EuCARD-BOO-2013-001
European Coordination for Accelerator Research and Development PUBLICATION
Advances in Conformal Radiotherapy - Using Monte Carlo Code to design new IMRT and IORT accelerators and interpret CT numbers; EuCARD Editorial Series on Accelerator Science and Technology (J-P.Koutchouk, R.S.Romaniuk, Editors), Vol.17
Wysocka-Rabin, A (NCBJ Swierk Poland)
04 March 2013
The research leading to these results has received funding from the European Commission under the FP7 Research Infrastructures project EuCARD, grant agreement no. 227579.
This work is part of EuCARD Work Package 2: DCO: Dissemination, Communication & Outreach.
The electronic version of this EuCARD Publication is available via the EuCARD web site EuCARD-BOO-2013-001 [WPISZ NAZWĘ FIRMY] Advances in Conformal Radiotherapy Using Monte Carlo Code to design new IMRT and IORT accelerators and interpret CT numbers Anna Wysocka-Rabin 2012-12-31 Contents Author’s Preface 3 1. Introduction and aim of the work 5 2. A new scanning photon beam system for IMRT 13 2.1 Intensity modulated radiotherapy (IMRT) techniques ...... 13 2.1.1 Conventional MLC based IMRT technique ...... 13 2.1.2 An alternative way to do IMRT ...... 14 2.2 Research objective ...... 16 2.3 Monte Carlo (MC) study on a new concept of a scanning photon beam ...... 17 2.3.1. Definition of requirements on the resulting photon beam ...... 17 2.3.2. First draft for a target-collimator system ...... 17 2.3.3 Influence of the collimator aperture ...... 18 2.3.5 Influence of the incident electron beam characteristics ...... 24 2.3.6 Influence of the geometry ...... 26 2.4 Summary: conclusions and discussion ...... 30 2.4.1 Simulated dose distribution of an intensity modulated field ...... 32 2.4.2. Discussion ...... 34 3 A new mobile electron accelerator treatment head for IORT 38 3.1 What is IORT? ...... 38 3.2 Research objective ...... 41 3.3 Monte Carlo study on a new model of a treatment head for a mobile electron accelerator .... 43 3.3.1. Radiation field and protection requirements ...... 43 3.3.2. First draft for a foils-collimator-applicator system ...... 45 3.3.3 Monte Carlo simulations ...... 47 3.3.4 Dose distributions for the first draft of a foils-collimator-applicator system ...... 48 3.3.5 Comparison of dose distribution for real and monoenergetic beams ...... 59 3.3.6 Acceptable tolerance for displacement and rotation of applicator axis relative ...... 62 to beam axis ...... 62 3.3.7 Second draft for a foils-collimator-applicator system ...... 63 3.4 Radiation protection studies for a new mobile IORT accelerator ...... 73 3.4.1. Dose equivalent inside and outside operating room ...... 75 3.4.2. Neutron DEQ ...... 78 3.5 Summary: conclusions and discussion ...... 80 4. A new approach to estimate the effect of CT calibration on range calculation 83 1 4.1 Treatment planning in Carbon ion therapy ...... 83 4.1.1 Radiotherapy with heavy charged particles ...... 83 4.1.2 CT in Carbon ion radiotherapy treatment planning ...... 86 4.1.3 Image representation in CT-numbers (Hounsfield Units) ...... 89 4.2 Research objective ...... 91 4.3 Materials studied: CT scanner, substitutes and phantoms ...... 91 4.3.1 Investigated CT scanner ...... 91 4.3.2 Investigated substitutes and phantoms ...... 91 4.4 MC simulation CT-numbers for a CT scanner and different phantom inserts ...... 93 4.4.1 Simulation work flow ...... 93 4.4.2 Optimization of parameters used in MC code...... 94 4.4.4 Reconstructing CT-images from PHSP ...... 95 4.4.5 CT-numbers of the various substitute materials ...... 96 4.4.6 Accuracy of the simulated CT-numbers ...... 98 4.5 Effect of X-ray voltage, phantom size and material on CT-numbers ...... 102 4.5.1 Effect of filters on energy spectrum and fluence ...... 102 4.5.2 Effect of voltage settings on energy spectrum , fluence and CT-numbers ...... 104 4.5.3 Effect of substitute material on energy spectrum , fluence and CT-numbers ...... 105 4.5.4 Effect of phantom size on CT-numbers ...... 106 4.5.5 Effect of phantom material on CT-numbers ...... 107 4.6 Effect of X-ray voltage, phantom size and material on range calculation ...... 109 4.6.1 CT calibration relation for ion therapy ...... 109 4.6.2 Effect of CT calibration on range calculation ...... 110 4.6.3 Effect of CT scanner and phantom parameters on range calculation in C-ion therapy . 113 4.7 Summary: conclusions and discussion ...... 117 References 119 List of Figures 126 Abbreviations 133 Appendix A 135 Appendix B 143 2 Author’s Preface The introductory chapter of this monograph, which follows this Preface, provides an overview of radiotherapy and treatment planning. The main chapters that follow describe in detail three significant aspects of radiotherapy on which the author has focused her research efforts. Chapter 2 presents studies the author worked on at the German National Cancer Institute (DKFZ) in Heidelberg. These studies applied the Monte Carlo technique to investigate the feasibility of performing Intensity Modulated Radiotherapy (IMRT) by scanning with a narrow photon beam. This approach represents an alternative to techniques that generate beam modulation by absorption, such as MLC, individually-manufactured compensators, and special tomotherapy modulators. The technical realization of this concept required investigation of the influence of various design parameters on the final small photon beam. The photon beam to be scanned should have a diameter of approximately 5 mm at Source Surface Distance (SSD) distance, and the penumbra should be as small as possible. We proposed a draft for this system based on the PRIMUS 6MV DKFZ accelerator and investigated new geometry of the source-target-collimator system. We assessed the influence of different collimator parameters, different target construction and various incident electron beam characteristics. Based on this work, it was possible to define adequate parameters for the target- collimator system and the scanning electron beam for new a IMRT system. Examples of the intensity modulated field produced by the resulting photon beam are shown. In Chapter 3, attention is turned to recent and ongoing work on a new mobile electron accelerator for Intraoperative Radiotherapy (IORT) at the Polish National Centre for Nuclear Research (NCBJ) in Świerk. Based on Monte Carlo calculations, we have designed, verified and optimized an electron beam forming system for IORT that uses two different docking systems for applicators. When developed, the accelerator will deliver electron beams in an energy range of 4 – 12 MeV. It will use thin-walled metal applicators with diameters ranging from 3 – 12 cm, possibly larger at lower energies, which can be attached to a universal therapeutic head. The treatment head uses a fixed system of collimators and scattering foils that is independent of beam energy and applicator diameter. Dose distribution in the patient plane, inside and outside operating room, meets all regulatory requirements for radiation protection. A prototype will now be constructed and tested in the laboratory. Chapter 4 describes work to improve treatment planning for hadron therapy with protons or heavy ions, which also took place at DKFZ in Heidelberg. Treatment planning is a complex process and the need to develop new strategies to reduce uncertainties in such planning remains an ongoing challenge to physicists. To calculate ion range in tissue, medical physicists who prepare treatment plans apply an empirical correlation between measured Carbon ranges and X-ray computed tomography (CT) numbers, the value of which depends on the parameters used during measurement. 3 We undertook a systematic study of the effect of various measurement parameters on CT-numbers. Monte Carlo simulations were used to model a complete CT machine and phantom with tissue substitute and receive projections. These results were then processed using a reconstruction algorithm that converted them to CT-numbers calculated in Hounsfield units (HU). We also systematically investigated deviations in CT-numbers that result from different voltage settings of the X-ray tube, composition of substitutes, and changes in the diameter and material of the phantom that is used for CT measurements. Subsequently we translated these into range uncertainties using CT data from an actual patient with a chondrosarcoma at the base of the skull. The studies described in this monograph all required teamwork. The IMRT study in Chapter 2 was performed in the laboratory of Prof Gunther Hartmann at DKFZ, who is an extremely creative medical physicist with three decades of experience in conformal radiotherapy, as well as a wonderful teacher, role model and friend. The author worked (and continues to work) on the IORT study described in Chapter 3 with a fine team of NCBJ colleagues in the Division of Accelerator Physics & Technology, including Dr Eugeniusz Pławski, Dr Przemek Adrich, Dr Adam Wasilewski, and our Division head, Dr Sławomir Wronka. Special recognition also goes to Prof Grrzegorz Wrochna, the Director NCBJ, for diverting his eyes from the cosmos for a time, taking note of the significance of radiotherapy accelerators here on Earth and greatly encouraging our work in IORT. We have also been advised by two recognized international experts in IORT, our friends Dr Peter Biggs of the Massachusetts General Hospital and Dr Frank Hensley of the University Clinic in Heidelberg. The study in Chapter 4 was performed together with Dr Sima Qamhiyeh, a very ambitious young physicist who received her PhD at Heidelberg. Our chief was Dr Oliver Jäkel, head of Medical Physics in the Heidelberg Ion-beam Therapy (HIT) Center, father of numerous new ventures in hadrontherapy, as well as the father of three fantastic children. This work would not have happened at all had I not been guided into radiotherapy by a number of fine mentors, including Prof Barbara Gwiazdowska, Prof Jerzy Tołwiński, Prof Gerhard Kraft, Prof Wolfgang Schlegel and Prof Jean Chavoudra, and helped along the way by many colleagues from Oncological Centers across Europe, all of whom believe, as I do, that radiotherapy is a challenging field that offers great opportunities for physicists. Nor would this monograph have been possible without the ongoing support of Prof Stanisław Kuliński and Prof Ryszard Romaniuk, who convinced me to write it and kept encouraging me to complete it. Finally, I want to thank my husband and editor, Dr Kenneth Rabin, for his understanding of the nuances of science writing in English, his frank advice, consistent support, and almost endless patience. 4 1. Introduction and aim of the work Cancer is a serious human health problem. The latest estimates from the International Agency for Research on Cancer’s GLOBOCAN database state that 12.7 million new cancer cases and 7.6 million cancer deaths occurred worldwide in 2008 [1][2]. It is predicted that as the world’s population continues to increase and grow older, the burden of cancer will inevitably increase. Even if cancer rates continue to stabilize and in some cases decrease, it is estimated that there will be almost 22.2 million new cases diagnosed annually worldwide by 2030, leading to over 13.2 million cancer deaths [3]. It is clear that cancer treatment will remain one of the biggest health care challenges of the 21st century. One of the most important and commonly used methods of cancer treatment is radiotherapy. The aim of radiotherapy is to deliver a dose of radiation into a volume of cancer that is sufficient enough to kill cancer cells, but to do so in a way that spares the healthy tissues surrounding the cancer. It is not easy to fulfill these two requirements even today, more than a century after the first attempts to use radiation in cancer treatment, which took place just a few months after W. K. Roentgen’s 1895 discovery of what was later called X-radiation. 1.1 Historical background The earliest radiation sources were provided by gas-filled X-ray tubes, and then by vacuum tubes containing a hot tungsten cathode [4]. However, the X-rays generated by these tubes were too “soft” from a medical point of view: the maximum dose was delivered at the skin surface but its potency fell off rapidly as tissue depth increased. For this reason, medical radiologists began making their earliest attempts to create more penetrating radiation, using gamma-emitting radionuclides. Beginning in 1912, medical radiologists treated cancer patients using radium-226, a radionuclide that emits gamma rays with energies ranging between 0.24 and 2.20 MeV, as their radiation source [5]. However, this option was restricted by high cost and low availability. In the early 1950s, the idea of using a radionuclide for treatment was considered once again, with the Co- 60 isotope as the radiation source. Co-60 was readily produced by irradiating Co-59 in high neutron flux in a nuclear reactor. It has a long half-life (5.27 years) and produces almost monochromatic high- energy photons of 1.17 MeV and 1.33 MeV in roughly equal quantities. In the early 1930s, however, radiologists began to turn their attention to a high voltage accelerator first developed in 1932 by R. Van de Graff . The first medical accelerator of this type, which had a beam energy of 1 MeV, was installed in Boston in 1937, but the technology did not achieve wider use until the start of commercial production of 2 and 2.5 MeV machines. Forty such accelerators were built, but their production ended in 1959 due to their immense size, poor 5 maneuverability and high operating costs, which were considered too great a drain on hospital resources to justify their purchase [6]. The years after World War II also saw a dramatic increase in the medical use of photon radiation energy, made possible by the development of a new accelerator, the betatron, which was developed by D. W. Kerst [7]. The first cancer patient treated with this technology was irradiated in 1949, with photons generated by 20 MeV energy electrons from a betatron installed in Urbana (USA). Commercial production of betatrons began fairly quickly thereafter, both in the USA and in Europe, and by the early 1970s about 200 such machines were in medical use worldwide [8]. The betatron was a clear advance over previous sources of therapeutic radiation beams. The depth dose distribution for photons from a 25 MV betatron had far better properties – skin sparing, higher depth dose, less side scatter – than radiation generated by a Co-60 source and 200 kV X-ray tube. Betatrons were also able to produce electron beams with an energy range of 5 to 25 MV, which were also used in radiotherapy. The major disadvantages of the betatron were its considerable weight, the low intensity of its photon beam and its small treatment field. Production of betatrons ended in the mid- 1970s. The real revolution in radiotherapy came with the introduction of the electron linear accelerator – a machine that uses high frequency, high power to accelerate electrons that travel in a straight line (which is why they are often referred to as “linacs”). Linac technology was made possible by technical advances in the construction of magnetrons (microwave generators) for radar applications during World War II [9] . The first “traveling-wave linear accelerator “ was demonstrated by D.W. Fry in England in 1946 [10]. A year later C.W. Miller, in cooperation with Metropolitan Vickers Ltd. and the Atomic Energy Research Establishment, designed the first British stationary radio frequency linear accelerator for medical use, which was installed at Hammersmith Hospital near London in 1952. The first patient was treated on this machine in 1953 [11]. At the same time in the USA, H.S. Kaplan at the Stanford Medical Center, in cooperation with a team from the Stanford High Energy physics laboratory, built a prototype linear accelerator for X- ray therapy at an energy of 5 MeV. The accelerator was installed at Stanford in 1955, and cancer treatments began in early 1966 [9]. Large-scale commercial construction of clinical linear accelerators was soon implemented in the USA [9], led by companies like Varian Associates, which designed and built a prototype isocentric accelerator that permitted full rotation around the patient. This machine was installed at UCLA Medical Center in 1962. Thus, by the mid-1960s, the ongoing era of radio-frequency (rf) linear accelerators had begun. Rf linear accelerators came to dominate the world market for medical accelerators and this domination has continued up to now. 6 Compared to linear accelerators, traditional cobalt units offer far less geometrical precision in treatment, are less penetrating and less flexible in respect to dose control. While cobalt units can no longer compete with linacs in modern, sophisticated radiation therapy, however, they may still be the best choice for radiotherapy in locations that do not have conditions suitable for the maintenance of linear accelerators. Moreover, there is one technology that uses cobalt sources to produce similar or even better treatment results than those seen with linacs – this is the Gamma Knife [12][13][14]. The total number of rf linear accelerators in radiotherapy in mid of 1990s exceeded 3000 worldwide[15][16]. Modern linear accelerators can not only rotate around the patient. They possess complex, movable collimating system, which have made it possible to introduce new irradiation techniques that limit irradiated volume “almost” to the volume of lesion – the target volume – with unprecedented precision and potency. In addition, the higher energy of modern linac therapeutic beams provides patients with better treatment dose distributions. 1.2 Radiotherapy today Now, at the beginning of the 21 century, thanks to better screening and earlier diagnosis, almost three cancers in five (about 58%) are discovered before they have spread (or metastasized) to other locations in the body. Tumors at this localized stage can potentially be cured by local therapeutic interventions – surgery, radiation therapy, or a combination of both approaches. About 22 percent of all cancer patients are cured by surgery alone. Twelve percent can be cured solely by presently available radiotherapeutic methods, while the combination of radiotherapy with surgery boosts the cure rate to as much as 18 percent [17]. Despite this admirable achievement, though, almost a third of all patients whose cancer is initially diagnosed prior to metastasis (or 18 percent of all diagnosed patients) are not able to be treated successfully. To obtain better results, further improvement of established techniques of local therapy is required, including more timely transfer of newly developed surgical and radiotherapeutic methods into clinical practice. This need is likely to remain fairly constant for some time, even if therapeutic concepts at the molecular level become clinically applicable in the longer term. Cure rates of cancer diagnosed in local stages have steadily improved in recent decades through the advancing development of diagnostic methods, such as computer-supported imaging, as well as increased precision in surgery and radiation therapy. In radiotherapy, additional advances may be expected in future with the increased use of extremely high precision therapy with photons and electrons. But for those patients who cannot be treated adequately with those conventional beam therapy, only the application of charged-particle beams – protons and ions – can promise greater curative success. Delivering a dose of radiation that is high enough to kill cancer tissues while exposing normal tissues to as little radiation as possible remains a technical challenge. To achieve this objective, 7 radiological oncologists today rely increasingly on the use of conformal radiotherapy – which applies various technological advances to assure that a high-dose volume “conforms “ as precisely as possible to the target volume. Target volume is defined as the full extent of the tumor including any marginal spread of disease and a “safety margin”. At the same time, it is also remains critical to minimize the dose to organs at risk. 1.2.1 Conformal radiotherapy Conformal radiotherapy is technologically complex, but it is evident that this added complexity results in improved dose distributions that, in turn, lead to improved local tumor control (LTC). The idea of conformal therapy is now almost a half century old[18][19]. The last 20 years have seen significant progress in this field, with the development of some advances that have contributed to the improved precision of procedures using this important technique. Today, a distinction is made between conventional or "classical" conformal radiation therapy and intensity modulated radiation therapy (IMRT). The basic idea of conformal radiation therapy is to deliver the beam from multiple directions, so that a higher dose is deposited within the overlapping region of the beams. When the apertures of the beams are tailored three-dimensionally to the shape of the planning target volume (PTV) and the organs at risk (OAR) are masked, the overlapping region should fit the PTV. However, the use of overlapping beams remains problematic. First, the dose distributions created by irradiating several target points at the same time are usually not homogeneous. Second, when shaped target volumes are close to radio-sensitive organs, a simple beam configuration does not offer sufficient precision. In these cases, a more complex beam configuration is needed in order to achieve acceptable dose distribution. This is done by using intensity modulated beams [20][21]. Błąd! Nie można odnaleźć źródła odwołania. shows a schematic treatment of a target volume, which surrounds an organ at risk (OAR) with three radiation fields. The left side of Fig.1. 1 shows the conventional approach, where the fields are collimated to the projected target volume. The illustration on the right shows how additional intensity modulation of the fields leads to improved conformity of target and treatment volume and increased sparing of the OAR. The improved field modulation seen here is achieved through a technique called inverse treatment planning, which is computed based on the amount of radiation required to treat the target volume alone [18] . 8 Fig.1. 1 Schematic treatment of a target volume, which surrounds an organ at risk (OAR), with three radiation fields. Left side- conventional approach. Right side- intensity modulation of the fields to optimize dose to target volume. 1.2.1.1 Intensity Modulated Radiotherapy (IMRT) At present the most common form of IMRT uses a high energy X-ray machine (linac) in conjunction with a conformal irradiation technique that employs multiple irregular-shaped fixed beams. Beam shaping is still often performed with blocks, but computer-controlled multi-leaf collimators (MLCs) are increasingly becoming the standard. MLCs are used primarily in a static mode, but they also have the potential for dynamic operation. Either the static or dynamic MLC operating mode can be used to generate intensity-modulated beams. The dynamic mode is also used in the slice-by-slice IMRT treatment technique called tomotherapy. Two important fields that use conformal radiotherapy are stereotactic radiotherapy (SRT) and stereotactic radiosurgery (SRS). While these techniques have been in practice since the 1950s [22], the subsequent discovery that linear accelerators can be used instead of the specialized gamma-knife has helped establish this form of radiotherapy as standard practice in many oncological centers [23][24][25][26], including Polish centers, where they were first introduced in 2002 [27][28][29][30][31][32][33][34]. The standard stereotactic beam delivery accessory for a linac is a set of circular-holed tertiary collimators. For conformal SRT and SRS, micro multileaf collimators are now used . IMRT can be achieved in several ways, but a very promising approach that has not yet been implemented in clinical practice utilizes scanned elementary beams. This is the subject of the study described in Chapter 2 here. The work was done at the Department of Medical Physics in the DKFZ (Deutsches Krebsforschungszentrum, German Cancer Research Center) Heidelberg. This department has been involved in the research and development of 3D conformal radiotherapy for more than 25 years. 9 In IMRT, a photon beam is delivered via multiport, rotational, dynamic and other techniques to assure that the radiation dose to OAR is significantly lower than the dose to target volume. However, all radiotherapy technologies that use photons are ultimately limited by the physics of the interaction of radiation with matter. This occurs because when a single beam is used to irradiate a target volume, the dose on the proximal side of the target volume is always higher than the dose received within in the target volume, while the dose on the distal side, although lower, is certainly not zero. For this reason, even combinations of beams do not always give acceptable dose distributions, which makes the concept of radiotherapy with charged particles an important alternative . Electron, proton, and heavy ion beams have all been used in lieu of photons to achieve more precise dose conformity with the target volume. 1.2.1.2 Intraoperative Radiotherapy (IORT) Electron beams with energies between 4 - 12 MeV have been used for some time in intraoperative radiotherapy (IORT), as an adjuvant to surgery and/or for fractionated external beam radiation of locally advanced cancers of the abdomen, pelvis, neck, cranium, thorax and extremities [35]. IORT involves the delivery of a single, large radiation dose to the exposed tumor at the time of the surgery or to the bed of a resected tumor. IORT requires a surgical suite and a medical linear accelerator. The simplest way is to introduce IORT in practice is to modify an existing radiation treatment room to accommodate a patient who is transported from a remote operation room (OR). However, the ideal solution for IORT is to have a dedicated radiation machine in the OR. In recent years, the commercial viability of a specially designed mobile linear accelerator for IORT has been explored. Three years ago, the National Centre for Nuclear Research (NCBJ) in Poland began competing with two other providers internationally to develop a new model of accelerator for IORT. Monte Carlo simulations to determine the best types of mobile accelerator treatment head for a prototype IORT unit are reviewed in Chapter 3 here. The studies that were performed concern the effects of different materials and geometry of accelerator head components on such critical beam properties as flatness, X-ray and neutron contamination, and on the amount of dose delivered outside the treatment field. Based on these findings, a treatment head and applicators for the new mobile electron accelerator are being designed. 1.2.1.3 Carbon C-12 Therapy When protons and carbon C-12 ions interact with human tissue, their inherent physical properties also make them ideal candidates for conformal therapy. Proton radiation therapy, in particular, is becoming increasingly popular [36] (PTCOG) because of its superior ability to conform dose distribution to target volumes, while reducing dose to the surrounding tissues in comparison to conventional cancer treatment methods, such as three-dimensional conformal radiation therapy (3D- CRT) and intensity modulated radiation therapy (IMRT). 10 C-12 ion beam have the same high physical selectivity as protons, and can also be scanned dynamically during dose delivery. They also offer some special advantages, specifically higher biological effectiveness (high positron emission tomography effect) and the possibility of dose- deposition verification by means of positron emission tomography (PET). The first heavy ion center built for clinical application, the Heavy Ion Medical Accelerator (HIMAC) in Chiba, Japan, opened in 1994. As of late 2011, proton therapy was being practiced in more than 34 centers worldwide, while heavy ion therapy was available at just five centers : 3 in Japan , one in Germany, and one in China. Some 26 additional facilities are planned for the next few years, mainly for proton beams and most of them with one or more gantries. C-ion therapy centers are now built in Austria, Italy, Germany (two of them) and China [37]. The enormous technological effort required to build a heavy ion facility is the main reason for the relatively low numbers of patients treated with this modality through the end of 2011, about 9800 cases, compared to more than 99500 treated with protons [36] (http://ptcog.web.psi.ch). Presently carbon ions are used in Chiba, Hyogo and Gunma in Japan and at Heidelberg Ion Therapy Center (HIT) in Heidelberg. In early 1990s, G. Kraft, head of the medical physics group at the SIS accelerator at GSI, Darmstadt, Germany began a hadron therapy project. This successful GSI project was the inspiration for the recently-opened HIT patient treatment facility in Heidelberg, which is a joint project of Heidelberg University and DKFZ and GSI [38]. Treatment planning for hadron therapy with protons or heavy ions is very complex, as it must account for both the possibility of patient movement and tissue inhomogeneity. Chapter 4 of this paper describes a project performed in DKFZ Heidelberg, which studied the effect of X-ray voltage, phantom size and material on CT-numbers and range calculations in treatment planning. Computer tomography (CT) is the basis for treatment planning. In the case of heavy charged particles, the X-ray CT serves two major purposes. First, it defines the contours of target and organs at risk (OAR). Second, the Hounsfield units in each voxel of the CT are used to calculate the ion's energy deposition on its path through tissue and, above all, its range. The delivered dose distribution in hadron therapy is much more sensitive to the calibration of CT numbers than is the case in photon therapy, and comprehensive range measurements in different tissues are necessary to establish a correlation between CT numbers and ion range. 1.3 Monte Carlo code The studies presented in Chapters 2, 3,and 4 here all apply MC code to calculate dose distributions, energy fluences and range of particles, for different radiotherapy modalities – intensity modulated radiotherapy (IMRT),intraoperative radiotherapy (IORT)and hadron therapy. 11 The Monte Carlo technique [39] is the most accurate approach to describe the microscopic processes of energy absorption and dose distribution. The transport and creation of particles, e.g., photons or electrons, is modeled as a sequence of stochastic processes at interaction points with the medium. The probability of the different possible processes is well-known based on our knowledge of physics. This allows us to calculate the path and the loss of energy for all particles, based on probability distributions. In respect to treatment planning calculation, the description of the heterogeneous medium is taken from the patient’s CT data sets. The desired macroscopic dose distribution is obtained by averaging the statistically distributed microscopic energy release from many particles. To reduce statistical uncertainties, the required number of particle histories should be on the order of 100 million. Two widely used program packages for Monte-Carlo simulations in this branch of medical physics are EGS (Electron Gamma Shower) [40] and Geant (Cern-Lab). In order to make use of the exact simulation predictions made possible by these programs, the delivered radiation has to be accurately described. This data, in particular the energy spectrum and angular distribution of the incoming photon beam, can be obtained from a Monte Carlo simulation of the linear accelerator head, as discussed subsequently . Dedicated programs have been developed to describe the accelerator head , e.g., the BEAM system [41]. As a result, the otherwise time- consuming simulation of the accelerator head above the patient’s jaws needs to be performed only once, and serves as input for all subsequent patient-dependent simulations. The MC code EGSnrc/BEAMnrc was used for studies of new accelerator models for IMRT and IORT (see Chapters 2 and 3) , and on the effects of different parameters of a CT scanner on the calculated C-12 range in treatment planning (Chapter 4). The Monte Carlo technique uses knowledge of the probability distributions governing the individual interactions of electrons and photons in materials to simulate the random trajectories of individual particles (see Appendix A). Appendix B contains a short description of the MC codes used for the type of simulations performed here. A well-designed computer simulation must accurately take into account all the relevant physical processes involved in electron-photon transport, which is necessary in order to interpret the multiple processes taking place within the energy range that is of interest. Every aspect of this work must include subsections that describe and analyze all parameters of the calculations that are performed. In sum, the aim of all the studies described in this paper has been to help make the latest generations of conformal therapy as accurate as possible, and to spare healthy tissue to the greatest 12 extent possible. Monte Carlo codes have proven to be an extremely useful tool to help achieve these critical treatment objectives. 