 280 0.1 0.1 0.1 0.2 0.6 0.1 0.1 0.3 0.8 0.1 0.5 0.1 0.8 0.0 0.3 0.3 0.2 0.5 0.2 0.1 0.1 2800 0 0 0 1 4 7 9 12 13 11 13 12 10 10 7 3 0 0 0 0 290 0.1 0.1 0.1 0.3 0.4 0.0 0.2 0.1 0.5 0.7 0.1 0.6 0.4 0.0 0.6 0.2 0.2 0.5 0.2 0.1 0.1 2900 0 0 0 1 5 6 9 12 13 11 12 12 12 9 8 2 0 0 0 0 300 0.1 0.1 0.2 0.3 0.5 0.3 0.2 0.2 0.5 0.7 0.1 0.4 0.3 0.7 0.0 0.7 0.5 0.4 0.2 0.1 0.1 3000 0 0 0 3 5 6 9 11 11 13 11 12 11 10 7 3 0 0 0 0 310 0.1 0.1 0.1 0.5 0.1 0.1 0.1 0.3 0.5 0.1 0.7 0.1 0.5 0.3 0.5 0.2 0.2 0.5 0.2 0.1 0.1 3100 0 0 0 3 6 8 7 10 11 13 11 12 11 10 7 3 0 0 0 0 320 0.1 0.1 0.2 0.5 0.0 0.2 0.5 0.3 0.4 0.1 0.8 0.1 0.5 0.3 0.5 0.2 0.2 0.5 0.2 0.1 0.1 3200 0 0 0 2 8 8 8 8 12 11 12 12 12 9 8 2 0 0 0 0 330 0.1 0.1 0.2 0.4 0.5 0.8 0.2 0.2 0.3 0.8 0.0 0.4 0.3 0.7 0.0 0.7 0.5 0.4 0.2 0.1 0.1 3300 0 0 0 3 7 10 8 9 10 10 13 12 10 10 7 3 0 0 0 0 340 0.1 0.1 0.2 0.5 0.1 0.2 0.8 0.1 0.1 0.3 0.1 0.7 0.4 0.1 0.6 0.2 0.2 0.5 0.2 0.1 0.1 3400 0 0 0 3 7 9 10 10 9 10 12 13 10 9 7 3 0 0 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Fig. 7. Prostate reconstruction image obtained by extracting the image data into Excel. A negative value was written in red letters.

Fig. 8. Schematic of a three-phase condense technique. a: filtered back-projected image obtained by graphing data on the uppermost stage (θ= 0) shown in Fig. 6b. b: Three-phase condensation image obtained by cutting of f the negative values from the back projection data and consolidating the intensity into three stages. c: Plan created by setting one direction to have three-stage intensity and operating a multileaf collimator. A negative value was written in red letters.

Fig.7

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with one port were expressed as three-stage intensity modulation. Therefore, the calculation was performed as 108-port conformation therapy (Fig. 4).

3.4. Density adjustment work and film verification All pixels in this program express density. When the principles of the conventional FBP method is used, the values of projections deriving from each port will be aggregated and exhibited through density. This value

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Fig. 9. Schematic of density adjustment methods. (Upper row) The results of a dose distribution calculation with the density of the original image set to 1 are shown, and the dose distribution is non-uniform. (Lower row) Results obtained by performing the density adjustment so that the density of the original image is not 1 but the density of the image reconstruction is 1, followed by the calculation of a dose distribution.

Fig. 10. The results of dose distributions estimated by a radiotherapy planning system (RTPS; left) and irradiated film (right) sandwiched in a phantom. A dose distribution of the RTPS is approximately identical to that of the film according to a DD-System verification system.

Fig. 11. Pharyngeal cancer images obtained by the input of planning target volume of the pharynx and the calculation of a dose distribution. A good dose distribution was created.

can be set to an arbitrary numerical value, in this study the PTV density of this original image was calculated as one. The calculation result in the case in which the density of the original image is 1 showed a non-uniform dose distribution (Fig. 9, upper row). The density of the original image was then purposely adjusted so that the density of the reconstructed image, but not that of the original image, would be uniform. As a result, a uniform dose distribution could be obtained (Fig. 9, lower row).

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This density adjustment work was necessary to obtain a uniform distribution since it was performed using the correlation between each cell of the original image and that of the reconstructed image. An analysis by the DD-System was made by irradiating the phantom, while the film was sandwiched according to the transplanted plan. The dose distribution of the R TPS was approximately identical to that of the film (Fig. 10).With the PTV obtained in the same manner of the pharyngeal cancer

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and the postoperative breast and lung cancer used as an original image, a dose distribution could be created from the back projection theory (Figs. 11-13).

