

ORIGINAL RESEARCH REPORT 

Year : 2017  Volume
: 14
 Issue : 2  Page : 7480 

Development of pelvis phantom for verification of treatment planning system using convolution, fast superposition, and superposition algorithms
Michael Onoriode Akpochafor^{1}, Chibuzo Bede Madu^{2}, Muhammad Yaqub Habeebu^{1}, Akintayo Daniel Omojola^{3}, Samuel Olaolu Adeneye^{1}, Moses Adebayo Aweda^{1}
^{1} Department of Radiation Biology, Radiotherapy, Radiodiagnosis and Radiography, College of Medicine, Lagos University Teaching Hospital, IdiAraba, Lagos, Nigeria ^{2} Department of Radiology, Medical Physics Unit, University College Hospital, Ibadan, Nigeria ^{3} Department of Radiology, Medical Physics Unit, Federal Medical Center, Asaba, Nigeria
Date of Web Publication  18Apr2017 
Correspondence Address: Chibuzo Bede Madu Department of Radiology, Medical Physics Unit, University College Hospital, Ibadan Nigeria
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/jcls.jcls_78_16
Background: The cost of commercial pelvis phantom is a burden to the quality assurance in radiotherapy of small and/or lowincome radiotherapy centers. That an algorithm is accurate with short treatment time is a prized asset in treatment planning. Objectives: The purpose of this study was to develop a hybrid algorithm that has balance between accuracy and treatment time and design a pelvis phantom for evaluating the accuracy of a linear accelerator monitor unit. Materials and Methods: A pelvis phantom was designed using Plaster of Paris, styrofoam and water with six hollows for inserting materials mimicking different biological tissues, and the ionization chamber. Computed tomography images of the phantom were transferred to the CMS XiO treatment planning system with three different algorithms. Monitor units were obtained with clinical linear accelerator with isocentric setup. The phantom was tested using convolution (C), fast superposition (FSS), and superposition (S) algorithms with respect to an established reference dose of 1 Gy from a large water phantom. Data analysis value was done using GraphPad Prism 5.0. Results: FSS algorithm showed better accuracy than C and S with bone, lung, and solid water inhomogeneous insert. C algorithm was better in terms of treatment time than S. There was no statistically significant difference between the mean doses for all the three algorithms against the reference dose. The maximum percentage deviation was ±4%, which was below ±5% International Commission on Radiation Units and Measurement minimal limit. Conclusion: This algorithm can be employed in the calculation of dose in advance techniques such as intensitymodulated radiation therapy and RapidArc by radiotherapy centers with multiple algorithm system because it is easy to implement. The materials used for the construction of the phantom are very affordable and simple for lowbudget radiotherapy centers. Keywords: Fast superposition, monitor unit, phantom, radiotherapy, superposition and convolution algorithms, treatment planning system
How to cite this article: Akpochafor MO, Madu CB, Habeebu MY, Omojola AD, Adeneye SO, Aweda MA. Development of pelvis phantom for verification of treatment planning system using convolution, fast superposition, and superposition algorithms. J Clin Sci 2017;14:7480 
How to cite this URL: Akpochafor MO, Madu CB, Habeebu MY, Omojola AD, Adeneye SO, Aweda MA. Development of pelvis phantom for verification of treatment planning system using convolution, fast superposition, and superposition algorithms. J Clin Sci [serial online] 2017 [cited 2018 Jan 17];14:7480. Available from: http://www.jcsjournal.org/text.asp?2017/14/2/74/204705 
Introduction   
During radiotherapy treatments, the prescribed absorbed dose delivered should be concentrated on the target volume while the doses to normal tissues and organs at risk are minimized. According to Nette and Svensson, “in principle, a quality assurance program should ensure that all patients treated with a curative aim receive the prescribed dose within a margin of about 5%.”^{[1]} This means that the uncertainty involved in the delivery of the prescribed dose must be within 5%.^{[2],[3],[4],[5]} Quality assurance program ensures that all treatment facilities used in radiotherapy are properly checked for accuracy and consistency and that all radiation facilities are functioning according to manufacturer's specification. After the acceptance and commissioning of a computerized treatment planning system (TPS), a scheduled quality assurance program should be established to verify the output of the TPS. Several ways of carrying out the quality assurance in TPS have been proposed by various reports. However, it is necessary for each department to develop its own program based on the availability of equipment and local requirements while using published methods as a guideline. Computerized TPSs are used in external beam radiotherapy to generate beam shapes and dose distributions with the intent to maximize tumor control and minimize normal tissue complications. Treatment simulations are used to plan the geometric and radiological aspects of the treatment using radiation transport simulations and optimization. TPS ensures that patients receive the prescribed doses in which a number of parameters of the tumor have to be taken into consideration such as the shape, size, and depth. There are several algorithms for TPSs that play different roles; however, the dose calculation algorithms play the central role of calculating dose within any position inside the patient. Algorithms are a sequence of instructions that operate on a set of input data, transforming the information into a set of output results that are of interest to the user.