2. A new scanning photon beam system for IMRT 2.1 Intensity modulated radiotherapy (IMRT) techniques 2.1.1 Conventional MLC based IMRT technique IMRT is a well-established technique in radiotherapy [20]. This technique has important potential to further reduce the absorbed dose to organs at risk (and thus the risk for normal tissue complications), while also delivering a conformal dose to irregularly shaped target volumes. It is expected that this technique of radiotherapy will play a dominant role in the years to come. Currently, IMRT is almost exclusively realized using a multi-leaf collimator (MLC). Fig.2. 1. Modern medical accelerator equipped with MLC shows a modern medical accelerator equipped with MLC, while Fig.2.2 shows the MLC itself. Here, the irregular field shaped by the tungsten leaves is visible. It is surrounded by the driving units and potentiometers used for leaf positioning. Fig.2. 1. Modern medical accelerator equipped Fig.2.2. Micro MLC with removed cover( courtesy of with MLC MRC Systems GmbH) 13 Other forms of IMRT use compensators, but these are very time consuming procedures. Dai and Hu studied the “jaws (of accelerator) only” (JO) technique [42] (Dai99), and Webb extended this idea by combining variable jaw positions with a variable beam mask (J+M) [43][44], but found that fabricating such a large mask presented several engineering difficulties. A number of MLC applications are well-known, such as. static “step and shot” IMRT [45], and the dynamic MLC (dMLC) technique [46]. However, each of these raises some areas of concern: a) The concept of IMRT is totally independent from the concept of an MLC, hence it is not certain that the use of MLCs is the best solution for IMRT. b) Although they may be suited for it, MLC’s were not originally designed for IMRT. c) With MLCs, the ratio of that part of beam that is used for treatment compared to total beam shape may seem problematic. This occurs because a medical linac is designed to provide large fields, while IMRT requires a large number of small field sections. d) For IMRT, both large fields and a high resolution (dependent on leaf width) are desirable. However, improving MLC based IMRT solutions by using large MLCs with a fine resolution, raises additional complex mechanical problems in the control system of the MLC. Therefore, it appeared useful to investigate alternative approaches to realize intensity modulated fields, i.e. methods of delivering beam therapy that are not based on an MLC. 2.1.2 An alternative way to do IMRT An alternative approach to realize IMRT is based on two technical developments: A) It has been shown that it is technically feasible to construct a scanning collimator with a small aperture in such a way that the collimator moves across the 2-dimensional (2D) surface of a sphere, with the beam source in the centre of this sphere [21]. An example of this scanning collimator, which was designed by O. Pastyr and G. Echner [47] from Deutsches Krebsforschungszentrum (DKFZ), is shown in the Fig.2. 3. Fig.2. 3. The DKFZ (O. Pastyr, G. Echner) design for a collimator, which can be moved across the surface of a sphere in such a way that whatever position is taken up by the collimator, it stays focused on the radiation source. As a consequence, a narrow photon beam can be scanned two-dimensionally across a desired radiation field. In this example, three different cylindrical apertures are provided by a revolving collimator system.[21]. 14 B) It is feasible to scan an electron beam, such as produced by a linear accelerator, in arbitrary directions using a 2D system of bending magnets These two devices can theoretically be combined in a radiation machine that constantly forces the scanning electron beam to hit to a bremsstrahlung target that is directly placed at the entrance side of the scanning collimator (see Fig.2. 4 and Fig.2. 5). two dimensional scanning electron beam Target system fixed at the collimator two dimensional variable aperture scanning collimator monitor ionization chamber two dimensional scanning photon beam Fig.2. 4. Schematic drawing of the target-collimator-monitor system. two dimensional scanning electron beam two dimensional scanning photon beam Fig.2. 5. Scanning movement of the electron and narrow photon beams In this configuration, the shape of the photon beam depends predominantly on the characteristics of the collimator. To provide a photon beam that is appropriate for a variety of intensity modulated fields (very large fields, very small fields, high intensity gradients, small intensity gradients), a variable 15 collimator aperture must provide a set of different beam profiles. To achieve this, construction of a collimator with a fixed set of quadratic apertures was studied. A prerequisite for a radiation machine of this type is that the center of the electron beam must be exactly correlated with the central axis of the collimator. To meet this requirement, a special control system must be developed to correctly steer the electron beam. In addition, it must be possible to modulate the intensity of the photon beam by controlled change of the intensity of the electron beam from pulse to pulse. The development of such new control systems is certainly a challenging task. Nevertheless, this concept of a scanning photon beam for IMRT appears technically feasible. 2.2 Research objective The objective of the project ”A scanning photon beam system for IMRT” was to investigate how this concept could be realized and to demonstrate its technical feasibility. In particular, producing an arbitrary intensity modulated field for IMRT would inevitably place certain requirements on the design of the target-collimator system as well as on the scanning electron beam. The influence of design parameters of the target-collimator-monitor system on the quality of the desired intensity modulation must also be well understood. Finally, a prototype should be described that would demonstrate the technical feasibility of the proposed concept. Since partial solutions were already available, the project was structured appropriately in several steps leading to the recommended prototype. The sub-steps of this project were: To investigate the influence of various design parameters on the final small photon beam. This is a typical problem that can be investigated using Monte Carlo Simulation methods, which were performed and was done by author of the present work, To simulate examples of an intensity modulated field from the resulting photon beam, To define adequate parameters for the target-collimator system as well as the scanning electron beam based on the previous step, To investigate technical solutions to realize these parameters, and To construct a prototype accelerator In the following discussion, we present the MC calculations that were performed to investigate the influence of various design parameters on the final small photon beam. Following these calculations, the results are analyzed and the most appropriate design parameters identified. Examples of an intensity modulated field from the resulting photon beam were simulated in a published paper [48] and are shown here to illustrate that the idea of a scanning photon beam is viable. 16 2.3 Monte Carlo (MC) study on a new concept of a scanning photon beam MC methods to simulate the complete gantry system of conventional linacs are well established. The scanning photon beam system for IMRT was proposed and modeled with the BEAMnrc/EGSnrc [49]. The input parameters for the complete existing target-collimator system (PRIMUS 6MV) were used to study the basic influence of the single components on the beam characteristic, i.e. on the photon fluence differential in energy and direction. 2.3.1. Definition of requirements on the resulting photon beam The photon beam to be scanned should have a diameter well less than 10 mm at SSD distance, and the penumbra should be as small as possible. 2.3.2. First draft for a target-collimator system A first draft for a target-collimator-ionization chamber system was proposed and modeled with the MC code. This system is simply a copy of the system used for PRIMUS accelerator (see Fig.2. 6 Scheme of simulated geometry of the target, ionization chamber and collimator .Fig.2. 6). The source of electrons used in the calculation was a “point source” at a distance of 2.86 cm from the target; the radius of the electron beam on the target re was 1 mm; and the energy spectrum of electrons ranged from 6.174 MeV up to 7.103 MeV (equal as in the PRIMUS accelerator) 17 isotropic point electron source beam radius =0.1 cm Target system 1.5 cm ionization chamber 1.0 cm 3.3 cm 0.8 cm 2.3 cm 3 cm 10 cm collimator SSD = 55.6 cm 40 cm scoring plane of phase space file z axis Fig.2. 6 Scheme of simulated geometry of the target, ionization chamber and collimator . 2.3.3 Influence of the collimator aperture Calculations were done for 108 incident electrons, using ECUT=0.7 MeV, and PCUT=0.01 MeV. Calculation time for each collimator was 14 hours. An example of the resulting energy fluence distribution is presented in Fig.2. 7. For each collimator aperture, the energy fluence was calculated in 20 rings, each of 1 mm thickness, ranging from the beam axis to 2 cm off-axis on the surface at a distance of 40 cm from the collimator exit. The distance of 40 cm was based on reasonable medical requirements (see Fig.2. 6). The terms r and R signify , respectively, the radius at the entrance and exit aperture of the collimator. Several combinations of r and R were investigated (see Table 1). We investigated the influence of different parameters for 8 different collimators. All MC calculations provided data as energy fluence/incident electron/energy bin in units of cm-2 at a distance of 40 cm from the source. Calculations of the dose (D) absorbed in water have been performed by: en D i Ei Ei Ei i for energy steps i = 1,2,3,.. 20, which means that 20 equally spaced energy bins were provided. Φi signifies the energy fluence per ring divided by the number of incident electrons used as input for the 18 simulation. ηen / ρ signifies the mass energy-absorption coefficient for water. E was 0.38 MeV for all i-s. D, the dose absorbed in water for the area of each ring, is expressed in units of MeV/g (1 MeV/g = 1.6 10-10 Gy). Parameters of collimators are given in Table 1. Fig.2. 7. Example of energy fluence distribution of photon beam calculated for the field with 2 mm diameter, in the distance of 40 cm from the exit of collimator (r = R = 2.8 mm) Results of the dose distribution calculated for different collimators are presented in Fig.2. 8 and in Table 2.1. FWHM and PM express the full width at half maximum and the penumbra of beam profile respectively. The best value for the width at half maximum was for collimators #3 , 6, 7, and 8, but for the last three the dose was very small (see Fig.2. 8). Other calculations were performed to estimate the influence of different target constructions on the photon beam dose distribution. This was done because the original target system of the PRIMUS used as manufactured using a layer of carbon of 1 cm thickness to minimize electron contamination. For a scanning photon beam system, however, any material that would contribute to scattering of the photons should be avoided in order to get a beam as narrow as possible. For this investigation, the energy fluence distribution was calculated already at a distance of 3.3 cm from the top of the target, i.e. before the collimator (see Fig.2. 6). Calculations were made for 107 particles. 19 Table 2.1. Full width at half maximum (FWHM) and penumbra (PM) of beam profile calculated for different collimators Collimator # entrance exit width at half penumbra aperture r aperture maximum PM (mm) (mm) R (mm) FWHM (mm) 1 1 2.8 20.92 3.20 2 2.8 2.8 17.64 6.47 3 1 1 6.56 3.14 4 2 1 7.70 3.17 5 3 1 8.56 3.40 6 2 0.5 5.46 2.69 7 1 0.5 5.18 2.24 8 0.5 0.5 5.52 2.30 20 collimator collimator (r=0.1cm, R=0.28 cm) (r=R=0.28cm) 2.00e-5 HW=20.92mm HW=17.64mm PM =3.20mm PM=6.47mm 1.50e-5 1.00e-5 Water absorbed dose 5.00e-6 0.00 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Distance from the beam axis (mm) collimator collimator collimator (r=R=0.1cm) (r=0.2cm, R=0.1cm) (r=0.3 cm, R=0.1cm) 2.00e-5 HW=6.56mm HW=7.70mm HW=8.56mm PM=3.14mm PM=3.17mm PM=3.40mm 1.50e-5 1.00e-5 Water absorbed dose 5.00e-6 0.00 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Distance from the beam axis (mm) collimator collimator collimator (r=0.2 cm, R=0.05cm) (r=0.1 cm, R=0.05cm) (r=0.05 cm, R=0.05cm) 2.00e-5 HW=5.46 mm HW=5.18 mm HW=5.72 mm PM =2.69 mm PM=2.24 mm PM=2.30 mm 1.50e-5 1.00e-5 Water absorbed dose 5.00e-6 0.00 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Distance from the beam axis (mm) Fig.2. 8. Photon beam profiles for different collimators. HW and PM mean the full width at half maximum and penumbra of beam profile, respectively. 21 Fig.2. 9 presents a comparison of photon beam profiles for different diameters of electron beam and for three types of target construction. In the first type, 0.965 mm of gold, the cooling system and a layer of carbon was used. In the second, air was used instead of carbon. For the third type, a small electron beam radius re equal 0.5 mm was used, and in the fourth type the layer of gold was reduced to 0.5 mm. The best result, i.e. the most distinct forward direction for the water absorbed dose to the beam axis was obtained for the fourth target with the thin layer of gold. However, the thickness of the gold also has an influence on the mean energy of the photon beam, as calculated and presented in Fig.2. 10. Calculations were performed for re equal 0.5 mm with energy spectrum of electrons from 6.174 MeV up to 7.103 MeV. A calculation was also performed at SSD distance with re=0.5mm and a collimator with r = R = 1 mm when air instead of carbon was used in the target construction. The change of FWHM and PM were: 7.42mm and 1.68 mm (with carbon) and 7.54 mm and 1.70 mm (with air). A method to further reduce scattering material by reducing the thickness of the gold foil appears less appropriate: when the thickness of the foil is reduced, a significant reduction of the mean photon energy occurs, as shown in Fig.2. 10. 22 0.008 target 2 0.006 target 3 target 1 target 4 0.004 Water absorbed dose 0.002 0.000 0 5 10 15 20 25 30 Distance from the z axis (mm) Fig.2. 9. Comparison of the water absorbed dose after target and ionisation chamber for the different target construction and different size of electron beam: Target 1 : re = 1 mm, 0.96mm of Au and C in the target Target 2 : re= 1 mm, 0.96mm of Au ,air instead of carbon in the target construction Target 3 : re =0.5 mm, 0.96 mm of Au, air instead of carbon in the target construction Target 4 : re =0.5 mm, 0.50 mm of Au, air instead of carbon in the target construction 23 Fig.2. 10. Mean energy of photon beam as the function of Au target thickness calculated for radius of electron beam re =0.5 mm and energy spectrum of electrons from 6.174 up to 7.103 MeV 2.3.5 Influence of the incident electron beam characteristics Calculations referring to the influence of electron beam characteristics on the dose distribution in the photon beam were also done. These calculations refer to the influence of a) the size of electron beam on the dose distribution of photon beam, b) the energy, c) the displacement of electron beam from the axis of system. 2.3.5.1 Size of electron beam Two values of the radius of electron beam, 1 mm and 0.5 mm, were selected. Results on FWHM and PM are presented in Table 2.2. The absorbed dose was calculated for the three collimators: #3, #4 and #5. Table 2.2. FWHM and PM of photon beam profile calculated for different collimators and different radius of incident electron beam. radius of electron beam radius of electron beam (mm) (mm) 1.0 0.5 1.0 0.5 Number of collimator FWHM (mm) PM (mm) #3 6.56 7.42 3.14 1.68 #4 7.70 8.20 3.17 2.07 #5 8.56 8.76 3.40 2.33 24 It can be seen from Table 2 that a reduction in the radius of electrons re from 1.0 mm to 0.5 mm gives only small increase in FWHM, however, and it considerably improves the penumbra. We concluded that a radius of electrons re =0.5 mm should be used in the scanning photon beam system. 2.3.5.2 Energy of the electron beam Absorbed dose for collimator #3 was calculated for two sets of electron energy: a spectrum from 6.174 up to 7.103 MeV and monoenergetic electrons of 4 MeV. Results are presented in Table2. 3. Table 2.3. Mean FWHM, PM and maximum dose D max of photon beam profile for different energy and re of incident electron beam. Energy (MeV) Energy (MeV) Energy (MeV) 6.174-7.103 4 6.174-7.103 4 6.174-7.103 4 Collimator#3 FWHM (mm) PM (mm) Dmax (MeV/g) *) r = 1mm e 6.56 6.16 3.14 3.35 1.93e-5 8.86e-6 and carbon r = 0.5 mm e 7.42 7.04 1.68 1.99 1.78e-5 9.34e-6 and carbon r =0.5mm and e 7.54 7.10 1.70 1.75 2.02e-5 9.43e-6 air *) Dmax values are very small because they describe the dose of radiation associated with only a single electron. For example a dose of 2 Gy/min will require just 2.4 μA of electron current. The simulations showed that the reduction of energy to 4 MeV does not have much influence on the values of FWMH and PM; however, it reduces the water absorbed dose of the photon beam by more than 2 times. In addition, the mean energy of the photon beam is reduced from 1.272 ± 0.008 MeV to 0.865 ± 0.008 MeV for re = 0.5 mm and for a target thickness of 0.965 mm.This led us to conclude that electron energy of close to 6 MeV should be used for the scanning photon beam system. For further calculations, therefore, a 6 MeV monoenergetic electron beam should be used.) 2.3.5.3 Displacement of the electron beam When an electron beam is forced to follow a moving collimator, the electron beam may not stay exactly adjusted to the aperture of the collimator. Therefore, we also simulated a possible displacement of the electron beam from the axis of the target-collimator system. This investigation was done only for collimator # 3 and a parallel beam with re=0.5 mm. The possible displacement was simulated by: 25 a) Parallel displacement of the electron beam of 0.5 mm radius from the system z axis in x direction, and b) Tilt of the electron beam direction of 0.50 from the z axis FWHM at a distance of 40 cm from the collimator was used to determine a possible influence. However, this simulation resulted in no changes in the parameter. 2.3.5.4 Shape of the electron beam profile Calculations to determine the influence of different electron beam profiles on the dose distribution in the photon beam were performed. Simulations were done for a 10 cm long collimator with a circular aperture of 1 mm and two different profile shapes for the electron beam: rectangular and Gaussian profile. A 6 MeV monoenergetic electron beam was used for calculation; the water absorbed dose distribution of the photon beam was normalized to 1 for the maximum obtained dose. The simulations showed that the change of the shape of electron beam does not significantly influence the value of FWHM and PM. For rectangular profile these values are: 5.1 mm and 2.4 mm, for Gaussian profile they are: 5.4 mm and 2.6 mm, respectively. We therefore concluded that since a Gaussian shape appears more realistic, this electron beam characteristic should be used for further simulations. 2.3.6 Influence of the geometry A “new geometry” of the simulated system of target, collimator, and chamber, was introduced in our subsequent simulation (Fig.2. 11) : (1). A new distance between target and collimator was introduced, and (2) the ionization chamber was moved behind the collimator. 1. The collimator is at a distance of 0.5 cm from the target. This ensures that more photons from the target will enter the collimator than at a distance of 5.6 cm. 2. The ionization chamber is placed at a distance of 0.5 cm behind the collimator. This makes it possible to measure the photon beam dose behind the collimator and to control the correlation between the scanning of the electron beam and the scanning of the collimator. In the “new geometry”, a water phantom was added at a distance of 40 cm from the collimator. The water absorbed dose was calculated in the voxels of this phantom at a depth between 1 and 1.5 cm. The DOSXYZnrc code was used for calculating dose distribution in further simulations. This code is an EGSnrc-based Monte Carlo simulation code for calculating dose distributions in a rectilinear voxel phantom. A variety of beams may be incident to the phantom, including full phase- space files from BEAMnrc, which we used in the next step of this work. 26 Gaussian distribution electron source FWHM =0.1 cm Target system 0.5 cm collimator 3 cm 10 cm 0.5 cm ionization chamber SSD = 53.3 cm 40 cm scoring plane of phase space file 1.0 cm voxels 1.5 cm z axis 10 cm 5.45 cm water phantom Fig.2. 11. “New geometry”- scheme of simulated system of target, collimator , ionization chamber and water phantom, used for the simulation in the second part of project. ECUT and PCUT are the two EGSnrc input parameters that define the cutoff energy for electron and photon transport in MeV. ECUT should be chosen so that the electron’s range at ECUT is less than about 1/3 of the smallest dimension in a dose scoring region. This ensures that the energy is transported and deposited in the correct region also for electrons, which are moving isotropically. In the present simulation ECUT = 0.15 MeV due to x y z dimensions of voxel are 1x 1 x 5 mm. PCUT is 0.01 MeV, as it should generally be used. A “Parallel Circular Beam with 2-D Gaussian X-Y Distribution” was used as the source type of incident electron beam in the BEAMnrc code. The value of FWHM of the Gaussian distribution was set to 1 mm. The energy of electron beam was set to 6 MeV. Three types of collimators were simulated with BEAMnrc code in this part of project: The phase space files, which were generated for these three types in BEAMnrc, were used as source input data for the DOSXYZ code. Parameters of these collimators as well as results for FWHM and PM of the obtained photon beam are given in Table 2.4 and in Fig.2. 12 and Fig.2. 13, 27 Table 2.4. FWHM and PM of beam profile calculated for different collimators Size of Circular rectangular width at half penumbra collimator in z aperture r aperture r’ maximum PM (mm) direction (cm) (mm) (mm) FWHM (mm) 10 0.5 - 5.42 2.64 15 1.0 - 7.16 2.56 10 - 0.5 5.8 2.7 circular aperture of 10cm collimator 7e-16 circular aperture of 15cm collimator square aperture of 10cm collimator 6e-16 5e-16 4e-16 3e-16 2e-16 1e-16 0 -15 -10 -5 0 5 10 15 Water absorbed dose per incident particle from original source [Gy] from original particle incident per dose Water absorbed Distance from the z axis [mm] Fig.2. 12. Comparison of photon beam profile calculated for different collimators: the 10 cm long collimators with the square of 1 mm x1 mm and circular aperture of 1 mm, and 15 cm long collimator with circular aperture of 2 mm. The comparison shows that the change of parameters influences the outcome of photons. 28 1.2 square aperture of 10cm collimator circular aperture of 10 cm collimator circular aperture of 15cm collimator 1.0 0.8 0.6 0.4 0.2 Water absorbed dose per particle from original source [Gy] 0.0 -15 -10 -5 0 5 10 15 Distance from the z axis [mm] Fig.2. 13. Water absorbed dose distribution of the photon beam calculated for different collimators and normalized to 1 for the maximum dose. This comparison shows that the change of parameters influences the gradient of the dose profile. Water absorbed dose distribution of the photon beam in the Fig.2. 13 were normalized to 1 for the maximum obtained dose. We concluded that a 10 cm collimator with either a square or circular aperture of 0.5 mm gives better photon beam profiles than 15 cm collimator with aperture of 1.0 mm. In addition, the field dose distribution of the photon beam was calculated for the 2 types of 10 cm collimators, as presented in Fig.2. 14 and Fig.2. 15, respectively. 29 Fig.2. 14. Field dose distribution for the photon beam from the collimator with a square aperture of 1 mm; the electron beam diameter was 1mm Fig.2. 15. Field dose distribution for the photon beam from the collimator with a circular aperture of 1 mm; the electron beam diameter was 1mm. 2.4 Summary: conclusions and discussion The main characteristics of the target-collimator-monitor system that was found to be appropriate for a scanning photon beam are summarized in this section. A schematic drawing is shown in Fig.2. 16 30 Electron source with Gaussian distribution (FWHM =1.0 mm) target system 0.5 cm tungsten 3 cm collimator 10 cm 0.5 cm transition ionization chamber 40 cm isocenter Fig.2. 16. Geometrical characteristics for the system of target-collimator-monitor as found to be appropriate for a scanning photon beam. An optimal system of target-collimator-monitor for a scanning photon beam should have the following characteristics: 1. The diameter of the incident electron beam should be smaller than 2.0 mm because when the diameter of the electron beam is reduced, an improved penumbra of the photon beam is observed. 2. The energy of the electron beam should not be less than 6 MeV, because the intensity of the photon beam substantially decreases with decreasing energy, and using lower energy is, therefore, of no advantage. 3. Using gold foil with a thickness of ~1 mm is an appropriate target, and avoids the need for any additional material. The mean energy of the photon beam decreases with foil thickness, which contributes to scattering. 4. Since the photon beam profile produced directly from the target is quite large, photon beam intensity after the collimator should increase with an increased collimator entrance opening. This, however, would produce an undesired effect on the photon beam profile after the collimator. Therefore, the collimator should have a non-divergent aperture with a diameter of ~1 mm. This aperture is necessary in order to obtain a photon beam diameter not larger than about 5 mm in isocenter distance. A quadratic-shaped aperture would be better than a circular- shaped one, if a variable opening is to be constructed. 31 5. The radiation monitor chamber must be placed behind the collimator, because any changes in photon beam intensity behind the collimator must be directly monitored. 6. In respect to geometry, the distance between the beam exit at the radiation monitor and the isocenter should not be larger than 40 cm. This is because any increase in the distance between the collimator and isocenter will contribute to an increase in the photon beam diameter. A minimum diameter not larger than about 5 mm in isocenter distance should be provided. 2.4.1 Simulated dose distribution of an intensity modulated field In a published paper [48], we showed simulated examples of the intensity modulated field produced by the resulting photon beam. We used a program that allows the user to determine the required intensity of a single beam, when a single beam is moved in raster-scan motion across a given field size to arrive at a desired dose distribution. The intensity weights were optimized in such a way that the obtained superimposed dose distribution matches a given input distribution of intensity. The single photon beam profile was expressed as a 15x15 matrix, each element representing the dose at isocenter distance in a 1mm x 1mm pixel element. The raster scanning was performed in a quadratic point raster with 1 mm spacing. An example of resulting dose distribution is shown in Fig.2. 17, right. The optimization procedure provided an individual, positive weight (intensity) for each raster point. Intensity Map from TPS Dose distribution obtained from Photon Beam Scanning 160 160 150 150 140 140 130 130 120 120 110 110 100 100 90 90 80 80 70 70 60 0.0 60 0.5 50 1.0 50 40 1.5 40 2.0 30 1.25 30 20 1.50 20 1.75 10 2.00 10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 Fig.2. 17. left: example for a desired intensity map as obtained from the treatment planning system right: dose distribution as obtained from a raster-scan with single photon beams, each produced by the target-collimator system with a dose distribution as shown in Fig.2. 15 (collimator with a circular aperture of 1 mm; electron beam diameter 1mm) 32 It might be useful to limit the variation of the weights between a maximum weight and a minimum weight. If a factor of 20 is introduced (wmin=wmax/20), the result of Fig.2. 18 is obtained. Dose distribution obtained from Photon Beam Scanning Dose distribution obtained from Scanning with wmin=wmax/20min=wmax/20 160 160 150 150 140 140 130 130 120 120 110 110 100 100 90 90 0.0 80 80 Y Data Y 0.2 70 0.4 70 60 0.6 60 50 0.8 50 1.0 40 40 1.2 30 1.4 30 20 1.6 20 10 10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 X Data Fig.2. 18. Intensity modulated beam map, shown as a greyscale, left: identical to Fig.2. 17 right; right: calculated with wmin=wmax/20 This shows that the very small dose area is not "painted" correctly. A factor of 40, however, would be sufficient. In Fig.2. 19 our intensity profiles are compared. This comparison again demonstrates that in a larger area of reduced dose (in a "hole") the selected limitation of wmin=wmax/20 would lead to a too big reduction, whereas a factor of 40 obviously is sufficiently wide. 33 1.8 1.6 all positive weights w =w /20 1.4 min max from TPS w =w /40 1.2 min max 1.0 0.8 intensity 0.6 0.4 0.2 0.0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 profile at Y = 90 Fig.2. 19. Comparison of intensity profiles at coordinate Y=90. 2.4.2. Discussion In the work presented here the Monte Carlo technique was applied to investigate the feasibility of performing IMRT by scanning a narrow beam across the field. It represents an alternative to techniques that generate beam modulation by absorption, such as MLC, individually manufactured compensators and special tomotherapy modulators [50][51]. More recently (2003-2008), a ‘Single-Arc’, rotational IMRT approach has been developed [52][53][54][55][56] and has generated user interest as a commercial product (RapidArc, VMAT). In the Single-Arc approach there is no intensity modulation for any one beam angle, but the radiation field shape is varied dynamically and rapidly with an MLC as the gantry rotates around the patient. In 2010 Webb et al [57] showed how the use of a rotate-translate methodology employing only jaws, which move dynamically with the beam continuously on, can lead to a delivery of a two-dimensional intensity-modulated beam, whose the modulation varies spatially slowly . In 2011 Bill J Salter [58] has presented a novel ‘burst mode’ modulated arc delivery approach, in which 2000 monitor units per minute (MU min−1) of high rate dose bursts are facilitated by a flattening-filter-free treatment beam on a Siemens Artiste (Oncology Care Systems, Siemens Medical Solutions, Concord, CA, USA) digital linear accelerator in a non-clinical configuration. 34 In the case of a scanning beam, intensity modulation has been obtained by superposing spots with different irradiation times. Satheberg et al.[59] and Svensson et al.