ASYMMETRIC COLLIMATION: DOSIMETRIC CHARACTERISTICS, TREATMENT PLANNING ALGORITHM, AND CLINICAL APPLICATIONS. by WILLIAM KW A B.Sc, The University of British Columbia, 1978 M.Sc.A., McGill University, 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT S FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Physics We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March, 1998 Â© William Kwa, 1998 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT Asymmetric collimation of photon beams produces non-trivial alterations in absolute output, depth dose and beam profile. The full potential of asymmetric collimation can only be realized with a proper treatment planning algorithm specific for asymmetric collimation. In this thesis the dosimetric characteristics of asymmetric fields are investigated and a new computation method for the dosimetry of asymmetric fields is described and implemented into an existing treatment planning algorithm. Based on this asymmetric field treatment planning algorithm, the clinical use of asymmetric fields in cancer treatment is investigated, and new treatment techniques for conformal therapy are developed. Dose calculation is verified with thermoluminescent dosimeters in a body phantom. An asymmetric field is referred to as an off-set radiation field whereby the central axis of the radiation field does not coincide with the collimator axis as the opposite pair of collimators no longer are equidistant from the collimator axis. Here, the corresponding symmetric field is a radiation field centered at the collimator axis with the opposite pair of collimators set equidistant from the collimator axis and to the largest asymmetric collimator setting. Usually the dose distribution in an asymmetric field is represented by some form of beam modeling. In this thesis, an analytical approach is proposed to account for the dose reduction when a corresponding symmetric field is collimated asymmetrically to a smaller asymmetric field. This is represented by a correction factor that uses the ratio of the equivalent field dose contributions between the asymmetric and symmetric fields. The same equation used in the expression of the correction factor can be used for a wide range of ii asymmetric field sizes, photon energies and linear accelerators. This correction factor will account for the reduction in scatter contributions within an asymmetric field, resulting in the dose profile of an asymmetric field resembling that of a wedged field. The output factors of some linear accelerators are dependent on the collimator settings and whether the upper or lower collimators are used to set the narrower dimension of a radiation field. In addition to this collimator exchange effect for symmetric fields, asymmetric fields are also found to exhibit some asymmetric collimator backscatter effect. The proposed correction factor is extended to account for these effects. A set of correction factors determined semi-empirically to account for the dose reduction in the penumbral region and outside the radiated field is established. Since these correction factors rely only on the output factors and the tissue maximum ratios, they can easily be implemented into an existing treatment planning system. There is no need to store either additional sets of asymmetric field profiles or databases for the implementation of these correction factors into an existing in-house treatment planning system. With this asymmetric field algorithm, the computation time is found to be 20 times faster than a commercial system. This computation method can also be generalized to the dose representation of a two-fold asymmetric field whereby both the field width and length are set asymmetrically, and the calculations are not limited to points lying on one of the principal planes. The dosimetric consequences of asymmetric fields on the dose delivery in clinical situations are investigated. Examples of the clinical use of asymmetric fields are given and the potential use of asymmetric fields in conformal therapy is demonstrated. A n alternative head and neck conformal therapy is described, and the treatment plan is compared to the iii conventional technique. The dose distributions calculated for the standard and alternative techniques are confirmed with thermoluminescent dosimeters in a body phantom at selected dose points. iv TABLE OF CONTENTS Page ABSTRACT ii TABLE OF CONTENTS v LIST OF TABLES viii LIST OF FIGURES ix ACKNOWLEDGMENTS xiv 1. INTRODUCTION 1 1.1. Objective and Contents of this Thesis 7 2. BACKGROUND 9 2.1. Radiation Absorbed Dose Calculations in External Beam Radiotherapy 9 2.1.1. The depth of maximum dose (dmax) 9 2.1.2. The monitor unit (MU) and output factor (OPF) 10 2.1.3. The percentage depth dose (PDD) 13 2.1.4. The tissue maximum ratio (TMR) and tissue air ratio (TAR) 15 2.1.5. The backscatter factor (BSF) or the peak scatter factor (PSF) 15 2.1.6. The scatter air ratio (SAR) 18 2.1.7. The off axis ratio (OAR) and the depth dose profile 20 2.1.8. The isodose curve, and isodose chart or distribution 20 2.1.9. The collimator scatter factor (CSF) or head scatter factor 22 3. MATERIALS AND METHODS 23 3.1. Linear Accelerator (linac) 23 v 3.2. Dosimetry Phantoms 23 3.2.1. Water tank system 23 3.2.2. Body phantom 24 3.3. Dosimetric Measuring Instruments 25 3.3.1. A thimble type ionization chamber 25 3.3.2. Thermoluminescent dosimeter (TLD) 27 3.4. Treatment Planning 28 3.4.1. Treatment planning algorithm 28 3.4.1.1. An in-house treatment planning algorithm 29 3.4.1.2. A commercial treatment planning system 29 3.4.2. Absorbed dose distribution in a patient 30 4. DOSIMETRIC CHARACTERISTICS OF ASYMMETRIC BEAMS 35 4.1. Overview/Historical Development 35 4.2. The Output Factor (OPF) of an Asymmetric Field (AF) 40 4.2.1. Direct implementation of the Day's equivalent field method 40 4.2.2. Derivation of a correction factor (CF) 47 4.2.3. Influence of the collimator settings on the output factor (OPF) 50 4.2.4. Influence of the collimator settings on the asymmetric field output factor (AF OPF) 56 4.3. Asymmetric Field Dose Calculation 72 4.3.1. The asymmetric field dose representation at depth 72 4.3.2. The wedge effect of asymmetric collimation 77 vi 4.4.. An Asymmetric Field Treatment Planning Algorithm 86 4.4.1. Generation of a set of correction factors 86 4.4.2. Implementation of the correction factors as a FORTRAN subroutine 93 4.4.3. Summary 98 4.5. Asymmetric Collimation in Both Field Dimensions 100 5. CLINICAL USE OF ASYMMETRIC COLLIMATORS 112 5.1. An Overview 112 5.2. Half-collimated Asymmetric Breast Treatment Technique 118 5.3. Head and Neck Conformal Therapy 124 6. CONCLUSIONS 137 BIBLIOGRAPHY 140 APPENDIX 1: AsymCorrFactor- a FORTRAN subroutine for the asymmetric field treatment planning algorithm 147 APPENDIX 2: Glossary of Terms 151 vii LIST OF TABLES Page Table 1. Ratios of calculated asymmetric field output factors to measured asymmetric field output factors for a 6 MV photon beam. 64 Table 2. Ratios of calculated asymmetric field output factors to measured asymmetric field output factors for a 10 MV photon beam. 65 Table 3. Difference in "T sym" readout of a Clinac 2100C linac with the Clinac dose servo disabled for different 6 MV asymmetric fields. 69 Table 4. Difference in "T sym" readout of a Clinac 2100C linac with the Clinac dose servo disabled for different 10 MV asymmetric fields. 70 Table 5. The measured ion chamber ratios of asymmetric fields and symmetric fields for a 6 MV photon beam at the asymmetric field center are compared to the calculated correction factors at the same point. 75 Table 6. The measured ion chamber ratios of asymmetric fields and symmetric fields for a 10 MV photon beam at the asymmetric field center are compared to the calculated correction factors at the same point. 76 Table 7. Table 8. The effective tissue air ratios at dm a x and at 10 cm depth are calculated based on the Clarkson's scatter-sector integration method. 82 The average percentage dose difference between the calculated and measured dose values for points within the radiation field and 1.5 cm away form the field edges along the asymmetric central plane and the principal plane are shown. 110 Table 9. TLD verification of doses received with the standard technique at discrete points in a prestwood head phantom is shown. 127 Table 10. TLD verification of doses calculated using the in-house treatment planning system with the alternative technique at discrete points in a prestwood head phantom is shown. 132 LIST OF FIGURES Page Figure 1. An illustration of a medical linear accelerator and its rotational and translational degrees of freedom. 2 Figure 2. A linear accelerator head assembly in photon beam mode is shown. 3 Figure 3. The upper and lower collimators defining a pyramid of useful radiation are illustrated. 4 Figure 4. The relationships between field sizes and distances in an asymmetric field and a symmetric field are illustrated. 6 Figure 5. A typical photon beam depth dose curve is shown. 11 Figure 6. The irradiation geometry used in the derivation of the output factor (OPF) is shown. 12 Figure 7. The irradiation geometry used in the derivation of the percentage depth dose (PDD) at a fixed source to surface distance is shown. 14 Figure 8. The irradiation geometry used in the derivation of the tissue maximum ratio (TMR) at a fixed source to axis distance with field size W x L is shown. 16 Figure 9. The irradiation geometry used in the derivation of the tissue air ratio (TAR) at a fixed source to axis distance with field size W x L is shown. 17 Figure 10. The irradiation geometry used in the derivation of the backscatter factor (BSF) or the peak scatter factor (PSF) at a fixed source to axis distance with field size W x L is shown. 19 Figure 11. The irradiation geometry used in the derivation of the off axis ratio (OAR) is shown. 21 Figure 12. A schematic diagram of a typical thimble ionization chamber is shown. 26 Figure 13. The storing of a matrix of dose points is shown. Dose points are represented by 13 fan lines and 5 transverse lines. 31 Figure 14. A schematic diagram illustrating the absorbed dose in a rectangular field of dimensions W x L at a point Q. 32 Figure 15. A three-dimensional representation of the patient outline by the superior (sup), central, and inferior (inf) transverse cross-sectional planes or slices. 33 Figure 16. Isodose distributions for a three field treatment are illustrated on several cross-sectional CT slices. 34 Figure 17. The equivalent field contributions used in the Day's equivalent dose calculation method are illustrated. 41 Figure 18. The off-axis ratios (OARs) for both the (A) 6 MV and (B) 10 MV photon beams at dmax and in-air are shown. 45 Figure 19. Illustration of primary and scattered radiation to points on center and at the edge of the radiation field. 46 Figure 20. The output factors (OPFs) were measured for square and rectangular fields with the upper Y collimator and the lower X collimator defining the field width for a 6 and a 10 MV photon beam. 52 Figure 21. The geometric relationships between x-ray target, flattening filter, and upper and lower secondary collimators relative to the isocenter are illustrated. 54 Figure 22. The asymmetric field output factors (AF OPFs) were measured at the asymmetric field center for a 6 MV 12 x 40 cm2 symmetric field collimated to 9, 6, and 4 x 40 cm2 asymmetric fields. 59 Figure 23. The asymmetric field output factors (AF OPFs) were measured at the asymmetric field center for a 10 MV 12 x 40 cm2 symmetric field collimated to 9, 6, and 4 x 40 cm2 asymmetric fields. 60 Figure 24. The asymmetric field output factors (AF OPFs) were measured at the asymmetric field center for a 6 MV 40 x 20 cm2 symmetric field collimated to 30, 20, 18, and 10 x 40 cm2 asymmetric fields. 61 Figure 25. The asymmetric field output factors (AF OPFs) were measured at the asymmetric field center for a 10 MV 40 x 20 cm2 symmetric field collimated to 30, 20, 18, and 10 x 40 cm2 asymmetric fields. 62 Figure 26. The collecting plate configuration of the beam monitor chamber is shown. 68 Figure 27. Typical absorbed dose profiles for a symmetric field, a half-collimated asymmetric field, and a symmetric field with the same field width as the half-collimated asymmetric field are shown. 78 Figure 28. Illustration of a 20 x 20 cm2 field with the 10Â° sectors used in the calculation of effective tissue air ratio (eff TAR) and effective peak scatter factor (eff PSF) at collimator axis and 7 cm off-axis is shown. 80 Figure 29. The measured and calculated asymmetric field dose profiles are compared for a 6 MV photon beam at dmax and at 100 cm source to axis distance. 83 Figure 30. The measured and calculated asymmetric field dose profiles are compared for a 10 MV photon beam at dmax and at 100 cm source to axis distance. 84 Figure 31. The measured and calculated dose profiles are compared for a 6 MV photon beam at depths of 2, 10 and 25 cm and at 100 cm source to axis distance. 87 Figure 32. A schematic diagram illustrating the dose profiles of a symmetric field and a smaller asymmetric field is shown. The positions where the various correction factors used in the present algorithm are applied for asymmetric fields are indicated. 89 Figure 33. The measured and calculated dose profiles are compared for a 10 MV photon beam at depths of 2, 10 and 25 cm and at 100 cm source to axis distance. 92 Figure 34. The measured and calculated isodose distributions for a 10 MV photon beam at 100 cm source to surface distance are shown. 94 Figure 35. The measured and calculated isodose distributions for a 6 MV photon beam at 100 cm source to surface distance are shown. 95 Figure 36. The calculated isodose distribution for two adjacent half-collimated beams and a single symmetric field for a 6 and a 10 MV photon beam are shown. 97 Figure 37. Illustration of the equivalent field principle for a 2-fold asymmetric field is shown. 