^{[6],[7],[8],[9],[10],[11]} For every algorithm, the quality of the dose depends on the data or parameters used in the algorithm. There are three types of dose calculation algorithms in the CMS Xio TPS for calculation of monitor unit in photon beams needed to deliver a given dose to a point, and these are the fast Fourier transform (FFT) convolution, the superposition, and the fast superposition (FSS). In the FFT convolution algorithm, the distribution of the dose is convoluted from the total energy released per unit mass (TERMA).^{[12]} The FFT algorithm increases the speed of calculation by calculating dose in the frequency domain while assuming kernels to be invariant with position. FFT convolution does not account for the presence of inhomogeneity during calculations which may lead to inaccurate dose calculations.^{[13],[14],[15],[16],[17],[18],[19],[20],[21],[22],[23],[24],[25],[26]} The following equation describes the distribution.^{[27]}
= Dose at a point
= Mass attenuation coefficient
= Primary photon energy fluence
= Convolution kernel, the distribution of fraction energy imparted per unit volume
= TERMA at depth includes the energy retained by the photon.
Superposition method is an adaptation of the “collapsed cone” dose calculation method.^{[15],[16]} Energy deposition kernels are modified to account for variations in electron density which makes it accurate for calculating dose in homogenous media compared to FFT convolution. Its calculation speed is, however, slow. The following equation is used in the superposition dose calculation.^{[27]}
Dose at point is the summation of the TERMA point times the value of the energy deposition kernel originating at point and evaluated at point r.
With FSS, the spherical kernels computation is improved by the ability to merge adjacent zenith rays in the kernel.^{[14]} This increases the speed of calculations with this algorithm; however, the accuracy of the calculated monitor unit is reduced compared to superposition algorithm. Depending on the user, a compromise between the accuracy and speed of calculation is required. Each algorithm surfers from its limitations; these include density of the material, due to interactions and dose deposition points not modeled, photon and electron contamination from certain treatment aids is not modeled, the spectrum which is assumed to be independent of the field size and shape, the mass attenuation coefficient used in patient is that of water, electron contamination is assumed to be independent of source to surface distance (SSD), and wedge/block trays are not modeled in the fluence calculations. As a result of these limitations, it is important to check the accuracy of these algorithms independently. This study aimed at evaluating the precision of monitor units obtained by the algorithms used in CMS XiO TPS using an inhouse designed phantom.
Materials and Methods   
An inhouse designed phantom was made in the shape of the human pelvic region. The design of the phantom was motivated by inability to use the Rando Anderson phantom with the diode system for the treatment planning verification measurements. The phantom has provision for six hollow inserts for materials mimicking different biological tissues and the ionization chamber. The yellow Plaster of Paris insert with computed tomography (CT) number also known as Hounsfield unit was used to mimic the bone (1100 HU) [Figure 1] while the styrofoam insert with CT number of 900 HU was used to mimic the lung and water for normal soft tissues [Figure 2]. The phantom was also tested with solid water.  Figure 1: Inhouse phantom filled with water having bone inhomogeneity made of Plaster of Paris
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 Figure 2: Inhouse designed phantom with lung inhomogeneity using styrofoam
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The Toshiba Asteion CTscanner was used to acquire images using the 5 mm slices. Two sets of scans were acquired first with the bone inserts and then lung. After the scans were acquired, the CTnumbers of the bone and lung inhomogeneities were determined using the CTnumber calculation algorithm present in the CTscanner. The scans were transferred into the CMS XiO TPS for planning [Figure 3].  Figure 3: The scans transferred to the CMS XiO treatment planning system for planning
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Several simple plans of single to multiple beams were made with the phantom using the different calculation algorithms configured to give 1.0 Gy at the isocenter with a 10 cm × 10 cm field size [Figure 4]. Plans were then transferred to the precalibrated ELEKTAPrecise clinical linear accelerator for measurements.