[60] studied this method at a Racetrack Microtron (50MeV electron energy) at Karolinska Institute in Stockholm. The investigators measured beam widths of about 33 mm with 20-25 mm penumbra at 100 cm SSD. The energy they used is outside of energy range used in radiotherapy, however. Subsequently, a dissertation was written [61] in which author used Geant MC code to examine the feasibility of using a lower-energy narrow photon beam for IMRT. At electron energies of about 20 MeV, using the combination of a thin beryllium target and a purging magnet, a photon beam width of about 40 mm at 100 cm source-to-surface distance with a penumbra of 25 mm could be achieved. However, using a very thin transmission target such as 0.2 mm beryllium results in a yield that is several factors smaller than the maximum yield achievable with this material although it is still comparable to the forward yield of the conventional photon mode of clinical accelerator. The partial conversion of incident electron energy into photon energy seen with this approach is compensated for by the higher incident energy, the enhanced forward emission and the absence of the flattening filter. However, this would also result in increased treatment time the field has to be built from superimposing spots. It was suggested that this problem could be resolved by installing an additional fixed collimator, which would consist of a tungsten plate with holes, that could be inserted into the accessory tray of accelerator. In the work we performed at DKFZ using EGSnrc MC code to examine the feasibility of using narrow photon beam for IMRT we determined that with the electron energies of 6 MeV, a gold target of 1 mm and a wolfram collimator with a 1 mm aperture, a photon beam with a width of about 5 mm at 55 cm source-to-surface distance with a penumbra of 2.5 mm could be achieved. Following a feasibility study of this type, the next step should be experimental testing of a moving collimator and target. Up to now, however, this has not taken place as it has proven to be a challenge to construct a collimator with the small aperture we require. This challenge has been addressed successfully by other workers, however, and is now available in the form of an IrisTM collimator mounted on the Accuray Cyberknife linear accelerator [62], whose smallest circular field is 5 mm at SSD, with a penumbra width of about 0.1 mm. A new compact micro-MLC prototype is also being developed at DKFZ. 35 Fig.2. 20. Dual-bank 12-sided collimator concept designs [63] 36 Fig.2. 21. Illustration of the major mechanical components of the Iris Collimator.(a) External view of the assembled device. (b) A view from beneath the lower segment bank toward the x-ray target, which illustrates how the gap between any two collimator segments in one bank is covered by the body of a segment in the other bank, thereby limiting the intersegment transmission [63]. The Iris collimator was developed based on the same type of technological assumptions about narrow beam delivery that we made at DKFZ. The Iris collimator, developed by Accuray Incorporated of Sunnyvale, CA, USA and DKFZ, permits field size to be varied during treatment delivery. This makes possible multiple-field-size treatments with no increase in treatment time, as there is no need to exchange collimators or make multiple traversals with the robotic manipulator [63]. The collimator has an array of two banks of six tungsten–copper alloy segments (see Fig.2. 20, Fig.2. 21). These are rotated by 30◦ with respect to each other in order to produce a 12-sided polygonal treatment beam while reducing the likelihood of radiation leakage between segments. In effect, this beam is almost perfectly circular. It has a root-meansquare (rms) deviation in the 50% dose radius of <0.8% (corresponding to <0.25 mm at the 60 mm field size) and an rms variation in the 20–80% penumbra width of about 0.1 mm at the 5 mm field size increasing to about 0.5 mm at 60 mm. The highest measured leakage dose rate was 0.07%. The Iris Collimator offers the potential to greatly increase the clinical application of multiple field sizes for robotic radiosurgery and it is another example of conformal therapy with narrow beams that was studied at DFFZ. 37 3 A new mobile electron accelerator treatment head for IORT 3.1 What is IORT? Intra Operative Radiation Therapy (IORT) is a technique that allows the patient to be irradiated directly during a surgical operation, using a moveable linear accelerator that is brought into the operating room. The radiation dose can be delivered to the surgical bed in a single fraction to pre- treat the tumor before the surgeon resects it, or post-surgery either to treat portions of tumors that remain after a partial resection, or to irradiate tissue that is adjacent to the surgical site and is suspected of containing microscopic tumor cells. Because IORT is performed during surgery, when normal tissue and organs are removed from the field, a higher dose of radiation can be delivered to the diseased area, thus increasing the local control of the disease. IORT is an important example of the growing multidisciplinarity of cancer treatment today. It can increase the likelihood of surgical success by (a) destroying microscopic lesions that may not have been removed during the surgery, (b) greatly increasing the amount of radiation applied to the tumor site in comparison to external beam radiotherapy, and (c) bringing the known benefits of radiotherapy to the patient earlier in the course of treatment. A special advantage of IORT is that it allows for the delivery of a high dose of radiation when the tumor may be particularly vulnerable to the biological effects of this radiation. When exposed human tissue undergoes surgical intervention, it becomes highly vascularized with a high rate of aerobic metabolism, which makes it more sensitive to radiation, and is referred to as the “Oxygen Effect”. Time is also a key factor in cancer treatment, especially so because it is known that remaining cancer cells tend to proliferate far more rapidly than usual, often exponentially so, after surgical resection. This repopulation of tumor cells is also accelerated between dose fractions of traditional beam radiotherapy. Thus, a single high dose of IORT given when surgery is performed can “buy time” for a patient in two ways – slowing the potentially rapid growth of post-surgical neoplasms and reducing the new tumor burden that will require treatment with external beam radiation. It is important to note, however, that the use of IORT does not mean that the patient will not require external beam therapy in the future. But its immediate anti-tumor benefits may well increase the likelihood of success of subsequent external beam treatments. The practice of IORT using megavoltage electron beams dates from the work of Abe et al., in Japan [64]; and Gunderson et al. [65], J. Tepper and W. F. Sindelar [66], and B. A. Fraass et al. [67], in the United States. Abe at the University of Kyoto in the early 1960s [68][69] combined surgical excision of advanced abdominal tumors with a single massive dose ( 25-30 Gy) of radiation during 38 operation. He used an even higher dose (up to 40 Gy) if the tumor was found to be unresectable. His first patients were treated with a cobalt-60 machine. In 1965, when a betatron was installed in an operating room within radiotherapy department, subsequent patients were treated with electrons. By the early 80s, this technique had spread to 27 hospitals in Japan, and several hundred patients were treated intraoperatively. The IORT technique was introduced United States at Howard University Hospital in Washington, DC, in 1977 [70]. By 1982, 114 patients had been treated with variable electron energies. The second US IORT was opened in 1978at Massachusetts General Hospital [65], followed by the US National Cancer Institute in 1979 [66], and in the early 1980s by the Mayo Clinic and the New England Deaconess Hospital [71]. In some of these centers, IORT was used in addition to conventional radiotherapy with electron beams, in others it was used alone. IORT began to be used in Europe in the 1980s, as well. The initial centers were in Caen, France (1983), followed by Pamplona, Spain and Innsbruck, Austria (1984), Lyon, France and Milan, Italy (1985) and Milan, Italy (1986). By the 1990s, European centers had begun pooling data on IORT outcomes and reporting them in the medical literature and through the International Society of IORT (ISIORT), which was established in the year 2000 and holds international IORT congresses biennially [72]. IORT was also introduced in Poland early in the 2000s. Two Mobetron devices are currently in operation, one at the Collegium Medicum UJ in Krakow (2003), the other at the Wielkopolskie Centrum Onkologii (WCO) in Poznan (2006). A third Mobetron system has recently been installed (2012) at the Centrum Onkologii in Bydgoszcz, . Although it was suggested in the 80s that an orthovoltage X-ray unit could be used for intraoperative radiation [71], the most common modality used for IORT was (and remains) a linear accelerator with electron beam of energy varying from 6 to 22 MeV. In the early days of IORT, hospital practitioners developed a number of different types of cone-holding assemblies to connect the intraoperative cones to collimator of the accelerator [73], [74], [75], [67], [76]. Today, however, such assemblies are available commercially [77]. IORT was for many years performed using stationary linear accelerators located either in a shielded section of an operating room (OR), or in a shielded radiotherapy treatment room. Now, new technology has made it possible to use mobile accelerator units that can be moved to any OR within a hospital. Three models are currently available for clinical use. Fig.3. 1, Fig.3. 2, Fig.3. 3 show the NovacTM7 (New Radiant Technology S.p.A., LiacR (SORDINA S.p.A.), and MobetronR1000 (IntraOp Medical Corporation) mobile IORT accelerators. More than 43 Mobetron systems are now (2012) in use worldwide. It is also known that 12 Novac and 11 Liac machines are now in use in Italy, which is their home market. According to Hensley [78] in 2004, IORT was available in 33 centers in Europe and that this number was increasing on a linear basis, so that the total now is closer to 50 centers. 39 Fig.3. 1. Mobile accelerator for IORT Novac 7 Fig.3. 2. Mobile accelerator for IORT Liac Fig.3. 3 Mobile accelerator for IORT Mobetron The design of the new, mobile units differs from that of conventional linear accelerators in several important ways. In particular, mobile IORT units are designed for use in an unshielded OR. In order to prevent excessive radiation exposure in surrounding rooms, maximum beam energy is limited to 10-12 MeV, and a beam stopper must be designed for every unit. Electron beam applicators for 40 IORT are also designed specifically for use in surgical areas; treatment is performed under sterile conditions; and the radiation is delivered in a single fraction. In addition, the treatment head should have a range of motion that provides flexibility in delivering a dose of radiation to an anesthetized patient. The fundamental techniques of IORT, including radiation protection issues, acceptance testing and commissioning, and a recommended quality assurance program for mobile systems were published in the report of the AAPM Radiation Therapy Committee Task Group No.72 [79]. 3.2 Research objective In 2009, the Polish National Centre for Nuclear Research (NCBJ) received an EU grant to underwrite the development of a number of new accelerators, including one a new mobile unit for IORT. Under this grant, we have undertaken a specific project, on which author of this work continue to serve as a team leader, to investigate a new IORT treatment head that is consistent with both the AAPM recommendations [79] and IEC standards [80][81]. The new treatment head will be a key component of a prototype IORT unit that will ultimately be developed and introduced for radiotherapeutic use by NCBJ. The IORT treatment head is the part of the accelerator where the electron beam used to treat the patient is formed. When the electron beam leaves the accelerating structure, it has a diameter of a few millimeters. At the Source-Surface Distance (SSD) where the beam is administered to the patient, it should cover the field with a diameter of from 3 - 12 centimeters. The treatment head must also be designed in a way that protects the patient and OR personnel against leakage radiation, in the form of electrons outside the radiation field. The main elements of the treatment head are the scattering foils, the primary collimators and the beam-defining collimating system (i.e. the applicators). The design of the treatment head should configure each of these elements in a way that enables precise delivery of electron beams that are appropriate for each patient. The applicator, which is used to apply the electron beam to the target volume in the patient, is a tube made of either metal (originally brass) or Plexiglas (methyl methacrylate). It can be circular, rectangular or other geometric shape. Since the applicator touches normal tissue surrounding the lesion in the patient, its walls must also shield this normal tissue from the primary radiation. To maintain dose homogeneity within the applicator and to control leakage outside of it, the applicator design must take into account such factors as wall thickness, material and the way in which the applicator interfaces with the machine. Based on clinical experience, applicators must be a minimum of 25-30 cm in length in order to reach tumors deep within the patient’s abdomen, and require an aperture of between 3-10 cm to be used depending on the tumor volume. Standardizing the length of 41 the entire set of applicators of different aperture enables one-time generation of all relevant dosimetric data and no source-to-skin distance (SSD) correction is needed. This is important because acquiring correct data for IORT can be a time consuming and labor intensive process [82]. There are two different methods of docking the applicator to the accelerator head, referred to as hard or soft docking. With hard docking, the applicator is rigidly attached to the accelerator head, while with the soft docking there is no physical contact between the applicator and the accelerator head. Because it creates an inflexible link between the applicator and the treatment head, hard docking carries the potential risk of crush injury to the patient. Soft docking (also referred to as air docking) does not fix the applicator to the accelerator head; it uses a rigid structure attached to the operating table with a clamp-and-post assembly to hold the applicator in place . The design and dosimetry of both hard docking [75][74][67][76][83] and soft docking [84][85][86][87][88][89] IORT systems have been described in the literature. In the “first draft” section of our work, we used a hard docking system in our “plastic” model and soft docking system in our “metal” model [92][90] . However, in the “second draft” of our design, we optimized the foils and collimators used in the “metal” model in a way that is compatible with both soft and hard docking systems, and permits a higher maximum aperture of the applicator [92] [93]. The design we developed also had to be compatible with a separately designed structure for accelerating electrons, and system for robotic operation of the mobile accelerator. Moreover, as the electron beams that leave the accelerating structure have an energy that exceeds the threshold for photoneutron production, we also had to calculate neutron leakage around the accelerator. We kept in consideration that the treatment head should be light and compact, because any feature that reduces the weight of the entire machine will make it easier to move to, from and within the OR. Our team’s specific project aim was to study the effects of different materials and geometry of accelerator head components on such critical beam properties as flatness, X-ray and neutron contamination, and the amount of dose delivered outside the treatment field. Based on these findings, a treatment head with applicators for a new prototype mobile electron accelerator was optimized and is now designed. The work of our treatment head optimization group was divided into several sub-steps that ran in parallel with the work the project groups assigned to optimize the electron accelerating structure and the mobile robot: To investigate the influence of various design parameters on the dosimetric characteristics of final electron beam, To calculate each of these characteristics (relative depth dose, profile, symmetry and flatness) for a whole set of different energies and different applicator apertures, 42 To simulate examples of dose distributions for different fields of irradiation and beam energies, To define adequate parameters for the foils-collimator-applicator system based on the previous steps, To investigate together with project engineers the technical solutions required to realize these parameters, and To provide the quantitative data the engineers will need to construct the treatment head of a prototype accelerator. 3.3 Monte Carlo study on a new model of a treatment head for a mobile electron accelerator 3.3.1. Radiation field and protection requirements The accelerator head parameters for the new mobile unit described in this paper were optimized for an IORT unit for use in any OR setting. As also mentioned, the requirements for radiation fields and radiation protection that we used in this study were consistent with the recommendations of the AAPM report [79] and fulfill IEC standards [80][81]. The flatness of the absorbed dose distribution in the radiation field was determined as (Dmax- Dmin)/Dmin x 100% in the central 80% of the beam field at dmax, where Dmax and Dmin are the maximum and minimum absorbed dose, and dmax is the depth of the maximum absorbed dose. According to [81], dose distribution should also be flat enough that, for a field diameter size greater than 5 cm, the distribution of isodoses in water should fulfill three criteria: 1. The value of parameter “A” – which is the distance between a 90% isodose and the border of the geometrical field measured at the standard depth of measurement (SDM), which is defined as one half of 80% isodose depth in the beam axis – should not be greater than 10 mm. 2. The value of parameter “B” – which is the distance between an 80% isodose and the border of the geometrical field measured at the base depth (BDM), which is defined as the depth of a 90% isodose measured in the beam axis – should not be bigger than 15 mm. 3. The absorbed dose, measured at the standard depth of measurement (SDM) anywhere in the radiation field, should not be higher than 103% of the maximum dose measured in the beam axis. Additionally, according to the international standard IEC60601-2-1[80], stray X-radiation that occurs during electron irradiation in the radiation field is allowable within a specific limit, described as follows: The percentage absorbed dose on the reference axis due to X-radiation at a depth of 100 mm beyond the practical electron range shall not exceed the values given 3,45; 3,75; 4,05; 4,35; 4,55 % of 43 absorbed dose in the axis for electron energies 4, 6, 8, 10 and 12 MeV respectively (figure 201.101 in [80]). Limits of leakage radiation in the patient plane are described by introducing definition of area M and M10. The geometrical field M is a projection of the distal end of the beam limiting devices on a plane perpendicular to the radiation beam axis. M10 is the area that results from extending the periphery of the geometrical field by 10 cm. The absorbed dose, as a percentage of the maximum absorbed dose on the reference axis at SSD, should not exceed a maximum of 10% in the area between a line 2 cm outside the geometrical field M and the boundary of M10. The average absorbed dose due to leakage radiation in the area between a line 4 cm outside the geometrical field and the boundary of M10, should not exceed the limits of allowable leakage radiation, which are 1% for electron energies up to and including 10 MeV, rising to 1,8 % for electron energies from 35 MeV to 50 MeV. Leakage radiation excluding neutrons in the patient plane outside the area M is limited in the following way: In the plane circular surface of radius 2m centered on and orthogonal to the reference axis at the isocenter, and excluding the area M, the absorbed dose due to leakage radiation, excluding neutron radiation, should not exceed a) a maximum of 0,2 % and b) an average of 0,1 % of the maximum absorbed dose measured at the center of the plane in a 10cm x 10 cm radiation field. Leakage neutron radiation in the patient plane outside the area M is limited as follows: In the plane circular surface of radius 2m centered on and orthogonal to the reference axis at the isocenter, and excluding the area M, the absorbed dose due to neutrons, should not exceed a) a maximum of 0,05 % and b) an average of 0,02 % of the X-radiation absorbed dose measured at the center of the plane in a 10cm x 10 cm radiation field. Leakage radiation excluding neutrons outside the patient plane is limited as follows: Except within the volume formed by a plane of radius 2m, centered on and orthogonal to the reference axis at the isocenter and the boundary for measurement in the distance of 1m from the electron beam path in the acceleration structure ( figure 201.103 in [80]), the absorbed dose due to leakage X-radiation at 1 m from: the path of the electron between the electron gun and the target or radiation window, and the reference axis, should not exceed 0,5 % of the maximum absorbed dose measured on the reference axis at SSD in a 10cm x 10 cm radiation field. Leakage neutron radiation outside the patient plane is limited as follows: 44 Except within the volume defined above, and under the same conditions, the absorbed dose due to leakage neutron radiation should not exceed 0,05 % of the maximum absorbed dose due to electron radiation or X-radiation. 3.3.2. First draft for a foils-collimator-applicator system As first draft of this system [91], we modeled two different treatment head assemblies and applicators using materials similar to those used in existing IORT systems. The first model was optimized for weight, the second for compactness. The first model (subsequently referred to as the “plastic” model) is characterized by a simple light-weight treatment head with a single scattering foil, without heavy collimators, and with plastic applicators (Fig.3. 4 right) and an SSD equal to 60 cm. The second model (subsequently referred to as the “metal” one) incorporates a more complex system of scattering and flattening foils fitted into a set of heavy collimators, and metallic applicators (Fig.3. 4 left). However, it is more compact, with an SSD equal to 50 cm. Multiple variants of each model were studied. Fig.3. 4. The “metal” (left) and “plastic” (right) models of treatment heads and applicators Details of the Accelerator Head Models (1) Scattering and flattening foils The scattering foil mechanism used to broaden electron beams with RF linacs typically has two 45 elements. The first is a higher-Z foil of uniform thickness, which broadens the linac pencil beam into a Gaussian profile. The second is a lower-Z shaped foil that is thickest at the center and thinnest at the edges, which minimally scatters electrons at the tail of the profile incident to the secondary foil, while maximally scatters electrons that are near the center of the profile. The resulting beam profile is relatively flat throughout the designated field area, and falls off sharply at the edges of the field. For the “metal” model, the scattering and flattening foils were selected according to a method described by K. K. Kainz et al.[94]. In this method, thickness of the primary foil is determined before the secondary foil is put in place. The primary foil is adjusted until the relative height of the Gaussian- shaped profile at the edges of the proposed treatment field at SSD reaches about 60% of the maximum fluence. We performed scattering foil simulations to test a number of different metals and foil thicknesses for minimization of electron energy loss, and decided to employ a primary foil made of gold, whose thickness ranges from 0.0006 to 0.004 cm for beam energies from 4 to 12 MeV, respectively, with an SSD of 50 cm. We placed an aluminum flattening foil of smooth Gaussian shape 10 cm below the gold scattering foil. The thickness of this foil (h) at each radial distance (r) is described by the equation: h = Hexp(−r2/R2). By varying the parameters R and H, the desired flatness of electron fluence distribution at the SSD can be achieved. In this study, the values of R and H were optimized to achieve flatness of fluence distributions better than 5 % for all beam energies and a field with a diameter of 10 cm, and better than 10 % for all beam energies and fields less than 10 cm in diameter. A single combination of a gold scattering foil and a Gaussian-shaped aluminum flattening foil was found sufficient to flatten the beam in the “metal” model for all considered beam energies and field sizes. For the “plastic” model a single, flat, scattering foil made of yellow brass was found sufficient to flatten the beam for all beam energies and field sizes. However, the use of only one foil it made it necessary to design a longer SSD. (2) Collimators In the “metal” model, the primary beam is substantially more scattered than in the “plastic” model. For this reason, a collimating system is needed to control leakage radiation. The shape, materials and dimensions of collimators were optimized to achieve acceptable control over the leakage radiation with minimal weight. (3) Applicators Cylindrical applicators in the “metal” model are made of aluminum, while those in the “plastic” model are made of polymethyl methacrylate (PMMA). We calculated thickness of the applicator walls to control leakage and scattered radiation levels in accordance with the European Standard [80]. The walls 46 are thinner for smaller diameter applicators. (4) Beam stopper and operating room shielding Beam stopper dimensions and operating room shielding were checked with FLUKA code simulations. The beam stopper was made of lead (Pb) and modeled as described by M. Ciocca et al., with dimensions of 40cm x 40cm x 15cm [95]. The size of the operating room was assumed to be 4m x 4m x 3m with 10 cm thick Portland concrete walls. 3.3.3 Monte Carlo simulations a) EGSnrc/BEAM simulations This study used the EGS system, version V4-r2-2-5, for an MC simulation with the user code BEAMnrc, version 2007 [96][97].Simulations were performed for monoenergetic electron beams,as well as, continuous energy spectra ranging from 4 to 12 MeV. Continuous energy spectra were obtained from calculations with the GPT code for a just-designed electron accelerating structure [98]. An electron beam with a Gaussian-distributed intensity profile of 3 mm full-width-half- maximum (FWHM), was directed onto the front of an accelerating structure vacuum exit window, through which it was transported to the treatment head and applicators. To assure statistical accuracy, these simulations were performed using 108 source particles. Transport parameters included an electron lower energy cut-off (ECUT) and AE of 0.7 MeV and photon lower energy cut-offs (PCUT) and AP of 10 keV. Other parameters included (a) maximum step size SMAX of 5 cm, (b) ESTEPE of 0.25, (c) XIMAX of 0.5, (d) spin effect turned on, (e) skin depth for BCA defaulted, (f) bremsstrahlung angular sampling and pair angular sampling both simple, and (g) bremsstrahlung cross-section Bethe-Heitler. The cross section data for all materials used in the simulations were obtained using PEGS4 code [99]. For each BEAMnrc run, information about each particle (such as energy, position, direction, and charge) that traversed the user-defined scoring planes was stored in phase-space files. Scoring planes were defined at different locations in each of the two accelerator head models, but for both models the last scoring plane was defined to be at the bottom of an applicator. The phase-space files were then used as an input for dose distribution calculations with EGSnrc/DOSXYZnrc [100]. Dose distributions were calculated for 109 particles at the entrance to a water phantom with dimensions of 40 x 40 x 20 cm3. The voxel size of 1 x 1 x 0.1 cm3 was set for the percentage depth dose (PDD). A phantom voxel size of 0.2 x 0.2 x 0.2 cm3 was used for the beam profile calculations. 47 From the PDDs the following properties were determined: (a) depth of the maximum dose, dmax, (b) depths of the 90% dose levels above and below the depth of maximum dose, d90%, (c) depths of the 50% and 80% dose levels, d50% , d80% , and (d) the relative dose due to Bremsstrahlung (stray radiation). Beam profiles were calculated at the depth of maximum dose. Flatness of a profile was determined as (Dmax - Dmin)/Dmin x 100% in the central 80% of the beam field at dmax. b) FLUKA simulations MC simulations using FLUKA code, version 2008.3c.0 October 2009, were performed to study radiation leakage in the operating room and to test the shielding of the entire system [101][102]. Simulations were performed for monoenergetic electron beams at energy ranging from 4 to 12 MeV. Calculations of beam transport started at a point located 1 mm from the beginning of the copper accelerating structure model, as the FLUKA program does not facilitate simulation of charged particle dynamics under an RF field in a resonant cavity. The primary electron beam of 0.3 mm FWHM and divergence of 4 mrad is transported via 89.9 cm of vacuum inside the linear accelerator model and up to the titanium window, where beam size reached FWHM of 3.6 mm, which is similar to that found under working conditions. Such beams were used to calculate the dose equivalent of radiation delivered to and around the patient plate, in order to determine how well the designed system meets operating standards. To assure statistical accuracy in a reasonable calculation time, these simulations were performed using 106 – 109 source electrons. Each FLUKA run provides complete information on such calculated quantities as fluence of particles or dose equivalents in the given areas, regardless of defined geometry. Binning of space can be defined in any arbitrary manner, depending on the situation. However, analysis of the results of a FLUKA run in the FLAIR graphical user interface is restricted to 640kB of data [103]. The FLAIR matrix presents dose analyses within a two-dimensional plane of approximately 800x800 cells. 3.3.4 Dose distributions for the first draft of a foils-collimator-applicator system A full range of performance data was collected for each model of the accelerator treatment head. Calculations were repeated for circular applicators with diameters ranging from 3 to 10 cm, and for monoenergetic beams with energies ranging from 4 to 12 MeV. Based on these data, we identified for each model a universal scattering foil and geometry of the treatment head and applicators that performed well independent of either the beam energy or the diameter. However, the simpler “plastic” model requires an SSD of 60 cm, which is 16.7% longer than the SSD of 50 cm in the heavier, “metal” model. 3.3.4.1 Dose Distribution in the Treatment Field 48 Fig.3. 5 (a) and (b) show percentage depth dose along the beam axis for the “metal” and “plastic” models with an applicator diameter of 10 cm for monoenergetic beams of energies ranging from 4 to 12 MeV. a) b) Fig.3. 5. Relative depth dose (PDD-percentage depth dose) along the beam axis for IORT (a)“metal” and (b) “plastic” model with applicator diameter of 10 cm and monoenergetic beams of energies ranging from 4 to 12 MeV. Fig.3. 6 and Fig.3. 7 show dose profiles at dmax for the “metal” and “plastic” models with applicator diameters of (a) 10 cm and (b) 5 cm for monoenergetic beams of energies ranging from 4 to 12 MeV. 49 a) b) Fig.3. 6. Dose profiles at dmax for an IORT “metal” model with applicator diameters of (a) 10 cm (b) of 5 cm, for monoenergetic beams of energies ranging from 4 to 12 MeV. 50 a) b) Fig.3. 