4. Discussion

FBP method is widely used in clinical for shor t computation time, and a tendency to reduce exposure doses and improve image quality has been observed. This study showed that beam intensities in an IMRT plan can be calculated by image reconstruction. This study will contribute to verification methods and the development of optimization algorithms.

In this study, appropriate dose distribution was established with intensity modulated data determined by our FBP method for IMR T. It was confirmed in the analysis of the DD-system of the phantom irradiation result from sandwiching a film that the dose distribution of the RTPS was approximately identical to that of the film. This shows the possibility that an IMR T dose distribution can be extracted by this method without the use of an optimization calculation by the conventional dose calculation algorithm. Since priority was placed on whether dose distribution of the objective PTV could be achieved, normal tissue was not evaluated.

In regards to the image reconstruction program creation and reproducibility, as the number of collection directions of projection data increased, noise was reduced and reproducibility was improved. This is a matter of course from the FBP theory and was seen as a tendency similar to that of the SPECT tests7). Therefore, even in rotational IMRT with a large number of irradiation ports, a dose gradient will increase and dose concentration will be improved. This point, however, could not be confirmed because of the restricted capacity of the TPS.

Fig. 12. Breast cancer images obtained by the input of planning target volume of the postoperative breast and the calculation of a dose distribution. A good dose distribution was achieved.

Fig. 13. Lung cancer images obtained by the input of planning target volume of the lung and the calculation of a dose distribution.

Fig.12.

Fig.13.

The intensity was consolidated to three stages, but it is possible that, if the number of stages can be increased, a dose distribution with higher conformality will be obtainable. Furthermore, it is also possible that irradiation can be delivered using a smaller number of ports. As stated above, the demonstration that irradiation via IMRT using theoretical image reconstruction has become possible is a great achievement.

Since image reconstruction of the PTV was performed in Excel and did not involve the concept of X-ray absorption, transplantation to the RTPS was performed without consideration of X-ray absorption. Currently, electron density and subject’s X-ray absorption are important points for dose calculation in radiotherapy, however, this study does not use this to determine beam intensity. Appropriate dose distribution could not be created although beam intensities determined as asymmetric ports were transplanted. In this method, it could not be adapted that it symmetrical having no rotational irradiation. If it is not an IMRT plan in which parallel opposing ports are assembled, appropriate dose distribution could not be achieved. It was thought that multiple-port rotational irradiation with opposing port decreased the influence of X-ray absorption.

In the density adjustment work and film verification processes, a phenomenon in which the PTV density distribution became non-uniform was seen during the reconstruction. In this study, in order to obtain an appropriate dose distribution, uniform density within image reconstruction is required. Therefore, it is necessary to secure the density adjustment process. This density adjustment is performed using the correlation between the cells of an original image and those of a reconstructed image in the same positions. With the same PTV and irradiation method, there was a correlation

Kouichi Shioya et al. / Radiation Environment and Medicine 2017 Vol.6, No.1 6–1212

between the cells of the original image and those of the reconstructed image in the same positions. This density adjustment work was made much more efficient with the identification of a coefficient of the correlation. We need to develop the automation method to control density and to transport the beam intensity to the treatment planning system.

In radiation treatment, changes over with time occur in the tumor and patient during treatment, and the influence exerted by the changes on dose distribution cannot be disregarded8). In the current radiation treatment, however, since the dose was considered an optimization calculation for a target dose distribution, the calculation requires a lot of time, and the treatment plan cannot be frequently changed8). Higher-speed calculation processing is expected to become possible using this method compared with conventional methods in addition to dose calculation according to a patient’s condition during the treatment period. If this method is established, it will become possible to accurately irradiate a tumor that changes during treatment with irradiation and will lead to the application of adaptive radiotherapy.

5. Conclusions

Here it was confirmed by self-writing using an image reconstruction program and slit irradiation with a back-projected image of the PTV as intensity modulation that a dose distribution of rotational IMRT could be created. In genetic algorithm nowadays, it takes a long time for calculation time in order to reiterate calculations to determine proper beam intensity. We suggest that the time taken by our method theoretically is almost as much as the time taken by CT reconstruction because the

beam intensity is determined by using image processing without the dose calculated by FBP. We expect that radiation planning time is getting shorter and we think this point is the advantage of this method compared to other algorithms. This trial study enabled the examination of an IMRT dose distribution from the FBP theory viewpoint.

Conflict of Interest Disclosure

The authors have no conflict of interest directly relevant to the content of this article.

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