Measurements were carried out with 6 MeV photons from the ELEKTAPrecise clinical linear accelerator using an isocentric setup. A precalibrated Farmertype ionization chamber along with its electrometer was used to measure the absorbed dose delivered. Six measurements were made for each plan using the different algorithms for comparison and to limit statistical uncertainties. Absorbed dose at reference depth was calculated as follows:^{[17]}
Where M_{Q} is the electrometer reading (charge) corrected for temperature and pressure. N_{D, W} is the chamber calibration factor and K_{Q, Qo} is the factor which corrects for difference in the response of the dosimeter at the calibration quality, Q, and at quality, Q of the clinical Xray beam according to the TRS398 protocol of the International Atomic Energy Agency.^{[17]} Deviation between expected and measured dose was obtained using:
Where D_{ref} is calculated dose from the large water phantom and D_{m} is measured dose result from the designed pelvic phantom for this study. The calculated value for D_{ref} was ≈ 100 cGy (1 Gy).
Ethical considerations
Ethical approval is not required since no human or animal subject was used.
Statistical analysis
Data analysis value was done using GraphPad Prism 5.0 (GraphPad Software, Inc., San Diego, California, USA). Descriptive statistics and unpaired t test were implored at 95% level of significance. A P < 0.05 was considered statistically significant.
Results   
The result of mean absorbed dose, standard deviation, and percentage deviation was measured for different field plans with bone inhomogeneity. The percentage deviation for single field for C, FSS, and S was 3.8%, 1.3%, and 2.0%, respectively, wedge field for C, FSS, and S was 4.0%, 2.8%, and 3.0%, respectively, oblique field for C, FSS, and S was 3.5%, 0.5%, and 1.7%, respectively, opposite field for C, FSS, and S was − 2.0%, −4.0%, and − 3.3%, respectively, and three field for C, FSS, and S was 2.7%, 0.7%, and 1.3%, respectively. The highest percentage deviation was noticed in the wedge field for convolution algorithm (4.00%) and opposite field for FSS (−4.00%), respectively. The least percentage deviation was noticed in the oblique field for FSS which was 0.5% [Table 1].  Table 1: Measured mean absorbed dose with bone inhomogeneity insert for different field plans with D_{ref}100 cGy (1 Gy)
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Furthermore, result of mean absorbed dose, standard deviation, and percentage deviation was measured for different field plans with lung inhomogeneity. The percentage deviation for single field for C, FSS, and S was 2.2%, 1.2%, and 2.2%, respectively, wedge field for C, FSS, and S was 2.0%, 1.2%, and 2.0%, respectively, oblique field for C, FSS, and S was 2.2%, 1.2%, and 2.2%, respectively, opposite field for C, FSS, and S was − 2.8%, −3.5%, and − 2.8%, respectively, and three field for C, FSS, and S was 1.3%, −0.2%, and 0.7%, respectively. The highest percentage deviation was noticed in the opposite field for FSS algorithm (−3.50%), and the least percentage deviation was noticed in the three field superposition which was 0.7% [Table 2].  Table 2: Measured mean absorbed dose with lung inhomogeneity insert for different field plans with D_{ref}100 cGy (1 Gy)
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In addition, result of mean absorbed dose, standard deviation, and percentage deviation was measured for different field plans with solid water inhomogeneity. The percentage deviation for single field for C, FSS, and S was 0.7%, 2.3%, and 1.0%, respectively, wedge field for C, FSS, and S was 3.2%, 2.5%, and 2.8%, respectively, oblique field for C, FSS, and S was 1.2%, 1.2%, and 1.3%, respectively, opposite field for C, FSS, and S was −0.8%, −1.8%, and − 0.3%, respectively, and three field for C, FSS, and S was 2.3%, 1.0%, and 0.8%, respectively. The highest percentage deviation was noticed in the wedge field for convolution algorithm (3.20%), and the least percentage deviation was noticed in opposite field for superposition which was − 0.3% [Table 3].  Table 3: Measured mean absorbed dose with solid water insert for different field plans with D_{ref}100 cGy (1 Gy)