7. Dose profiles at dmax for an IORT- “plastic” model with applicator diameters of (a) 10cm (b) 5 cm for monoenergetic beams of energies ranging from 4 to 12 MeV. Tables 3.1 and 3.2 show examples of electron beam characteristics for “metal” and “plastic” models with applicator diameter of 10 cm. 51 Table 3.1 Electron beam characteristic for “metal” model with applicator diameter of 10 cm. Input Rp E(Rp) dmax d90% d80% Flatness energy (cm) (MeV) (cm) (cm) (cm) (%) (MeV) 4 1.56 3.32 0.55 0.83 0.95 3.1± 0.4 6 2.58 5.35 1.05 1.46 1.64 1.8± 0.3 8 3.60 7.38 1.45 2.11 2.36 3.5± 0.2 10 4.62 9.42 1.85 2.76 3.09 4.7± 0.3 12 5.61 11.41 1.95 3.37 3.79 4.0± 0.2 For both models, beam flatness is better than 5% for a field of 10 cm diameter and better than 10% for all fields with a diameter greater than or equal to 5 cm. The “metal” model delivered beams of greater flatness at lower beam energies while the “plastic” model delivered better flatness at higher electron beam energies. Table 3.2 Electron beam characteristic for “plastic” model with applicator diameter of 10 cm. Input d Rp E(Rp) max d90% d80% Flatness energy (cm) (MeV) (cm) (cm) (cm) (%) (MeV) 4 1.6 3.41 0.60 0.87 0.98 4.7 ± 0.5 6 2.6 5.44 1.00 1.47 1.65 5.1 ± 0.4 8 3.6 7.50 1.30 2.05 2.30 3.6 ± 0.4 10 4.6 9.48 1.50 2.60 2.96 1.7 ± 0.2 12 5.6 11.48 1.60 3.15 3.60 1.2 ± 0.2 3.3.4.2 Leakage and Stray Radiation 52 For both models, we also determined stray radiation in the treatment field, as well as leakage around the end of applicator and through the side wall. Tables 3.3 and 3.4 show sample results of these calculations in comparison to the limits set by the European Standard IEC 60601-2-1[80]. Geometrical field M is a projection of the distal end of the beam limiting devices on a plane perpendicular to the radiation beam axis. M10 is the area that results from extending the periphery of the geometrical field by 10 cm. Leakage radiation, as calculated on the circular surface with a radius of 2 m, centered in the isocenter and perpendicular to the beam axis, fulfills radiation safety requirements for both models [80]. Table 3.3 Stray and leakage radiation on the patient plate, calculated for the “metal” model with an applicator diameter of 10 cm. Applicator Input energy (MeV) Φ = 10 cm 4 6 8 10 12 Stray radiation at a depth of 100 mm beyond Rp IEC standard (%) 3,45 3,75 4,05 4,35 4,55 Results (%) 0.13 0.17 0.24 0.30 0.39 Leakage radiation through beam limiting devices Maximum dose in the area between a line 2 cm outside the periphery of geom. field and the boundary of M10 IEC standard (%) 10,00 Results (%) 0.08 0.10 0.53 1.37 1.62 Average dose in the area between a line 4 cm outside the periphery of geom. field and the boundary of M10 IEC standard (%) 1,00 1,00 1,00 1,00 1,06 Results (%) 0.02 0.02 0.21 0.68 0.83 53 Table 3.4 Stray and leakage radiation on the patient plate, calculated for the “plastic” model with an applicator diameter of 10 cm. Applicator Input energy (MeV) Φ = 10 cm 4 6 8 10 12 Stray radiation at a depth of 100 mm beyond Rp IEC standard (%) 3,45 3,75 4,05 4,35 4,55 Results (%) 0,18 0,36 0,66 1,03 1,59 Leakage radiation through beam limiting devices Maximum dose in the area between a line 2 cm outside the periphery of geom. field and the boundary of M10 IEC standard (%) 10,00 Results (%) 0,17 0,30 1,60 3,0 4,00 Average dose in the area between a line 4 cm outside the periphery of geom. field and the boundary of M10 IEC standard (%) 1,00 1,00 1,00 1,00 1,06 Results (%) 0,01 0,06 0,17 0,48 0,88 Leakage radiation at a distance of 1 m from the beam axis was calculated for both models and compared with the maximum absorbed dose on the beam axis for the 10 cm diameter applicator. These values were less than 0.025% for the “metal” model and 0.06% for the “plastic” model. According to the standards these values should not exceed 0.5% [80]. 3.3.4.3 Shielding Assessment Fig.3. 8 (a) and (b) show two-dimensional distributions of relative dose equivalents inside and outside the operating room calculated for a maximum energy of 12 MeV, using a 10 cm diameter applicator for the “metal” and “plastic” models, respectively. Calculations were performed for 2 x 109 source electrons. Besides the collimator and applicator assemblies, the simulated setups included a 54 copper accelerating structure, a 60 x 60 x 30 cm3 water phantom and a 40 x 40 x 15 cm3 lead beam stopper. The setup was placed inside a 4 x 4 x 3 m3 box with 10 cm thick concrete walls approximating an operating room. The assumption of 10 cm thick wall is considered as a very conservative lower limit [104]. Fig.3. 8 (a), (b) Two-dimensional distribution of relative dose equivalents inside and outside the operating room were calculated for a maximum energy of 12 MeV, with a 10 cm diameter applicator for the (a) “metal” and (b) “plastic” models respectively. Spatial dimensions (X and Y axis) are in cm. Note that the vertical axis is rotated by 90 degrees: the X axis represents height of a hypothetical OR; the floor of the OR is on the right side of each figure. The highest doses are deposited in the beam direction, which makes shielding of the floor the most critical requirement. By comparing dose equivalents in a water phantom at depth dmax and in the space directly below the floor of the OR, one can estimate limits of allowable number of treatments per year. 55 A dose of 10 Gy delivered to a patient over a single treatment results in a dose equivalent of about 6.8 μSv delivered directly beneath the floor of the OR for the “metal” model, and 2.2 μSv for the “plastic” model. Assuming three treatments per week, the cumulative yearly dose outside the OR would be no greater than 1.05 mSv for the “metal” and 0.33 mSv for the “plastic” model, both of which are comparable to or below the annual limit of 1 mSv for non-controlled areas. Fig.3. 9 (a), (b) 2D distributions of relative dose equivalent due to neutron radiation inside and outside the operating room calculated for a maximum energy of 12 MeV, with a 10 cm diameter applicator for the (a)” metal”: and (b) “plastic” model. Spatial dimensions (X and Y axis) are in cm. Note that the vertical axis is rotated by 90 degrees: The X axis represents the height of an OR; the floor of the OR is on the right side of each figure. Two-dimensional distributions of dose equivalent from neutrons, inside and outside the operating room, were calculated for a maximum beam energy of 12 MeV, with a 10 cm diameter applicator. Calculations were performed with the FLUKA code for 2 x 109 source electrons. Fig.3. 9 (a) and (b) shows resulting distributions for the “metal” and “plastic” models, respectively. 56 The main source of neutrons is the beam stopper and it generates a similar number of neutrons in both models. Based on FLUKA calculations, we estimated an annual dose equivalent from neutrons beneath the floor of an operating room. In case of 12 MeV beam energy and 10 cm applicator and assuming three treatments per week (10 Gy per treatment) the doses are 0.09 mSv/year and 0.013 mSv/year for the „metal” and the „plastic” models, respectively. It must be recognized that the above calculations are reasonable estimates only. It was clearly impossible to simulate all viable structural setups in this study. 3.3.4.4 Applicators with diameters of more than 10 cm In IORT practice it is often desirable to irradiate fields with diameters larger than 10 cm, especially when the tumor is in the abdomen or pelvis. In the two treatment head models described above, we simulated applicators with an aperture greater than 10 cm for energy of 12 MeV. The conclusions we reached are as follow: a) Beam flatness was good for both treatment head models (“metal” and “plastic”) with a 12 cm applicator (aluminum and PMMA), b) The level of leakage radiation was higher than that allowed by the standards for a PMMA applicator ( Fig.3. 10,) c) Beam flatness for applicators with a diameter >12cm was not sufficient in a “metal” model whose foils were optimized for a 10 cm applicator Relativ absorbed dose Relativabsorbed Off-axis position [cm] 57 Fig.3. 10 Dose profiles at dmax for an IORT- “plastic” (blue line) and “metal”( red line) model with 12 cm applicator diameter for energy of 12 MeV. In addition, we studied larger applicators with diameters of 15 and 22 cm. Based on the conclusions observed in the 12 cm models, we limited this part of our investigation to a “plastic” model with one foil, and no collimators. To achieve acceptable beam flatness in a large field, we modeled new scattering foils with complex shapes. The resulting flatness of the beam in the treatment field is equal to 2.9±0.3% and 7.0±0.4% for applicators with diameters of 15 cm and 22 cm, respectively. Calculations were performed at a beam energy of 12.5 MeV. Results are shown in Fig.3. 11. Fig.3. 11 Dose profiles at dmax for an IORT- “plastic” model with steel applicator diameters of 15 cm (blue line) and 22 cm ( red line) for monoenergetic beams with energies of 12.5 MeV The large diameter applicators, we modeled, were made of steel in order to keep leakage radiation within the limits set by the European Standards. The maximum dose in the area between a line 2 cm outside the geometrical field and the boundary of M10 is 1.4 % and 2.0 % of maximum dose on the beam axis for 15 and 22 cm applicator diameter, respectively (limit is 10 %). The average dose in the area between a line 4 cm outside the geometrical field and the boundary of M10 is 0.77 % and 0.88 % of maximum dose on the beam axis for the 15 and 22 cm applicator diameters, respectively (limit is 1.06 %). While it would be possible to build foils that would provide acceptable parameters of therapeutic beams to irradiate larger fields, however, there is no standardized system for doing this.. 58 This would make it necessary to change foils whenever the larger applicators were used, which is impractical. 3.3.5 Comparison of dose distribution for real and monoenergetic beams All the simulations we did used monoenergetic electron beams. To verify this simpler assumption, we also calculated examples using continuous energy spectra ranging from 4 to 12 MeV. Continuous energy spectra were calculated with GPT code for a just-designed electron accelerating structure, and are shown in Fig.3. 12 and Fig.3. 14 ntensity Electron beam i beam Electron Fig.3. 12. Example of the realistic energy distribution of a beam received from the accelerating structure. Calculations were performed with GPT code for a beam with a maximum energy of approximately 4 MeV. 59 Fig.3. 13. Comparison of the depth dose distribution and profiles calculated for a monoenergetic beam (blue curves) and for a beam with real energy distribution (red curves) for 3cm ( upper figures) and 10cm applicators (lower figures). ntensity Electron beam i beam Electron Fig.3. 14 Example of the realistic energy distribution of a beam received from the accelerating structure. Calculations were performed with GPT code for a beam with a maximum energy of approximately 12 MeV. 60 Fig.3. 15 Comparison of the depth dose distribution and profiles calculated for a monoenergetic beam (blue curves) and for a beam with real energy distribution (red curves) for 3cm ( upper figures) and 10cm applicators (lower figures). These calculations demonstrate that the main beam parameters (percentage depth dose and profiles) are almost identical when the energy of the monoenergetic beam is similar to the average energy of a beam with continuous energy distribution, and when the most probable energy in this spectrum does not differ greatly from the average energy of spectrum. Fig.3. 13 and Fig.3. 15 show the comparative depth dose distribution and profiles for a monoenergetic beam (blue curves), and for a beam with real energy distribution (red curves) for a 3cm applicator (upper figures) and 10cm applicator (lower figures). 61 3.3.6 Acceptable tolerance for displacement and rotation of applicator axis relative to beam axis We also did a number of calculations to estimate acceptable tolerance for the displacement and rotation of the applicator axis relative to the beam axis. We simulated the dose distribution at the patient surface for different applicator positions relative to beam axis and as a function of the rotation of these axes. Fig.3. 16 illustrates these calculations and results. Fig.3. 16 Visualization of calculations for estimating the tolerance of displacement (upper left) and rotation (upper right) of two axes: applicator and beam; sample results for displacement in metal model (lower left and right). The calculations we did for the “metal” model, show that an acceptable displacement of the axes is no more than 1 mm, while rotation should not be displaced by more than 0.5 degree. In the ”plastic” model, we found that the tolerance for displacement of the axes was greater (around 5 mm) but that tolerance for displacement of rotation was smaller (around 0.25 degree) in comparison to the “metal“ model. 62 Our findings on beam flatness versus different axis displacements for the metal and plastic model applicators with a diameter of 10 cm and a 12 MeV beam are displayed in Tables 3.5 and 3.6. Table 3.5 Flatness versus axis displacement (Δx) for the “metal” model Δx (mm) dmax (cm) Flatness (%) 0 1.75 3.6± 0.3 0.1 1.95 5.3±0.4 0.2 1.85 4.1±0.4 0.5 1.95 5.8±0.4 1.0 1.95 7.8±0.4 5.0 1.75 19.9±1.1 Table 3.5 Flatness versus axis displacement (Δx) for the “plastic” model Δx (mm) dmax (cm) Flatness (%) 0 1.55 1.2± 0.1 0.5 1.75 2.9±0.3 1.0 1.45 1.6±0.5 2.0 1.65 3.8±0.4 5.0 1.45 5.5±0.5 3.3.7 Second draft for a foils-collimator-applicator system Both models of the treatment head assembly described above fulfilled basic requirements for quality of the therapeutic beam, as well as for radiation protection against stray and leakage radiation. The primary disadvantage of the “plastic” model is that it requires relatively thick applicator walls (from 4-6 mm depending on the beam energy and size of applicator) if the patient is to be irradiated at an SSD equal to, or less than 60 cm. In the metal model, it is possible to make the applicator walls much thinner using a material other than aluminum for their construction.. A second 63 advantage of the “metal” model is that is better suited for use with a soft docking system, with which it is also easier to use large diameter or rectangular applicators. We also learned subsequently from discussions with practitioners that the soft docking system, where there is no physical contact between the applicator and the accelerator head, is considered much safer for the patient and easier for the physicians to use. Only a small number of oncological radiotherapists who treat breast cancer found a hard docking system to be more comfortable. In the second draft of our treatment head design, we therefore decided to study the use of both docking systems with the “metal” model. First, we performed calculations for the “metal” model described above with both steel and brass applicators. The results were favorable: use of either of these materials made it possible to reduce wall thickness to less than 3 mm. Fig.3. 17 shows examples of the results obtained at 12 MeV beam energy with an applicator of 10 cm diameter. Fig.3.17 (a) Relative dose distribution ( PDD) for beam energy equal to 12 MeV and 10 cm applicator diameter with reduced wall thickness. Fig.3. 17 (b) Beam profile at the dmax for beam energy equal 12 MeV and 10 cm applicator diameter with reduced wall thickness . 64 In the next step, we designed a final, universal model treatment head with a fixed set of foils and collimators that could be used with either a soft or hard docking system, depending on the needs and preferences of the accelerator user. We studied a treatment head with source to surface distance (SSD) equal to 60 cm and a two-part applicator whose total length is 45 cm. The two sections of the applicator permit both hard docking (Fig.3. 18, right) for the entire applicator assembly, and soft docking for the lower 30 cm section, which has an air distance of 15 cm from the collimator (Fig. 3.18, left) We optimized all key components of this treatment head model: Foils system, Collimator apertures, Applicator materials and wall thickness, and Maximum diameter of the applicator. Subsequently, we also studied the possibility of using rectangular applicators [92][93]. Fig.3. 18. Accelerator treatment head with soft-docking (left) and hard-docking (right). We also studied the effects of different docking systems on such critical beam properties as flatness, X-ray contamination, and the amount of dose delivered outside the treatment field. Based on these findings, we were able to provide our engineers with the basic data for a treatment head with either docking option. 3.3.7.1 Dose distributions in the treatment field 65 Simulations covering beam energy ranging from 4 to 12 MeV were repeated for circular applicators with diameters ranging from 4 – 12 cm, and for applicators made of steel and brass. Fig.3. 19 and Fig.3. 20 show examples of results for 12 cm applicator, for both docking systems, at different energies. Fig.3. 19 Depth dose distribution for 12 cm diameter applicator, for different beam energy; soft or hard docking. Fig.3. 20. Beam profile at dmax for 12 cm diameter applicator, for different beam energy, soft and hard docking system, with input beam energy ranging from 4 to 12 MeV. Table 3.6 Therapeutic beam properties extracted from Monte Carlo calculated dose distributions for input beam energy ranging from 4 to 12 MeV and applicator diameter of 12 cm. 66 . Table 3.7 Beam flatness calculated for 12 cm applicator at dmax, with input beam energy ranging from 4 to 12 MeV, for soft or hard docking. Depth doses, profiles and main therapeutic beam characteristics are almost identical for both docking systems, which suggests that our optimization of scattering and flattening foils and the collimator system was adequate, as shown in Fig.3. 19 and Fig.3. 20 and Table 3.6 and 3.7 Small differences in flatness are illustrated in Table 3.7 but these are acceptable. 3.3.7.2 Leakage and Stray Radiation For both docking systems, we simulated both doses delivered outside the treatment field and stray radiation in the treatment field, as well as leakage around the end of applicator and through the side wall. Results were similar for both docking systems, and fell within range of statistical error. Calculations were performed for initial beam energies ranging from 4 to 12 MeV and for circular applicators with diameters ranging from 3 to 12 cm. Table 3.8 and 3.9 show sample results of these calculations for an applicator diameter of 12 cm, compared against the limits recommended in the European Standard IEC 60601-2-1[80]. For both docking systems used with a 12 cm. applicator, we calculated leakage radiation at a distance of 1 m from the beam axis and compared with the maximum absorbed dose on the beam axis. These values were less than 0.05 %, i.e. about 10 times below the recommended limit. Table 3.8. Stray radiation at a depth of 100 mm beyond Rp, calculated for 12 cm applicator. 67 Input energy (MeV) 4 6 8 10 12 IEC standard (%) 3.45 3.75 4.05 4.35 4.55 Results (%) 0.13 0.17 0.24 0.30 0.39 Table 3.9 Leakage radiation on the patient plane, calculated for a 12 cm applicator. Maximum dose in the area between a line 2 cm outside the periphery of the geometric field and the boundary of M10 Input energy (MeV) 4 6 8 10 12 IEC standard (%) 10 10 10 10 10 Results (%) 0.08 0.10 0.53 1.37 1.62 Average dose in the area between a line 4 cm outside the periphery of geometric field and the boundary of M10 Input energy (MeV) 4 6 8 10 12 IEC standard (%) 1 1 1 1 1.06 Results (%) 0.02 0.02 0.21 0.68 0.83 3.3.7.3 Circular applicators with diameters of more than 12 cm and non-circular applicators As elongated field shapes are often desirable for IORT procedures, we also studied potential applicators with diameters larger than 12 cm, and also applicators non-circular in shape. We observed based on these calculations that it is impossible to generate a field size equal to or greater than 15 cm without changing the foil system. Achieving acceptable flatness at an SSD equal to 60 cm, would require thicker scattering and flattening foils, which would also mean more energy loss. Further study led us to find what appeared to be a reasonable compromise between foil thickness and field size, which enabled us to simulate fields with a diameter of 12-13 cm for 12 MeV beam energy, and 14 cm for 6 MeV beam energy. We calculated dose profiles at dmax for a soft docking applicator at energies of 6 and 12 MeV: for a 14 cm applicator at an energy of 6 MeV, and a 13 cm applicator at an energy of 12 MeV, as shown in Fig.3. 21 and Fig.3. 22 68 Fig.3. 21 Dose profile at dmax calculated for 14 cm applicator and beam energy 6 MeV, for a universal model using soft docking. Fig.3. 22. Dose profiles at dmax calculated for 13 cm applicator and beam energy 12 MeV, for universal model using soft docking. According to [81], dose distribution in radiation field should be flat enough that with a field diameter size greater than 5 cm, the distribution of isodoses in water should fulfill three criteria that were noted initially in section 3.3.1 above: 1. The value of parameter “A” – which is the distance between a 90% isodose and the border of the geometrical field measured at the standard depth of measurement (SDM), which is defined as one half of 80% isodose depth in the beam axis – should not be greater than 10 mm. 2. The value of parameter “B” – which is the distance between an 80% isodose and the border of the geometrical field measured at the base depth (BDM), which is defined as the depth of a 90% isodose measured in the beam axis – should not be bigger than 15 mm. 3. The absorbed dose, measured at the standard depth of measurement (SDM) anywhere in the radiation field, should not be higher than 103% of the maximum dose measured in the beam axis. 69 To determine whether our model met these criteria, we verified isodose distribution in water for beams generated with either docking system. Sample results are shown in Fig.3. 23. Based on this, we concluded that the criteria were met for either docking system, for an energy range of 4 – 12 MeV, with applicator head diameters less than or equal to 12 cm. At energies less than 12 MeV, the three criteria were also met for applicators slightly larger than 12 cm in diameter: at beam energies of 6 and 9 MeV, isodose distribution was satisfactory with a field diameter of 13 cm, and at a beam energy of 6 MeV good distribution was achieved with a 14 cm diameter applicator. 12 MeV, 10 cm (soft 9 MeV, 13cm (soft docking) docking) A = 5.9 mm (Norma A < 10 Fig.3. 23. Examples of isodose distribution in water. Left site: isodose distribution for soft docking system, for beam energy of 12 MeV and radiation field of 10 cm. Right site: isodose distribution for soft docking system, for beam energy of 9 MeV and radiation field of 13 cm. As mentioned above isodose distributions fulfill all criteria of IEC standards. We also modeled the second draft version of the treatment head with a non-circular shaped applicator and soft docking, simulating a rectangular yellow brass applicator with a cross section of 10 x 5 cm and wall thickness of 2 mm [92]. 70 Fig.3. 24 Scheme of applicator with the rectangular cross section. A good quality therapeutic beam was generated with the rectangular applicator. Fig.3. 25 shows dose distribution in water at the depth of maximum dose in the beam axis using this applicator. Fig.3. 26 shows depth dose distribution and profiles along the X- and Y-axis at the depth of maximum dose in the beam axis. These results suggest that this treatment head has broad potential for clinical use. 71 dose [%] Fig.3. 25 Dose distribution at d max for a rectangular 10 cm x 5 cm applicator. 72 X-profile on dmax Stray radiation=0.37% Y-profile on dmax Fig.3. 26 Dose distribution for a 10x5 cm rectangular applicator and beam energy of 12 MeV: (left) depth dose distribution, (right) beam profiles along the X- and Y-axis at maximum dose depth in the beam axis. 3.4 Radiation protection studies for a new mobile IORT accelerator Using an accelerator to directly irradiate surgically-exposed organs in a standard operating room (OR) raises specific concerns about radiation safety for the patient and medical personnel. Therefore, we also needed to calculate the external shielding necessary to meet safety requirements for our new treatment head model [105][106]. Our secondary objective was to assess safety risk related to generation of neutron leakage radiation when employing electron beams with energies higher than 10 MeV. The extended therapeutic range of 12 MeV electron beams can be highly desirable in some clinical situations.. The added energy permits better coverage of thick lesions [107]. Mobile linear accelerators are built with several features to reduce the need for any additional shielding. They include a beam stopper to intercept the primary beam and work at lower energies than those a conventional accelerator. They also do not have bending magnets, which produce neutrons in conventional accelerators. 73 We used FLUKA code to study dose distribution inside and outside the OR. To assess the risks related to exposure to leakage radiation, we modeled a hypothetical surgical suite consisting of an OR and a Control Room, as illustrated in the Fig.3. 27 and Fig.3. 28. We assumed 10 cm thick concrete walls and a 30 cm thick concrete floor and ceiling. We performed calculations without any additional shielding, as well as with a lead shielding plate of dimensions 140 x 150 cm2 and variable thickness, which was designed to protect the personnel in the control room. We analyzed dose levels in several locations inside and outside the suite, at points located 1 m above the floor and 30 cm from the walls, as indicated in Fig.3. 27. The points indicated in Fig.3. 28 are located on the beam axis. MC simulations using FLUKA code, version 2.13 (2011), were performed in the same way as described previous in section 3.3.3, with 109 source electrons. Fig.3. 27. Layout of OR and Control Room. Points selected for detailed dose analysis are indicated with a + sign (top view: x, y axis). 74 Fig.3. 28. Layout of OR and Control Room. Points selected for detailed dose analysis are indicated with the + sign (side view: y, z axis). 3.4.1. Dose equivalent inside and outside operating room Two-dimensional distribution of relative dose equivalent (DEQ) inside and outside the operating room (OR) was calculated specifically for a maximum beam energy of 12 MeV and a 12 cm diameter applicator, both with (Fig.3. 30) and without (Fig.3. 29) additional lead shielding. Based on an anticipated dose of 20 Gy delivered to a patient over a single treatment, and assuming three treatments per week, we estimated a DEQ of about 0.03(2) mSv/year in a room directly above the OR and 1.1(2) mSv/year in the space directly beneath the floor of the OR. Both results are equal to or less than the annual limit of 1 mSv for non-controlled areas. A different situation was found behind the 10 cm concrete walls of the modeled OR. At points Z1 and X4, DEQ was equal to 11.54(4) and 4.22(2) mSv/year, suggesting that it would be necessary to restrict the number personnel allowed in those areas, or to increase wall protection at these points. 75 Fig.3. 29. Two-D distribution of relative dose equivalent inside and outside the operating room were calculated for a maximum energy of 12 MeV, with a 12 cm diameter applicator without OR shielding. Spatial dimensions (X, Y and Z axis) are in cm. The upper illustration is a side view of the OR, the lower shows a top view. 76 Fig.3. 30. Two-D distribution of relative dose equivalent inside and outside the OR were calculated for a maximum energy of 12 MeV, with a 12 cm diameter applicator and OR shielding. Spatial dimensions (X, Y and Z axis) are in cm. The upper figure shows a side view of the OR, the lower shows a top view. We determined dose equivalent from all particles (DEQ) and from neutrons only (neutron DEQ), at points Y2,Y2a, Z2, Z3 for energies 12 and 9 MeV, with a 12 cm diameter applicator and different lead shielding thickness. Table 3.10 shows sample results of these calculations at a location labeled “Y2a”, which is inside the control room where the control console might be located and thus where a technician would be working during patient irradiation. The calculations suggest that the 10 cm concrete walls of the OR near points Z1 and X4 will require additional metal protection if the rooms on the other sides of them are occupied during treatments. To protect people working in the control room, it would be sufficient to place a 1 x 140 x 150 cm (x,y,z axes, respectively) mobile lead shield between the accelerator and the control room. 77 Table 3.10 DEQ from all particles and neutron DEQ at OR point Y2a, for 9 and 12 MeV energies, with a 12 cm diameter applicator and different lead shielding thickness. 12 MeV 9 MeV Lead shielding (cm) DEQ Neutron DEQ DEQ Neutron (mSv/y) (mSv/y) (mSv/y) DEQ (mSv/y) 0 1.98(4) 0.0878(8) 1.99(4) 0.00039(2) 1 0.93(2) 0.0860(7) 0.96(2) 0.00035(2) 2 0.67(3) 0.0829(7) 0.65(2) 0.00036(2) 3 0.44(2) 0.0809(6) 0.428(9) 0.00036(2) 4 0.37(2) 0.0804(5) 0.316(8) 0.00031(2) 5 0.32(2) 0.0779(6) 0.252(5) 0.00030(2) 3.4.2. Neutron DEQ An electron beam produces neutrons primarily through absorption of the bremsstrahlung photons produced the electrons. A neutron may be produced when the absorbed photons have energy greater than the binding energy of the neutron to the nucleus. Neutron production will take place in any material struck by an electron or bremsstrahlung radiation above a threshold energy (Eth), which varies in general from 10 to 19 MeV for light nuclei (A< 40) and from 4 to 6 MeV for heavy nuclei. The dominant reaction is (γ, n), with smaller quantities of neutrons produced by (γ, p n) and ( γ, 2n) at higher energies. The average energy of neutrons emitted by (γ , n) reactions in the primary beam is in the range of 1-2 MeV and the angular distribution of neutron fluence is nearly isotropic [108]. We also used FLUKA calculations to estimate annual neutron DEQ beneath the OR floor. For a 12 cm applicator diameter, at 9 or 12 MeV beam energy, assuming three treatments per week at 20 Gy per treatment, neutron DEQ would be 0.0062(6) and 0.00006(9) mSv/year. Fig.3. 31 shows two- dimensional distributions of relative neutron DEQ inside and outside the OR. The main source of neutrons is a 40×40×15 cm (x,y,z axes, respectively) lead beam stopper. Neutron DEQ in the control room was very low, only 0.086 and 0.0003 mSv/y, at 12 and 9 MeV electron beam energy, respectively. It must be recognized that the above calculations are reasonable estimates only. To assure the safety of patients and personnel, actual measurements should be performed after the accelerator is installed, and then compared with measurement results obtained by other investigators [109][110][111] [112]. 78 Fig.3. 