101 Figure 38. The measured and calculated dose profiles along one of the principal planes at dmax, 10 and 25 cm depths and at 100 cm source to axis distance are compared for a 6 MV photon beam. 105 Figure 39. The measured and calculated dose profiles along one of the principal planes at dmax, 10 and 25 cm depths and at 100 cm source to axis distance are compared for a 10 MV photon beam. 106 Figure 40. The measured and calculated dose profiles along the asymmetric central plane (2.5 cm away from the principal plane) at dmax, 10 and 25 cm depths and at 100 cm source to axis distance are compared for a 6 MV photon beam. 107 Figure 41. The measured and calculated dose profiles along the asymmetric central plane (2.5 cm away from the principal plane) at dm a x, 10 and 25 cm depths and at 100 cm source to axis distance are compared for a 10 MV photon beam. 108 Figure 42. The measured and calculated dose profiles of a 20 x 40 cm2 symmetric field collimated in both dimensions to a 10 x 20 cm2 asymmetric field along the asymmetric central plane (10 cm away from the principal plane) at dm a x, 10 and 25 cm depths and at 100 cm source to axis distance are compared for a 6 MV photon beam. 111 Figure 43. Comparison of treatment plans for a concavely shaped planning target volume typical of nasopharyngeal cancer with retrostyloid tumor extension using a multiple asymmetric fields technique and a conventional three-field technique. 115 Figure 44. A treatment plan for an L-shaped planning target volume typical of nasopharyngeal cancer. 117 Figure 45. Schematic illustrating the set-up of the conventional tangential breast treatment with gantry tilt. 119 Figure 46. Schematic illustrating the SSD set-up of the half-collimated asymmetric field breast treatment. 120 Figure 47. The dose distributions for breast irradiation with two tangential opposed beams using the conventional and the half-collimated asymmetric field technique. 121 Figure 48. Schematic illustrating the isocentric SAD set-up of the half-collimated asymmetric field breast treatment. 123 Figure 49. The dose distributions in the central plane of a prestwood head phantom for a standard technique and an alternative technique. 126 Figure 50. The dose distribution for a single arced asymmetric field in a circular phantom as calculated with the proposed asymmetric field algorithm and with the GE Target system. 130 Figure 51. The dose distributions for a standard technique and an alternative technique along the mid-plane of a patient's neck are shown. 133 Figure 52. The dose distributions of the same patient using the same alternative technique at a plane 5 cm superiorly is shown. Figure 53. The dose distribution of the same patient is shown at a plane 5 cm inferiorly using the alternative technique but with the large lateral pair angled at an oblique angle so as to avoid the shoulder. ACKNOWLEDGMENTS I would like to express my gratitude to the following people: Dr. E. El-Khatib, my thesis supervisor and head physicist, for her continuous support and guidance. Dr. R. O. Kornelsen, my retired head physicist, for his original suggestion towards this topic. Dr. S. Hussein, my colleague and mentor, for his encouragement and advice. My co-authors, and in particular, Mr. R. W. Harrison, whose work constitutes invaluable contributions to our joint projects. My colleagues in the Clinical Physics Department, oncologists in the Division of Radiation Oncology, and staff of the Medical Illustration Department for their patience, assistance, and support. Dr. J. Scrimger and Ms. O. L. Chow for their help. My dear wife Joyce, parents, relatives and friends for their patience, encouragement, and support. xiv 1. INTRODUCTION Radiotherapy is a major treatment modality for cancer. In external beam radiotherapy a radiation emitting device is used to aim a beam of photons or electrons at the tumor volume from some distance away. The equipment of choice for external beam therapy is the linear accelerator (linac). As illustrated in Figure 1, the gantry of the linear accelerator rotates along an axis that is centered at the isocenter as represented by GG. The isocenter is a reference point in space that is the common axis of rotation for the gantry, collimator and turntable. The couch rotates with the turntable as represented by 0T and moves vertically, longitudinally and laterally in order to align the patient's treatment center with the isocenter. The collimator consists of the field-defining jaws that also have the isocenter as the axis of rotation as represented by 9c. The collimator is part of the structure of the treatment head of the linear accelerator as shown in Figure 2. In photon mode, electrons strike a target and produce bremsstrahlung photons. These photons are first collimated by the primary collimator to form a cone of radiation. The bremsstrahlung photons produced are forward peaked in intensity and therefore to produce a uniformly intense radiation field need to pass through a flattening filter. This radiation beam is then collimated by two pairs of continuously moveable collimators or jaws to produce a pyramid of useful radiation where the radiation field size can have any square or rectangular shape typically between 0 x 0 to 40 x 40 cm2 at 100 cm from the target as shown in Figure 3. The two pairs of collimators are perpendicular to each other and are referred to as the upper and lower collimators. For the Varian Clinac linear accelerators used (Varian Associates, Palo Alto, CA), the upper pair of collimators are 1 Figure 1. An illustration of a medical linear accelerator and its rotational and translational degrees of freedom. 2 Figure 2. A linear accelerator head assembly in photon beam mode is shown. Â«m target Figure 3. The upper and lower collimators defining a pyramid of useful radiation are illustrated. 4 referred to as the Y i and Y 2 collimators, and the lower collimators are labeled X i and X 2 . With the collimator angle 0c set at 0Â°, the lower pair defines the radiation field width, W, and the upper pair defines the radiation field length, L. Normally, each pair moves equidistant from the center of the field so as to define a symmetric radiation field of rectangular or square shape. By convention, the position of each collimator is defined as the projected dimension at the cross plane of the isocenter which is normally 100 cm from the radiation source. For example, a symmetric field of 10 x 20 cm2 has the collimators set at X i = 5 cm, X 2 = 5 cm, Y i = 10 cm, and Y 2 = 10 cm. Some newer linear accelerators allow the independent movement of each pair of the upper and lower collimators. This feature is called asymmetric collimation. With this feature, each pair of the upper and lower collimators do not need to be set equidistant from each other. For example, X i is set at 5 cm whereas X 2 is set at 2 cm. The result is a radiation field width of 7 cm wide whose center is now located at r a s y m which is 1.5 cm offset towards the X i collimator (Fig. 4). This off-centered field is referred to as the asymmetric field and has a width AW. The clinical use of asymmetric collimation is quite limited.1 This is because most radiotherapy centers do not have the proper treatment planning algorithm to calculate the dose distribution within an asymmetric field. In radiotherapy, accurate dose delivery is crucial since the aim is to deliver maximum absorbed dose to the tumor but minimum dose to normal tissue. In particular, the absorbed dose to critical structures such as the spinal cord must not exceed organ tolerance or else the treatment will fail because of treatment complication. 5 Figure 4. The relationships between field sizes and distances in an asymmetric field (AF) and a symmetric field (SF) are illustrated. 6 1.1. Objective and Contents of this Thesis The aim of this thesis is to develop a dose computation method that would accurately predict the radiation dose at any point in an asymmetric field and that requires minimal data acquisition and minimal computation time. Some of the dosimetric characteristics of asymmetric fields are investigated. The clinical use of asymmetric fields is discussed and new treatment techniques are developed. In Chapter 2, some of the dosimetric parameters commonly used in radiotherapy physics are explained. Materials and Methods are covered in Chapter 3. Topics include the linear accelerators and phantoms used in the work of this thesis. The dose measuring methods and the algorithms used in treatment planning are also described. In Chapter 4.1, some of the published papers on the dosimetry of asymmetric fields are described. In Chapter 4.2, the influence of the asymmetric field settings on radiation output is investigated and a correction factor is derived to account for the difference in radiation dose in symmetric and asymmetric fields. In Chapter 4.3, the correction factor is extended to represent absorbed dose at any off axis point and at any depth along the principal plane parallel to the asymmetric field dimension. The correction factor is also shown to account for the observed tilt of the radiation dose profile (wedge effect) of an asymmetric field. In Chapter 4.4, the implementation of the correction factor into an existing treatment planning program is discussed. Comparisons are made between this correction factor method and the dose calculations made with those obtained from a commercial system based on the Cunningham's IRREG program.2 In Chapter 4.5, the correction factors are extended for dose 7 representation of two-fold asymmetric fields, i.e., with both the field width and length collimated asymmetrically. In Chapter 5.1, the clinical use of asymmetric collimators and its implication in dose optimization are investigated. In particular, the wedge effect (as discussed in Chapter 4.3) on treatment optimization is illustrated. An improved tangential breast treatment technique in terms of ease of patient set-up is introduced in Chapter 5.2. Again, the importance of the use of a proper asymmetric field dose calculation algorithm for the optimal optimization and delivery of a treatment plan is illustrated. In Chapter 5.3, a head and neck treatment technique with static and rotational asymmetric fields is proposed. The calculated dose distributions are confirmed by thermoluminescent dosimeter measurements in a body phantom. 8 2. B A C K G R O U N D 2.1. Radiation Absorbed Dose Calculations in External Beam Radiotherapy The use of external beam radiotherapy involves careful treatment planning. The aim of external beam radiotherapy planning is to deliver maximum absorbed dose to a well defined planning target volume in a patient to obtain the desired biological or clinical effects while at the same time sparing the surrounding normal tissues. As a result, a precise knowledge of the absorbed dose at all points of interest in an irradiated patient is required. Unfortunately, verification of dose using direct measurement is seldom possible within the patient. Indirect methods are therefore employed. Conventionally, absorbed dose measurements are carried out in a well defined manner with some water-equivalent phantom. The dose distributions are then used to relate and predict the dose distributions within the patient. Ultimately the dose at all points in an irradiated 3 dimensional volume is related to the dose at the point where the accelerator is calibrated. Some of the terminology used in the dose representation for external beam radiotherapy is described here. 2.1.1. The depth of maximum dose (dmax) This is the depth in an irradiated medium at which maximum dose is observed. For megavoltage photon beams, the photon interaction sets in motion electrons that deposit their energies at some distance away from the site of photon interaction. Thus, the maximum 9 absorbed dose occurs at some depth beyond the irradiated surface as shown in Figure 5 where all doses are shown normalized to 100% at the maximum. The actual depth of maximum dose depends on the photon energy used. For photon energies below the megavoltage range, the dmax is just below the surface, but for megavoltage photon beams, the dm a x in water ranges from 0.5 cm for Cobalt 60 radiation to 5 cm for a 25 MV photon beam. 2.1.2. The monitor unit (MU) and output factor (OPF) The radiation beam emanating from a medical linear accelerator is pulsed and the radiation output over time may fluctuate. In order to monitor the dose delivered to the patient, most linear accelerators employ a beam monitor chamber situated in the treatment head to integrate the radiation delivered over a set period. The unit used is the monitor unit (MU). Upon the delivery of a preset MU, the linear accelerator terminates the radiation production automatically. Since the actual dose delivered to the patient is dependent on various factors such as the size of the radiation field used, the term output factor (OPF) is used to relate the dose delivered at a particular point in a water phantom with the MU given. Linear accelerators are typically calibrated for a reference field size of 10 x 10 cm2 at 100 cm from the source at a depth of maximum dose, d,^, on the central axis in a water phantom. At this point the MU is adjusted so that 1 MU = 1 centigray. The output factor for a 10 x 10 cm2 field as shown in Figure 6A is then defined as: 10 max depth (cm) Figure 5. A typical photon beam depth dose curve is shown. 11 Figure 6. The irradiation geometry used in the derivation of the output factor (OPF) is shown. The absorbed dose at depth of maximum ionization (d^x) and at 100 cm source to axis distance (SAD) along the collimator axis is obtained for (A) a 10 x 10 cm2 field and (B) a radiation field W x L. 12 OPF (10x10) = D (dmax, 10x10) / M U . (1) where D(dmax,10xl0) is the absorbed dose measured for the number of MU delivered. It is specified in units of centigray per monitor unit, cGy / MU. The output factor for any other field size W x L as shown in Figure 6B is then given as: Therefore the output factors give the relationship between radiation absorbed doses at point of maximum dose in a water phantom for different radiation field sizes. 