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Treatment time with the convolution (C) was determined with lungs  single field (t = 0.5 s), lungs  opposite field (t = 0.7 s), lungs  12 fields (t = 7.0 s), bone  12 fields (t = 9.0 s), solid water  12 fields (t = 6.0 s), lungs  30 fields, intensitymodulated radiation therapy (IMRT) plan (t = 45 s), and lungs  57 fields, RapidArc plan (t = 98 s). Superposition (S) algorithms was as well determined with lungs  single field (t = 1.0 s), lungs  opposite field (t = 1.2 s), lungs  12 fields (t = 8.0 s), bone  12 fields (t = 11.0 s), solid water  12 fields (t = 8.0 s), lungs  30 fields, IMRT plan (t = 66 s), and lungs  57 fields, RapidArc plan (t = 123 s). The results show that convolution has a good treatment time than superposition algorithm [Table 4].  Table 4: Calculation of treatment time of the different algorithms for different plans for 6 MeV photon beam
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Discussion   
The result for this study using C, FSS and S algorithms were within ±4% limit. The results were seen to be consistent with van Dyk et al.^{[7]} and follow similar trend to Butts and Foster ^{[25]} whose deviation were also within ±4% limit. The results were as well within the range of ±5% as recommended by International Commission on Radiation Units and Measurement.^{[28]}
A large deviation was observed with the convolution (P = 0.0992) and superposition (P = 0.0884) algorithm with bone inhomogeneity and solid water, respectively, which could be due to unaccounted scattered radiation contribution from the inhomogeneous material by the algorithm.^{[14],[18]}
FSS algorithm showed better accuracy with bone homogeneous insert with P = 0.8306 than C algorithm with P = 0.0992 and S algorithm with P = 0.440. Furthermore, FSS algorithm showed better accuracy with lung homogeneous insert with P = 0.9835 than C algorithm with P = 0.3648 and S algorithm with P = 0.4196. In addition, FSS algorithm showed better accuracy with the solid water with P = 0.2474 than C algorithm with P = 0.1263 and S algorithm with P = 0.0884. These results indicate that FSS algorithm can be useful in planning a patient with lung and bone tumor. Although there was still good accuracy for C algorithm for bone and solid water, C and S algorithm for lung.
In general, oblique field was more accurate for convolution, FSS, and superposition algorithm for bone inhomogeneous insert (P = 0.1611) with the poorest accuracy noticed with wedge field [P = 0.0127, [Table 1], three field was more accurate for convolution, FSS, and superposition algorithm for lung inhomogeneous insert (P = 0.3025) with the poorest accuracy noticed with opposite field [P = 0.0059, [Table 2], and opposite field was more accurate for convolution, FSS, and superposition algorithm for solid water insert (P = 0.1597) with the poorest accuracy noticed with oblique field [P = 0.0007, [Table 3].
There was a statistically significant difference for wedge and opposite field with bone inhomogeneous insert with respect to the reference dose where P = 0.0127 and P = 0.0339, respectively, with the three algorithms. This implies that deviation from the reference dose will be encountered using wedge and opposite field for bone insert. There was also statistically significant difference for single, wedge, oblique, and opposite field with lung inhomogeneous insert with respect to the reference dose where P = 0.0304, P = 0.0229, P = 0.0304, and P = 0.0059, respectively, with the three algorithms. The results show that only three fields showed better accuracy. Furthermore, there was a statistically significant difference for wedge and oblique field with solid water phantom with the reference dose which was P = 0.0051 and P = 0.0007, respectively, with the three algorithms. Convolution algorithm average treatment time was better than superposition algorithm [Table 4].