31. Two-D distributions of relative dose equivalent due to neutron radiation inside and outside the operating room calculated for a maximum energy of 12 MeV with a 12 cm diameter applicator. Spatial dimensions (X Y and Z axis) are in cm. (upper) side view (lower) top view. 79 3.5 Summary: conclusions and discussion To summarize the work presented in this section: We used MC code to simulate a number of treatment head models and operating conditions for a new IORT accelerator to be built at the Polish National Center for Nuclear Research (NCBJ), Prior to performing these simulations, we extensively reviewed the literature on IORT, and developed our initial planning assumptions for a new IORT machine and the parameters to be studied, Based on the information gathered, we arrived at an advanced draft of the technical specifications for a treatment head (foils, collimators and applicators) for a new mobile IORT accelerator, We also tested the model for radiation safety against existing technical standards, and simulated operating room radiation shielding requirements to determine optimal safety conditions for normal accelerator operations, and We consulted with third-party experts as well as our own engineering staff to make sure that we were creating simulations that were rational given the real-world conditions in which IORT is used now and may be used in the future. Our simulations led us finally to recommend a “universal” IORT accelerator treatment head that can uses either hard or soft docking applicator system. The accelerator we developed will deliver electron beams in an energy range of 4 – 12 MeV. It will use thin-walled metal applicators with diameters ranging from 3 – 12 cm, possibly larger at lower energies, which can be attached to a universal therapeutic head. The treatment head uses a fixed system of collimators and scattering foils that is independent of beam energy and applicator diameter. A double foil scattering system was designed to minimize beam energy loss and bremsstrahlung production. Collimator weight and shape was optimized, and different applicator materials were studied. The treatment head is compatible with both cylindrical and non-cylindrical applicators. Using only one set of two foils limits the diameter of irradiated field to about 12-13 cm, but it will also simplify treatment head construction, and result in a treatment head is simpler and lighter than treatment heads found in a classic electron accelerator. In the first stage of our work, we studied two treatment head models: a ”plastic” model with one foil and plastic applicators, and a “metal“ model with a double foil scattering system and collimators and metal applicators. The primary disadvantage of the “plastic” model was that it required relatively thick applicator walls (from 4-6 mm, depending on the beam energy and size of 80 applicator) if the patient is to be irradiated at an SSD equal to or less than 60 cm. Applicator walls in the “metal” model, which are made of steel, can be much thinner (2 mm). A second advantage of the “metal” model is that is better suited for use with a soft docking system, with which it is also easier to use large diameter or rectangular applicators. We also learned from subsequent discussions with practitioners that, as there is no physical contact between the applicator and the accelerator head, the soft docking system is considered much safer for the patient and easier for physicians to use. Only a small number of oncological radiotherapists who treat breast cancer felt that a hard docking system was more comfortable; so, in the second draft of our treatment head design, we decided to study both docking systems with the “metal” model. The second draft model fulfills basic requirements for quality of the therapeutic beam, as well as for radiation protection against stray and leakage radiation. Using an electron accelerator inside a regular OR is not a trivial issue in respect to radiation dose. In this work, we showed that when we use a “beam stopper“ as radiation absorber directly on the beam axis, accelerator operation is possible without compromising the radiation safety of the patient and medical staff. It was determined that dose distribution in the patient plane meets existing radiation protection requirements. It was further found that safe operation of the accelerator in a conventional OR may require some additional light shielding, depending on details of the wall construction, patient workload and occupancy factors. We showed that relatively light and mobile lead shielding panels may be successfully used for that purpose. Investigation of leakage and scatter radiation provides a resource to evaluate shielding and to set some limit on the number of IORT procedures performed weekly in an operating room. Assuming three treatments per week in certain OR, the cumulative yearly dose outside the OR would be well below the annual limit of 1 mSv for non-controlled areas in the locations above and under OR. The model of the treatment head assembly for a new mobile electron accelerator for IORT have been designed. As a next step, a prototype IORT accelerator will be constructed and tested in the laboratory. The medical need for a new IORT that is movable, flexible, safe and price-competitive is demonstrable. Only three IORT manufacturers currently exist, despite an ever-strengthening scientific case for increased use of this technology. IORT has now been in use worldwide for over 30 years, delivering a supplementary or alternative radiotherapy option to treatment cancer patient. Results have shown promise. Retrospective analyses of clinical experience with IORT in the treatment of such operable cancers as pancreatic tumors, locally advanced or recurrent rectal cancer, head and neck carcinomas, sarcomas 81 and cervical cancer (Fig.3. 32) have shown local tumor control comparable to clinical experience with alternative modalities [113]. Fig.3. 32 Using of mobile accelerator for IORT for different tumor sites [78] Recently, electron beam IORT (also called ELIOT) has shown promise as the sole treatment for patients with earlier-stage cancers, especially breast tumors. This work started at the European Institute of Oncology in Milan. Orecchia and Veronesi describe the rationale and techniques associated with ELIOT, and present the results of different clinical studies [114] [111], and conclude that ELIOT may be an excellent alternative to external-beam radiation therapy (EBRT) for the treatment of patients with early-stage breast cancer. Intensive long-term follow-up to fully evaluate local control and possible side effects is ongoing in several countries [115]. A new IORT accelerator could help advance these developments in radiotherapy practice. 82 4. A new approach to estimate the effect of CT calibration on range calculation 4.1 Treatment planning in Carbon ion therapy 4.1.1 Radiotherapy with heavy charged particles Physical Properties and delivery systems Heavy charged particles and photons interact differently with matter. The physical interactions of conventional photon beams of 4 - 25 MV with matter consist mainly of Compton scattering with atomic electrons, followed by showers of high energy secondary electrons. Charged particle beams, such as. proton beams of 70 MeV - 250 MeV, lose energy mainly through Coulomb interaction. High energy therapeutic heavy ion beams can also lose a substantial fraction of their energy through direct hadronic interactions. Both effects result indifferent biological effectiveness for therapeutic hadron beams compared to conventional photon beam therapy. The principal difference between photons and charged particles is that charged particles have in their depth dose curve a strongly peaked part (see Fig. 4. 1), called the Bragg peak. However, because this peak is a very narrow one, its usefulness in treatment is limited by the tumor size. Fig. 4. 1. Depth dose curves for photons, protons and carbons-ions: The broad Bragg peak of 135 MeV protons (green line) exhibits no exit dose. The narrow Bragg peak of 254 MeV/n and 300MeV/n carbons ions (red lines) - clearly show the distal dose tail caused by light beam fragmentation [old GSI materials]. 83 To improve the clinical utility of the Bragg peak, it is necessary to produce a spread-out Bragg peak (SOBP), which gives a uniform dose at a depth sufficient to cover the intended target volume thickness (tumor-thickness) Fig. 4. 2. Two different techniques have been developed to deliver an effective dose to the patient: passive and active systems. The principal components of a passive system, which is currently the most common modality for dose delivery, are scattering devices[42], a modulator wheel [117], collimators and apertures and compensator. This system delivers a beam simultaneously to the plane perpendicular to the direction of the beam at a given depth. In contrast, the active delivery system moves, or scans, the beam spots over the whole target. Two different approaches have also been implemented to move the beam spot in the active system: (a) scanning magnets, which locate the particle at any position in the transverse plane (at GSI) [118] and (b) a wobbler magnet, which laterally deflects the particles in directions parallel to the x-z plane (at PSI) ) [119]. In order to control the range of the particle in an active system, the energy of the beam is adjusted by the accelerator itself (usually a synchrotron is used). In a passive system (where a synchrotron or cyclotron can be used) the beam is slowed down by a slab of plastic material in the modulator wheel. Fig. 4. 2. Comparison of depth dose profiles of different radiation types. The depth-dose profiles of ions lead to a decreased integral dose. The enhanced RBE of Carbon ions in the Bragg-peak leads to a higher biologically effective dose within the tumor [17] ( Schleg 3D) 84 Although dose distribution with a single field looks highly conformal in Carbon ion therapy, treatment teams often use irradiation techniques that superimpose several fields on the same Planning Treatment Volume (PTV) of a tumor. This approach makes it easier to spare organs-at-risk (OAR), particularly when an OAR is situated directly behind the PTV, as it reduces the risk of over-ranges due to misalignment of the beam. Fig. 4. 3 shows the dependence of the entrance dose and the dose to healthy tissue in front of and behind the PTV on tumor depth. It is clear that using more than one entrance port will spare healthy tissue and skin. Fig. 4. 3. Carbon ion physical depth dose distributions in water for SOBPs of different sizes lying in different depths. Blue: 2.5cm SOBP in 5 cm depth, red: 2.5cm SOBP in 20 cm depth, green: 10 cm SOBP in 12.5 cm depth [17] (Schlegel 3D) Biological Properties Heavy charged particles also show some biological characteristics that differ significantly from those of photons or electrons [120]. Their relative biological efficiency (RBE), which is the ratio of a photon dose to a biologically isoeffective particle dose, rises with increasing linear energy transfer (LET). This means that a biologically equivalent dose has to be introduced in order to evaluate the effect of particle radiation on tissue. This enhancement in RBE results from the larger LET of particles in matter [120][121]. While LET for protons is low, it rises with increases in the atomic number of the incident particle. LET is 85 also higher in the Bragg peak than on the plateau of the depth dose profile. This makes high-LET radiation of interest for radiotherapy[122][123][124][38], because it makes it possible to increase the biologically effective dose in the tumor without raising the dose in surrounding tissue (see Fig. 4. 2) . The ratio of the RBE of the Bragg peak to the plateau is highest for carbon ions. Therefore, most ongoing studies in heavy charged particle irradiation focus on carbon ion therapy [125][126]. At present, the RBE of protons is modeled by a constant value of 1.1 over the entire Bragg peak, independent of the particle energy. This implies that the selectivity of protons is mainly physical. For heavier ions, however, more sophisticated models are needed. For carbon ions, such models result in a mean RBE of about 3 inside the target volume, and about 1 to 1.5 outside of it. This suggests that carbon ions possess enhanced biological selectivity. Their additional advantages include less scattering compared to protons, as well as a homogeneous cell response after irradiation. Within the Bragg peak, moreover, no relevant cell cycle dependence is observed for carbon ions. The dependence on tissue oxygenation is also less than for low-LET irradiation. Thus, this type of radiation is of particular interest in the treatment of hypoxic tumors that show a high radio-resistance to photon therapy. PET analysis as a control tool Heavy charged particle beams also present a unique possibility for "visualization" of the in- vivo delivered dose distribution. This is achieved by measuring the distribution of positron emitters produced in nuclear reactions between the incident particles and target nuclei during or shortly after irradiation. The comparison of measured and expected positron emitter distributions gives information about the distribution of received to patient dose. 4.1.2 CT in Carbon ion radiotherapy treatment planning The aim of treatment planning for heavy charged particles is to cover the PTV with the constant biologically equivalent dose of a spread-out Bragg peak (SOBP), using the treatment angle (or angles) and beam parameters that result in a minimum dose to healthy tissue and are thus most sparing of OAR. As the stopping powers within the patient’s body change, the ion range changes and the position of the Bragg peak is shifted. When we deliver a dose at a specified position in the presence of heterogeneity in the beam path, the energy of the beam has to be changed. To take heterogeneity into account in the treatment planning systems (TPS) at GSI and the HIT center at Heidelberg, the concept of Water-Equivalent-Path-Length (WEPL) was used. The WEPL of a material sample is defined as 86 the magnitude of the shift of the Bragg peak after the sample is located in front of the beam, when compared to reference measurements [127] (see Fig. 4. 4). Fig. 4. 4.WEPL approach for dose calculation in a treatment planning - (a) Schematic experimental set up for WEPL measurements. (b) Depth dose curves obtained by using different absorbers. The shift in the location of the Bragg Peak corresponds to the WEPL value [127] Replacing heterogeneous slabs with their equivalent water depths preserves the information on particle range while facilitating the calculation of beam energy. The ratio of WEPL to the thickness of a slab (T) is called its relative range. With small slabs, where stopping power (S) is nearly constant, the relative range is proportional to the stopping power ratio of the medium, compared to the stopping power of water. Hence, relative range is proportional to the electron density of the medium, relative to the electron density of water (according to the first approximation). Relative range measurements performed in muscle substitute [127] show that the relative range is independent of the energy of the incident Carbon ions for energies greater than 50 MeV/u . As this information makes clear, the transport of ions in tissue, and thus their range of therapeutic effectiveness, depends on the electron density of the tissue, which can only be calculated from high- quality CT images. The empirical calibration relation between CT-numbers and ion range is used for treatment planning in heavy ion radiotherapy (see Fig. 4. 5) [127]. This is estimated as a piecewise linear 87 relation between measured CT-numbers and the range of ions in tissues and tissue-like plastic materials. Any variation in measured CT-numbers will cause a drift in the calibration curve of the CT scanner, and these relations will vary for each machine and measurement condition [128][129] . It is estimated [127] that an uncertainty of 2-3% in CT-numbers will result in a 3mm inaccuracy in the absolute range of C-ions at a depth of 10 cm. To ensure a higher accuracy of 1% in the 3D dose plan, it is estimated that the uncertainty of the CT-number should not exceed 10 Hounsfield Units (HU) in the soft tissue region. Fig. 4. 5. WEPL approach for dose calculation in a treatment planning - Example of a HU-to-WEPL calibration [127]. The value of CT-numbers depends on the following parameters: Characteristics of the scanned object (e.g., dimensions, geometry, inhomogeneity, position in the CT gantry and patient movement), Characteristics of the CT-machine (e.g., filtration, dimensions, and collimation), Energy of the X-ray tube in the CT machine, and Reconstruction algorithms. The value of measured CT-numbers is also affected by the presence of image artifacts, which may result, for example, from beam hardening or strong absorption in metals. Some of these factors, such as X-ray tube energy, beam hardening, field of view and reconstruction algorithm, can cause a systematic deviation that can be measured and corrected. 88 4.1.3 Image representation in CT-numbers (Hounsfield Units) In X-ray Computed Tomography (CT), an X-ray source and an arc of detectors rotate around the patient’s body. The patient receives X-ray projections from different directions, which are measured and translated into cross-sectional images using reconstruction algorithms [130]. The resulting CT-images are used as a quantitative measure of tissue properties for radiotherapy treatment planning. A CT image is essentially a distribution of X-ray attenuation coefficients (relative to water) in the scanned object. The image can be represented on a grey scale. The grey values or CT-numbers are the attenuation coefficients of the object relative to the attenuation coefficients of water. m w (0.1) CTnumber 1000 HU w Here, m is the linear attenuation coefficient of material, and w is the linear attenuation coefficient for water. By definition, the CT-number of water equals zero. Since the attenuation coefficient of air is nearly zero, the CT number of air for any measurement condition is -1000. Although there is no limit on the higher end of the CT-number scale, most manufacturers set the scale for a 12-bit representation of the CT-number between -1024 and +3071 HU. CT-numbers that are larger than this maximum, as is the case with metals, are set at the maximum value. Values of CT-numbers can be used to identify different tissues and bone types (see Fig. 4. 6) 89 Fig. 4. 6. Scale of CT-number and the corresponding tissue types. The left, a sample CT image of the abdomen [17] Due to the dependence of CT numbers on the X-ray spectrum, the value of CT-numbers is affected by the size and material of the phantom used for the CT measurements, the kilovolt setting of the X-ray tube [131][132][133], the field of view (FOV), the elemental composition of the scanned media [131] and its temperature[134], as mentioned above. Simulations of CT scanners, several of which have been published, are all driven by the need to maximize image quality and minimize radiation dose to the patients. Simulations are based on approaches that calculate the energy spectrum of a CT, including empirical models and Monte Carlo simulations. The accuracy of various simulation approaches has been studied by Bhat et al.[135], Caon et al.[136] and later by Ay et al. [137][138]. The effect of beam shaping filters is an important aspect of all of these simulations and several methods have been used to calculate it. Atherton and Huda [139] developed a look-up table containing information on the angle of incidence and the amount of material in the beam path, an approach seen more recently in the work of Jarry et al.[140]. In the latter work, the information was translated into weighted factors, as opposed to a look-up table of linear attenuation coefficients. Full Monte Carlo simulations of filter geometry were carried out in other work [141], [142]. The work presented here represents the first time that simulations were performed to establish an approach to calculate the accuracy of CT-numbers directly. 90 4.2 Research objective The objective of the work was to investigate and quantify the effects of CT scanner parameters on measured values of CT-numbers and on the CT-number-to-range conversion relation, that is used in treatment planning . The project included following steps: 1) Develop an approach to calculate CT-numbers by performing Monte Carlo simulations of a CT scanner and phantom with substitutes, 2) Reconstruct the simulated projections into images represented in Hounsfield units, 3) Assess the accuracy of the simulation approach and the effect of different approximations, 4) Validate this approach by comparing the calculated CT-numbers with experimental measurements, and 5) Apply this approach to predict how different parameters directly affect the uncertainty of CT- numbers, and indirectly affect the empirical relation between the measured CT numbers and the carbon ion range used in treatment planning. 4.3 Materials studied: CT scanner, substitutes and phantoms 4.3.1 Investigated CT scanner The Siemens Emotion CT unit was simulated based on design data provided by Siemens Medical Solutions (see Fig. 4. 7). This scanner is equipped with a DURA 352-MV X-ray tube, two beam shaping filters (a bow-tie filter made from Al and a Teflon filter). The detector-arc is made out of 672 elements and is equipped with an anti-scatter grid. The material of the detector elements is Gadolinium Oxysulfide (Gd2O2S), for which the energy response function has been published in the work of Heismann et al[143]. The X-ray tube of the CT-scanner has three nominal voltages: 80, 110 and 130 kV. However, the air calibration of this particular scanner is maintained by changing the voltage settings of the X-ray tube. The voltage can vary by up to ±10 kV. 4.3.2 Investigated substitutes and phantoms Electron density substitutes, manufactured by Gammex-RMI (Middletown, WI, USA), were chosen as tissue equivalent substitute materials (see Fig.4. 8). Another group of substitutes (H- 91 materials) has been experimentally investigated by Jäkel et al[127] [127]. H-materials are based on polyethylene, and simulate actual tissue in terms of photon absorption, although their elemental composition includes high percentages of silicon and tin. CT-numbers of Gammex substitutes were measured using the Siemens Emotion CT-scanner. The measurements were performed using the nominal tube voltages 80, 110 and 130 kV, 200 mAs tube current, 3 mm slice thickness, H40s reconstruction filter and 287 mm diameter FOV. Measurements were carried out as described in [144][145] . The reported CT-measurements for the H- materials were done by Jäkel et. al. in [127]. A cylindrical phantom (16 cm diameter) of PMMA was simulated. Gammex substitutes and H-materials were simulated as phantom inserts (2.8 cm diameter). Their parameters were chosen based on the phantoms used for measurements. Air and water were simulated as reference media in order to present the simulated results in terms of Hounsfield Units. The elemental composition of all simulated materials is presented in Table 4.1. Fig. 4. 7. Emotion CT scanner with 16 cm diameter Fig.4. 8.Cylindrical PMMA phantom with cylindrical phantom from PMMA positioned for CT- Gammex tissue equivalent substitutes. value measurements. 92 4.4 MC simulation CT-numbers for a CT scanner and different phantom inserts 4.4.1 Simulation work flow As mentioned above, the CT unit modeled in this work was based on the design of the SIEMENS Somatom Emotion CT-scanner. Data on product specifications is protected by a non- disclosure agreement between Siemens Medical Solutions and the Medical Physics department of the German cancer research center (DKFZ). The Monte Carlo code BEAMnrc/EGSnrc was used to model the CT scanner and a phantom with different inserts. The EGSnrc MC code [49] was chosen, as it has the most advanced interaction library for physics modeling of electron, positron and photon interactions in low energy applications (1-150 keV) [146][147][148][149]. The Monte Carlo (MC) simulation investigates the propagation of X-ray photons from the X-ray tube to the detectors, taking into calculation all media in their path. CT- images are then calculated from the simulation results. A schematic diagram of the simulated system is shown in Fig. 4. 9 . Measurement using a 16 cm phantom of PMMA in the center of FOV was simulated. Fig. 4. 9 . Scheme of CT scanner and phantom simulation. 93 4.4.2 Optimization of parameters used in MC code. A. General settings of MC parameters Throughout the simulation, the photon cut-off energy (PCUT) and the electron cut-off energy (ECUT) were 0.001MeV and 0.516 MeV, respectively. These values ensured accurate electron transport of photons and secondary electrons throughout the simulation. A regional ECUT of 0.521 MeV was used in the simulation of collimators, which reduced calculation time by 18%. In a simulation performed using a monoenergetic photon source with an energy of 70 keV, it was found that the deactivation of Rayleigh scattering in the MC simulation will decrease the value of counts in the spectral distribution by up to 3 % of the total signal. Similarly, introducing bound Compton scattering and an electron relaxation effect will affect the spectrum of simulated photons by 2% and 1% respectively. Therefore, the simulation was performed while the following physical processes were activated: bound Compton scattering, Rayleigh scattering, atomic relaxation and relativistic spin effects. The ESTEPE was set to 0.25. B. Cross-Section data The cross-section database was created by the code PEGS4. The parameters AP and AE are the low-energy thresholds for the production of secondary bremsstrahlung photons and knock–on electrons, respectively. AP and AE should be defined lower than any used ECUT or PCUT values. Hence, an AE of 0.516 MeV and AP of 0.001 MeV were used to calculate the cross- sections that define the interactions of X-ray and secondary electrons with the different simulated media. The cross-section data was also based on the elemental composition of the materials. 4.4.3 Simulation set up Each hardware component was simulated as a separate unit (compound module) to allow for studying the effect of individual modules on the CT-image. The efficiency of X-ray generation by electrons is very low (0.5%). Therefore, it would have been inefficient to simulate the CT from the tube to the detectors in one run. Instead, the X-ray tube was approximated by a collimated point source with the pre-calculated photon spectra. The source was defined at a distance of 3.4 cm from the 94 simulated components. Photon spectra with maximum energies of 80, 110 and 130 keV (manufacturers’ specification) were used as input data to the point source. The spectral distributions of the three different X-ray tube voltages were calculated using the standard X-ray tube compound module of the simulation code and the manufacturer’s parameters. The influence of different parameters of the X-ray tube on X-ray spectra has been discussed by Romanchikova [150]. Simulation of the CT hardware and phantom was divided into 2 parts, CT1 and CT2. Each part of the simulation terminated with a so-called scoring plane. A phase space file (PHSP) was calculated at each scoring plane. The simulated particles are referred to as events. Each PHSP contains data relating to energy, position, direction, charge, etc., for every event crossing a scoring plane. The source, filters and collimator were simulated in CT1, the first part of the calculations. The modeled CT scanner has an aluminum bow-tie filter, followed by a Teflon filter. The collimator aperture was chosen to provide a field size of 50 cm by 1 cm in the center of the CT. The resulting PHSP is identified as PHSP1 in the CT1 part of work.. A phantom with different substitutes was simulated in CT2, the second part of the calculations. PHSP1 was used as input toCT2. The PHSP that resulted from CT2 is identified here as PHSP2. In this phase, various phantoms with different inserts were modeled. A cylindrical phantom from PMMA was simulated using the side-tube compound module. It was designed in three layers, which represent the inserts (2.8 cm diameter), the phantom (16 cm diameter) and the air in the FOV (50 cm diameter), respectively Fig. 4. 9 displays a schematic graph showing the location of the scoring planes and the simulated hardware for each part of the simulation. The number of incident particles was 109 and 5 x108 photons in CT1 and CT2, respectively. To analyze the PHSP data, the BEAMDP program was used to derive photon spectral distributions and energy fluence as a function of the position in the different scoring planes on PHSP1 and PHSP2. 4.4.4 Reconstructing CT-images from PHSP Obtaining CT–images from Monte Carlo simulation results requires representation of the output of the simulation in projection-data (signal per detector element). PHSP2 is the output of the simulation at the last scoring plane, which represents the detectors. The signal of each detector was calculated based on the energy and position of each photon in PHSP2 and the design parameters of the detector-arc. In a real CT machine the detectors are arrayed in an arc that is focused on the source. In 95 the simulation, the detectors were considered to be equi-angularly spaced with an angle of 27° between central and edge detectors. As noted above, the detectors were made of gadolinium oxysulfide, and their energy response function was calculated previously by Heismann et al [143]. As the energy of each photon is given in the PHSP file, each photon was assigned an efficiency-weight, which was estimated from the energy response function of the detectors [143]. Then, the photons were re-sampled into detector elements using the information on their position in the scoring plane. Re-sampling also required knowing the number of detectors in the array, the length of each detector’s active area and the dark areas between adjacent detectors. Finally, the signal was calculated for each detector as the sum of efficiency- weighted photons. Each CT-image was reconstructed from the detector signals using an algorithm that is equivalent to manufacturers’ specifications [151]. The reconstruction algorithm was developed by the Image Reconstruction group of the medical physics department of the Institute of Medical Physics in Friedrich-Alexander-University, Erlangen-Nürnberg, Germany. The code was used with permission of developers for our specific calculations. Fig. 4. 10 schematically summarizes the different steps used to calculate CT-numbers starting from a point source with given photon spectra. Fig. 4. 10. Scheme of the calculation of CT-numbers: from X-ray tube spectrum to CT-numbers (HU) that are extracted from the CT-image 4.4.5 CT-numbers of the various substitute materials The X-ray tube spectra corresponding to the voltage settings 80, 100, 120 keV (Fig. 4. 11) were used for the calculation of CT-numbers. 96 Fig. 4. 11. Photon spectra of X-ray tube for different tube voltage. The mean energy of the incident photons after the filters and collimators in CT1 for the X-ray tube voltage 100, 110 and 120 kV is shown in Fig. 4. 12. Fig. 4. 12. Mean energy of the incident photons as a function of the distance from the center of the FOV after filters and collimator. The peak voltage of the incident photons is shown in the legend. In Table 4.2 ( see Chapter 4.4, end) the measured and simulated CT-numbers are reported for the Gammex substitutes (lines1-8), H-materials (lines 9-14) and PMMA (line15). Measurements done previously by Jäkel et. al.[127] indicate that H-materials behave differently from Gammex substitutes, which closely imitate soft tissues. Fig. 4. 13 shows the simulated CT-numbers as a function of the electron-density for Gammex substitutes, H-materials and PMMA. The results of simulation successfully predicted the behavior of H-substitutes compared to Gammex substitutes. 97 Fig. 4. 13. The simulated CT-numbers as a function of the electron-density for Gammex substitutes, H-materials and PMMA. The simulations of CT-numbers were calculated using five independent projections for the 80 and 120 kV settings. However, only one projection was used for the 100 kV simulations. Using one independent projection instead of five resulted in a higher uncertainty in the simulated CT-numbers for the 100kV voltage settings. 4.4.6 Accuracy of the simulated CT-numbers Two distinct factors affect the accuracy of the simulation: uncertainties in the calculated CT-numbers and the deviation between calculated and measured CT-numbers. The number of events used as source in the CT1 phase of the simulation strongly affected the uncertainties of the results in PHSP2, which increased with the number of times PHSP1 was recycled. The PHSP also recycled if the number of requested events was less than the statistics available in PHSP. This statistical uncertainty was reduced by 50% when the number of initial particles from the source was increased from 108 to 109 photons in CT1. 4.4.6.1 Uncertainty of the calculated CT-numbers The photons in CT2-PHSP are dependent on the distribution of photons in CT1-PHSP. Using different random number seeds for the simulations of the CT2 part cannot completely eliminate this dependency. The statistical effect of the number of independent views on the reconstructed image was 98 investigated for a PMMA phantom with a Gammex cortical bone substitute as insert. As an example, recon Fig. 4. 14A and B show reconstructed attenuation coefficients ( m ) along a line through the center of the image. In Fig. 4. 14A, was calculated with a single independent view compared to five views in Fig. 4. 14.B. Despite the fact that the number of incident photons per view is the same, more fluctuations are seen in profile in A. The reconstructed CT images are shown in Fig. 4. 14 C and Fig. 4. 14 D. Ring artifacts are visible in the image, which was reconstructed using only one independent projection (C). However, the rings disappear when the image is reconstructed from five independent projections (D). A B C D Fig. 4. 14. The effect of number of independent projections on a profile in the center of a calculated CT-image (A and B) and the reconstructed images (C and D) is presented. The reconstructed CT image (512x512 pixels) represents a 16 cm PMMA phantom with cortical bone substitute as an insert. 99 4.4.6.2 Deviation between measured and simulated CT-numbers The deviation of the simulated CT-numbers from the measured value was always within the uncertainty of the simulation. Fig. 4. 15 shows simulated CT-numbers as a function of measured CT- numbers for Gammex substitutes, H-materials and PMMA. A histogram of the deviation between calculated CT-numbers and measured values is shown in Fig. 4. 16. The simulation results are randomly distributed around the measured values. The distribution can be described by the Gaussian function (G) such that: x x2 G(x) A exp . (0.2) 2 2 Here, x is the difference between measured and calculated CT-numbers; the average deviation ( x ) is 4±4 HU. The standard deviation ( ) is 49±4 HU and A is 12±1. Fig. 4. 15.Comparison of calculated and measured results of CT-numbers for Gammex, H-materials and PMMA for the 120kV voltage setting. Fig. 4. 