2.1.3. The percentage depth dose (PDD) To relate the absorbed dose at depth d and at d m a x along the collimator axis for a particular field size and photon energy, the term percentage depth dose (PDD) is used. For PDD the source to phantom surface distance (SSD) remains fixed, typically at 100 cm, and the distance of the measurement point from the source is SSD + d for a point located at depth d and SSD + d m a x for a point located at depth d m a x as shown in Figures 7A and B, respectively. The percentage depth dose is defined as the ratio of the absorbed dose at depth d, D(d,WxL,SSD), to the absorbed dose at d^x, D(dmax,WxL,SSD), and is given as: The percentage depth dose (an example of which is shown in Fig. 5) varies with photon energy, field size and source to surface distance. OPF (WxL) = OPF (10x10) x D (dmax,WxL) / D (d^, 10x10). (2) PDD (d,WxL,SSD) = 100 % x D (d,WxL,SSD) / D (dmax,WxL,SSD). (3) 13 D(d,WxL,SSD) E K d m a x , W x L , S S D ) Figure 7. The irradiation geometry used in the derivation of the percentage depth dose (PDD) at a fixed source to surface distance (SSD) is shown. The absorbed dose, D(d,WxL,SSD), at depth d is shown in (A) and that at depth d m a x , D(dmaX,WxL,SSD), is shown in (B). Both doses are measured on the collimator axis and for the same field size defined at SSD. 14 2.1.4. The tissue maximum ratio (TMR) and tissue air ratio (TAR) Alternatively, the relationship between two doses at different depths can also be related by the tissue maximum ratio (TMR). For the TMR, however, the distance from the source to the measurement point (source to axis distance, SAD) is kept constant at 100 cm and depth is varied by changing the water level above the measurement point. This is illustrated in Figure 8 with the tissue maximum ratio given as: TMR (d,W*L) = D (d ,WxL) / D ( d m a x ,WxL) . (4) The field size W x Lis defined at SAD which is the position of the measurement point. Hence for a given MU in a radiation field W * L and at 100 cm source to axis distance, the absorbed dose at a depth d along the collimator axis can be calculated from Eqs. 1, 2 and 4 as: D (d,WxL) = MU x OPF (W*L) x TMR (d,WxL). (5) Another useful term is the tissue air ratio (TAR). It is defined as the ratio of the absorbed dose at a depth d, D(d,WxL), to the absorbed dose "in air", Dair(WxL), at the same source to axis distance (Fig. 9A and B, respectively) and is given as: TAR (d ,WxL) = D (d,WxL) / D a i r ( W x L ) . (6) The Dair(WxL) is the absorbed dose in air or in free space with field size W x L , where the dosimeter is surrounded by sufficient phantom-like material to establish electronic equilibrium but not enough to significantly attenuate the primary radiation fluence. 2.1.5. The backscatter factor (BSF) or the peak scatter factor (PSF) 15 SAD D(d,WxL) D C d ^ W x L ) Figure 8. The irradiation geometry used in the derivation of the tissue maximum ratio (TMR) at a fixed source to axis distance (SAD) with field size W x L i s shown. The absorbed dose, D(d,WxL), at depth d is shown in (A) and that at depth dm a x, D(dmax,WxL), is shown in (B). 16 Figure 9. The irradiation geometry used in the derivation of the tissue air ratio (TAR) at a fixed source to axis distance (SAD) with field size W x L is shown. The absorbed dose, D(d,WxL), at depth d is shown in (A) and the dose in air, Dair(WxL), is shown in (B). 17 The backscatter factor (BSF) or the peak scatter factor (PSF) is the special case of a TAR at d m a x and is given as: BSF ( W * L ) or PSF ( W x L ) = TAR (dm ax,WxL) = D(dmax , W x L ) /D a i r ( W x L ) . (7) This is a measure of the phantom scatter contribution at dmax for the specified field size W x L since the absorbed dose at dmax, D(dm ax,WxL), would include phantom scatter contribution whereas the absorbed dose in free space, D a i r ( W x L ) , has minimal scatter contribution (Fig. 10A and B). The peak scatter factor generally, increases with field size as more scattered radiation reaches the collimator axis but levels off at large field sizes as the scattered radiation can no longer reach the point where absorbed dose is measured. 2.1.6. The scatter air ratio (SAR) The scatter air ratio (SAR) is a measure of the contribution from scattered radiation at depth. It is the difference between the tissue air ratio (TAR) for a radiation field of finite size W X L and for a zero area field size. SAR (d,WxL) = TAR (d,W><L) - TAR (d,0><0). (8) The tissue air ratio for zero area field size, TAR(d,0><0), can be determined from a measured narrow beam attenuation curve or from a plot of tissue air ratio versus field size extrapolated to zero field size. It represents the attenuation of the primary photon beam in material of thickness d. ' 18 S A D D ( d m a x > W x L ) Dai/WxL) Figure 10. The irradiation geometry used in the derivation of the backscatter factor (BSF) or the peak scatter factor (PSF) at a fixed source to axis distance (SAD) with field size W x L is shown. The absorbed dose in water at dmax, D(dmax,WxL), is shown in (A) and the dose in air, Dair(WxL), is shown in (B). 19 2.1.7. The off axis ratio (OAR) and the depth dose profile The previously defined parameters all relate doses measured on the center of the beam at the collimator axis. For any points away from the collimator axis, the off axis ratio (OAR) is used to relate the absorbed dose at the off axis point to a point along the collimator axis and at the same depth. The OAR is the ratio of absorbed dose at a point a distance r away from the collimator axis, D(r,d,W><L), (Fig. 11 A) to the absorbed dose at a point at the same depth along the collimator axis, D(0,d,WxL), (Fig. 1 IB) for the same field size W x L and photon beam and is given as: OAR (r,d,WxL) = D (r,d,WxL) / D (0,d,WxL). (9) Thus, the absorbed dose at an off axis point is related to the MU given by Eqs. 5 and 9 as: D (r,d,WxL) = MU x OPF (WxL) x TMR (d,W*L) x OAR (r,d,W*L). (10) If all dose points at a particular depth in water are joined and normalized to 1.0 or 100% on collimator axis the resultant continuous line is called a dose profile. A typical dose profile is shown in Figure 31. 2.1.8. The isodose curve, and isodose chart or distribution The isodose curve is a continuous line joining points that have the same absorbed dose value in a 2-dimensional cross-sectional plane and is usually expressed as a percentage of the maximum dose in the plane. An isodose chart or distribution is formed when a set of isodose curves, for a range of dose values, are displayed (an example of which is shown in Fig. 34). 20 SAD D(r,d,WxL) D(d,WxL) Figure 11. The irradiation geometry used in the derivation of the off axis ratio (OAR) is shown. The absorbed dose at distance r from the collimator axis, D(r,d,WxL), is shown in (A). The dose at the same depth on the collimator axis D(d,WxL) is shown in (B). 21 2.1.9. The collimator scatter factor (CSF) or head scatter factor. The collimator scatter factor (CSF), also known as the head scatter factor, is the ratio of the absorbed dose in free space at the isocenter for a given field size W x L to the absorbed dose at the same point for a reference field size, normally 10 x 10 cm2, and is given as: CSF ( W x L ) = D a i r ( W x L ) / D a i r (10x10). (11) Since the absorbed dose in free space is assumed to have minimal phantom scatter, the collimator scatter factor is therefore a measure of the difference in radiation output due to different collimator settings. The relationships between output factor (OPF), peak scatter factor (PSF) and collimator scatter factor (CSF) can be expressed by Eqs. 2, 7 and 11 as: OPF ( W x L ) = OPF (10x10) x CSF ( W x L ) x PSF ( W x L ) / PSF (10x10). (12) 22 3. MATERIALS AND METHODS 3.1. Linear Accelerator (linac) The linacs used for the work described in this thesis are two Clinac 2100C and a Clinac 2100C/D (Varian Associates, Palo Alto, CA). All three linacs are dual energy machines with 6 and 10 MV (megavoltage) photon beams. The nominal accelerating potentials for the photon beams are 4.7 and 8.9 MV respectively as defined by the AAPM 3 TG21 protocol. Both the lower X and the upper Y collimators can move independently past the collimator axis. The limits of travel for the upper Y and the lower X collimators are -10 to +20 cm and -2 to +20 cm relative to the collimator axis, respectively. 3.2. Dosimetry Phantoms 3.2.1. Water tank system Since it is impractical to measure the absorbed dose inside a patient, absorbed dose measurements are carried out with water equivalent phantoms. For most beam data collection, a water tank made of an acrylic container is used. A waterproofed measuring ionization chamber is mounted and immersed in the water tank. The measured signal is corrected for any machine output fluctuations that would have been detected by a reference chamber placed in the beam outside the water tank and away from the measuring chamber. 23 The position and movement of the measuring chamber is computer controlled. Both the position of the chamber and the measured signals are fed back to the computer. Two commercial automatic scanning water tanks were used. They are the PTW (Physikalisch-Technische-Werkstatten, Freiburg, Germany) and the Wellhofer (Wellhofer Dosimetrie, Schwarzenbruck, Germany) water tank systems. For the PTW system, the PTW waterproof chamber used (Type No. N233641) has a collection volume of 0.3 cm3 with an active diameter and length of 0.55 and 1.6 cm, respectively. For the Wellhofer system, two Wellhofer waterproof ion chambers (Model IC10) were used. Each ion chamber had an active volume of 0.14 cm3, with a diameter of 0.6 cm and an active length of 0.33 cm (see Fig. 12). The percentage depth dose curves are obtained by moving the measuring chamber along the collimator axis from the water surface to some distance at depth. The depth dose profiles are obtained by moving the chamber across the radiation field at a fixed depth and then the procedures are repeated for additional depths. The isodose distributions are obtained by computer-control with the measuring chamber searching a fixed dose value within the radiation field and the position of the chamber is plotted as a continuous line. 3.2.2. Body phantom Body phantoms are used in radiotherapy dosimetry to evaluate treatment procedures and the suitability of treatment planning algorithms. Body phantoms range from those with simple geometry, such as stacked sheets of tissue substitutes, to the complex anthropomorphic phantoms that are available commercially which have a high degree of external and internal 24 conformity to a standard human. The body phantom used in the work described in this thesis was an existing head phantom made of prestwood of unit density, in 5 mm slices. Small holes were drilled to accommodate thermoluminescent dosimeters. An immobilization device with head rest and acrylic shell was constructed, and a computed tomography (CT) scan of the phantom in the immobilization device was done to obtain contour and density information which is required for dose calculations. 3.3. Dosimetric Measuring Instruments 3.3.1. A thimble type ionization chamber A thimble chamber is used with the water tank to obtain beam data. It is the most common and widely used instrument in the measurement of absorbed dose. As shown in Figure 12, it has a semi-spherical volume of air at the tip. The chamber wall is usually matched to the air or a water-equivalent medium, i.e., its effective atomic number is the same as that of air although its density is not, or it is water-equivalent. The wall thickness is usually less than 1 mm and is sometimes supplemented with close-fitting caps of acrylic or other plastic to bring the total wall thickness up to that needed for electronic equilibrium at the chamber center for the radiation in question. The inner chamber wall is coated with a thin conducting layer and is grounded and acts as one electrode. The other electrode is centered and is insulated from the chamber wall and attached by a long cable to the electrometer. 25 To Electrometer Insulators Chamber Wall A / Central Collecting Air Volume Electrode Figure 12. A schematic diagram of a typical thimble ionization chamber is shown. 26 3.3.2. Thermoluminescent do simeter (TLD) Because of the finite size of the thimble chamber and the electrical cable attached to it, it is usually impractical to use a thimble chamber for dose measurement within a patient. However, thermoluminescent dosimeters (TLD) can be used and inserted in body cavities or located at various positions on a patient. The TLD used in the work described in this thesis is the lithium fluoride (LiF) rod with dimensions of 1 mm diameter by 6 mm length (TLD-100, Harshaw/Bicron, Solon, OH.). Lithium fluoride has an effective atomic number of 8.2 compared to 7.4 for soft tissue with a physical density of 2.64 gm/cc. Hence, the sensitivity of the lithium fluoride is slightly energy dependent in the kilovoltage photon energy range but is more or less constant at megavoltage energy which is the energy range used in this work. The thermoluminescent dosimeter is first annealed by heating at 400Â°C for 1 hr to remove residual effects from their previous radiation history and thermal history. Three thermoluminescent dosimeters are then packaged together and are placed at selected pre-drilled holes in the prestwood body phantom prior to irradiation. The thermoluminescent dosimeters were batched according to relative sensitivity (Â± 2 % variation within each batch). The thermoluminescent dosimeter dose was read with a commercial thermoluminescent dosimeter reader (Teledyne System 310, Teledyne Brown Engineering, Westwood, NJ.). The typical heating cycle was that the temperature was (1) raised to 150Â° C for the first 5 seconds, (2) maintained at 150Â° C for 10 seconds, (3) then raised to 240Â° C within the next 5 seconds, (4) and finally maintained at 240Â° C for the next 15 seconds. The light output was integrated at 5 seconds to the end of the heating cycle (35 seconds). No post-irradiation annealing was 27 performed prior to readout. Each measurement was accompanied by a calibration of the full relevant dose range measured in reference conditions with the appropriate photon or electron beams. For dose calibration of either a 6 MV photon beam or a 12 MeV (mega electron volt) electron beam, the TLD were placed at a dmax of 1.5 cm and 3.0 cm respectively, and were irradiated with a 10 x 10 cm2 field at 100 cm source to surface distance. 3.4. Treatment Planning 3.4.1. Treatment planning algorithm Computerized treatment planning is a numerical simulation procedure in which the absorbed dose distribution within a patient is predicted from models based on phantom measurements. It involves the superposition of one or more radiation field isodose curves to produce a composite isodose distribution. The treatment plan is finalized by a process of optimization with field combinations chosen to ensure maximum dose is delivered to the planning target volume and minimum dose to underlying or overlying normal tissues. Two treatment planning algorithms are used in the work of this thesis. A new dose calculation method for asymmetric fields is developed and implemented into our in-house treatment planning program. The use of this new treatment algorithm is then compared to that of a commercial treatment planning system. 