The maximum percentage deviation recorded for this study was approximately ± 4%. This result was relatively higher than that obtained by Muralidhar et al. whose maximum percentage variation was ± 3.7% in a comparative study of convolution, superposition, and FSS algorithm in conventional radiotherapy, threedimensional conformal radiotherapy, and IMRT using CMS XIO planning system. FSS for this study for lung insert was consistent with Muralidhar et al. whose study showed that FSS was better in terms of accuracy for all dose points. Average percentage deviation for lung insert for FSS algorithm for this study was 1.52% against Muralidhar et al. whose percentage variation value was 0.4% for all dose volume points.^{[18]}
Conclusion   
The choice of which algorithm to use should not be based on the speed of computation alone but also on the accuracy, especially for advanced radiotherapy techniques such as IMRT, where high accuracy of delivered dose is required. Hence, the goal would be to strike a balance between speed and accuracy. Each algorithm has its advantages and shortfalls based on the assumptions made during design. However, our results show that all three algorithms may be used successfully for the calculation of the monitor unit to an accuracy of ±4%. There was no statistically significant difference between the mean doses for all the three algorithms against the reference dose. The best was FSS algorithm for bone, lung, and solid water. This shows that the materials used in the design of the inhouse phantom were suitable and that the phantom can be used successfully for verification exercise. Furthermore, the cost of designing the phantom is minimal, and it is easier to use compared to other modern verification phantoms such as Rando Anderson phantom. Smaller radiotherapy centers without diode and TLD systems in place can still perform verification exercise using this phantom with their local ionization chamber.
Acknowledgment
The authors would like to thank the coauthors who gave out their time and contributed immensely to this research work.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
References   
1.  Nette P, Svensson H. Radiation dosimetry in health care; expanding the reach of global networks. Vienna: IAEA Bulletin; 1994. 
2.  International Commission on Radiation Units and Measurement (ICRU). Determination of Absorbed Dose in a Patient Irradiated by Beams of X or Gamma Rays in Radiotherapy Procedures. ICRU Reports 24. Washington, DC: ICRU Publication; 1976. 
3.  Brahme A. Dosimetric precision requirements in radiation therapy. Acta Radiol Oncol 1984;23:37991. 
4.  Brahme A. Optimization of stationary and moving beam radiation therapy techniques. Radiother Oncol 1988;12:12940. 
5.  Mijnheer BJ, Battermann JJ, Wambersie A. What degree of accuracy is required and can be achieved in photon and neutron therapy? Radiother Oncol 1987;8:23752. 
6.  Podgorsak EB. Radiation Oncology Physics: A Handbook for Teachers and Students. Vienna: IAEA Publication; 2005. 
7.  van Dyk J, Barnett RB, Cygler JE, Shragge PC. Commissioning and quality assurance of treatment planning computers. Int J Radiat Oncol Biol Phys 1993;26:26173. 
8.  van Dyk J. Quality assurance. In: Khan FM, Potish RA, editors. Treatment Planning in Radiation Oncology. Baltimore, MD: Williams and Wilkins; 1997. p. 12346. 
9.  Shaw JE. A guide to commissioning and quality control of treatment planning systems. Institution of Physics and Engineering in Medicine and Biology. Report Series. No.68. England, YorK: Institution of Physics and Engineering in Medicine and Biology; 1996. 
10.  Fraass B, Doppke K, Hunt M, Kutcher G, Starkschall G, Stern R, et al. American Association of Physicists in Medicine radiation therapy committee task group 53: Quality assurance for clinical radiotherapy treatment planning. Med Phys 1998;25:1773829. 
11.  Fraass BA. Quality assurance for 3D treatment planning. In: Palta J, Mackie TR, editors. Teletherapy: Present and Future. Madison: Advanced Medical Publishing; 1996. p. 253318. 