16. Distribution of the simulated CT-numbers around measured values. The graph shows the histograms of the data points as a function of the difference between the simulated and measured CT- 100 numbers. The histogram of all the data points and the Gaussian fit (G(x) in equation (0.2) are shown. Table 4. 1.Composition of materials used CT-simulation (phantom & inserts) [127] [152][153] MATERIAL %H %C %N %O %Mg %Si %P %Cl %Ca %Ti %Sn %Ar Density Physical Physical Electron to Water Relative Density Gammex substitutes Lung (LN300) 0.30 0.29 8.46 59.38 1.96 18.14 11.19 0.78 0.10 Lung (LN450) 0.45 0.44 8.47 59.57 1.97 18.11 11.21 0.58 0.10 Adipose fat 0.92 0.90 9.06 72.30 2.25 16.27 0.13 Muszle 1.05 1.02 8.10 67.17 2.42 19.85 0.14 2.32 Brain 1.05 1.05 10.83 72.54 1.69 14.86 0.08 CB230 1.34 1.29 6.68 53.48 2.12 25.61 0.11 12.01 CB250 1.56 1.47 4.77 41.63 1.52 32.00 0.08 20.02 Cortical bone 1.82 1.69 3.41 31.41 1.84 36.50 0.04 26.81 Inner Bone 1.13 1.09 6.67 55.64 1.96 23.52 3.23 0.11 8.86 H-materials H-800 0.23 0.22 7.96 64.21 16.29 11.48 0.06 H-500 0.47 0.46 8.04 45.93 19.41 26.48 0.14 H+200 1.04 1.01 7.70 31.50 22.99 35.66 1.96 0.19 H+400 1.12 1.07 6.35 28.07 27.38 29.40 8.64 0.16 H+900 1.43 1.33 3.72 21.41 35.93 17.21 21.64 0.09 H+1200 1.65 1.52 2.40 18.07 40.21 11.10 28.16 0.06 Phantom materials Air 10-3 0.00 0.01 75.27 23.17 1.28 Water 1.00 1.00 11.19 88.81 PMMA 1.18 1.15 8.05 59.98 31.96 RW3 1.05 1.01 7.59 90.41 0.80 1.20 101 Table 4. 2. Simulated and measured CT-numbers for Gammex susbstitutes, H-materials and PMMA. Measured CT-numbers Simulated CT-numbers 80 kV 110 kV 130 kV e-density (79.3) (101.9) (121.7) 80 kV 100 kV 120 kV 1 Lung (LN450) 0.438 -578±20 -577±23 -583±20 -549±102 -541±193 -532±87 2 Adipose fat (AP6) 0.902 -137±4 -121±4 -114±4 -143±106 -140±220 -116±115 3 Brain(SR2) 1.045 -17±4 1±5 7±4 -2±150 -46±235 -10±115 4 Muscle(RMI452) 1.021 40±5 35±5 31±5 44±91 10±188 35±103 5 Inner bone(IB) 1.093 391±9 311±7 274±6 277±113 220±189 200±115 6 CB2 30% (CB230) 1.286 723±16 600±13 546±11 681±134 556±256 548±135 7 CB2 50% (CB250) 1.470 1332±28 1088±24 987±22 1253±97 1042±428 1006±145 8 Cortical bone(SB3) 1.692 1999±41 1616±36 1459±36 1862±196 1575±360 1462±166 9 Hm800 0.223 -- -- -798±11 -- -- -729±75 10 Hm500 0.456 -- -- -485±10 -- -- -436±83 11 H200 1.006 -- -- 227±10 -- -- 289±176 12 H400 1.070 -- -- 420±15 -- -- 461±187 13 H900 1.334 -- -- 962±35 -- -- 1013±189 14 H1200 1.520 -- -- 1250±65 -- -- 1407±137 15 PMMA 1.146 -- -- 138±7 -- -- 147±182 4.5 Effect of X-ray voltage, phantom size and material on CT-numbers 4.5.1 Effect of filters on energy spectrum and fluence Photon spectra resulting from the simulation of the three X-ray tube voltages (80, 110 and 130 kV) were used as input [150]. The effect of filters was investigated in terms of photon spectral distribution at the center and the edge of FOV. The spectral distribution resulting from transporting X-rays through the two filters with the three input spectra (80, 110 and 130 kV) is shown in Fig. 4. 17(a) at the central axis and in Fig. 4. 17(b) at the edges of FOV. 102 Fig. 4. 17. Photon spectral distribution after transport through CT filters and collimator, calculated with the 3 different spectra of X-ray tube in the centre of FOV (a) and at the edge of FOV (b). The effect of filters on the spectral distribution was also investigated by simulating each filtes individually, and then simulating both simultaneously. To aid in interpreting the results, a simulation using no filters (X-ray travel through air) was also performed. The spectral distribution resulting from these different simulated filter arrangements was carried out using 109 photons with an incident energy of 110kV. The resulting figures show a different spectral distribution that depends on the length and composition of the transverse material. For simplification, only the results at the center of FOV and at the edge of FOV are presented in Fig. 4. 18(a) and Fig. 4. 18(b), respectively. Fig. 4. 19 presents energy fluence vs. position, calculated for different filters arrangements and 110 keV X-ray tube voltages. Fig. 4. 18. Photon spectral distribution after transport through CT different filters. The spectral distribution was calculated using 110 keV X-ray spectrum as calculated from the X-ray tube simulation. The image shows the Photon spectral distribution for different filters in the center of FOV (a) and at the edge of FOV (b). 103 Fig. 4. 19. Energy fluence vs position due to different filters. The results were calculated using the spectrum simulating 110 keV X-ray tube voltage. 4.5.2 Effect of voltage settings on energy spectrum , fluence and CT-numbers The spectral distribution for cortical bone insert and for different voltages of incident photons ( 80, 110, 130 keV) is presented in Fig. 4. 20. Energy fluence as a function of position was calculated after the cylindrical phantom with the cortical bone insert for the three incident photon energies (Fig. 4. 22). To study the effect of voltage settings of X-ray tube on CT-numbers , CT1_PHSP files were calculated using seven peak energies (80 kV, 100 kV, 105 kV, 110 kV, 115 kV, 120 kV, 130kV) Fig. 4. 20. Comparison of spectral distribution after transport of X-rays through Cortical bone insert for different X-ray spectra ( 80, 110, 130 keV). 104 Only bone-like materials are significantly affected by the change of voltage (see Fig. 4. 21). The change in CT-number of the cortical bone substitute is -9.6 HU/kV. The figure also shows the change of simulated CT numbers with voltage as a function of the electron density of the different substitutes. Fig. 4. 21. Change of simulated and measured CT-numbers per kV as a function of the electron density of the Gammex substitutes. Based on these calculations, we observed that the CT-numbers of bone-like substitutes increase with decreasing energy of the spectrum. This sensitivity of CT-numbers based on voltage setting is visible also in Fig. 4. 21. This occurs because the possibility of photoelectric interactions is proportional to (Z/E)3. For bone tissues, Z =13.8. It is 7.5 for other tissue and 7.4 for water [154]. CT-numbers are attenuation coefficients relative to water; therefore, only bone like tissues show significant variations in CT-number with different voltages. The simulation correctly predicted these results. 4.5.3 Effect of substitute material on energy spectrum , fluence and CT-numbers From the resulting PHSP2, spectral distributions reflecting the transport of X-rays through the phantom and inserts were calculated. Energy fluence as a function of position was calculated for the cylindrical phantom with the different inserts Fig. 4. 22. 105 Fig. 4. 22. Comparison of energy fluence vs position after transport through phantom with Cortical bone insert. The X-ray spectra simulating the X-ray tube voltage ( 80, 110, 130 keV) are used. To study the effect of phantom inserts, the phantom was assumed to be made of PMMA with a 16 cm diameter. The simulated CT-numbers of Gammex substitutes, H-materials and PMMA are shown as a function of the electron density in Fig. 4. 23. From the measurements of the CT-numbers as a function of the electron density of the substitutes, we observed that the CT-number of bone-like H-materials is about 500 HU higher than expected from the Gammex substitutes [127]. The deviation between the measured and simulated CT-numbers is 4±4 with a standard deviation of 49±4. Thus, our simulation successfully predicted the behaviour of H-substitutes compared to Gammex substitutes [155], which suggests that the simulation can be used to select suitable substitute materials based on their composition. The composition of the H-materials can also explain different behavior observed in the CT- imaging. In addition to H, C, N O and Ca, the H-materials also contain significant amounts of Si (10- 30%) and Sn (0.06-0.19%). The density of Si is 2.33 g/cm3; the density of Sn is 7.31 g/cm3. These are higher than the densities of any other element used in Gammex substitutes. Therefore, the presence of Si and Sn can be expected to cause more photoelectric interactions and larger attenuation of the X-ray photons than in Gammex substitutes. 4.5.4 Effect of phantom size on CT-numbers A PMMA phantom with a variable diameter (from 12 to 32 cm in steps of 4 cm) was used to study the effect of phantom size on CT-numbers of substitutes inside the phantom. 106 We observed that CT-numbers increase with increasing phantom diameter. The effect also increases with the electron density of the substitute, which is -12 HU/cm for the cortical bone substitute but only -2 HU/cm for the inner bone substitute. Fig. 4. 23 shows the change of CT-numbers as a function of electron density of substitute material. Fig. 4. 23. Change of simulated CT-numbers per phantom diameter as a function of the electron density of the substitutes. Phantom size in fact affects the CT-numbers of all substitutes. Beam hardening increases with the increasing diameter of the PMMA phantom. Therefore, CT-numbers decrease with the increasing phantom diameter. The beam hardening correction applied in the scope of this work treats all materials like water. It should, however, also detect the effect of different sizes of the PMMA phantom. 4.5.5 Effect of phantom material on CT-numbers To investigate the effect of phantom material on CT-numbers of phantom inserts, we used: air, water, muscle substitute and cortical bone substitute from Gammex, and RW3 water equivalent material from PTW and PMMA . We observed that the CT-numbers of Gammex substitutes decreased with the increasing electron density of the phantom materials. Lung substitutes were also affected by the extreme electron density of the air and cortical bone phantoms. In another test, the phantoms were simulated with water as an insert, and the effect of phantom material on the CT number of water was calculated. From the results, it was clear that value calculated by assuming a cortical bone phantom is unrealistic compared to the other data points. 107 Change in simulated CT-numbers was calculated twice, once when results of cortical bone phantom was taken into account and another when it was discarded. The resulting change per electron density of the phantom materials is shown as a function of the electron density of the substitutes in Fig. 4. 24 Fig. 4. 24. Change of simulated CT-numbers per electron density of the phantom materials is shown as a function of the electron density of the substitutes. The points represent the calculated change when the results of the cortical bone phantom are discarded. CT-numbers decrease as the density of the phantom material increases. Again, the effect appears due to increased beam hardening. Compared to water, muscle (e-density is 1.02), RW3 (e-density is 1.01) and PMMA ( e-density is 1.15) only small deviations in CT-numbers were found, which suggests that. these phantom materials could be used as water equivalent phantoms. Maximum deviation was recorded when air (e-density is 0) and cortical bone (e-density is 1.69) were simulated as phantom materials. Since the purpose of the CT phantom is to resemble attenuation in patients, it would not be useful to use cortical bone or air as a phantom material. However, in the work of Schaffner and Pedroni, measurements of substitutes in air were used to estimate the effect of beam hardening on CT-numbers [133]. Schaffner and Pedroni also reported that if the HB/SR4 bone substitute is scanned free in air, the CT numbers are 4% higher than when a 15 cm phantom is used. In a standard Hounsfield scale, the CT number of the HB/SR4 substitute increases by about 70 HU from the value measured by Schneider 108 et al. (783 HU) [156]. The deviation in CT-number due to scanning of the substitute in a 15 cm diameter phantom or in air is indeed about 9% in the standard Hounsfield scale. The corresponding change in CT-number of CB250, which is comparable to the HB/SR4 substitute, is 9.6% from the simulation. Therefore, our simulation results are accurate for bone substitutes in air. Beam hardening corrections (BHC) were applied to all simulations of phantom materials. However, the applied correction is strictly valid only for a water-like medium. Therefore, CT-numbers measured in cortical bone phantom are expected to be under corrected and lower than expected. The simulated CT-numbers of water confirm that the simulation results obtained with the cortical bone phantom are inaccurate. Another problem is the large uncertainties in the simulated CT- numbers (between 400 and 1000 HU). The main reason is the insufficient number of incident photons, as most of the photons were absorbed within the phantom. When a cortical bone phantom is simulated, the number of photons registered in the detector elements is 18 times less than number registered when a water phantom is simulated. 4.6 Effect of X-ray voltage, phantom size and material on range calculation 4.6.1 CT calibration relation for ion therapy Empirical calibrations were used to study the effects of simulated CT-numbers on Carbon range calculations. We build an empirical calibration relation, by performing a piecewise linear fit representing the relative range as a function of CT-numbers and using the Sigma Plot 8.0 fit-package. The relative range data were measured values . The CT-numbers were simulated values. We calculated a total of six calibration relations. The simulations for the standard phantom settings (number 1 in Table 3) were set as the base of the comparison. Calibrations were based on CT- simulations of 110 ±10 kV voltage of the X-ray tube, H-materials as substitutes, phantom diameter of 30 cm and air as phantom material (i.e. no phantom). The parameters defining the calibrations are listed in Table 4.3, and calibrations 1-6 can be written as: mk HU bk 1000 HU 0 Cal k 1 k k m2 HU b HU 0 k k k The values m1 , m2 and b are given in Table 4.3. 109 The change in the simulated CT-numbers of the standard simulation (110kV with 16 cm PMMA phantom) was calculated by interpolation of the simulated data. For example, the effect of voltage change was calculated by interpolating simulations at 80, 100, 105, 110, 115, 120 and 130 kV. Change in CT-number resulting different phantom size was calculated by interpolating 12-32 cm diameter phantoms of PMMA. From the simulation of different phantom materials, the results of the simulations of substitutes in air were then used to build a calibration relation. The CT-numbers of the H-materials were also used to build a calibration relation. Table 4.3. List of parameters defining calibrations which were calculated based on simulated CT-numbers Phantom Phantom Calibration kV Inserts number diameter(cm) material 1 16 PMMA 110 Gammex substitutes 2 16 PMMA 100 Gammex substitutes 3 16 PMMA 120 Gammex substitutes 4 16 PMMA 120 H-materials 5 30 PMMA 110 Gammex substitutes 6 16 Air 110 Gammex substitutes 4.6.2 Effect of CT calibration on range calculation To study the effect of these calibrations on the relative range of Carbon ions in tissue, we used CT data from an actual patient with chondrosarcoma at the base of the skull. Fig. 4. 25 is a delineated CT-slice showing the clinical target volume (CTV) in red and the surrounding critical organs. 110 Fig. 4. 25. Transverse slice of the CT-data of selected patient. The tumour (CTV) is marked in red; the organs at risk are the brain stem which is marked in blue, the left optical nerve which is marked in green, the chiasm (not shown in this slice), the eyeballs and the other optical nerve. We calculated the CT-numbers along the central line through the CT-image. The line through the CT- image was defined by the pixel coordinates of y = 131. The profile is shown in Fig. 4. 26. The tumour is between pixels 110 and 160. Fig. 4. 26. Profile through a central CT slice of a head of a patient with skull base tumor. The arrows indicate the position of skull bone. In between is a mixture of soft tissue and spongy bone (lower skull base). The patient was treated using two opposing fields. The water equivalent path length of each pixel was calculated to be the relative range of the pixel times the length of the pixel (1.12 mm). The relative range was calculated from empirical calibration relations, which are based on simulated CT-numbers. The accumulated WEPL was calculated by adding up the contributions from each pixel in the beam path. 111 The energy and intensity of the beam spots were optimized for SOBP, based on the standard calibration. Assuming a single field irradiation from the left, the distal edge of the SOBP is set at pixel 110 for the optimized field. The shift in the position of the distal end ( WEPL ) is then calculated as the difference between the position of the distal edge calculated using a given calibration and the position calculated using the standard calibration. k k k The values m1 , m2 and b are given in Table 4. The resulting calibrations and measured data points for Gammex and tissue samples are shown in Fig. 4. 27. We calculated the accumulated WEPL along the beam path by adding up the WEPL from the pixels in the beam path. The shift in the position of the distal edge of a SOBP of a single field ( WEPL ) is shown in Table 4.4. Table 4.4. Fit parameters for the calibration relations 1-6 and the difference in position of the distal end of the SOBP due to using the different calibration curves From left From right k Cal k WEPL (mm) WEPL (mm) 1 cal 1 (standard) 1.07E-03 3.67E-04 1.04E+00 0.0 0.0 2 cal 2 (100 kV) 1.07E-03 3.46E-04 1.04E+00 -0.2 -0.4 3 cal 3 (120 kV) 1.07E-03 3.90E-04 1.04E+00 0.2 0.4 4 cal 4 (H-materials) 7.88E-04 4.68E-04 8.64E-01 -13.8 -15.2 5 cal 5 (30 cm phantom) 1.22E-03 4.16E-04 1.02E+00 -1.5 -1.3 6 cal 6 (air) 1.03E-03 3.17E-04 1.06E+00 2.4 2.2 112 Fig. 4. 27. Calibration curves derived from simulated CT-numbers of Gammex substitutes for different voltage settings in comparison to measurements in Gammex substitutes and animal tissues. The calibration relation based on measurements in H-materials and the actual measured values are also shown for comparison. The calibrations are parameterized in Table 4.4. Calibrations 3 and 6 caused the SOBP to stop before the assigned target margin, while in calibrations 2, 4, and 5, the SOBP overshot the target volume. The deviation between the calculated WEPL of both fields appears to be a result of the different distribution of CT-numbers on both sides of the patient’s head and the different number of pixels traversed by the beams. 4.6.3 Effect of CT scanner and phantom parameters on range calculation in C-ion therapy The uncertainty in patient positioning is about 1-2 mm [157]. The resolution of the voxels in the CT image is estimated as half the diagonal of the voxel. The length of the side of the square voxels in CT-images is about 1 mm; the slice thickness is 3 mm. The resolution of the voxel is 1.7 mm [158]. WEPL is considered critical if it exceeds 2 mm. 113 4.6.3.1. Effect of voltage settings of the X-ray tube on range calculation In patient treatment planning, the effect was stronger when the beam was applied from the right, as there are more bone structures in the beam path from that direction (see Fig. 4. 26). However, the total WEPL is only 0.4 mm. This suggests that the Siemens Emotion CT scanner can be used for radiotherapy treatment planning despite the fact that the air-water calibration is maintained by changing the voltage of the X-ray tube without notifying the user. However, it should be emphasized that each of the nominal voltage settings of the Emotion scanner should be represented by a separate calibration relation when it is used for radiotherapy. Calibrations affecting bone are likely to cause negligible effects in range calculations because bone represents less than 20 % of the human body. Furthermore, there are different types of bone, distributed between 200 - 1800 HU. 4.6.3.2 Effect of substitute materials on range calculation Calibration 4, which is based on measurements in H-materials, caused the highest WEPL . It underestimated the relative range for the entire scale of HU. WEPL of -14.5 mm is not surprising, however, and it confirms that H-materials are not suitable substitutes for CT-calibrations for heavy ion therapy. 4.6.3.3 Effect of phantom size on range calculation The diameter of the measurement phantom is 16 cm. It was designed specifically to simulate attenuation in the head of the patients, since more than 90% of the patients treated with Carbon ion radiotherapy at GSI were treated for head and neck tumors. Commercially available calibration phantoms are usually larger than this. For example, the diameter of the Gammex-RMI phantoms for CT-calibration is 33 cm [152]. Effect of phantom size on CT-calibration was discussed in earlier studies [132][133][160][161]. The results we simulated were consistent with previous findings for bone substitutes. For example, Schaffner and Pedroni used phantoms with diameters of 15 and 30 cm to measure CT-numbers [133]. They measured a 5% deviation of CT-numbers of a bone substitute (HB/SR4) due to the different phantom sizes .However, their values were reported in scaled HU, i.e .the CT-number plus 1000 HU. In the standard Hounsfield scale, the change in CT-number due to 15 cm difference in the diameter of the phantom is -5.9 HU/cm. In this work, the CB250 Gammex 114 substitute (e-density is 1.47) is comparable to the HB/SR4 substitute (e-density is 1.39) . The respective change in the CT-number of CB250 is simulated as –5.6 HU/cm. This suggests that our simulation results are accurate for bone substitutes. Minohara et al.[160] and Schaffner and Pedroni [133] measured the change of CT-numbers in bone and soft tissue substitutes. The effect of phantom size was seen only with bone substitutes. However, in this work, it was found that phantom size also affects the CT-numbers of lung substitutes (see Fig. 4. 23). This behavior of lung substitutes was only significant for 28 and 32 cm phantom diameters. However, the uncertainty of the simulated CT-number was almost 100% for the substitutes in a phantom of 32 cm diameters even when 3x109 incident photons are used. Calibrations by Minohara et al.[160] and Schaffner and Pedroni [133] are compared with our calibrations cal 1 and cal 5 in Fig. 4. 28. Neither the voltage of the X-ray tube nor the material of the phantom was noted in either previous work [132][151]. Our simulation results are very similar to the calibrations found in literature. The main difference is in the region of HU<0 where simulation suggests that phantom size affects lung substitutes. However, prior literature on the effect of phantom size on range calibration is only available for bone substitutes [133][160]. Minohara Schaffner Fig. 4. 28. Comparison of calibration relations for ion treatment with literature data for different phantom sizes. 115 The magnitude of change in relative range caused by changing the phantom size can be estimated by dividing the change of the slope of the calibration curves by the change in the diameter of the phantom ( slope/ diameter) as shown in Table 4.5. The effect estimated in this work is comparable with results in the literature for CT- numbers larger than zero. However ,the difference in is considerably larger for the range of CT-numbers below zero. By comparison, the slope of the standard calibration (cal 1) is 3.86E-04 HU-1 for bone and 1.09E-03 HU-1 for CT-numbers below zero. A change by 3.57E-06 HU-1 cm-1 in the slope is equivalent to a 9.2% variation in the CT-number of the phantom insert for a 10 cm change in phantom diameter. Quantitatively, the effect of the diameter of PMMA phantom on WEPL is about -1.4 mm, which is considerable but only for CT-numbers less than -200 HU. Fortunately, less than 10% of the all the pixels in the CT-image of a patient have a CT-number below the -200 HU limit (Fig. 4. 26). Table 4.5. Change of slope of the calibration curve due to change of phantom size ( ) estimated from results of Minohara et al. [160] Schaffner and Pedroni [133] and the values for cal 1 and cal 5 in Table 4.4 slope/ diameter (HU-1 cm-1) CT-number < 0 HU CT-number > 0 HU Minohara et al. 1.00E-06 3.21E-06 Schafner and Pedroni 0.00E+00 3.57E-06 This work 1.03E-05 3.57E-06 The effect of the phantom size is systemic. Therefore, it is recommended that the phantom that is used for calibration purposes represents the body part of interest to the treatment planner. 4.6.3.4 Effect of phantom material on range calculation Calibration 6 (scanning the substitutes in air) has a different slope compared to the standard calibration (cal 1). The effect of the calibrations on WEPL is about 2.3 mm, which is not negligible. Such a calibration does not represent the attenuation of photons in the body, however, and should not 116 be used for treatment planning, but it can be used to estimate safety margins, as shown by Schaffner and Pedroni [133] 4.7 Summary: conclusions and discussion The work presented here was the first study of the accuracy of CT-numbers based on MC simulations of a CT-scanner. Previous studies were based on measurement results of known substitutes. A more detailed discussion of approach we used to calculate CT-numbers is in [162]. The results of using our approach demonstrate that: Changing the settings of an X-ray tube by ±10 kV causes only a small effect on the calculated range, as the change only affects the part of the calibration that affects bone, Substitutes that do not represent tissues (e.g. H-materials) are not suitable for CT-calibration, especially for heavy ion therapy, Phantom size has an effect on CT-calibration. The size of the phantom should represent the body part under study, and The calibration that is calculated when the substitutes are scanned without a phantom (i.e., in air) has a totally different slope than the standard calibration, and should not be used for treatment planning in heavy ion therapy [163]. Changes in CT-number due to voltage settings and phantom size have been quantified in this study. Future applications of MC-simulated CT-numbers could be used to investigate the effect of metal artifacts on range calibrations. However, due to the strong absorption of X-rays in metal and a cut-off for large CT-numbers in the software of most CT-scanners, a range calculation in metals cannot be based on the measured CT-numbers. Patients with gold fillings or hip prostheses close to the treatment volume thus represent a potentially serious problem for treatment planners. In order to obtain a correct position of Bragg peak of ions after traversing a metal implant, it is necessary to assume a correct value of the range in the metal in the region of implant. Values for the range of carbon ions relative to water were measured and analyzed for various metals used as implants by Jäkel [164]. The same investigator has also studied the issue of CT artifacts due to metal implants and their impact on ion range uncertainties [165]. It is clear that the accuracy of dose calculation is strongly connected with correct modeling of the patient. The value of CT numbers, which are the main parameter that characterizes the physical properties of the patient body voxel, must be known with low uncertainties. Lomax [166] has shown that variations of 3% in CT numbers leads to range errors of the order of 5%, that is 5 mm for every 10 117 cm in water. The study presented here provides useful concepts that could be used to find diminish the uncertainties of CT numbers. In particular, we successfully quantified the way the value of CT-numbers changes with changes in X-ray energy in a CT machine. The uncertainties in the empirical calibration of the CT numbers (CT number - WEPL), which have been described by a number of investigators [128][129][144][145][167][168], is one of the major sources of uncertainties in the ion treatment planning process. Recently, efforts have been made to better describe the physical properties of each voxel using alternative imaging modalities. Bazalova [169] [170] used Dual Energy CT to provide a better material segmentation. Hünemohr et al [171] used Dual Energy CT to provide a better HU-to- WEPL calibration. In the latter paper, the authors investigated the use of dual energy CT in order to improve ion range determination. Dual energy CT (DECT) technology [172] provides the means to obtain two CT numbers by scanning an object with two X-ray spectra of different energy.. The former study [171] measured materials, including tissue surrogates, using a second-generation dual source CT scanner. The authors established a new approach for CT data calibration by calibrating the electron density to the WEPL, and compared this to a standard empirical HU-WEPL calibration in a treatment planning study based on tissue surrogates. The results are very promising. Simultaneous imaging in a dual source CT scanner clearly opens up the possibility of providing additional tissue information, which can further reduce the inaccuracy of CT data translation for ion radiotherapy [173][174]. However, accurate dose calculation in Treatment Planning Systems and the impact of errors in calculation on the dose delivered remains an open problem today, despite these important recent contributions. 118 References [1] Ferlay, J., et al.,Estimates of worldwide burden of cancer in 2008: GLOBOCAN 2008. Int J Cancer, 127(12): p. 2893-2917, (2010) [2] Ferlay J, Shin HR, Bray F, Forman D, Mathers C, Parkin DM. GLOBOCAN 2008 v1.2, Cancer Incidence and Mortality Worldwide: IARC CancerBase No. 10 [Internet]. Lyon, France: International Agency for Research on Cancer, 2010. Available from: http://globocan.iarc.fr. Accessed May (2011) [3] Bray F, Jemal A, Grey N, Ferlay J, Forman D. Global cancer transitions according to the Human Development Index (2008-2030): a population-based study. Lancet Oncol.; doi:10.1016/S1470- 2045(12)70211-5, (2012) [4] Saunders W.M. “Radiation oncology: the use of beams of photon or particles for the treatment of tumors”, Radiat. Phys. Chem. 24, no 3/4, 357-64 , (1984) [5] M. D. Schutz, “The supervoltage story”, Am. J. Roentgenology, 124, 541-59, (1975) [6] W.F. Hanson ,”The changing role of acceleratorsin radiation therapy”, IEEE Trans.Nucl.Sci. NS-30, 1781-83, (1983) [7] D.W. Kerst, “The betatron”, Radiology 40, 115-19, (1943) [8] P. Wideroe, “Tumor therapy with high energy ionizing radiation”, Kerntechnik 11, 312-17, (1969) [9] E.L. Ginzton, C.S.Nunan,”History of microwave electron linear accelerators for radiotherapy”, Int.J.Radiat. Oncol. Biol. Phys 11, 205-16 , 1985 [10] D.W.Fry, W.Walkinshaw, “Linear accelerators”, reports on progress in Physics 12, 102-132, (1949) [11] D.K. Bewley,” he 8 MeV linear accelerator at the MRC Cyclotron Unit”, Brit.J.Radiology 58, 213-17, (1985) [12] L.Leksell, Stereotaxis and Radiosurgery, Charles C. Thomas, Springfield, IL, (1971) [13] L.Walton, C.K. Bomford, D. Ramsden, “The Sheffield stereotactic radiosurgery unit: physical characteristicsand principles of operation, Br. J. Radiol., 60, p897-906, (1987) [14] C. Lindquist, Gamma knife radiosurgery, Semin.Radiat.Oncol., 15, 197-202, (1995) [15] W. Sharf, Akceleratory Biomedyczne, PWN, Warszawa 1994, Scharf W H. Biomedical Particle Accelerators. New York.American Institute of Physics Press, 1994; with up-todated supplement published also in Japanese by Iryou-Kagaku-Sha. Tokyo (1998) [16] W. Maciszewski, W,Sharf, Particle Accelerators for Radiotherapy,Present Status and Future, Physica Medica Vol. XX, N. 4, , 137-145, (2004) [17] Schlegel W, Mahr A. 3D Conformal Radiation Therapy-A multimedia introduction to methods and techniques. Springer Verlag Berlin Heidelberg New York, Editors; Schlegel W, Mahr A. (2001) [18] Webb Steve. The physics of three-dimensional radiation therapy, Institute of Physics Publishing Bristol and Philadelphia, IOP publishing Ltd., (1993) [19] Webb, The physics of conformal radiotherapy, Institute of Physics Publishing Bristol and Philadelphia, IOP publishing Ltd., (1997) [20] Webb S. Intensity Modulated Radiation Therapy 2001 Institute of Physics Publishing Bristol and Philadelphia, IOP publishing Ltd., (2001) [21] Webb S, Hartmann G, Echner G, Schlegel W . Intensity-Modulated Radiation Therapy using a Variable-Aperture Collimator. Phys. Med. Biol.; 48(9):1223, (2003) [22] Leksell, L.,The stereotaxis methodand radiosurgeryof the brain, Acta Chir. Scand., 102, 316-319, (1951) [23] Betti, O. Derechinski, V., Multiple-beam stereotaxic irradiation, Neurochirurgie,29,295-98, (1983) [24] Colombo f., Benedetti, A., Pozza, F. et all Stereotactic radiosurgery utilizing a linear accelerator, Appl. Neurophysiol., 48, 133-45, (1985) [25] Hartmann, GH., Schlegel, W., et all Celebral radiation surgery using moving field irradiadion at a linear accelerator facility, Int. J. Radiat. Onco. Biol. Phys., 28, 1185-1192, (1985) [26] Lutz, W., Winston, K.R., and Maleki, N., A system for stereotactic radiosurgery with linear 119 accelerator, Int.J. Radiat. Oncol. Biol. Phys., 14, 373-381, (1988) [27] Wysocka A, "Physical Aspects of Stereotactic Radiosurgery with Application of the Linear Acceler- ator Arc Method", Polish Journal of Medical Physics and Engineering, 1, No.1, p. 157(1995) [28] Wysocka A. Physical aspects of stereotactic radiosurgery with application of the linear accelerator arc method. Nukleonika Vol. 41 No. 2: 11-20, (1996) [29] Wysocka A. Physical Aspects of Treatment Planning in Linac-Based Radiosurgery of Intracranial Lesions” Reports of Practical Oncology and Radiotherapy, Vol.3, No.3, p. 59-66,(1998) [30] Wysocka A, J. Rostkowska, M. Kania, W. Bulski, J. Fijuth “ Dosimetry of Small Circular 6-MV X- Ray Beams for Stereotactic Radiotherapy with a Linear Accelerator” Proc.XXVI Mazurian Lakes School of Physics 1-11 September, Krzyże, Poland, (1999) [31] Wysocka A, J. Rostkowska, M. Kania, W. Bulski, J. Fijuth. Dosimetric Characteristics of Circular 6-MV X-Ray Beams for Stereotactic Radiotherapy with a Linear Accelerator", Acta Physica Polonica B, , Vol.31, No 1, p. 81-87, (2000) [32] Wysocka A, W. Maciszewski. The Photon Beam Characteristics of Linear Accelerator Equipped with Additional Narrow Beam Collimator, Nukleonika , 46(3), p. 91-93, (2001) [33] Wysocka A, “Collimation and Dosimetry of X-Ray Beams for Stereotactic Radiotherapy with a Linear Accelerator”, Ph.D. Dissertation presented to the Scientific Council of the Andrzej Sołtan Institute for Nuclear Studies, Warsaw (2002) [34] Rostkowska J, M.Kania, W.Bulski, A.Wysocka “Dosimetry of X-Ray Beams in Stereotactic Radiosurgery” Polish J Med. Phys & Eng , ,8:3:143-156, (2002) [35] Palta J.R, Biggs P.j, Hazle JD, Huq MS, et.all.Intraoperative electron beam radiation therapy: technique, dosimetry, and dose specification:report of task force 48 of the radiation therapy committee, American Association of Physicist in Medicine Int. J. Radiat.Oncol. Biol. Phys. Vol.33. No .3. pp 725-746, (1995) [36] PTCOG 2010 http://ptcog.web.psi.ch [37] Amaldi U, Kraft G. European Developments in Radiotherapy with Beams of Large Radiobiological Effectiveness J.Radiat.Res.,48:Suppl.A27-A41, (2007) [38] Jakel O, Schulz-Ertner D, Debus J. Specifying Carbon Ion Doses for Radiotherapy:The Heidelberg Approach. J.Radiat.Res., 48:Suppl.,A87-A95, (2007) [39] Andreo P. Monte Carlo techniques in medical radiation physics Phys.Med.Biol.36:861-920, (1991) [40] Nelson WR, Hirayama H, Rogers DWO. The EGS4 code system. SLAC-Report-265, (1985) [41] Rogers DWO, Faddegon BA, Ding GX, Ma CM, We J, Mackie TR. BEAM: a Monte Carlo code to simulate radiotherapy treatment units. Med. Phys. 22:503-524, (1995) [42] Dai J-R, Hu Y-M Intensity-modulation radiotherapy using independent collimators: an algorithm study Med.Phys.236 :2562-70, (1999) [43] Webb S, “Intensity modulated radiation therapy using only jaws and mask”, Phys. Med. Biol.47 : 257- 75, (2002) [44] Webb S, “Intensity modulated radiation therapy using only jaws and mask: II. A simplified concept of relocatable single-bixel attenuators”, Phys.Med.Biol.47:1869-79, (2002) [45] Bortfeld TR, Boyer A L, Schlegel W, Kahler D L and Waldron T J Realisation and Verification of three-dimensional conformal radiotherapy with modulated fields.Int.J. Radiat. Oncol. Biol. Phys. 30: 899-908, (1994) [46] Stein J, Bortfeld T, Dorschel B and Schlegel W, “Dynamic X-ray compensation for conformal radiotherapy by means of multileaf collimation”, Radiother. Oncol. 