28 3.4.1.1. An in-house treatment planning algorithm Our in-house treatment planning program for conventional symmetric fields is based on the Kornelsen and Young empirical equations for the representation of depth dose data.4 The absorbed dose at any depth is related to the tissue maximum ratio (TMR) for a symmetric field W x L by an equation of the form TMR = \-(l-e~dlQ)m where d' denotes depth beyond the peak of the dose curve, and m and Q are constants. The form of the equation ensures that after an initial shoulder, the curve will gradually become exponential, the extent of the shoulder being determined by m and the gradient of the exponential portion by Q. The values of m and Q are determined empirically and are functions of the radiation energy and of the radiation field size. The absorbed doses at points distant from the collimator axis along the principal planes are represented by the off axis ratios (OARs). With our in-house treatment planning system, the off-axis distance corresponding to a specific off axis ratio is stored in the computer for specific depths. The off axis ratio at a point between the stored off axis ratio points is then obtained by interpolating between the stored off axis ratio values. 3.4.1.2. A commercial treatment planning system The Target 2 Radiation Treatment Planning System (GE Medical Systems, Milwaukee, WI.) is used for comparing the dose calculation based on our in-house system to that obtained with a commercial system. The commercial system uses 47 fan-lines and 5 29 cross-lines to represent the dose matrix in an irradiated field as illustrated in Figure 13. The storage of a sufficient number of radiation fields is required for each photon energy. Other field sizes are interpolated between the stored database. For blocked or irregular photon fields, the calculation is based on the Cunningham's ERREG program2 as illustrated in Figure 14. This method was first described by Clarkson5 whereby the absorbed dose at any point in an irradiated medium is the sum of the primary and scatter contributions (Fig. 14). 3.4.2. Absorbed dose distribution in a patient Three-dimensional patient data can be obtained from contiguous transverse slices as illustrated in Figure 15. Accurate external contours as well as contours and densities of internal organs can be obtained from multiple computed tomography (CT) cross-sectional slices. In treatment planning, a combination of radiation fields are chosen to aim at the target volume while at the same time avoiding the critical organs if possible. The dose distributions for each slice are calculated using a treatment planning algorithm and are displayed as sets of isodose lines as illustrated in Figure 16. 30 /A /(Â», i t n \ //", n'u* / I I ' M * / / ' / , ' Â» I ' M W / / ' / , Â» I ' M \ \ / 'I I ' M \ \ I I 1 1 , II 11 \ \ \\ / ; " I M H I I \ \ / / ' I i II I 1 I \ \ \ / / ' ' / l l | l \ \ \ \ / / ' I | I I I 1 I I \ \ / / ' I i M I 1 I \ \ \ I I 1 I l I I I ' 1 I l l - f 7 J - 1 - , - M 4 U Vâ€” \ â€”v - \ - ' / / ' / , I ' ' ' I \ \ \" / / ' / , I I I 1 I \ \ ' \ _ y _y _ _ | H 4. 4 ^ ^ / / ' I i I I I ' \ I > I / y ' / , I I I 1 I 1 \ I / I 1 1 , I 1 1 1 I I I \ _ _ _ r (- n n i - i - r r T -\ / / ' I , I I I 1 I \ I \ / / ' I , I I I 1 I \ \ I I _ l_ i J _,_ i J J _ Â± J _ \_ A _ _ / i 1 I. , I I I ' 1 I \ V / I 1 i , I I I 1 I \ \ V / I 1 I â€¢ , I I I 1 I I \ I / _ _ / _ ! _ ' _ 4. _ L i J _ L _ L i _Â» _ / i ' 1 i i i i i i \ \ \ I I 1 I , I I I 1 I V \ \ / / ' / I I I 1 I I I ' ; ; ' > ; i i i 1 i \ i â€” t / , ' I I I I I 1 I I I \ / , ' I , I I I I > 1 I V / / ' ' I I I I 1 I I I \ / / ' I i I I I I I \ v \ / / ' I I I I I I \ \ \ \ y I I I 1 \ ' \ \ Figure. 13. The storing of a matrix of dose points is shown. Dose points are represented by 13 fan lines and 5 transverse lines. 31 J Primary i i i i I i u 0 2 4 6 8 radius (cm) Figure 14. A schematic diagram illustrating the absorbed dose in a rectangular field of dimensions W x L at a point Q. The absorbed dose at point Q is the average absorbed dose for sectors of radius n, r2 ... into which the field is divided. The primary contribution is constant and is independent of the radius, whereas the scatter contribution is a function of the radius, increasing with the radius of the radiation field. 32 Figure 15. A three-dimensional representation of the patient outline by the superior (sup), central, and inferior (inf) transverse cross-sectional planes or slices. 33 Figure 16. Isodose distributions for a three field treatment are illustrated on several cross-sectional CT slices. 34 4. DOSIMETRIC CHARACTERISTICS OF ASYMMETRIC BEAMS Some modern linear accelerators (linacs) are equipped with asymmetric collimators or jaws. The independent jaw movement allows closing down one side of the field without affecting the opposite side. For instance, a 10 x 10 cm2 symmetric field has collimator settings of Xi, X 2 , Yi, and Y 2 each equal to 5 cm. This is the distance from the collimator axis at 100 cm from the source. When a 7 cm wide asymmetric field is desired, one can close down one of the jaws, for example, Xi to 2 cm. Consequently, the resultant asymmetric field is smaller in dimension than the corresponding symmetric field of 10 x 10 cm2 (Fig. 4) and the absorbed dose is therefore reduced. This absorbed dose reduction is non-trivial producing alterations in output at collimator axis, depth dose and beam profile. The data that is required for dose calculations are: percentage depth doses, profiles, off axis ratios, and output factors. 4.1. Overview/Historical Development Klemp et al.6 have measured and stored beam data for half-collimated photon fields in a commercial treatment planning system (GE Target 2 system). Such a practice is time consuming and is limited to the fixed number of asymmetric fields one can store. Several investigators have developed calculation methods to determine the output factor of asymmetric fields.7"10 Others have developed methods to account for the dosimetry of asymmetric fields at depths along the asymmetric field axis.11'12 Palta et al} have demonstrated that the percentage depth dose along the asymmetric field axis (i.e., the center 35 of the asymmetric field), and the shape of the isodose distribution of an asymmetric field differ from that of a symmetric field having the same field size as the asymmetric field. They have attributed the observed difference to the difference in primary beam profile produced because the off-set asymmetric field and the centrally-positioned symmetric field having the same field size as the asymmetric field intercept different positions of the flattening filter. Khan et al.13 have proposed to correct for the variation in beam quality observed at positions away from the collimator axis by using narrow beam attenuation, which is determined either by transmission measurements or by scatter subtraction technique. They have incorporated their primary beam modification method into an older version of the TP 11 treatment planning system (Atomic Energy of Canada Limited, Ottawa, Canada). Woo et a/.14 have evaluated the accuracy of a newer version of the commercially available TP 11 (Theraplan versions 4.2 and 5, Theratronics International Limited, Kanata, Canada) specifically as applied to the dosimetry of asymmetric fields, which in this system is based on Khan's methodology. A totally different approach to dose calculation in asymmetric fields has been proposed by Chui et al.15 Their method is an extension of their off-center ratios (OCRs) method for 3D dose calculation,16 and hence is only applicable to their specific treatment planning system, or similar systems that compute the OCR at a point using the product of the primary OCR (POCR) and the boundary factors (BFs). Because of the approximation used in deriving the POCR, Loshek and Keller17 have observed some discrepancy between calculations and measurements for large field size and/or heavily collimated asymmetric field with large field offset. They have refined and minimized the errors by using a piecewise re-construction technique to model the POCR, however, this requires an additional set of dose profiles to be 36 measured and manipulated for each depth. Thomas and Thomas1" have modeled the POCR using only a single measured beam profile in air, in addition to a number of narrow beam attenuation coefficients measured at various positions to account for the radial variation of beam quality at depth. Combining both the techniques of Palta8 and Chui16, Loshek and Parker19 have used the OCR method to determine the variation in primary dose at dmaX across the field, while employing an attenuation function to account for the scatter and primary beam attenuation at depths and at off axis distances. Recently, Cadman has extended his field edge correction (FEC) method7 to generate accurate POCRs and OCRs for asymmetric fields.20 Alternatively, Storchi and Woudstra have represented the off-axis profiles by a computed envelope profile and two boundary profiles.21 Some commercial treatment planning systems do not have specific algorithms for calculating dose in asymmetric fields, but allow blocking of a field by an externally mounted block. Simulating the collimators as blocks, the calculation would then account for the asymmetric collimation. Most blocked field calculations and, in particular the one used in the GE Target 2 system, are based on the Clarkson's scatter-sector integration method5 or the Cunningham's IRREG program.2 Such an algorithm is well suited for irregular field calculation but is rather inefficient for asymmetric rectangular or square field calculation. This is because the irregular field calculation method calculates the absorbed dose by separating the primary and the scatter contributions with the scatter contribution calculated over 360Â° and is very time consuming. A more efficient approach is to use the Day's equivalent field calculation method22 as the basis for asymmetric field calculation.9'11'23 Several examples of this method include the 37 direct implementation of the Day's method by Tenhunen and Lahtinen,9 the use of the effective field for the field size dependent factors by Rosenberg et al.11 and the use of the ratio of the equivalent field contributions between the asymmetric and symmetric fields by Kwa et al2' In this thesis, an analytical approach that accounts for the dosimetric characteristics of an asymmetric field is proposed.23 It is based on the concept that for every asymmetric field, where the field center is not aligned with the collimator axis, there is a corresponding symmetric field in which the opposite pair of collimators are equidistant from the axis and this distance is equal to the distance in the asymmetric field where the collimator is furthest away from the axis (Fig. 4). This approach is unique in that it does not need to separate the dose into the primary and the scatter contributions. The method calculates the difference in absorbed dose at any point between the smaller asymmetric field and the corresponding symmetric field. Therefore, the absorbed dose in an asymmetric field can be determined from existing beam data for symmetric fields. As a result, minimal data acquisition is required. This correction method can be applied to most existing treatment planning algorithms, and computation time is not significantly longer than that for symmetric fields. Furthermore, the correction factor proposed can account for differences in collimator settings and hence output factors as observed for rectangular fields when the collimators defining field width and length are switched (collimator exchange effect). In this thesis, it is also shown that part of this collimator exchange effect with asymmetric fields is due to the asymmetric collimator backscatter effect (i.e., radiation scattered from the collimators back into the beam monitor chamber). Since the proposed correction factor is also position specific with respect to the 38 asymmetric and symmetric field settings, it is also shown to account for the scatter contributions and thereby the observed tilt of the radiation dose profile (wedge effect) of an asymmetric field. In a symmetric field the radiation dose profile would be symmetric and uniform whereas in an asymmetric field it may be tilted to one side because some scatter dose is missing on that side (see Fig. 27). 39 4.2. The Output Factor (OPF) of an Asymmetric Field (AF) The absorbed dose at a given point in an irradiated medium is conventionally represented by the product of MU, OPF, TMR and OAR as given in Eq. (10) for symmetric fields. Various methods to determine the output factor of an asymmetric field have been described. Khan et al.13 have suggested the use of the output factor of the symmetric field having the same field size as the asymmetric field. Others require extensive measurements to account for the effects of each of the four collimator positions on dose.12'15 In between, there are the straightforward and efficient approaches of using the Day's equivalent field method.9'11'23 The use of the Day's method for the dosimetry of asymmetric fields and some of its limitations are discussed below. 