12.  Mackie TR, Scrimger JW, Battista JJ. A convolution method of calculating dose for 15MVxrays. Med Phys 1985;12:18896. 
13.  Boyer AL, Zhu YP, Wang L, Francois P. Fast Fourier transform convolution calculations of xray isodose distributions in homogeneous media. Med Phys 1989;16:24853. 
14.  Animesh. Advantages of multiple algorithm support in treatment planning system for external beam dose calculations. J Cancer Res Ther 2005;1:1220. 
15.  Ahnesjö A. Collapsed cone convolution of radiant energy for photon dose calculation in heterogeneous media. Med Phys 1989;16:57792. 
16.  Miften MM, Beavis AW, Marks LB. Influence of dose calculation model on treatment plan evaluation in conformal radiotherapy: A threecase study. Med Dosim 2002;27:517. 
17.  International Atomic Energy Agency (IAEA). Absorbed Dose Determination in External Beam Radiotherapy: An International Code of Practice for Dosimetry Based on Standards of Absorbed Dose to Water. IAEA Technical Report Series 398. Vienna: IAEA Publication; 2000. p. 10114289. 
18.  Muralidhar KR, Murthy NP, Raju AK, Sresty N. Comparative study of convolution, superposition, and fast superposition algorithms in conventional radiotherapy, threedimensional conformal radiotherapy, and intensity modulated radiotherapy techniques for various sites, done on CMS XIO planning system. J Med Phys 2009;34:1222. [ PUBMED] [Full text] 
19.  Mackie TR, Ahnesjo A, Dickof P, Snider A. Development of a convolution/superposition method for photon beams, in the use of computer in radiotherapy. Netherlands, NorthHolland: Elsevier Science Publisher; 1987. p.10710. 
20.  Mackie TR, Reckwerdt PJ, Holmes TW, Kubsad SS. Review of Convolution/Superposition Methods for Photon Beam Dose Computation: Proceedings of the X ^{th} ICCR; 1990. p. 203. 
21.  Mackie TR, Reckwerdt PJ, Gehring MA, Holmes TW, Kubsad SS, Thomadsen BR, et al . Clinical Implementation of the Convolution/Superposition Method: Proceedings of the X ^{th} ICCR; 1990. p. 3225. 
22.  Hasenbalg F, Neuensch Wander H, Mini R, Born EJ. Collapse cone and analytical anistropic algorithm dose calculations compared to VMC++ Monte Carlo simulations in clinical cases. J Phys Conf Ser 2007;74:111. 
23.  Vanderstraeten B, Reynaert N, Paelinck L, Madani I, De Wagter C, De Gersem W, et al. Accuracy of patient dose calculation for lung IMRT: A comparison of Monte Carlo, convolution/superposition, and pencil beam computations. Med Phys 2006;33:314958. 
24.  Born E, FogliataCozzi A, Ionescu F, Ionescu V, Tercier PA. Quality control of treatment planning systems for teletherapy. SSRPM Recommendations No. 7. Zurich: Swiss Society for Radiobiology and Medical Physics; 1997. 
25.  Butts JR, Foster AE. Comparison of commercially available threedimensional treatment planning algorithms for monitor unit calculations in the presence of heterogeneities. J Appl Clin Med Phys 2001;2:3241. 
26.  Mackie TR, elKhatib E, Battista J, Scrimger J, van Dyk J, Cunningham JR. Lung dose corrections for 6 and 15MVxrays. Med Phys 1985;12:32732. 
27.  Kohno R, Kitou S, Hirano E, Kameoka S, Goka T, Nishio T, et al. Dosimetric verification in inhomogeneous phantom geometries for the XiO radiotherapy treatment planning system with 6MV photon beams. Radiol Phys Technol 2009;2:8796. 
28.  International Commission on Radiation Units and Measurements (ICRU). Dose Specifications for Reporting External Beam Therapy with Photons and Electrons. ICRU Report 29. Baltimore: Bethesda; 1978. 
[Figure 1], [Figure 2], [Figure 3], [Figure 4]
[Table 1], [Table 2], [Table 3], [Table 4]