32: 163-73,(1994) [47] Pastyr O, Echner G, Schlegel W, Hartmann G, “Kollimator und Programm zur Steuerung des Kollimators”, German Patent pending 101 57 523.8, (2002) [48] Wysocka-Rabin A, Hartmann G. Monte Carlo study on a new concept of a scanning photon beam system for IMRT. Nukleonika, Vol. 56, No 4: 291-296 (2011) [49] Kawrakow I, Rogers DWO. The EGSnrc code system: Monte Carlo simulation of electron and photon transport. National Research Council of Canada (CA); Report No.: PIRS-701, (2001) 120 [50] Mackie T, Holmes T, Swerdloff S, Reckwerdt P, Deasy J,Yang J, Paliwal B, Kinsella T, “ Tomotherapy a new concept for the delivery of dynamic conformal radiotherapy”, Med. Phys. 20: 1709–19, (1993) [51] Carol M P, “Integrated 3D conformal multi-vane intensity modulation delivery system for radiotherapy”, 11th Int Conf. on the Use of Computers in Radiation Therapy (Christie Hospital NHS Trust, Manchester, UK) pp 172–3: (1994) [52] Crooks S M, Wu X, Takita C, Watzich M and Xing L, “Aperture modulated arc therapy”, Phys. Med. Biol. 48 1333–44, (2003) [53] Cameron C, “Sweeping-window arc therapy: an implementation of rotational IMRT with automatic beam-weight calculation”, Phys. Med. Biol. 50: 4317–36, (2005) [54] Ulrich S, Nill S and Oelfke U, “Development of an optimization concept for arc-modulated cone beam therapy”, Phys. Med. Biol. 52: 4099–119, (2007) [55] Otto K, “Volumetric modulated arc therapy: IMRT in a single gantry arc”, Med.Phys.35:310–17, (2008) [56] Wang C, Luan S, Tang G, Chen D Z, EarlMA and Yu C X” Arc-modulated radiation therapy (amrt): a single-arc form of intensity-modulated arc therapy Phys. Med. Biol. 53: 6291–303, (2008) [57] Webb S and Poludniowski G, ”Intensity-modulated radiation therapy (IMRT) by adynamic-jaws-only (DJO) technique in rotate-translate mode”, Phys. Med. Biol. 55 N495–N506 (2010) [58] Salter B, Sarkar V, Wang B, Shukla H, Szegedi M and Rassiah-Szegedi P,2011, Rotational IMRT delivery using a digital linear accelerator in very high dose rate ‘burst mode’ Phys. Med. Biol. 56: 1931–1946, (2011) [59] Satherberg A, Andreo P, and Karlsson M, Bremsstrahlung Production at 50 MeV in different Target Materials and Configurations. Med. Phys. 23, 495,(1996) [60] Svensson, R., Asell, M., Nafstadius, P., and Brahme, A. Target, Purging Magnet and Electron Collector Design for Scanned High-Energy Photon Beams. Phys. Med. Biol. 43 (1998), 1. [61] Kuster G, Monte Carlo Untersuchungen zur Optimierung von Techniken fur die konforme Strahlentherapie, PhD thesis, Ruprecht-Karls-Universit at Heidelberg,(1999) [62] Kilby W al Platforms for image-guided and adaptive radiation therapy Image Guided and Adaptive Radiation Therapy ed R Timmerman and L Xing (Philadelphia, PA: Lippincott Williams and Wilkins) at press, (2009) [63] Echner G, Kilby W, Lee M, Earnst E, Sayeh S, Schlaefer A, Rhein B, Dooley J, LangC, Blanck O, Lessard E, Maurer C and Schlegel1 W,2009, The design, physical properties and clinical utility of an iris collimator for robotic radiosurgery Phys. Med. Biol. 54:5359–5380, (2009) [64] Abe M, “Intraoperative radiotherapy-past, present and future”, Int. J. Radiat. Oncol. Biol. Phys. 10, 1987-1990, (1984) [65] Gunderson L. LShipley., W. U., and Suit H. D., ”Intraoperative irradiation, a pilot study external beam photons with “boost” dose intraoperative electrons”, Cancer 49, 2259-2266 (1982) [66] Tepper J. and Sindelar W. F., “Summary of the workshop on intraoperative radiation therapy”, Cancer Treat. Rep. 65, 911-918 (1981) [67] Fraass J. B. A. et al., “Intraoperative radiation therapy at the National Cancer Institute, technical innovation and dosimetry”, Int. J. Radiat. Oncol. Biol. Phys. 11, 1299-1311 (1985) [68] Abe M, Fukada M, Yaniano K, et al. Intraoperative irradiation in abdominal and cerebral tumours, Acta Radiol, 10;408-16, (1971) [69] Abe M,Shibamoto Y, Ono K, Takahashi M , Intraoperative radiation therapy for carcinoma of the stomach and pancreas, Front. Radiat. Ther. Oncol;25:258-69,(1991) [70] Goldson AL, Preliminary clinical experience with intraoperative radiotherapy, J.tl. Med. Assoc;70:493-5, (1978) [71] Rich T.A, Cady B, McDermott W. V , Orthovoltage Intraoperative Radiotherapy:A new look at an old idea, Int J. Radiat. Oncol.Biol. Phys. 10, 1957 (1984) [72] Calvo F A, Meirino R. M, Orecchia R, Intraoperative radiation therapy ;First part: Rationale and techniques, Critical reviews in Oncology/Hematology 59 ; 106-115 (2006) 121 [73] Papanikolau N and Paliwal B, Effect of cone shielding in intraoperative therapy, Med.Phys.Vol.22, No 5, 571-75 (1995), [74] Biggs PJ, Epp ER, Ling CC, Novack DH, Michaels HB. Dosimetry, field shaping and other considerations for intra-operative electron therapy. Int J Radiat Oncol Biol Phys.;7(7):875–84. (1981) [75] Bagne FR, Samsami N, Dobelbower RR Jr. Radiation contamination and leakage assessment of intraoperative electron applicators. Med Phys.;15(4):530–37,(1988) [76] McCullough EC, Anderson JA. The dosimetric properties of an applicator system for intraoperative electron-beam therapy utilizing a Clinac-18 accelerator. Med Phys.;9(2):261–68. (1982) [77] Nevelsky A. et al.: Intra-operative electron beam therapy utilizing ELEKTA Precise accelerator , Journal of Applied Clinical Medical Physics, Vol. 11, No. 4, 57-69 (2010) [78] Hensley F. et al. “Survey of IORT Activities in Europe”, private communication, (2004) [79] Beddar A. S., Biggs P. J., Chang S., Ezzell G. A., Faddegon B. A., Hensley F. W., Mills M. D., “Intraoperative radiation therapy using mobile electron linear accelerators: Report of AAPM Radiation Therapy Committee Task Group No.72” Med. Phys. 33, 1476-1489 (2006) [80] European Committee for Electrotechnical Standardization (CENELEC), “European Standard IEC 60601-2-1:1998 + A1:2002, Medical Electrical Equipment Part2-1: Particular requirements for the safety of electron accelerators in the range of 1 MeV to 50 MeV”, (2002) [81] IEC Technical Report, IEC/TR60976 and IEC/TR60977, Medical electrical equipment-Medical electron accelerators - Guidelines for functional performance characteristics, International Elecrotechnical Commision, Edition 2.0, (2008) [82] Palta J. R., Biggs P. J., Hazle D. J., Huq M. S., Dahl R. A., Ochran T. G., Soen J.,. Dobelbower R. R, and McCullough E. C., "Intraoperative electron beam radiation therapy, technique, dosimetry, and dose specification, report of Task Group 48 of the radiation therapy committee, American Association of Physicists in Medicine," Int. J. Radiat. Oncol. Biol. Phys. 33, 725-746 (1995). [83] Price R. A. and Ayyangar K. M., "IORT apparatus design improvement through the evaluation of electron spectral distributions using Monte Carlo methods," Med. Phys. 27, 215-220 (1999). [84] Palta J. R. and Suntharalingam N., "A nondocking intraoperative electron beam applicator system," Int. J. Radiat. Oncol. Biol. Phys. 17, 411-417 (1989). [85] Hogstrom K. R., Boyer A. L., Shiu A. S., Ochran T. G., Kirsner S. M., Krispel F., and Rich T. A., "Design of metallic electron beam cones for an intraoperative therapy linear accelerator," Int. J. Radiat. Oncol. Biol. Phys. 18, 1223-1232 (1990). [86] Jones D., Taylor E., Travaglini J., and Vermeulen S., "A non-contacting intraoperative electron cone apparatus," Int. J. Radiat. Oncol. Biol. Phys. 16, 1643-1647 (1989). [87] Kharrati H., Aletti P., and Guillemin F., "Design of a non-docking intraoperative electron beam applicator system," Radiother. Oncol. 33, 80-83 (1994). [88] Björk P., Knöös T., Nilsson P., and Larsson K., "Design and dosimetry characteristics of a soft- docking system for intraoperative radiation therapy," Int. J. Radiat. Oncol. Biol. Phys. 47, 527-533 (2000). [89] Björk P., Nilsson P., and Knöös T., "Dosimetry characteristics of degraded electron beams investigated by Monte Carlo calculations in a setup for intraoperative radiation therapy," Phys. Med. Biol. 47, 239- 256 (2002). [90] Adrich P., Wysocka-Rabin A., Wasilewski A., “Modeling of the treatment head of a new mobile electron accelerator for IORT”, Radiother. Oncol. Vol. 96 No S1:560, (2010) [91] Wysocka-Rabin A, Adrich P, Wasilewski A, “Monte Carlo Study of a new Mobile Electron Accelerator Head for Intra Operative Radiation Therapy (IORT)” Prog. Nucl. Sci. Technol. Vol. 2: 181-186 (2011) [92] Wysocka-Rabin A., Adrich P, ”Monte Carlo study of hard and soft-docking system for a new mobile intraoperative accelerator”, Radiother. Oncol. Vol. 99 No S1:16, (2011) [93] Wysocka-Rabin A., Adrich P., ”Method and system of forming electron beam for a treatment head of a mobile intraoperative accelerator”, patent P.397929 (2012) [94] Kainz K. K. et al., „Dual scattering foil design for poly-energetic electron beams”, Phys. Med. Biol. 50, 755-767 and references therein (2005) 122 [95] Ciocca M. et al., "Radiation survey Liac around a mobile electron linear accelerator for intraoperative radiation therapy", J. Appl. Clin. Med. Phys., 10 (2), (2009) [96] Kawrakow I., ”Accurate condensed history Monte Carlo simulation of electron transport: I. EGSnrc, the new EGS4 version”, Med. Phys. 27, 485-98 (2000) [97] Rogers D. W. O. et al., ”BEAM: a Monte Carlo code to simulate radiotherapy treatment units”, Med. Phys. 22, 503-24 (1995) [98] General Particle tracer (GPT), Version 2.82, Pulsar Physics [99] Kawrakow I. and Rogers D. W. O., “The EGSnrc Code System: Monte Carlo simulation of Electron and Photon Transport”, National Research Council of Canada Report PIRS-701 (Ottawa: NRC), (2003) [100] Walters B. et al., “DOSXYZnrc Users Manual”, National Research Council of Canada Report PIRS- 794, rev B, (Ottawa: NRC), (2004) [101] Ferrari A., Sala P. R., Fasso A., and Ranft J., "FLUKA: a multi-particle transport code", CERN 2005- 10, INFN/TC_05/11, SLAC-R-773,(2005) [102] Battistoni G., Muraro S., Sala P. R., Cerutti F., Ferrari A., Roesler S., Fasso A., Ranft J., "The FLUKA code: Description and benchmarking", Proceedings of the Hadronic Shower Simulation Workshop 2006, Fermilab 6-8 September 2006, M. Albrow, R. Raja eds., AIP Conference Proceeding 896, 31-49 (2007) [103] Vlachoudis V., "FLAIR: A Powerful But User Friendly Graphical Interface For FLUKA", Proc. Int. Conf. on Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs, New York, 2009, Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs, New York, (2009) [104] Wysocka-Rabin A., Adrich P., Wasilewski A., ”Shielding assessment of a new mobile electron accelerator for Intra Operative Radiation Therapy (IORT)”, Radiother. Oncol. Vol. 96 No S1, 564, (2010) [105] Wysocka-Rabin A., Adrich P., Wasilewski A., „Design, Dosimetry Characteristics and Shielding Assessment of a New Mobile Electron Accelerator for Intraoperative Radiation Therapy (IORT) Developed Using Monte Carlo Methods”, Radiother. Oncol. Vol. 102 No S1: 46, (2012) [106] Wysocka-Rabin A., Adrich P., Wasilewski A., „Radiation Protection studies for a new mobile electron accelerator for Intra Operative Radiation Therapy (IORT)”, Prog. Nucl. Sci. Technol. ( submitted),(2013) [107] Soriani A. et al., “Setup verification and in vivo dosimetry during intraoperative radiation therapy (IORT) for prostate cancer”, Med. Phys. 34(8), 3205-3210 (2007) [108] Ongaro C, Zanini A, Nastasi U, Rodenas J, Ottaviano G and Manfredotti C “Analysis of photoneutron spectra produced in medical accelerators”, Phys. Med. Biol. 45 L 55-61, (2000) [109] Daves J.L. and Mills M.D., “Shielding assessment of a mobile electron accelerator for intraoperative radiotherapy”, J. Appl. Clin. Med. Phys. 2(3), 165-173 (2001) [110] Loi G. et al. “Neutron production from a mobile electron accelerator operating in electron mode for intraoperative radiation therapy”, Phys. Med. Biol. 51(3),695-702 (2006). [111] Jaradat A.K. and Biggs P.J, “Measurements of the neutron leakage from a dedicated intraoperative radiation therapy electron linear accelerator and conventional linear accelerator for 9, 12, 15, (16), and 18 (20) MeV electron energies” Med. Phys. 35(5), 1711-1717 (2008). [112] Soriani A. et al. ”Radiation protection measurements around a 12 MeV mobile dedicated IORT accelerator”, Med. Phys. 37 (3), 995-1002, (2010) [113] Calvo F A, Meirino R. M, Orecchia R, “Intraoperative radiation therapy Part 2. Clinical results”, Critical Reviews in Oncology/Hematology 59 ; 116-127 (2006) [114] Orecchia R., Veronesi U., “Intraoperative electrons”,Serminars in Radiation Oncology, Vol 15, 2, : 76- 83 ( 2005) [115] Mannino M, Yarnold J., “Accelerated partial breast irradiation trials: Diversity in rationale and design”, Radioth. Oncol.91 :16-22, ( 2009) [116] Gottschalk B., “Passive beam spreading in proton radiation therapy.” http://huhepl.harvard.edu/gottschalk/ 123 [117] RR. Wilson. Radiological use of fast protons. Radiology, 47:487-491, (1946) [118] Haberer T, Becher W, Schardt D, and Kraft G, “Magnetic scanning system for heavy ion therapy”. Nucl. Instrum. Methods Phys. Res. A 330, pages 296-305, (1993) [119] Pedroni E, Bacher R, Blattmann H, Bohringer T, Coray A, Lomax A, Lin G., G. Munkel, S. Scheib, and U. Schneider. Proton therapy status reports, PSI, Life Sciences Newsletter 1989/1990, (1989) [120] Kraft G., The radiobiological and physical basis for radiotherapy with protons and heavier ions. Strahlenter.Oncol.166; 10-13, (1990) [121] Kraft G, “Tumor therapy with heavy charged particles”. Prog Part Nucl Phys 45; 473-544, (2000) [122] Linz U (ed.) Ion beams in tumor therapy.Chapman & Hall, Weinheim, (1995) [123] Debus J, Jäkel O, Kraft G, Wannenmacher M, “ Is there a role for heavy ion beam therapy? Recent Results”, Cancer Res.150:171-182(1998) [124] Debus J, Engenhart-Cabillic R, Kraft G, Wannenmacher M “The role of high-LET radiotherapy compared to conformal photon radiotherapy in adenoid cystic carcinoma”. Strahlenther. Onkol. 175(Suppl 2):63-65(1999) [125] Kanai T, Endo M, Minohara S et al. Biophysical characteristics of HIMAC clinical irradiation system for heavy-ion radiation therapy. Int.J.Radiat.Oncol.Biol.Phys.44:201-210 (1999) [126] Tsujii H, Mizoe J, Kamada T, Baba M, et.all.” Clinical Results of Carbon Ion Radiotherapy at NIRS”. J. Radiat. Res., 48: Suppl., A1-A13 (2007) [127] Jäkel O, Jacob C, Schardt D, Karger CP, Hartmann GH. Relation between carbon ion ranges and X- ray CT numbers. Med. Phys.; 28(4):701-703, ( 2001) [128] Qamhiyeh S, A. Wysocka-Rabin, M. Ellerbrock, C. Penssel, M. Kachelriess, O. Jaekel, , Simulation of CT-images: from X-ray spectrum to CT-numbers”,13th UK Monte Carlo User Group Meeting (MCNEG 2007), National Physical Laboratory Teddington, Middlesex, UK, 2007-03-28 2007-03-29 Programme and Abstract Book, p.7, (2007) [129] Qamhiyeh S, Wysocka-Rabin A, Ellerbrock M, Jäkel O. Effect of voltage of CT-scanner, phantom size and phantom material on CT-calibration and carbon range. 9th Biennial ESTRO Meeting on Physics and Radiation Technology for Clnical Radiotherapy. Sep 8-13; Barcelona, Spain. Radiother Oncol. 2007, 84(Supp.1) p.232, (2007) [130] Kalender WA. Computed tomography: fundamentals, system technology, image quality, applications. Ed John Wiley & Sons; (2000). [131] Mustafa A A, Jackson D F, “The relation between X-ray CT numbers and charged particle stopping powers and its significance for radiotherapy treatment planning”, Phys. Med. Biol. 28 169-176, (1983) [132] Verhaegen F, Devic S, “Sensitivity study for CT images in Monte Carlo treatment planning”, Phys. Med. Biol. 50 937-946, ( 2005) [133] Schaffner B, Pedroni E, “The precision of proton range calculations in proton radiotherapy treatment planning : experimental verification of the radiation between CT-HU and proton stopping power”, Phys. Med. Biol. 42 1579-1592, (1998) [134] Homolka P, Gahleitner A, Nowotny R, “Temperature dependence of HU values for various water equivalent phantom materials”, Phys. Med. Biol. 47 2917-2923, (2002) [135] Bhat M Pattison J Bibbo G Caon M “Diagnostic X-ray spectra: a comparison of spectra generated by different computational methods with a measured spectrum” Med. Phys. 25 114-120, (1998) [136] Caon M Bibbo G Pattison J Bhat M The effect on dose to computed tomography phantoms of varying the theoretical X-ray spectrum: a comparison of four diagnostic spectrum calculating codes Med. Phys. 25 1021-1027, (1998) [137] Ay M R Shahriari M Sarkar S Zaidi H Monte Carlo simulation of X-ray spectra in diagnostic radiology and mammography using MCNP4C Phys. Med. Biol. 49 4897-4917, (2004) [138] Ay M R, Sarkar S Shahriari M Zaidi H, “Assessment of different computational models for generation of x-ray spectra in diagnostic radiology and mammography”,Phys. Med. Biol. 32 1660-1675, (2005) [139] Atherton J V, Huda W, “CT dose in cylindrical phantoms”, Phys. Med. Biol. 40 891-911, (1995) [140] Jarry G, DeMacro J, Beifuss U, Cagnon C,”A Monte Carlo-based method to estimate radiation dose 124 from spiral CT : from phantom testing to patient-specific models”,Phys. Med. Biol. 48: 2645- 2663(2003) [141] Salvado M, Lopez M, Morant J J, Calzado A,”Monte Carlo calculations of radiation dose in CT examination using phantom and patient tomographic models”, Rad. Prot. Dos. 114 364-368, (2005) [142] Tzedakis A Perisnakis K, “The effect of Z overscanning on radiation burden of pediatric patients undergoing head CT with multidetector scanners: A Monte Carlo study”, Med. Phys. 33 7 2472-2478, (2006) [143] Heismann BJ, Leppert J, Stierstorfer K. Density and atomic number measurements with spectral x-ray attenuation method. J Appl Phys; 94 (3):2073-9, (2003) [144] Qamhiyeh S, Wysocka-Rabin A., Ellerbrock M., Penssel C., Kachelriess M., Jakel O,”Analysis of tissue substitutes using a Monte Carlo Simulation of Hounsfield Units”, abstract in Radiother. Oncol. Vol. 81 No supp1: p357,(2006) [145] Qamhiyeh S A Monte Carlo study of the accuracy of CT-numbers for range calculations in Carbon ion therapy PhD for The University of Heidelberg 2007 [146] Kawrakow I, “ Accurate condensed history Monte Carlo simulation of electron transport. EGSnrc, the new EGS4 version”, Med. Phys. 27 485-498, (2000) [147] Verhaegen F Nahum A E Van de Putte S Namito Y Monte Carlo modelling of radiotherapy kV X-ray units Phys. Med. Biol. 44 1767-1789, (1999) [148] Verhaegen F “ Evaluation of the EGSnrc Monte Carlo code for interference near high-Z media exposed to kilovolt and 60Co photons” Phys. Med. Biol. 47 1691-1705, (2002) [149] Kawrakow I. and Rogers D. W. The EGSnrc Cod System: Monte Carlo simulation of electron and photon transports Technical report PRIS-701 National Research Council of Canada Ottowa, Canada (2003) [150] Romanchikova M. Monte Carlo Simulation des Röntgenspektrums einer computertomographischen Röntgenröhre[master’s thesis]. [Heidelberg (GE)]: University of Heidelbeg; March (2006). [151] Sennst D A Kachelriess M Leidercker C Schmidt B Watzke O Kalender W, “ An Extensible Software- based Platform for Reconstruction and Evaluation of CT images” Radiographics 24 (2) 601-613, ( 2004) [152] Constantinou C Harrington J C DeWerd L A An electron density calibration phantom for CT-based treatment planning computers Med. Phys. 19 325-327, (1992) [153] [Gammex] Gammex data sheet [154] Dowset D J Kenny P A. and Johnston R E The physics of diagnostic imaging (Chapman and Hall Medical, London (1998) [155] Qamhiyeh S, Wysocka-Rabin A, Jäkel O, Monte Carlo simulation of X-ray CT-numbers. In progress [156] Schneider U Pedroni E Lomax A The calibration of CT Hounsfield units for radiotherapy treatment planning Phys. Med. Biol. 41 111-124,(1996) [157] Karger C P Jäkel O Debus J Kuhn S Hartmann G H, “ Three-dimensional accuracy and interfractional reproducibility of patient fixation and positioning using a stereotactic head mask system” IJROBP 49 1493-1504, ( 2001) [158] Jäkel O Hartmann G H Karger C P Heeg P Rassow J Quality assurance for treatment planning system in scanned ion beam therapy Med. Phys. 27 1588-1600, (2000) [159] Marianno CM, Higley KA, Palmer TS. A comparison between default EGS4 and EGS4 with bound Compton cross sections when scattering occurs in bone and fat. Health Phys, 78(6):716-720, (2000) [160] Minohara S Kanai T Endo M Kawachi K Effects of object size on a function to convert X-ray CT numbers into the water equivalent path length of charged particle beam In Proceedings Third Workshop on Physical and Biological Research with heavy ions, Chiba 14-15,(1993) [161] Siegel M J Schmidt B Bradley D Suess C Hildebolt C Radiation dose and image quality in pediatric CT: effect of technical factors and phantom size and shape Radiology 233 515-522,(2004) [162] Wysocka-Rabin A, Qamhiyeh S, Jakel O, “Simulation of computed tomography (CT) images using a Monte Carlo approach”. Nukleonika, 56 (4), 299-304, (2011) 125 [163] Qamhiyeh S, Wysocka-Rabin A, Ellerbrock M, Jaekel O,” The effect of X-ray voltage, phantom size and material on CT-numbers and range calculations in Carbon ion therapy” , in progress [164] Jäkel O, ”Ranges of ions in metals for use in particle treatment planning”. Phys. Med. Biol. 51, N173- N177, (2006) [165] Jäkel O, Reiss P, “ The influence of metal artefacts on the range of ion beams”, Phys. Med. Biol. 52, 635-644, (2007) [166] Lomax A, ”Intensity modulated proton therapy and its sensitivity to treatment uncertainties 1:the potential efects of calculational uncertainties”. Phys Med Biol, 53:1027-1043, (2008) [167] Qamhiyeh S, Jäkel O, Wysocka-Rabin A, 2004, “Verification of measured CT numbers for heavy ion therapy”,/poster/ 40th Particle Therapy Cooperative Group Conference, Paris, June 16-18,(2004) [168] Qamhiyeh S, Wysocka-Rabin A, Jäkel O, “The effect of HU uncertainty on calculated Carbon ion range”; 43th Particle Therapy Cooperative Group Conference, Munich, December, (2005) [169] Bazalova M, Carrier JF, Beaulieu L, and Verhaegen F,” Dual-energy CT-based material extraction for tissue segmentation in Monte Carlo dose calculations”. Phys Med Biol, 53(9):2439-2456, ( 2008) [170] Bazalova M., JF. Carrier, L. Beaulieu, and F. Verhaegen. “Tissue segmentation in Monte Carlo treatment planning: a simulation study using dual-energy CT images”. Radiother Oncol, 86(1):93-98. (2008) [171] Hünemohr N. et al. “Ion range estimation by using dual energy computed tomography”. (submitted). (2012) [172] Flohr, T., McCollough, C., Bruder, H., Petersilka, M., Gruber, K., Süss, C.,Grasruck, M., Stierstorfer, K., Krauss, B., Raupach, R., Primak, A., Küttner, A., Achenbach,S., Becker, C., Kopp, A., and Ohnesorge, B. First performance evaluation of a dualsourceCT (DSCT) system. European Radiology, 16:1405–1405, (2006). [173] Yang, M., Virshup, G., Clayton, J., Zhu, X. R., Mohan, R., and Dong L, “Theoretical variance analysis of single- and dual-energy computed tomography methods for calculating proton stopping power ratios of biological tissues”. Physics in Medicine and Biology, 55(5):1343, (2010). [174] Yang M, Zhu X, Park, P, Titt U, Mohan R, Virshup G, Clayton J, and Dong L, “Comprehensive analysis of proton range uncertainties related to patient stopping-power-ratio estimation using the stoichiometric calibration”. Physics in Medicine and Biology, 57(13):4095, (2012). List of Figures Fig.1. 1 Schematic treatment of a target volume, which surrounds an organ at risk (OAR), with three radiation fields. Left side- conventional approach. Right side- intensity modulation of the fields to optimize dose to target volume. Fig.2. 1. Modern medical accelerator equipped with MLC Fig.2.2. Micro MLC with removed cover( courtesy of MRC Systems GmbH) Fig.2. 3. The DKFZ (O. Pastyr, G. Echner) design for a collimator, which can be moved across the surface of a sphere in such a way that whatever position is taken up by the collimator, it stays focused on the radiation source. As a consequence, a narrow photon beam can be scanned two-dimensionally across a desired radiation field. In this example, three different cylindrical apertures are provided by a revolving collimator system.[21]. 126 Fig.2. 4. Schematic drawing of the target-collimator-monitor system. Fig.2. 5. Fig.2. 6 Scheme of simulated geometry of the target, ionization chamber and collimator . Fig.2. 7. Example of energy fluence distribution of photon beam calculated for the field with 2 mm diameter, in the distance of 40 cm from the exit of collimator (r = R = 2.8 mm) Fig.2. 8. Photon beam profiles for different collimators. HW and PM mean the full width at half maximum and penumbra of beam profile, respectively. Fig.2. 9. Comparison of the water absorbed dose after target and ionisation chamber for the different target construction and different size of electron beam: Target 1 : re = 1 mm, 0.96mm of Au and C in the target Target 2 : re= 1 mm, 0.96mm of Au ,air instead of carbon in the target construction Target 3 : re =0.5 mm, 0.96 mm of Au, air instead of carbon in the target construction Target 4 : re =0.5 mm, 0.50 mm of Au, air instead of carbon in the target construction Fig.2. 10. Mean energy of photon beam as the function of Au target thickness calculated for radius of electron beam re =0.5 mm and energy spectrum of electrons from 6.174 up to 7.103 MeV Fig.2. 11. “New geometry”- scheme of simulated system of target, collimator , ionization chamber and water phantom, used for the simulation in the second part of project. Fig.2. 12. Comparison of photon beam profile calculated for different collimators: the 10 cm long collimators with the square of 1 mm x1 mm and circular aperture of 1 mm, and 15 cm long collimator with circular aperture of 2 mm. The comparison shows that the change of parameters influences the outcome of photons. Fig.2. 13. Water absorbed dose distribution of the photon beam calculated for different collimators and normalized to 1 for the maximum dose. This comparison shows that the change of parameters influences the gradient of the dose profile. Fig.2. 14. Field dose distribution for the photon beam from the collimator with a square aperture of 1 mm; the electron beam diameter was 1mm Fig.2. 15. Field dose distribution for the photon beam from the collimator with a circular aperture of 1 mm; the electron beam diameter was 1mm. Fig.2. 16. Geometrical characteristics for the system of target-collimator-monitor as found to be appropriate for a scanning photon beam. 127 Fig.2. 17. left: example for a desired intensity map as obtained from the treatment planning system right: dose distribution as obtained from a raster-scan with single photon beams, each produced by the target-collimator system with a dose distribution as shown in Fig.2. 15 (collimator with a circular aperture of 1 mm; electron beam diameter 1mm) Fig.2. 18. Intensity modulated beam map, shown as a greyscale, left: identical to Fig.2. 17 right; right: calculated with wmin=wmax/20 Fig.2. 19. Comparison of intensity profiles at coordinate Y=90. Fig.3. 1. Mobile accelerator for IORT Novac 7 Fig.3. 2. Mobile accelerator for IORT Liac Fig.3. 3 Mobile accelerator for IORT Mobetron Fig.3. 4. The “metal” (left) and “plastic” (right) models of treatment heads and applicators Fig.3. 5. Relative depth dose (PDD-percentage depth dose) along the beam axis for IORT (a)“metal” and (b) “plastic” model with applicator diameter of 10 cm and monoenergetic beams of energies ranging from 4 to 12 MeV. Fig.3. 6. Dose profiles at dmax for an IORT “metal” model with applicator diameters of (a) 10 cm (b) of 5 cm, for monoenergetic beams of energies ranging from 4 to 12 MeV. Fig.3. 7. Dose profiles at dmax for an IORT- “plastic” model with applicator diameters of (a) 10cm (b) 5 cm for monoenergetic beams of energies ranging from 4 to 12 MeV. Fig.3. 8 (a), (b) Two-dimensional distribution of relative dose equivalents inside and outside the operating room were calculated for a maximum energy of 12 MeV, with a 10 cm diameter applicator for the (a) “metal” and (b) “plastic” models respectively. Spatial dimensions (X and Y axis) are in cm. Note that the vertical axis is rotated by 90 degrees: the X axis represents height of a hypothetical OR; the floor of the OR is on the right side of each figure. Fig.3. 9 (a), (b) 2D distributions of relative dose equivalent due to neutron radiation inside and outside the operating room calculated for a maximum energy of 12 MeV, with a 10 cm diameter applicator for the (a)” metal”: and (b) “plastic” model. Spatial dimensions (X and Y axis) are in cm. Note that the vertical axis is rotated by 90 degrees: The X axis represents the height of an OR; the floor of the OR is on the right side of each figure. Fig.3. 10 Dose profiles at dmax for an IORT- “plastic” (blue line) and “metal”( red line) model with 12 cm applicator diameter for energy of 12 MeV. Fig.3. 11 Dose profiles at dmax for an IORT- “plastic” model with steel applicator diameters of 15 cm (blue line) and 22 cm ( red line) for monoenergetic beams with energies of 12.5 MeV 128 Fig.3. 12. Example of the realistic energy distribution of a beam received from the accelerating structure. Calculations were performed with GPT code for a beam with a maximum energy of approximately 4 MeV. Fig.3. 13. Comparison of the depth dose distribution and profiles calculated for a monoenergetic beam (blue curves) and for a beam with real energy distribution (red curves) for 3cm ( upper figures) and 10cm applicators (lower figures). Fig.3. 