4.2.1. Direct implementation of the Day's equivalent field method The Day's equivalent field method has been adopted to calculate absorbed dose distributions in water irradiated by symmetric megavoltage photon beams.24 It has also been used for calculations in asymmetric photon fields. ' ' The Day's equivalent field method calculates the scattered dose at any off-axis point in a radiation field by making it equal to the average scattered dose contribution of the four quarter fields centered at the same point. For example, for a W x L field with the point R along the transverse principal plane being a distance r away from the collimator axis, the two rectangular fields providing contribution to the dose at R would be (W + 2r) x L and (W - 2r) x L as shown in Figure 17(A). This 40 Figure 17. The equivalent field contributions used in the Day's equivalent dose calculation method are illustrated. For (A), the absorbed dose to a point R in a symmetric field WxLis equivalent to the average of the two doses at the center of the two symmetric fields of (W + 2r) x L and (W - 2r) x L. For (B), the absorbed dose at a point R in an asymmetric field AW x L is equivalent to the average of the two doses at the center of the two symmetric fields of (W + 2r) x L and (2AW - W - 2r) x L. For (C), the absorbed dose at a point P along the collimator axis in an asymmetric field is equivalent to the average of the two doses at the center of the two symmetric fields of W x L and (2 AW - W) x L. 41 equivalent field method is a simplified version of the widely used Clarkson's method.5 One limitation is that unlike the Clarkson's method, the Day's method is not suited for irregular field dose calculation but can only be applied to square or rectangular fields. However, the Day's method is much more efficient than the Clarkson's method for the dose computation of rectangular and square asymmetric fields. This is because with the Day's method two equivalent field contributions need to be determined, whereas, with the Clarkson's method 72 scatter contributions need to be calculated based on a 5Â° per sector integration. Most asymmetric field algorithms use some form of beam modeling to generate asymmetric field dose profiles. Usually, they separate the dose into primary and scatter components. For example, Tenhunen and Lahtinen9 use the off axis ratio in free space, OARa^r,40x40), to represent the primary component of dose at distance r from the center of a 40 x 40 cm2 field, and then use the Day's method to account for the scatter component of dose originating in the phantom. In the situation when one of the collimators is set asymmetrically to width A W (Fig. 17B), the asymmetric field output factor (AF OPF) at an off-axis point a distance r away from the collimator axis (Fig. 4) and at dmax in water would be Here the AF OPF(r,AWxL) is a function of the off axis distance r, the asymmetric field size AW x L , and the corresponding symmetric field W x L . The symmetric field width W is defined as twice the largest collimator setting of the asymmetric field. For the example given in Figure 4, the largest collimator setting of an asymmetric field width of 7 cm is 5 cm, the setting of the X ] collimator. Therefore the corresponding symmetric field width is 10 cm with both X i and X 2 collimators set at 5 cm. The asymmetric field offset is then defined as 42 (W - AW) / 2. This is represented by the asymmetric field (AF) axis in Figure 4, and the offset distance is defined as r a s y m and is 1.5 cm away from the collimator axis for the example given in Figure 4. The OARair(r,40x40) is the off-axis ratio in free space at the off-axis point for the maximum field opening of 40 x 40 cm2. It gives the ratio of the dose at an off axis position such as R (Fig. 17) to the dose on the center of the axis and therefore relates the doses in air at those two points. The output factors relate doses in water at dmax for different field sizes and unless specified otherwise are all defined at the collimator axis or central axis. For example, OPF((W+2r)xL) is the output for a field of length L and width (W + 2r) on the central axis of this field. Here, the off-axis distance r is positive when the off-axis point is on the asymmetrically collimated side and is negative when it is on the opposite side. Hence, rasym would always be negative (Fig. 4). Kwa and El-Khatib25 have suggested that Eq. (13) which represents a direct implementation of the Day's method for the output factor calculation of an asymmetric field would lead to some discrepancy with measured values. This is because when the asymmetric field width AW approaches the symmetric field width W (Fig. 17A), Eq. (13) leads to: AFOPF(r,AW^W* L) - OAR.JrA0 x 40) * ^ ' L ) * Â° P F ^ ~ Â» > * L Â» (14) But AF OPF(r,AW->WxL) is basically the output factor for the symmetric field W x L at the off-axis point r, in which, OPF(r,W x L) = OAR(dmax,r,W x L) x OPF(W x L). (15) Note that OAR(dmax,r,WxL) is the ratio of the doses at positions r and on center in water at dmax and for field size W x L . The OARair(r,40x40) and OAR(dmax,r,WxL) are generally 43 equal as shown in Figure 18 except at points when r is in close proximity to the field edge. The difference in the off axis ratios at points close to the field edge between in-air and in-phantom (at dmax) measurements is attributed to the relative lack of side-scatter contribution at points near the field edge within the irradiated medium (Fig. 19). Hence based on Eqs. (14) and (15), AF OPF(r,AW->WxL) < OPF(r,WxL) in general.25 This is because output factors do not increase linearly with field width but level off at large field width (see Fig. 20). Therefore, OPFÂ«W + 2r) x L) + OPF((W - Ir) x L) ^ Q p f { } y ^ Â£ ) ( 1 6 ) An example is given using measured off axis ratios from Figure 18 and output factors from Figure 20. For an off-axis point with r = 5 cm in a 6 MV 20y x 20x cm2 photon field (superscripts x and y indicate collimator positions X and Y), the calculated output factor based on Eq. (14) would be 1.034 x (1.016 + 1.076) / 2 = 1.082 cGy/MU but the actual output factor at the off axis point (based on Eq. (15)) would be 1.033 x 1.058 = 1.093 cGy/MU. Thus, the calculated output factor for an off-axis point using this direct implementation of the Day's method would be in error (1% for the example shown above) when the asymmetric collimator setting approaches that of the symmetric field.25 However, this error will vanish when r approaches zero since the two equivalent field sizes would become the same, W x L . The inequality in Eq. (16) will increase with increasing off axis distance r but this inequality will be compensated for somewhat as OARair(r,40x40) > OAR(dmax,r,WxL) (Errors up to 1.5% are expected with r = 8.5 cm for points close to the field edge of a 6 MV 20 x 20 cm2 field). 44 A. 6 MV 1.08 1.04 + 1.00 0.96 â€¢ â€¢ . â€¢" S. -in air jrf^ * dmax \ \ . *. in air 40x40 cm2 d V max \ â€¢ 20x20 cm2 1 1 â€” i 1 0 B. 10. MV 1.08 1.04 1.00 0.96 10 15 Off axis distance, r (cm) 20 â€¢ in air 40x40 cm2 20x20 cm2 1 1 10 15 Off axis distance, r (cm) 20 25 25 Figure 18. The off-axis ratios (OARs) for both the (A) 6 MV and (B) 10 MV photon beams at d^x and in-air are shown. 45 Figure 19. Illustration of primary and scattered radiation to points on center and at the edge of the radiation field. (A) In air the dose contribution is predominantly from primary radiation (dashed arrows) and radiation scattered from the head and collimators and therefore differences along the profile are mainly due to primary transmission through the flattening filter. (B) At d^x in phantom in addition to the primary transmission through the flattening filter and head scatter, there is phantom scatter (solid arrows) which is relatively less for points near the edge of the field than for points near the center. 46 4.2.2. Derivation of a correction factor (CF) A new approach is proposed here that can avoid the inherent limitations of using the Day's method directly in the absorbed dose representation of asymmetric fields. Instead of generating asymmetric field profiles using some beam modeling as is conventionally done, a correction factor (CF) that modifies the existing symmetric field profiles to account for the dose reduction in an asymmetric field is proposed.9 The symmetric field can either be square or rectangular in shape and the resultant asymmetric field could be a square or rectangular field of smaller dimension. The correction can then be applied to dose distributions in symmetric fields to obtain those in asymmetric fields. The method is first described as it applies to situations where only one independent jaw is closed down along the field width and with the dose calculation plane along the transverse principal plane (Fig. 17B or C). However, it can readily be extended to situations where the field length is being collimated asymmetrically or where both field dimensions are being collimated asymmetrically as discussed in Chapter 4.5. Let's consider the radiation output of an asymmetric field AW x L and the corresponding symmetric field WxL. As discussed in Chapter 2.1.1, the output factor at dmax along the collimator axis in a symmetric field of W x L is defined as OPF(WxL). The output factor along the collimator axis in an asymmetric field (where r = 0), AF OPF(AWxL), is then approximated by the arithmetic mean of OPF(WxL) and OPF((2AW-W)xL) (Fig. 17C), which is given as: AF OPF(AWxL) - {OPF(WxL) + OPF((2AW-W)xL)}/2. (17) 47 The dose reduction in an asymmetric field AW x L as compared to the corresponding symmetric field WxL can be represented by a correction factor which consists of the ratio of the output factor in an asymmetric field to the output factor in a symmetric field. This correction factor (CF) at the collimator axis is given as: AFOPF(AWxL) CF(dmBX,AW x L) V max ' OPF(W x L) {OPF(W x L) + OPF((2AW -W)x L)} 12 (18) OPF(W x L) Since the equivalent field W x L is common between the asymmetric field and the symmetric field, the above CF (Eq. 18) is expressed as the geometric mean instead of the arithmetic mean of the output factors so as to minimize the computation steps and time, i.e., OPF(W x L) â€¢ = V OPFÂ«2AW -W) x L)_ OPF'W x L) Then, the output factor along the collimator axis in an asymmetric field can be calculated from the correction factor as: AF OPF (A W x L) = OPF(W x L) x CF(dmax , AW x L) = OPFiW x L) x pPHJ2AW-W)Â»L) V OPF(W x L) = <JOPF(W x L) x OPF((2AW - W) x L) (20) Therefore along the collimator axis, the correction factor proposed here (Eq. 20) gives the output factor as the geometric mean of the equivalent field contributions, whereas, Tenhunen and Lahtinen use the arithmetic mean.26 Tenhunen and Lahtinen26 have demonstrated experimentally that both methods are in good agreement with the largest discrepancy of only 48 0.5% between calculated and measured output factors. This is because with their method the deficiency of using the Day's method does not occur at the collimator axis as stated in Chapter 4.2.1. However for any off-axis points, the two methods are no longer similar. The reason for this is discussed below. Similar to Eq. (17), the output factor at an off-axis point a distance r away from the collimator axis along the transverse plane in an asymmetric field would be given as (Fig. 17B) : ^ Â« ^ x L ) = 0 ^ , , ^ x ^ (2!) Note that Eq. (21) is different from Eq. (13) in that Eq. (21) uses the OAR (d m a x , r ,WxL) whereas Eq. (13) uses the in air off axis ratio, OARair(r,40x40). Similarly, the output factor at the same off-axis point in a symmetric field would be (Fig. 17A) : OPF(r,W x L) = OAR^.r.W * L) l Â° ^ + 2r) Â» L) , OPF((W - 2r) x Â» ) ^ Hence using Eqs. (21) and (22) to calculate a correction factor for the dose off axis in an asymmetric field: AFOPF(r,AWxL) CF(dtnB!,r,AWxL) = V nBX' ' J OPF(r,WxL) {OPF((2AW- W-2r) x L) + OPF((W+2r) x L)}/2 {OPF{(W+2r) x L) + OPF{(W-2r) xL)}/2 Here again the magnitude of the parameter r is positive or negative depending on whether the off axis point is towards or away from the asymmetric collimator field edge, respectively. Again by using the geometric means, the output factor for the equivalent field W + 2r cancels out. Hence, the computation time can be cut in half because less numbers of equivalent output factors are used in the computation of CF: 49 CF(d max ' r, A W x L OPF'((2AW - W - 2r) x I ) OPF((W - 2r) x Z,) (24) Then the asymmetric field output factor at dm a x and at any off axis point can be calculated from the correction factor given in Eq. (24) as: AFOPF(r,AWx L) = OPF(W xL)x OAR(r,d^,Wx L) x CF(d^,r,AWx L) Aside from the use of different off axis ratios, there is another difference between Eqs. (25) and (13). Eq. (13) uses the arithmetic mean of the two output factors for field sizes (W + 2r) x L and (2AW - W - 2r) x L, whereas because of the r term in the square root, Eq. (25) does not reduce to the geometric mean of the two output factors for field sizes (W + 2r) x L and (2AW - W - 2r) x L except along the collimator axis (Eq. 20). Furthermore, when the asymmetric field width approaches the symmetric field width, the proposed correction factor (Eq. 24 and also for the special case when r = 0 with Eq. 20) reduces to unity and the output factor in Eq. (25) is the same as the output factor of a symmetric field, thus avoiding the limitation of using the Day's method directly. 4.2.3. Influence of the collimator settings on the output factor (OPF) By convention, the radiation output of a linac is calibrated at the center of a reference field size of 10 x 10 cm2 to be 1.000 cGy/MU. For other square and rectangular fields, the measured outputs are usually expressed as the output factors. The output factor is defined as the ratio of the absorbed dose of any square or rectangular field at dm a x to the dose at the same = OPF(W xL)x OAR{r,dm,W y. L) x OPF((2A W - W - 2r) x L) OPF((W-2r)xL) (25) 50 depth in the reference field. In general, the output factor increases with increasing field size but levels off at large field size as shown in Figure 20(A) and (B) for both the 6 and 10 MV photon beams, respectively, of the Varian Clinac 2100C and 2100C7D linacs. This is partly due to an increase in scattered radiation from the phantom reaching the point of measurement and partly due to the increase in collimator scatter with increasing field size. As observed by others,27"33 the output factors for rectangular fields are also dependent on the settings of the upper and lower collimators (Fig. 20), that is, the output factors are different for the same field size when the upper and lower collimator dimensions are reversed. The dashed curves in Figure 20 are for the output factors with the upper Y collimator defining the field width and the lower X collimator defining the field length. The dotted curves are for the output factors with the lower X collimator defining the field width and the upper Y collimator defining the field length. The difference between the two sets of output factors is as much as 5% for a 3y x 40x cm2 field and a 3X x 40y cm2 field. As stated the x and y superscripts indicate the collimator position used. This influence of the upper and lower collimator setting on the radiation output, also known as the collimator exchange effect, has been studied extensively. It is generally acknowledged that for a wide open field, scattered radiation originating in the linac head accounts for 8 to 12% of the total photon fluence,34"36 with the peak scatter factor (representing phantom scatter) accounting for less than 10%. Of this head scatter, 20% originates from the target, 40% from the primary collimator, 32% from the flattening filter and 8% from the monitor chamber, as determined by Chaney et al. based on their Monte Carlo studies.36 The scatter from the upper and lower secondary collirnators accounts for less than 1% of the primary photon fluence reaching the point of measurement.36'37 Therefore, the 51 A . 1.15 r-1.10 1.05 U OPF LOO h 0.95 6MV square field 20 cm length 0.90 10 20 30 Field Width (cm) B. 10MV 1.15 1.10 H 1.05 U OPF 1.00r-0.95h 0.90 h square field 10 20 30 Field Width (cm) Figure 20. The output factors (OPFs) were measured at d m a x in water for square fields (solid curves) and rectangular fields with the upper Y collimator (dotted curves) and the lower X collimator (dashed curves) defining the field width for (A) a 6 MV and (B) a 10 MV photon beam. The outputs for all field sizes were normalized to the output for a 10 x 10 cm2 field. The five fixed field lengths used were 3, 5, 10, 20 and 40 cm. 52 position of these field defining collimators is expected to have a minimal effect on the output factor due to the negligible scatter originating from the secondary collimator itself. Consequently, the effect of secondary collimator positions on the output factor is attributed to their presence in blocking the head scatter that originates upstream from the treatment head.34' 36,38,39 -pj^ r e a s o n j n g c a n b e explained by the two source model which assumes the x-ray sources of a linac are comprised of both focal and extra-focal radiation. ' ' The focal radiation comprises the forward scattered photons originated from the electrons hitting the target. The extra-focal radiation consists of the head scatter which is considered to originate predominantly from the plane of the flattening filter. The dimension of the area from which this extra-focal radiation originates is then assumed to be 6.8 cm in diameter at the plane of the flattening filter, which corresponds to the distance between the two opposite corners of the maximum field size of 40 x 40 cm2 defined at 100 cm source to axis distance (Fig. 21). Because of the close proximity of the upper collimator to the flattening filter, the upper collimator begins to block the isocenter's field of view of the flattening filter sooner than the lower collimator as the collimators are closed down. These correspond to field widths of 19.9 cm and 13.7 cm (half width of 9.95 and 6.85 cm, respectively as illustrated in Fig. 21) projected at 100 cm source to axis distance for the upper and lower collimators, respectively. Thus, there would be more reduction in extra-focal radiation and thereby radiation output at the isocenter when the upper collimator instead of the lower collimator is set smaller than 20 cm. This two source model would imply that there would be no difference in extra-focal radiation and thereby radiation output when the upper collimator or the lower collimator is used to set field sizes greater than 20 cm,40 since both collimators are clear from the path of 53 isocenter Figure 21. The geometric relationships between x-ray target, primary collimator, flattening filter, upper and lower collimators relative to the isocenter are illustrated. The primary collimator limits the spread of primary photons to 28.3 cm in radius (as represented by the dotted line) as projected to 100 cm. This would provide coverage of a 40 x 40 cm2 radiation field. The flattening filter is the main source of head scatter radiation and, thereby, the extra-focal radiation. Since the spread of the primary photons corresponds to a diameter of 6.8 cm at a distance of 12 cm from the source, the dimension of the extra-focal radiation is assumed to be 6.8 cm in diameter at the plane of the flattening filter (as indicated by the dashed lines). When the upper collimator is set smaller than 9.95 cm as projected at 100 cm (left solid line), the upper collimator begins to block the extra-focal radiation (left dashed line). On the other hand, the lower collimator would have to be set smaller than 6.85 cm (right solid line) in order to block the extra-focal radiation (right dashed line). 54 the extra focal radiation reaching the isocenter. However for these large fields as shown in Figure 20 for the Varian Clinac 2100 C and C/D, the output factors differ by 1% between the 20y x 40x and 20x x 40y cm2 fields for both the 6 and 10 MV photon beams. Yu et a/.38 have recognized this discrepancy and have added an additional term in their analytical modeling of output factor to account for this discrepancy. Other studies have attributed this collimator exchange effect to the collimator backscatter effect based on electron filter experiment,40"43 telescopic measurement technique,44"46 and beam current monitoring.46"48 Scrimger49 has demonstrated that when photons hit high atomic number materials, a significant amount of backscattered electrons are produced. These backscattered electrons are then picked up by the beam monitor chamber upstream in the machine head assembly (Fig. 2). As a result, the beam monitor chamber will pick up signals from the collimators in addition to the signal from the radiation source. These extra signals will cause the feedback mechanism built into the linac to terminate the exposure sooner. Since the upper collimator is closer to the beam monitor chamber, the beam monitor chamber will pick up relatively more backscattered radiation from the upper collimator. Thus for the same rectangular field, the output factor will be lower when the upper collimator is used to set the smaller field dimension. However, this collimator backscatter effect is very much dependent on the design of the machine head, in particular, the distance between the beam monitor chamber and the upper collimator, and the presence of any electron filter between the beam monitor chamber and the upper collimators. As a result, this collimator backscatter effect might not be significant with some linacs. For example, some Clinac 1800, 2100 and 2300 series (Varian Associates, Palo Alta, CA) with the Kapton beam monitor chamber will exhibit collimator backscatter effect,29'44'46 whereas other Clinac models 55 such as the 4/6/18 and 600 series with mica chamber and copper plated steel window will not "?fi A"i A$ AQ have this collimator backscatter effect. ' ' " Another example is the Therac 20 or Saturne linac (manufactured jointly by AECL of Canada and CGR MeV of France). With the Therac 20 or the Saturne linac, the output factors are lower when the lower collimators are setting the smaller field size. This is because the lower collimators are actually attached to a set of upper trimmers that are closer to the beam monitor chamber than the upper collimators.28'41"44 Hence for certain linacs, the collimator exchange effect is not only due to the head scatter as represented by the extra-focal radiation but also due to the collimator backscatter effect. 4.2.4. Influence of the collimator settings on the asymmetric field output factor (AF OPF) With the asymmetric collimation option on linacs that exhibit collimator backscatter effect, the dosimetry for the asymmetric field will also be affected by this collimator backscatter effect.11'39'45 This collimator backscatter effect may become even more significant as the independent collimator may actually move past the collimator axis and therefore create even more backscattered radiation. Several authors have commented on the possible influence of the collimator settings on the asymmetric field output factor,8'11'14'15'45 but some authors have suggested that there is no collimator dependence.7'10 To verify this effect for asymmetric fields on our Varian Clinac 2100C and C/D linacs, the measured asymmetric field output factors are compared with various calculated asymmetric field output factors using different calculation methods. 56 The output factors were measured at dm a x along the asymmetric field center for both the asymmetric and symmetric fields, namely, AF OPF(rasym,AWxL) and OPF(rasym,WxL), respectively. The r a s y m is the distance from central collimator axis corresponding to the asymmetric field center (Fig. 4). The dmax's were at depths of 1.7 and 2.5 cm for the 6 MV and 10 MV photon beams, respectively. Both the upper Y and the lower X collimators were used alternately to define the asymmetric fields. The collimator was rotated by an angle of 90Â° so that the same amount of the chamber assembly was being irradiated in both cases. The measured data are compared to calculated asymmetric field output factors using two different methods. One method of calculation is based on the proposed CF (Eq. 25) with r defined at rasym. Since OPF(WxL) x OAR(r,dm,WxL) in Eq. (25) is the measured OPF(rasym,WxL), the asymmetric field output factor (AF OPF) can be calculated using Eqs. (26) and (27) with the collimator specific CFs given in Eqs. (28) and (29). AF OPF based on the CFX s AF OPF(rasym, AWX x U) = measured OPF(rasym,WX x 77) x CFX (26) and AF OPF based on the CFy = AF OPF(rasym, AWy x U) = measured OPF(rasym,Wy x Lx) x CFy (27) where CFX = ^OPF(AWx x Ly)/OPF((2W - AW)X x l ' ) (28) and CFy = ^OPF(AWy x Lx)/(OPF((2W - AW)y x Lx) (29) 57 Eqs. (28) and (29) are the collimator specific correction factors at dmaX along the asymmetric field center and are derived from Eq, (24) with r = -r a s y m where r a s y n i = (W - AW) / 2. Alternatively, the asymmetric field output factors can be calculated using the method proposed by other authors.8"10'12'13'15 Except for Marinello and Dutreix,12 most approaches end up with the same equation as proposed by Khan et al.13 for the asymmetric field output factor at the asymmetric field center, namely, AF OPF based on OPFx = OPF(AW x If) x OAR'(#^,40 x 40) (30) and AF OPF based on OPFy = OPF (A WxL') x OAR' {ras)m ,40 x 40) (31) where OAR'(ra9ym,40x40) is the off axis ratio for a point at r a s y m away from the collimator axis either in air or at d^x, and usually for the maximum field size of 40 x 40 cm2. For the work in this thesis, the OAR'(rasym,40x40) was measured in phantom and at dm,*, i.e., OAR(dmax,rasym,40x40) for which the values are given in Figure 18. The OPF(AWxL) is the output factor at d m a x along the collimator axis for the symmetric field with field dimension of A W x L . In Figures 22 and 23 are shown the plots of measured and calculated asymmetric field output factors (AF OPFs) for a 12 x 40 cm2 rectangular field asymmetrically collimated to 9, 6, and 4 x 40 cm2 asymmetric fields and for a 6 MV and a 10 MV photon beam, respectively. The corresponding rasym's are 1.5, 3, and 4 cm from the collimator axis, respectively. Figures 24 and 25 show the measured and calculated asymmetric field output factors for a 40 x 20 cm2 symmetric field collimated to 30, 20, 18 and 10 x 20 cm2 asymmetric fields, and for both 58 Figure 22. The asymmetric field output factors (AF OPFs) for various asymmetric fields are shown for the 6 MV photon beam. The symmetric field has a field width of 12 cm and a field length of 40 cm. The widths of the asymmetric field are 9, 6 and 4 cm. One set of AF OPFs was for the lower X collimator (measured AF OPFx) defining the asymmetric field width, and the other set was for the upper Y collimator (measured AF OPFy) defining the asymmetric field width. The other two sets are for the calculated AF OPFs based on the proposed correction factors CFX and CFy (Eqs. 26 and 27, respectively), and on the symmetric field output factors, OPF (AWxxLy) and OPF (AWyxLx) as given in Eqs. 30 and 31 (based on OPFx and OPFy, respectively). The error bar represents one standard deviation. 59 Figure 23. The asymmetric field output factors (AF OPFs) for various asymmetric fields are shown for the 10 MV photon beam. The symmetric field has a field width of 12 cm and a field length of 40 cm. The widths of the asymmetric field are 9, 6 and 4 cm. One set of AF OPFs was for the lower X collimator (measured AF OPFx) defining the asymmetric field width, and the other set was for the upper Y collimator (measured AF OPFy) defining the asymmetric field width. The other two sets are for the calculated AF OPFs based on the proposed correction factors CFX and CFy (Eqs. 26 and 27, respectively), and on the symmetric field output factors, OPF (AWxxLy) and OPF (AWyxLx) as given in Eqs. 30 and 31 (based on OPFx and OPFy, respectively). The error bar represents one standard deviation. 60 1.13 Figure 24. The asymmetric field output factors (AF OPFs) for various asymmetric fields are shown for the 6 MV photon beam. The symmetric field has a field width of 40 cm and a field length of 20 cm. The widths of the asymmetric field are 30, 20, 18 and 10 cm. One set of AF OPFs was for the lower X collimator (measured AF OPFx) defining the asymmetric field width, and the other set was for the upper Y collimator (measured AF OPFy) defining the asymmetric field width. The other two sets are for the calculated AF OPFs based on the proposed correction factors CFX and CF y (Eqs. 26 and 27, respectively) and on the symmetric field output factors, OPF (AWxL 5) and OPF (AWyxLx) as given in Eqs. 30 and 31 (based on OPFx and OPFy, respectively). The error bar represents one standard deviation. 61 1.13 Figure 25. The asymmetric field output factors (AF OPFs) for various asymmetric fields are shown for the 10 MV photon beam. The symmetric field has a field width of 40 cm and a field length of 20 cm. The widths of the asymmetric field are 30, 20, 18 and 10 cm. One set of AF OPFs was for the lower X collimator (measured AF OPFx) defining the asymmetric field width, and the other set was for the upper Y collimator (measured AF OPFy) defining the asymmetric field width. The other two sets are for the calculated AF OPFs based on the proposed correction factors CFX and CFy (Eqs. 26 and 27, respectively) and on the symmetric field output factors, OPF (AWxxLy) and OPF (AWyxLx) as given in Eqs. 30 and 31 (based on OPFx and OPFy, respectively). The error bar represents one standard deviation. 