14 Example of the realistic energy distribution of a beam received from the accelerating structure. Calculations were performed with GPT code for a beam with a maximum energy of approximately 12 MeV. Fig.3. 15 Comparison of the depth dose distribution and profiles calculated for a monoenergetic beam (blue curves) and for a beam with real energy distribution (red curves) for 3cm ( upper figures) and 10cm applicators (lower figures). Fig.3. 16 Visualization of calculations for estimating the tolerance of displacement (upper left) and rotation (upper right) of two axes: applicator and beam; sample results for displacement in metal model (lower left and right). Fig.3. 17 (b) Beam profile at the dmax for beam energy equal 12 MeV and 10 cm applicator diameter with reduced wall thickness . Fig.3. 18. Accelerator treatment head with soft-docking (left) and hard-docking (right). Fig.3. 19 Depth dose distribution for 12 cm diameter applicator, for different beam energy; soft or hard docking. Fig.3. 20. Beam profile at dmax for 12 cm diameter applicator, for different beam energy, soft and hard docking system, with input beam energy ranging from 4 to 12 MeV. Fig.3. 21 Dose profile at dmax calculated for 14 cm applicator and beam energy 6 MeV, for a universal model using soft docking. Fig.3. 22. Dose profiles at dmax calculated for 13 cm applicator and beam energy 12 MeV, for universal model using soft docking. Fig.3. 23. Examples of isodose distribution in water. Left site: isodose distribution for soft docking system, for beam energy of 12 MeV and radiation field of 10 cm. Right site: isodose distribution for soft docking system, for beam energy of 9 MeV and radiation field of 13 cm. As mentioned above isodose distributions fulfill all criteria of IEC standards. Fig.3. 24 Scheme of applicator with the rectangular cross section. Fig.3. 25 Dose distribution at d max for a rectangular 10 cm x 5 cm applicator. 129 Fig.3. 26 Dose distribution for a 10x5 cm rectangular applicator and beam energy of 12 MeV: (left) depth dose distribution, (right) beam profiles along the X- and Y-axis at maximum dose depth in the beam axis. Fig.3. 27. Layout of OR and Control Room. Points selected for detailed dose analysis are indicated with a + sign (top view: x, y axis). Fig.3. 28. Layout of OR and Control Room. Points selected for detailed dose analysis are indicated with the + sign (side view: y, z axis). Fig.3. 29. Two-D distribution of relative dose equivalent inside and outside the operating room were calculated for a maximum energy of 12 MeV, with a 12 cm diameter applicator without OR shielding. Spatial dimensions (X, Y and Z axis) are in cm. The upper illustration is a side view of the OR, the lower shows a top view. Fig.3. 30. Two-D distribution of relative dose equivalent inside and outside the OR were calculated for a maximum energy of 12 MeV, with a 12 cm diameter applicator and OR shielding. Spatial dimensions (X, Y and Z axis) are in cm. The upper figure shows a side view of the OR, the lower shows a top view. Fig.3. 31. Two-D distributions of relative dose equivalent due to neutron radiation inside and outside the operating room calculated for a maximum energy of 12 MeV with a 12 cm diameter applicator. Spatial dimensions (X Y and Z axis) are in cm. (upper) side view (lower) top view. Fig.3. 32 Using of mobile accelerator for IORT for different tumor sites [78] Fig. 4. 1. Depth dose curves for photons, protons and carbons-ions: The broad Bragg peak of 135 MeV protons (green line) exhibits no exit dose. The narrow Bragg peak of 254 MeV/n and 300MeV/n carbons ions (red lines) - clearly show the distal dose tail caused by light beam fragmentation [old GSI materials]. Fig. 4. 2. Comparison of depth dose profiles of different radiation types. The depth-dose profiles of ions lead to a decreased integral dose. The enhanced RBE of Carbon ions in the Bragg-peak leads to a higher biologically effective dose within the tumor [17] ( Schleg 3D) Fig. 4. 3. Carbon ion physical depth dose distributions in water for SOBPs of different sizes lying in different depths. Blue: 2.5cm SOBP in 5 cm depth, red: 2.5cm SOBP in 20 cm depth, green: 10 cm SOBP in 12.5 cm depth [17] (Schlegel 3D). Fig. 4. 4.WEPL approach for dose calculation in a treatment planning - (a) Schematic experimental set up for WEPL measurements. (b) Depth dose curves obtained by using different absorbers. The shift in the location of the Bragg Peak corresponds to the WEPL value [127]. 130 Fig. 4. 5. WEPL approach for dose calculation in a treatment planning - Example of a HU-to-WEPL calibration [127]. Fig. 4. 6. Scale of CT-number and the corresponding tissue types. The left, a sample CT image of the abdomen [17]. Fig. 4. 7. Emotion CT scanner with 16 cm diameter cylindrical phantom from PMMA positioned for CT-value measurements. Fig.4. 8.Cylindrical PMMA phantom with Gammex tissue equivalent substitutes. Fig. 4. 9 . Scheme of CT scanner and phantom simulation. Fig. 4. 10. Scheme of the calculation of CT-numbers: from X-ray tube spectrum to CT-numbers (HU) that are extracted from the CT-image. Fig. 4. 11. Photon spectra of X-ray tube for different tube voltage. Fig. 4. 12. Mean energy of the incident photons as a function of the distance from the center of the FOV after filters and collimator. The peak voltage of the incident photons is shown in the legend. Fig. 4. 13. The simulated CT-numbers as a function of the electron-density for Gammex substitutes, Fig. 4. 14. The effect of number of independent projections on a profile in the center of a calculated CT-image (A and B) and the reconstructed images (C and D) is presented. The reconstructed CT image (512x512 pixels) represents a 16 cm PMMA phantom with cortical bone substitute as an insert. Fig. 4. 15.Comparison of calculated and measured results of CT-numbers for Gammex, H-materials Fig. 4. 16. Distribution of the simulated CT-numbers around measured values. The graph shows the histograms of the data points as a function of the difference between the simulated and measured CT-numbers. The histogram of all the data points and the Gaussian fit (G(x) in equation (0.2) are shown. Fig. 4. 17. Photon spectral distribution after transport through CT filters and collimator, calculated with the 3 different spectra of X-ray tube in the centre of FOV (a) and at the edge of FOV (b). Fig. 4. 18. Photon spectral distribution after transport through CT different filters. The spectral distribution was calculated using 110 keV X-ray spectrum as calculated from the X-ray tube simulation. The image shows the Photon spectral distribution for different filters in the center of FOV (a) and at the edge of FOV (b). Fig. 4. 19. Energy fluence vs position due to different filters. The results were calculated using the spectrum simulating 110 keV X-ray tube voltage. 131 Fig. 4. 20. Comparison of spectral distribution after transport of X-rays through Cortical bone insert for different X-ray spectra ( 80, 110, 130 keV). Fig. 4. 21. Change of simulated and measured CT-numbers per kV as a function of the electron density of the Gammex substitutes. Fig. 4. 22. Comparison of energy fluence vs position after transport through phantom with Cortical bone insert. The X-ray spectra simulating the X-ray tube voltage ( 80, 110, 130 keV) are used. Fig. 4. 23. Change of simulated CT-numbers per phantom diameter as a function of the electron density of the substitutes. Fig. 4. 24. Change of simulated CT-numbers per electron density of the phantom materials is shown as a function of the electron density of the substitutes. The points represent the calculated change when the results of the cortical bone phantom are discarded. Fig. 4. 25. Transverse slice of the CT-data of selected patient. The tumour (CTV) is marked in red; the organs at risk are the brain stem which is marked in blue, the left optical nerve which is marked in green, the chiasm (not shown in this slice), the eyeballs and the other optical nerve. Fig. 4. 26. Profile through a central CT slice of a head of a patient with skull base tumor. The arrows indicate the position of skull bone. In between is a mixture of soft tissue and spongy bone (lower skull base). Fig. 4. 27. Calibration curves derived from simulated CT-numbers of Gammex substitutes for different voltage settings in comparison to measurements in Gammex substitutes and animal tissues. The calibration relation based on measurements in H-materials and the actual measured values are also shown for comparison. The calibrations are parameterized in Table 4.4. Fig. 4. 28. Comparison of calibration relations for ion treatment with literature data for different phantom sizes. 132 Abbreviations AAPM American Association of Physicists in Medicine BDM Base Depth of Measurement BHC Beam hardening Correction CRT Conformal Radiation Therapy CT Computer Tomography CTV Clinical Target Volume DEQ Dose Equivalent ECUT electron lower energy cut-off EGS Electron Gamma Shower DKFZ Deutsches Krebsforschungszentrum German Cancer Research Center ( Heidelberg, Germany) FOV Field of View FWHM Full Width at Half Maximum GSI Gesellschaft fur Schwerionenforschung HIMAC Heavy Ion Medical Accelerator Center HIT Heidelberg Ion Beam Therapy Center HU Hounsfield unit IMRT Intensity Modulated Radiotherapy IORT Intraoperative Radiotherapy ISIORT International Society of IORT 133 LTC local tumor control LET Linear Energy Transfer Linac Linear accelerator LLUMC Loma Linda University Medical Center (US) MC Monte Carlo MLC Multi-leaf collimator NCBJ National Centre for Nuclear Research (Świerk, Poland) OAR Organs at risk OR Operation room PCUT Photon lower energy cut-off PDD Percentage Depth Dose SSD Source Surface Distance PET Positron Emission Tomography PHSP Phase Space File PM Pnumbra of beam profile( PMMA Polymethyl methacrylate PSI Paul Scherrer Institute (Switzerla nd) PTCOG Particle Therapy Co-Operative Group PTV Planning target volume RBE Relative Biological Efficiency RMS Root-meansquare SDM Standard Depth of Measurement SOBP Spread-out Bragg peak SSD Source Surface Distance Rf radio-frequency TPS Treatment Planning System WEPL Water-Equivalent-Path-Length 134 Appendix A: Monte Carlo method Probability theory and sampling methods The are many good references on probability theory and Monte Carlo methods so only the elements of probability theory necessary to understand Monte Carlo method will be mentioned in this section [Nel85]. The primary entities of interest will be random variables which take values in certain subsets of their range with specified probabilities. Random variables will be denoted by putting a ˆ above them (e.g. xˆ ). If E is e logical expression involving some random variables, then one can write Pr{E} for the probability that E is true. F will called the distribution function (or cumulative distribution function) of if F(x) Pr{xˆ x}. (1) When F(x) is differentiable, then f (x) F'(x) (2) b Pr{a xˆ b} f (x)dx . (3) a is the density function (or probability density function) of xˆ and In this case is called a continuos random variable. 135 xˆ In the other case that is commonly of interest, takes on discrete values xi with probabilities pi and F(x) pi . (4) xi x We call P the probability function of xˆ if P(x) pi if x xi (5) = 0 if x equals none of the xi Such a random variable is called a discrete random variable. When we have several random variables xi (i = 1,n), we define a joint distribution function F by F(x1,...., xn ) Pr{xˆ1 x1 &...& xˆn xn}. (6) The set of random variables is called independent if n Pr{xˆ x1 &...& xˆn } Pr{xˆ1 xi }. (7) i1 n f (x1,..., xn ) F(x1..., xn )/ x1...., xn . (8) If F is differentiable in each variable, then we have a joint density function given by Then, if A is some subset of Rn (n-dimensional Euclidian Space), Pr{xˆA} f (x)d n x. (9) A 136 With this preliminary introduction one can move to sampling methods. In practice almost all sampling is based on the possibility of generating (using computers) sequences of numbers which behave in many ways like sequences of random variables that are uniformly distributed between 0 and ˆ 1.Uniformly distributed random variables well be denoted by i and values sampled from the uniform distribution F( ) 0, if 0, , if 1, (10) 1, if 1 ; ˆ by i . Clearly, if F and f are distribution and density functions, respectively, of , then they are given by f(ζ )= 1, if ζ ε(0,1), = 0, otherwise, We assume, in what follows, that we have an unlimited number of uniform variables available. Now, suppose that xˆ and ŷ are related by ŷ = h( ) (with h monotonically increasing), and that and ŷ have distribution functions F and G; then, F(x) Pr{xˆ x} Pr{h 1 (yˆ) x} Pr{yˆ h(x)} (11) G(h(x)). Thus, we can find F given G and h. In particular, if we define by then G(y) = y xˆ F 1(ˆ), (12) 137 and h(x) = F(x), so that Pr{xˆ x} G(h(x)) f (x). This is the basis of the so called direct method of sampling xˆ in which we set F(x) = ζ and solve for x. The x-values so chosen will have the distribution F. Particle transport The correct simulation of an electromagnetic cascade shower can be decomposed into a simulation of the transport and interactions of a single particle, along with some necessary bookkeeping. Initially, only the properties of the incident particle are stored in the first position of the corresponding arrays. The basic strategy is to transport the top particle until an interaction takes place, or until its energy drops below a predetermined cutoff energy, or until it enters a particular region space. In the latter two cases, the particle is taken off the stack and simulation resumes with the new top particle. If an interaction takes place, and if there is more than one product particle, the particle with the lowest energy is put on the top of the stack. When a particle is removed from the stack and none remain, the simulation of the shower event is complete. The mean free path, λ, of a particle is given in terms of its total cross section, σt - or alternatively, in terms of its macroscopic total cross section, ∑t - according to the expression 1 M (13) t Na p t where 138 Na = Avogadro's number, p = density, M = molecular weight, σt = total cross section per molecule. The probability of an interaction is given by Pr{interaction in distance dx} = dx/λ. In general, the mean free path may change as particle moves from one medium to another, or when it loses energy. The number of mean free paths traversed will be x dx N . (14) x0 (x) Nˆ If is a random variable denoting the number of mean free paths from a given point until the next interaction, then it can be shown that Nλ has the distribution function ˆ Pr{N N } 1 exp(N ) for N 0. (15) Using the direct sampling method and the fact that 1 - ζ is also uniform on (0,1) if ζ is, we can sample Nλ using Nλ = - lnζ. (16) This may be used in Eqn. 14 to obtain the location of the next interaction. One can now consider the application of the above to the transport of photons. Pair production, Compton scattering (from a "free" electron), and photoelectric processes are usually considered in EGS4 (Rayleigh scattering is included as a non-default option). These processes all have cross sections that are small enough that all interactions may be simulated. This means that photons travel in a straight line with constant energy between interactions. Thus, if the space in which the simulation 139 takes place is composed of a finite number of regions, in each of which the material is homogeneous and of constant density, then the integral in Eqn. 14 reduces to a sum. If x0, x1, ...are the boundary distances between which λ is constant, then Eqn. 14 becomes i1 x x x x N j j1 i1 , (17) j1 j i where x Є (xi-1, xi). The photon transport procedure is then as follows. First, pick the number of mean free paths to the next interaction using Eqn. 16. Then perform the following steps: Compute λ at the current location. Let t1 = λNλ. Compute d, the distance to the nearest boundary along the photon's direction. Let t2 equal the smaller of t1 and d. Transport by distance t2 . Deduct t2 / λ from Nλ. If the result is zero (this happens when t2 = t1 ), then it is time to interact - jump out of the loop. This step is reached if t2 = d. Thus, a boundary was reached. Do the necessary bookkeeping. If the new region is a different material, go to Step 1. Otherwise, go to Step 2. In regions where there is a vacuum, σ = 0 (λ = ∞) and special coding is used to account for this situation. Now, it will be considered charged particle transport. The relevant interactions considered in EGS are elastic Coulomb scattering off the nucleus, inelastic scattering off the atomic electrons, positron annihilation, and bremsstrahlung. Difficulties with charged particle transport arise from the fact that the cross sections for all of the above processes (with the exception of annihilation) become infinite as the transferred energy approaches zero (the infrared catastrophe, etc.). In actuality, these cross sections, when various corrections are taken into account (i.e., screening for nuclear scattering, electron binding for electron scattering, and Migdal corrections for bremsstrahlung), are not infinite, but they are very large and the exact values for the total cross sections are not well known. Therefore, it is not practical to tray to simulate every interaction. On the other hand, the low momentum transfer events which give rise to 140 the large cross section values do not result in large fluctuations in the shower behavior itself. For this reason, they are lumped together and treated in a continuous manner. Cutoff energies are used to distinguish between continuous and discrete interactions. The electron and photon cutoff energies used by EGS (and set up by PEGS) are given by the variables AE and AP, respectively. Any electron interaction that produces a delta-ray with total energy of at least AE, or a photon with energy of at least AP, is considered to be a discrete event. All other interactions are considered continuous and give rise to continuous energy losses and direction changes to the electron between discrete interactions. The energy losses are due to soft interactions with the atomic electrons (excitation and ionization loss) and to the emission of soft bremsstrahlung photons. The changes in direction are mostly due to multiple Coulomb scattering from the nucleus, with some contribution coming from soft electron scattering. The above considerations complicate charged particle transport in several ways. First of all, due to continuous energy loss the cross section varies along the path of the electron; in addition, the electron path is no longer straight. The fact that the electron total cross section for discrete interactions decreases with decreasing energy - and hence, decreases along the path of the electron - makes possible the following trick, which is used to account for the change in λ along the path. An additional fictitious interaction is introduced which, if it occurs, results in straight - ahead scattering (i.e., no interaction at all). The magnitude of this cross section is assumed to be such that the total cross section is constant along the path. That is, f (x) (x) (x) cons tant (x ). (18) t1 ict t1real fict t1real 0 The location of the next "interaction" is then sampled using Eqns.16 and 14 along with the total fictitious cross section, σt1fict. When the point of interaction is reached, a random number is chosen. If is larger than σt1real(x)/σt1real(x0), then the interaction is fictitious and the transport is continued from that point without interaction. Otherwise, the interaction is real and is dealt with in the way described later. It can be shown that this scheme samples the distance between interactions correctly provided that the total cross section decreases with decreasing energy. Unfortunately, this is not the case for very low values of AE (e.g., for AE ≤ 580 keV for low Z materials). This introduces a small systematic error in low energy problems. The transport of an electron between interactions is divided into smaller steps. Along each of these steps the electron is assumed to follow a straight line, and the multiple scattering is accounted for by changing the electron's direction at the end of the step. The angle between the initial and final direction is sampled from the appropriate distribution and the azimuthal angle is selected randomly. These steps must be kept small enough so that neglecting the lateral deflection of the electron along a step does not 141 introduce significant errors. A related effect is that of path length correction. The steps must be kept small enough so that the true electron path length is not much larger than the straight line path length. Otherwise, a systematic error in the distance to the next interaction will result. Particle interactions When a point of (real) interaction has been reached it must be decided which of the competing processes has occurred. The probability that a given type of interaction occured is proportional to its cross section. Suppose the types of interactions possible are numbered 1 to n. Then î, the number of the interaction to occur, is a random variable with distribution function i j F(i) j1 , (19) t n where σj is the cross section for the jth type of interaction and σt is the total cross section (= ∑ j=i σj ). The F(i) are the branching ratios. The number of the interaction to occur, i, is selected by picking a random number and finding the i which satisfies F(i 1) F(i). (20) Once the type of interaction has been selected, the next step is to determine the parameters for the product particles. In general, the final state of the interaction can be characterized by, say, n parameters μ1,μ2,...... ,μn. The differential cross section is some expression of the form d n g()d n (21) with the total cross section being given by g()d n . (22) Then f(μ)=g(μ)/ ∫g(μ) dn μ is normalized to 1 and has the properties of a joint density function. This may be normalized using the method given in a previous section or using some of the more general 142 methods mentioned in the literature. Once the value of μ determines the final state, the properties of the product particles are defined and can be stored on the stack. As mentioned before, the particle with the least energy is put on top of the stack. The portion of code for transporting particles of the type corresponding to the top particle is then entered. Appendix B B.1 EGS (Electron-Gamma-Shower ) code The EGS (Electron-Gamma-Shower ) system of computer codes is a general purpose package for the Monte Carlo simulation of the coupled transport of electrons and photons in an arbitrary geometry for particles with energies above a few keV up to several hundreds of GeV. The new, enhanced version called EGSnrc is used to simulate the all 3 subject in this work. EGSnrc is based on the popular EGS4 system but includes a variety of enhancements introduced by I. Kawrakow and D.W.O.Rogers [Kaw00]. The original EGS4 implementation as: PRESTA algorithm, the inclusion of angular distribution of bremsstrahlung photons, the low energy photon cross section have been developed in EGSnrc. Recent advances in the theoretical understanding of the “condensed history” (CH) [Kaw98] technique and multiple elastic scattering were used for the simulation of charged particle transport. The EGS Code System has been written in an extended Fortran language known as Mortran. The EGS code itself consists of two User-Callable subroutines, HATCH and SHOWER, which in turn call the other subroutines in the EGS code , some of which call three User- written subroutines, HOWFAR, HOWNEAR and AUSGAB. This is illustrated with the Fig.2.9. To use EGS the user must write a “User Code”. This consists of a MAIN program and the subroutines HOWFAR, HOWNEAR and AUSGAB, the latter three determining the geometry and output (scoring), respectively. Additional auxiliary subprograms might be included in the User Code to facilitate matters. The user can communicate with EGS by means of various COMMON variables. Usually MAIN performs any initialization needed for the geometry routines, HOWFAR and HOWNEAR, and sets the values of certain EGS COMMON variables which specify such things as names of the media to be used, the desired cutoff energies, and the distance unit to be used. MAIN then calls the HATCH subroutine which “hatches EGS” by doing necessary once-only initialization and by reading material data for the media from a data set that had been previously created by PEGS. This initialization completed, MAIN may then call SHOWER when desired. Each call to SHOWER specify the parameters of the incident particle initiating the cascade. In addition, macro definitions can be included in MAIN in order to control or over-ride various functions in EGS as well as in the User-Written codes. 143 In EGSnrc there are many new options compared to EGS4. The system defaults to a set of options which will do the most complete and accurate simulation that EGSnrc is capable of. In some cases this will imply overkill and a reduction in efficiency with no gain in accuracy ( e.g. including atomic relaxation or bound Compton scattering for high energy photon calculations). The user has the ability to switch things on or off by setting various flags. So, e.g., one can choose to model Klein Nishina Compton scattering instead of bound Compton scattering by setting a flag. Once other class of new features in EGSnrc is the implementation within the code itself of several variance reduction techniques (range rejection and bremsstrahlung splitting being the main two) since by doing so, a much more efficient implementation is allowed. The user can, of course, completely ignore these features if so desired. Fig.2.9. The structure of the EGSnrc code system when used with a user-code ( from [Kaw00]). 144 B.2 DOSRZnrc user code Calculations of the dose distribution of electron and photon beams (Chapter 3 and 4) have been performed with “user code” DOSRZnrc. DOSRZnrc scores dose in a two different geometries : cylindrical geometry or x y z geometry. The user defines the geometry via the input of a number of planar and cylindrical coordinates which divide the cylinder or cubic into a number of regions, each region composed of a user specified material. One can specify in which of these regions the dose is to be scored. The user selects either the energy if monoenergetic beam is to be used or specifies an energy spectrum consisting of energy points and corresponding probabilities. The control over the simulation is possible by selecting the number of histories, time limit and statistical limit. All histories run unless time runs out or the variance calculated in the peak region drops below the statistical limit. Transport is controlled by such the parameters as the fractional energy loss per charged particle step, the maximum step size, particle energy cutoffs, range rejection parameters User must choose values of these parameters. The following options connect with physical phenomena: Atomic relaxations, Rayleigh scattering, Photoelectron angular sampling and Bound Compton scattering can be turned On/Off on a region -by region basis. Depth dose curves and lateral dose profiles at 7.5 cm in the water phantom were obtained for 6 MeV photon beams. Two separate calculations with different cube phantoms were done; one phantom had a high resolution along the beam axis to obtain depth doses, the other one had a high resolution in the xy-plane at 7.5 cm, to obtain lateral dose profiles. Broad beam photon spectra calculated by Mohan et al. was used as input. The preliminary results obtained by the author are interesting and will be continued. In the next step it would be good to have possibility of introducing real photon spectrum for each individual narrow beam collimator and then compare dose calculation with measurements. Energy cut-off parameters used, were ECUT = 0.521 MeV, PCUT=0.01MeV. EGSnrc simulations were performed for 1 x 108 particles. For the calculations of Scatter Output Factors (SOF), area of the dose scoring region at the central axis was established taking into account the lateral dimensions of the detector that was used to determine SOF experimentally. The radiation field with a diameter of 5 cm was used as reference field . to remoove later B.3 BEAM/EGSnrc code 145 A study of the photon and electron spectra of narrow photon beams were performed in this work with the code BEAM/EGSnrc. BEAM/nrc is a Monte Carlo simulating system [Rog95] for modelling radiotherapy sources which was developed as part of the OMEGA project to develop 3-D treatment planning for radiotherapy (National Research Council Canada and University of Wisconsin). BEAMnrc is built on the EGSnrc Code System [Kaw00] and must be run on a Unix-based system. The EGSnrc system was released in February 2000 and the BEAM code system was ported to using EGSnrc in 2001 and released in Oct 2001. The OMEGA/BEAM system has a well defined structure of directories. It can be thought of as having two or possibly three general parts. The first sub-system is generally referred to as OMEGA_HOME and contains all the source code and scripts needed to run BEAMnrc and associated codes such as DOSXYZnrc, readphsp, BEAMDP etc.. Fig. 2.10 outlines this subsystem. This part of the system contains no execute modules related to beam simulation. Fig.2.10. Main components of the OMEGA_HOME directory structure in the BEAMnrc/DOSXYZnrc/EGSnrc system. HEN_HOUSE contains the EGSnrc system (from 146 Within this sub-system resides another sub-system which could be considered separate, the HEN_HOUSE, which contains the NRCC Unix-based version of the EGSnrc system. The final component of the OMEGA/BEAM structure is the user’s area HOME which is not shown in Fig. 2.10. In the user’s area there are beamnrc and egsnrc scripts. These scripts will set up automatically if it is not in place, as will the INSTALL_OMEGA script. One of the main complications is that the EGSnrc and BEAMnrc systems are set up to use one disk system to support multiple Unix/Linux systems and their associated compilers. Thus , all execute modules and various compiler options etc. must be handled separately for each Unix system ( in this work was used one Unix system-Linux only). Fig.2.11. The steps involved in using the BEAMnrc system, (from [Rog95]). Figure 2.11. presents a schematic of the overall steps required to do an accelerator simulation. At the specify accelerator and build accelerator steps, the user is instructing the system how to pull together the source code and make an executable module. During the execution stage, the program reads in a large quantity of data related to photon and electron cross section data for the specific materials in this accelerator model (generated by a code included with the EGSnrc system called PEGS4) and also the user has an input file which specifies all the details about the particular accelerator. Also the user must 147 specify all the parameters controlling the radiation transport modelling and must also select and control the various variance reduction techniques being used. In this work the accelerator Clinac 2003CD is modelled. The confidential accelerator head data were obtained from Varian Oncology Systems. All accelerator components: the bremsstrahlung target, the flattening filter, the primary, secondary and tertiary ( narrow beams) collimators, and the monitor ionization chamber are modeled as accurately as possible based on information provided by the manufacturer. The simulations are carried out in several steps. First, 3 x 108 monoenergetic electrons (6 MeV) in a monodirectional pencil beam are allowed to interact with the bremsstrahlung target and the spatial coordinates, energy, weight factors and directional cosines of all particles passing the plane at the entrance of the narrow circular beam collimator, are scored in a phase space file. Next, starting from this phase space file , the narrow beam collimator is included into the simulation and particle transport information is scored again in two phase planes: at the circular collimator exit plane in air and at a plane which is located in water phantom at 100 cm SSD. These simulations are performed for 1 x 108 particles using cylindrical geometry. With the BEAM code, the accelerator is modelled for radiation fields with a diameter as small as 0.25 cm. Different electron and photon transport cut-off values, ECUT and PCUT, are used in the different parts of calculations. In the accelerator geometry ECUT is chosen as 1.5 MeV, PCUT as 100 keV. In the water phantom ECUT is set to 200 keV and PCUT to 10 keV. The code BEAMDP is used to extract the spectral and mean energy distributions of photons and electrons from a phase space data files. 148