62 the 6 and 10 MV photon beams, respectively. The corresponding rasym's are 5, 10, 11 and 15 cm from the collimator axis, respectively. Since the upper Y collimator can be set 10 cm past the collimator axis, the smallest asymmetric fields achieved with the Y collimators defining the field width is 10 cm for the 40 cm symmetric field. On the other hand, since the lower X collimator can only be set 2 cm past the collimator axis, the smallest asymmetric fields are 4 and 18 cm for the two symmetric fields of 12 and 40 cm, respectively. In general, the measured asymmetric field output factors are lower when the Y collimator is used to define the narrower field dimension than when the X collimator is used. This collimator exchange effect is particularly apparent in Figures 22 and 23 when the Y collimator is used to define the narrower field dimension whereby the asymmetric field output factors are always lower. In Figures 24 and 25, the measured AF OPFx for an asymmetric field size of 30x x 20y is lower than that for the asymmetric field 30y x 20" because the former has the Y collimator defining the narrow dimension. For the more or less square asymmetric fields of 18 x 20 and 20 x 20 cm2, the difference in measured AF OPFs between the two sets of collimator setting is minimal since there is no collimator exchange effect between square fields. In order to evaluate the two methods of calculation, the difference between the calculated and measured AF OPFs (Figs. 22-25) are expressed as the ratio of calculated to measured AF OPFs in Table 1 and 2 for both the 6 and 10 MV photon beams, respectively. The calculated AF OPFs (Eqs. 26 and 27) using the collimator-specific CFX and CFy, (Eqs. 28 and 29, respectively) are within Â±0.3% of the measured AF OPFs as set by the upper Y and the lower X collimator, respectively, for both the 6 and 10 MV photon beams, except in the extreme cases, when the 12 cm field width is collimated to a 4 cm asymmetric field width and 63 Table 1. Ratios of calculated AF OPFs to measured AF OPFs for a 6 MV photon beam. The calculated AF OPFs are (Column 3) based on CFX and CFy (Eqs.26-27), (Column 4) based on OPFx and OPFy (Eqs.30 and 31) and (Column 5) derived from Eq. 32. Symmetric Asymmetric ratios of calculated to measured AF OPF field field based on based on derived from (AF) CF x &CF y OPFx&OPFy Eq. (32) (Eqs. 26-27) (Eqs.30-31) 12xx40y 9xx40y .998 .999 1.000 6xx40y 1.000 .999 1.001 4xx40y 1.004 1.005 1.006 40xx20y 30xx20y 1.002 1.001 1.001 20xx20y 1.003 .997 .996 18xx20y 1.002 .995 .994 12yx40x 9yx40x .998 .996 1.000 6yx40x .999 .994 .998 4yx40x 1.000 .992 .995 40yx20x 30yx20x .998 1.003 .996 20yx20x .996 .996 .989 18yx20x .997 .995 .989 10yx20x 1.007 .990 .984 64 Table 2. Ratios of calculated AF OPFs to measured AF OPFs for a 10 MV photon beam. The calculated AF OPFs are (Column 3) based on CFX and CFy (Eqs. 26-27), (Column 4) based on OPFx and OPFy (Eqs. 30 and 31) and (Column 5) derived from Eq. 32. Symmetric Asymmetric ratios of calculated to measured AF OPF field field based on based on derived from (AF) CF x &CF y OPF x&OPF y Eq. (32) (Eqs. 26-27) (Eqs. 30-31) 12xx40y 9xx40y .998 1.003 .997 6xx40y .999 1.001 .996 4xx40y 1.005 1.002 .998 40xx20y 30xx20y .999 1.001 .996 20xx20y .999 .995 .990 18xx20y 1.001 .994 .989 12yx40x 9yx40x .999 .996 1.000 6yx40x .999 1.003 .997 4yx40x 1.002 .995 .992 40yx20x 30yx20x .998 1.005 .994 20yx20x .997 1.000 .986 18yx20x .998 .999 .986 10yx20x 1.008 .994 .983 65 when the 40 cm field width is collimated to a 10 cm asymmetric field width. With the former, the difference is still within 0.5% and is attributed to the uncertainty in the dose representation and measurements for such a small field. With the latter, the difference is within 0.8% and is attributed to the uncertainty in the extrapolation of output factors for field sizes greater than the maximum attainable field size of 40 cm which may be necessary to calculate 2W-AW in Eqs. (28) and (29). Generally, the ratios of AF OPFs based on OPFx and OPFy (Column 4) deviate from unity more than the ratios based on CFX and CFy. (Column 3). Since the calculated AF OPFs based on OPFx and OPFy (Eqs. 30 and 31) are derived from previously established data in symmetric fields and are independent of present measurements, any experimental deviation in measurement due to variations in set-up, such as, source to chamber distance, depth of measurement and off axis distance, will not be accounted for. For example, if the measured output factor at an off-axis point rasym away from the collimator axis, OPF(rasym,WxL), is greater than the calculated OPF(WxL) x OAR(dmax,rasym,WxL) from previously established data, then the measured AF OPFs at the same point, i.e., AF OPF(rasym,AWxL), might also be greater. These experimental uncertainties can be minimized by re-normalizing the ratio of AF OPF with the equality OPF(WxL) x OAR(dmax,rasym,WxL) = OPF(rasym,WxL). Then: AF OPF based on OPFx orOPFv lOPF{Wx L) x OAk\d^,r,Wx L) ratio of AF OPF= / â€” measured AF OPFjr^, AWxL)j measured OPFjr^ ,WxL) OPFjAWx L) xOARjd^r^AOx 40) jOPFjWx L) x OARjd^r^W x L) measuredAFOPFir^, AW xL) j measuredOPFjr^W'x L) = OPFjAWx L) x OARjd^r^AO x 40) j measuredAFOPFjr^, AWx L) OPFjWx^xOARjd^r^WxL) / measuredOPFjr^Wx L) 66 Hence, the numerator of the ratio of AF OPF (Eq. 32) is derived from established data for symmetric fields; whereas, the denominator is obtained from directly measured data. Column 5 in Table 1 and 2 are the derived ratio of AF OPFs based on Eq. (32) for both the 6 and 10 MV photon beams, respectively. In general, the derived ratios of AF OPF (Column 5) for both the 6 and 10 MV photon beams deviate from unity with increasing asymmetrically collimated fields when the Y collimator is set asymmetrically. This deviation may be due to the collimator backscatter effect. This is because as one of the Y collimators is closed down, one of the two inner D-shaped plates of the beam monitor chamber that is above the asymmetrically set collimator (between plates A and B or C and D of Fig. 26) will pick up more backscatter radiation. The Clinac feedback mechanism will interpret the extra signal as an angular deviation, i.e., the beam intensity is no longer symmetric away from the collimator axis. With the Clinac dose servo enabled, the linac will automatically compensate for it by steering the beam towards the other side thereby increasing the radiation output even when the net A + B or C + D signal is the same as with a symmetric field having the same field size as the asymmetric field. A quick and simple experiment to verify this asymmetric collimator backscatter effect is to disable both the positional and angular dose servo of the linac. In Table 3 and 4 are shown the differences in "T sym" readout when either the X or Y collimators are collimated asymmetrically for both the 6 and 10 MV photon beams, respectively, with both dose servos disabled. The "T sym" readout indicates deviations from symmetry as indicated by the beam monitor chamber. The Clinac showed a slight asymmetry in the readout "T sym" when the Y collimator is set asymmetrically (collimator angle at 90Â°) but not with the X collimator (collimator angle at 0Â°). This is because the X collimator 67 Table 3. Difference in "T sym" readout of the linac with the Clinac dose servo disabled for different 6 MV asymmetric fields. T sym indicates deviations from symmetry as indicated by the beam monitor chamber. Symmetric field Asymmetric field (AF) "T sym" readout of the Clinac 2100C (%) AWxxLy AW yxL x 12x40 9x40 0.03+0.04 0.17+0.13 6x40 0.02+0.00 0.10+0.01 4x40 0.01+0.01 0.06+0.04 40x20 30x20 0.02+0.01 0.16+0.03 20x20 0.05+0.03 0.27+0.10 18x20 0.05+0.01 0.11+0.11 10x20 N/A 0.16+0.16 20x10 10x10 0.01+0.01 0.01+0.05 69 Table 4. Difference in "T sym" readout of the linac with the Clinac dose servo disabled for different 10 MV asymmetric fields. T sym indicates deviations from symmetry as indicated by the beam monitor chamber. Symmetric field Asymmetric field (AF) "T sym" readout of the Clinac 2100C (%) AW xxL y AW yxL x 12x40 9x40 0.01Â±0.01 0.07+0.04 6x40 0.01+0.01 0.06+0.01 4x40 0.01+0.02 0.07+0.01 40x20 30x20 0.03+0.04 0.24+0.10 20x20 0.02+0.05 0.26+0.10 18x20 0.03+0.05 0.29+0.16 10x20 N/A 0.28+0.08 20x10 10x10 0.01+0.01 0.06+0.06 70 exhibits minimal collimator backscatter effect and hence will not exhibit much asymmetry in "T sym" when set asymmetrically. On the other hand as discussed in Chapter 4.2.3, the Y collimator exhibits collimator backscatter effect and will affect the beam monitor chamber signal. 71 4.3. Asymmetric Field Dose Calculation 4.3.1. The asymmetric field dose representation at depth The proposed correction factor (CF) discussed in Chapter 4.2.2 applies only to points at depth of maximum ionization (dmax). The proposed correction factor is now extended to any point at any depth d along the transverse principal plane within a radiation field (Fig. 4). This is achieved by expanding the collimator specific correction factors with the depth dependent term, TMR (tissue maximum ratio). As discussed in Chapter 2.1.4 (Eq. 5), the absorbed dose D(d,WxL) to a given point P along the collimator axis at depth d of a symmetric field is given as: where MU is the number of monitor units given. Now for the same point P in an asymmetric field AW x L, the two contributing fields would be W x L and (2AW - W) x L (Fig. 17C) and the dose D(d,AWxL) to point P is given as: D(d,W xL) = MU x OPF{W x L) x TMR(d,W x L) (33) D(d,AW xL) = MU x OPFjW x L) + OPF{(2AW -W)xL) 2 TMR(d,W xL) + TMR(d,(2AW -W)xL) 2 (34) Expressing in terms of the geometric mean, we have: D(d,AW x L) = MU x yjOPF{W xL)x OPF{{2AW -W)xL) XyJTMR{d,W xL)x TMR(d,{2AW - W) x L) (35) 72 A correction factor can then be calculated as the ratio of the absorbed dose in the asymmetric field to that in the symmetric field at the same point P, i.e., by combining Eqs. 35 and 33: D(d,AWxL) CF{d,AWx L) = D(d,WxL) OPF((2AW-W) x L) x TMR(d,(2AW-W) x L) OPF(W x L) x TMR(d, WxL) Similarly for an off-axis point R at off-axis distance, r, where r is not within the penumbral region nor outside the field edge, the two rectangular fields for the asymmetric field would be (W + 2r) x L and (2AW - W - 2r) x L and for the symmetric field they would be (W + 2r) x L and (W - 2r) x L (Figs. 17B and 17A, respectively). Hence, the correction factor CF(r,d,AWxL) for an asymmetric field at any off-axis point R would be the ratio D(r,d,AWxL) / D(r,d,WxL) where D(r,d,W x L) = MU x yjOPF((W - 2r) x L) x OPF((W + 2r) x L) xjTMR(d,(W - 2r) x L) x TMR(d,(W + 2r) x L) (37) D(r,d, AW x i ) = MU x ^OPF{{W + 2r) xL)x OPF((2AW - W - 2r) x L) xyJTMR(d, (W + 2r) x L) x TMR(d, (2AW - W - 2r) x L) (38) and D(r,d,AW x L) CF(r,d,AW x L) D(r,d,W x L) If" OPF((2AW -W -2r)x L) TMR(d,(2AW - W - 2r) x L) ( . OPF{(W - 2r) x L) * TMR(d,(W - 2r) x L) The proposed correction factor, therefore, is a function of the sizes of the asymmetric and symmetric fields, beam energy, depth, off-axis distance and, more importantly, distances with respect to the four field-defining collimators. Note the output factors are collimator 73 specific as discussed in Ch. 4.2.4 whereas the tissue maximum ratios are not. The absorbed dose D at point R in an asymmetric field can therefore be expressed as D(r,d,AW x L) = MU x OPF(W x L) x TMR(d,W x L) x OAR(r,d,W x L) xCF(r,d,AW x L) (40) At the asymmetric field center (or the field offset) which is r a s y m away from the collimator axis, the correction factor will be (Eq. (39) with r = -rasym = (AW - W) / 2): CF(r dAWv.D-f OPHAWxL) TMR(d,AW x L) ' }~ \OPFÂ«2W - AW)x L) TMR(d,(2W - AW) x L) K J For example, for a 6 MV 20 x 20 cm2 symmetric field collimated to a 10 x 20 cm2 asymmetric field, the asymmetric field center would be 5 cm from the collimator axis. The width and length are defined by the Y and X collimators, respectively. The OPF( 10x20) for the 6 MV photon beam was 1.016 and the OPF(30x20) was 1.076 (Fig. 20A). At a depth of 10 cm, the TMR(10x20) and the TMR(30x20) were 0.795 and 0.820 respectively. Hence, the CF(rasym,d,AWxL) at the asymmetric field center (Eq. 41) is given by 1.016 0.795 n CF(5,10,10 x 20) = t x t = 0. v V 1.076 V 0.820 957 The ratios of ion chamber readings at the asymmetric field center between the asymmetric and symmetric fields are shown in Tables 5 and 6 for the 6 and 10 MV photon beams, respectively, and are compared to the correction factor calculated using Eq. 41. For both photon energies, the agreement between measured and calculated correction factors for the three asymmetric fields at various depths was in most cases within half a percent. The largest discrepancy of one percent was with the heavily collimated 10 MV asymmetric field 74 Table 5. The measured ion chamber ratios of asymmetric fields and symmetric fields for a 6 MV photon beam at the asymmetric field center are compared to the calculated correction factors at the same point. A 20 x 20 cm2 field is blocked to a 5 x 20, 10 x 20 and 15 x 20 cm2 field. The corresponding asymmetric field centers are respectively 7.5, 5, and 2.5 cm away from the collimator axis and toward the unblocked field edge. asymmetric depth ratio of calculated % difference field (cm) chamber correction between cal'd (cm2) readings factor and meas'd 5 x 20 2 .947 .946 -0.1 10 .912 .912 0 25 .855 .857 +0.2 10 x 20 2 .975 .972 -0.1 10 .958 .957 0 25 .925 .925 0 15 x20 2 .988 .988 -0.1 10 .983 .982 -0.1 25 .968 .967 -0.1 75 Table 6. The measured ion chamber ratios of asymmetric fields and symmetric fields for a 10 MV photon beam at the asymmetric field center are compared to the calculated correction factors at the same point. A 20 x 20 cm2 field is blocked to a 5 x 20, 10 x 20 and 15 x 20 cm2 field. The corresponding asymmetric field centers are respectively 7.5, 5, and 2.5 cm away from the collimator axis and toward the unblocked field edge. asymmetric depth ratio of calculated % difference field (cm) chamber correction between cal'd (cm2) readings factor and meas'd 5 x20 2 .932 .941 +1.0 10 .917 .928 +1.2 25 .877 .887 +1.1 10 x 20 2 .966 .970 +0.4 10 .962 .965 +0.3 25 .937 .942 +0.5 15 x 20 2 .990 .987 -0.3 10 .984 .986 ' +0.2 25 .972 .976 +0.4 76 (5 x 20 cm2). The discrepancy was probably due to the lack of electronic equilibrium which occurs when the field radius was less than the electron range of the scattered electrons. In most asymmetric field algorithms the dose distribution of an asymmetric field is modified by accounting for the primary and scatter dose contributions separately. Here, the dose profile of a symmetric field is modified by a correction factor that accounts for the dose reduction within an asymmetric field as compared to the corresponding symmetric field. With this approach, the Day's equivalent field method is not used directly since there is no explicit attempt to separate the primary and scatter contribution. Instead, the correction factor uses the ratios of the OPFs and TMRs with field sizes determined by the equivalent fields between the asymmetric field and the symmetric field (Eq. 39). One limitation of this correction factor is that the correction factor can only be applied across the radiation field to within 1.5 cm from the field edges. This cutoff point is chosen since output factor and tissue maximum ratio for field sizes smaller than 3 cm are usually not available and are difficult to measure accurately. For points within the penumbral region and outside the radiation field, the correction factor can be approximated semi-empirically. The exact method of correction in the penumbral region will be discussed in a later section. 4.3.2. The wedge effect of asymmetric collimation A typical dose profile at d^x for an asymmetric field (dotted curve) and a symmetric field (solid curve) are shown in Figure 27. The dose profile of an asymmetric field tends to resemble that of a wedged field with the thick end towards the asymmetric field edge. Several 77 Figure 27. Typical absorbed dose profiles for a symmetric field, a half-collimated asymmetric field, and a symmetric field with the same field width as the half-collimated asymmetric field are shown. 78 authors have suggested that the wedge effect is the result of the primary beam variation between the asymmetric field and the symmetric field of the same field size.8'13 The asymmetric field algorithm proposed by Khan et al.13 thus modifies the primary transmission to account for this primary beam effect. The wedge effect of an asymmetric field can be explained from a different perspective using the correction factor proposed. For a given point in an asymmetric field and a symmetric field, the primary dose contribution is expected to remain unaltered unless the point is close to the field edge whereby the primary intensity will be altered by the collimator penumbral effect as illustrated by the abrupt drop in OAR,;, in Figure 18. The dose reduction in the asymmetric field versus the symmetric field is therefore due to the missing scattered radiation that would have originated within the irradiated phantom behind the asymmetric collimator.50 Obviously, this missing scatter effect is greatest near the asymmetric collimated edge (Fig. 19B). Hence, the resultant isodose profile is no longer flat but sloped towards the asymmetric collimated edge. Mathematically, this explanation can be demonstrated by the Clarkson's scatter-sector integration method5 and the Cunningham's IRREG program.2 Based on the Clarkson's method,5 the effective tissue air ratio (eff TAR) at a point at depth d in a rectangular or irregular field is represented as: eff TAR = TAR(d,rt) (42) n i=, where n is the number of sectors with each sector subtending an angle of 10Â°, r; are the radii from the center to the edge of the field at the center of each sector, and TAR(d,rj) are the tissue air ratios for circular fields of radius rj at depth d (Fig. 28). For points at dm a x, the eff TAR reduces to: 79 Figure 28. Illustration of a 20 x 20 cm2 field with the 10Â° sectors used in the calculation of effective tissue air ratio (eff TAR) and effective peak scatter factor (eff PSF) at the collimator axis and 7 cm off axis is shown. 80 ef/TAR(dmax) = eff PSF = - Â± PSF(rt) (43) where PSF(rj) are the peak scatter factors for circular fields of radius r, at dm a x. The data in Table 7 demonstrates that at dm a x and at 10 cm depth the eff PSF and eff TAR and thereby the scatter dose contributions are always lower for points close to the field edge (7 cm) than along the collimator axis. Experimentally, this is also reflected by the difference in measured off axis ratios at dm a x and in air (Fig. 18). For the same 7 cm off axis point, the off axis ratio at dm a x is 1% lower than the off axis ratio at the same point in air with a typical 6 MV 20 x 20 cm2 field (Fig. 18). This is in agreement with the calculated 1% difference in eff PSF between a point 7 cm away from the collimator axis and a point along the collimator axis (Table 7). This missing scatter effect is further illustrated in Figures 29 to 30 by comparing the measured asymmetric field dose profiles at dmax and those calculated based on various asymmetric field algorithms for both the 6 and 10 MV photon beams, respectively. The relative dose is normalized to the absorbed dose at dm a x along the collimator axis for a 10 x 10 cm2 photon field. The upper Y collimator is used to define the asymmetric field width and the lower X collimator is used to define the constant field length. The calculated asymmetric field dose profiles based on the average output factor (ave OPF) as suggested by Tenhunen and Lahtinen9 are calculated by multiplying the in air off axis ratio OARair(r,40x40) with the average output factor for the two field sizes as determined by the Day's equivalent field method (Eq. 13). The calculated dose profiles based on the proposed CF (Eq. 24) are calculated by multiplying the dose profile of the symmetric field and the correction factor proposed in Chapter 4.3.1 (Eq. 25) with the output factors being collimator specific. The 81 Table 7. The effective tissue air ratios (eff TARs) at dm a x and at 10 cm depth along the collimator axis and at a point 7 cm off the collimator axis are calculated based on the Clarkson's scatter-sector integration method. Data for a typical 6 MV photon beam with a 20 x 20 cm2 field size are used. angle (6) point along collimator axis point at 7 cm off axis radius (cm) PSF TAR radius (cm) PSF TAR 0 10.00 1.059 .858 17.00 1.080 .897 10 10.15 1.060 .860 17.26 1.081 .898 20 10.64 1.062 .863 18.09 1.082 .902 30 11.55 1.065 .869 19.63 1.084 .907 40 13.05 1.070 .877 15.55 1.077 .891 50 13.05 1.070 .877 13.05 1.070 .877 60 11.55 1.065 .869 11.55 1.065 .869 70 10.64 1.062 .863 10.64 1.062 .863 80 10.15 1.060 .860 10.15 1.059 .859 90 10.00 1.059 .858 10.00 1.059 .858 100 10.15 1.060 .860 10.15 1.059 .859 110 10.64 1.062 .863 8.77 1.053 .848 120 11.55 1.065 .869 6.00 1.037 .813 130 13.05 1.070 .877 4.67 1.027 .789 140 13.05 1.070 .877 3.92 1.021 .773 150 11.55 1.065 .869 3.46 1.017 .762 160 10.64 1.062 .863 3.19 1.015 .755 170 10.15 1.060 .860 3.05 1.013 .752 180 10.00 1.059 .858 3.00 1.013 .751 Ave = eff 11.13 1.063 .866 9.95 1.051 .838 82 (A) 20x20 SF & 15x20 AF 1.100 1.040 1.020 1.000 - A â€” based on ave OPF - X- - â€¢ based on CF â€¢ O - - based on OFF(AF) -10 -8 -4 -2 Off axis distance (cm) (B) 20x20 SF& 10x20 AF 1.100 1.080 CD g 1.060 3 1.040 <u CC 1.020 1.000 -10 - ~ ^ = * > â€” < t \ â€” 0 â€” measured SF â€” B â€” measured AF ) U â€” â€” u c n c u u i I a v e w r i . . . x- - - based on CF ._ . - based on 0PF(AFj -6 -4 Off axis distance (cm) 20x20 SF&5X20AF -10 -8 -7 Off axis distance (cm) Figure 29. The measured and calculated asymmetric field (AF) dose profiles relative to the OPF( 10x10) are compared for a 6 MV photon beam at dmax and at 100 cm source to axis distance. The calculated AF dose profiles based on ave OPF are determined by multiplying the OARair(r,40x40) with the average OPF for the two field sizes as determined by the Day's equivalent field method (Eq. 13). The calculated AF dose profiles based on CF are determined by multiplying the dose profile of the symmetric field (SF) and the proposed CF (Eq. 25). The calculated AF dose profiles based on OPF(AF) are determined by multiplying the OARair(r,40x40) with the OPF having the same field size as the AF (as Eq. 31 with r instead of rasym). 83 (A) 20x20 SF& 15x20 AF 1.100 1.080 a> in g 1.060 .1 5 1.040 a> DC 1.020 1.000 < ) I r ' A measured S F â€” B â€” measured AF â€” A â€” based on ave OPF . . . X- - - based on CF - o - - based on OPF(AF) I I -10 -8 -4 -2 Off axis distance (cm) (B) 1.100 1.080 CD ,Â§1.060 11.040 1.020 20x20 SF 8.10x20 A F 1.000 -10 < r~~ â€”0â€”rr teasured SF teasured AF -i â€” r\cc â€” B â€” r r a udbcu un ave wrr - - -X- - - based on CF - - o - - based on 0PF(AFj -8 -6 -4 Off axis distance (cm) (C) 20x20 SF & 5x20 A F 1.100 1.080 CD S 1.060 1 1.040 CD at 1.020 1.000 â€¢0 ^ > o < â€” 6 â€” measure d S F d AF l ave OPF â€” 6 â€” based or . . . X- - - based on CF - - o - - oasea or l u r ^ - ^ M ^ ; x -V T s^t: X Â£ â€”â€” 4< â€”a -10 -8 -7 Off axis distance (cm) Figure 30. The measured and calculated asymmetric field (AF) dose profiles relative to the OPF( 10x10) are compared for a 10 MV photon beam at dm a x and at 100 cm source to axis distance. The calculated AF dose profiles based on ave OPF are determined by multiplying the OARair(r,40x40) with the average OPF for the two field sizes as determined by the Day's equivalent field method (Eq. 13). The calculated AF dose profiles based on CF are determined by multiplying the dose profile of the symmetric field (SF) and the proposed CF (Eq. 25). The calculated AF dose profiles based on OPF(AF) are determined by multiplying the OARairO",40x40) with the OPF having the same field size as the AF (as Eq. 31 with r instead of rasym). 84 calculated dose profiles based on OPF(AF) are calculated by multiplying the OARair(r,40x40) with the output factor having the same field size as the asymmetric field (as Eq. 31 with r instead of rasym as off axis distance). The second method based on the proposed CF uses correction factors that vary across the asymmetric field, and thereby accounts for the difference in scatter dose contribution across the asymmetric field. Similarly, the first method based on the average output factor (ave OPF) as suggested by Tenhunen and Lahtinen9 also uses values, ave OPF, that vary across the asymmetric field. As shown in Figures 29 and 30, both methods give asymmetric field dose profiles that are in close agreement with measurement. Unlike the first two methods, the third method applies a constant value, OPF(AF), and thereby assumes a constant scatter dose contribution across the asymmetric field. As illustrated, the calculated asymmetric field dose profiles based on the OPF(AF) resemble the off axis ratio curves (Fig. 18) and fail to account for the lower dose at both ends of the field edges. In particular with the 20 x 20 cm2 symmetric field one-quarter collimated to a 15 x 20 cm2 asymmetric field, the calculated dose value at a point 2 cm from the asymmetrically collimated field edge follows the shape of the off axis ratio curve and does not slope towards the field edge as observed experimentally. As a result, Gibbons and Khan51 have modified the off axis ratio (OAR) in Khan's original equation13 with a varying scatter component that is similar to the equation suggested by Kwa et al23 85 4.4. An Asymmetric Field Treatment Planning Algorithm The correction factor (CF) proposed in Chapter 4.3.1 (Eq. 39) is used to account for the dose reduction when a symmetric field is asymmetrically collimated to a smaller asymmetric field. The absorbed dose at any point in an asymmetric field can then be determined from existing symmetric field data. One limitation is that the correction factor can only be applied across the radiation field to within 1.5 cm from the field edges. For points beyond this cutoff point, a set of correction factors to be used in the penumbral region is derived. These correction factors can then be represented by a subroutine or a function call in an existing treatment planning program. 4.4.1. Generation of a set of correction factors The details of the correction factors used across a radiation field are discussed here. The aim is to derive a set of correction factors based on equations that use similar beam, and position specific parameters, such as AW, W, L, d, r, OPF, TMR, etc. As demonstrated, they can then be used for a wide range of photon beams and asymmetric fields. These correction factors are first derived semi-empirically by beam fitting with a typical measured dose profile, such as a 6 MV half collimated 10 x 20 cm2 asymmetric field at a depth of 10 cm (Fig. 3 IB). The dose profiles at different depths are then calculated based on these parametrized correction factors and are compared with measured dose profiles. Additional parametrization of these correction factors might be required to obtain a better fit for the beam profiles at 86 -15.0 -5.0 0.0 off axis distance (cm) 15.0 ft '"â€¢^Sfru -5.0 0.0 5.0 off axis distance (cm) 15.0 E -15.0 0.0 5.0 off axis distance (cm) 15.0 Figure 31. The measured (solid line) and calculated (dashed line) dose profiles are compared for a 6 MV photon beam at depths of 2 (open triangle), 10 (cross) and 25 (open circle) cm and at 100 cm source to axis distance. A 20 x 20 cm2 symmetric field is (A) one-quarter collimated to a 15 x 20 cm2, (B) half collimated to a 10 x 20 cm2 field, and (C) three-quarter collimated to a 5 x 20 cm2 field. Ion chamber readings were normalized to a point at a depth of 2 cm along the collimator axis of the 20 x 20 cm2 symmetric field. 87 other depths (Fig. 3 IB). Once it is done for a particular field size, one can confirm the appropriateness of the correction factors by comparing to other asymmetric field profiles, such as a symmetric field of 20 x 20 cm2 one-quarter and three-quarter collimated to a 5 x 20 cm2 and a 15 x 20 cm2 asymmetric field (Figs. 31A and 31C, respectively). At present, these correction factors are specific to our in-house treatment planning program but can be readily applied to other treatment planning programs. Based on the original treatment planning algorithm as discussed in Chapter 3.4.1.1, the correction factors are categorized into eight groups labeled from CFA to CFH and the positions where they are applicable are shown in Figure 32 where: 1. CFA- -y/l-(l- AWIW)2 for points with OAR < 0.3 on the symmetrically collimated side where OAR is the off-axis ratio at the specified point in the symmetric field. The magnitude of the correction is small and the correction factor is approximated empirically based on some function of the width of the asymmetric field, AW, and the symmetric field, W. 2. CFB = CFA + (CFC - CFA ){OAR - 0.3) / 0.2 for points with off axis ratios between 0.3 to 0.5 on the symmetrically collimated side. Basically, CFB is used to smooth the transition from CFA to CFC. 3. CFC is used for points with OAR > 0.5 and to a cutoff point that is 1.5 cm away from the geometric field edge but within the radiation field on the symmetrically collimated side (Fig. 32). For a 20 x 20 cm2 field, this cutoff point would be 8.5 cm from the collimator axis. The magnitude of the correction is still small and is approximated by the correction factor at the cutoff point. Hence, it is a function of the sizes of the asymmetric and symmetric fields and depth of interest as follows: 88 Figure 32. A schematic diagram illustrating the dose profiles of a symmetric field (continuous line) and a smaller asymmetric field (dashed line) is shown. The positions where the various correction factors used in the present algorithm are applied for asymmetric fields are indicated. 89 CFC=^0PF((2AW-3) x L)/0PF((2W-3) x L) x ^ TMR(d,{2AW - 3) x L)/TMR(d,(2W-3) x L) 4. CFD is the correction factor (Eq. 39) used within the main radiation field between the two cutoff points 1.5 cm within both the symmetric and asymmetric field edges, and is given by: CFD = ^OPF((2AW-W-2r) x L)/OPF((W-2r) x L) x^TMR(d,(2AW-W-2r) x L)/IMR(d,(W-2r) x L) where r is the off-axis distance. For points within the penumbral region of the asymmetrically collimated side and outside the radiation field, the shape of the symmetric field edge is used as the basis upon which the asymmetric field edge calculation is done. Hence, the entire field edge is shifted laterally onto the asymmetric field edge, and the off axis ratio value of the symmetric field at the field edge is used to represent the off axis ratio at the field edge of the asymmetric field (shifted off axis ratio). For example, let's say the off axis ratio at the symmetric field edge is 50%, then the shifted off axis ratio (SOAR) at the asymmetric field edge is also given a value of 50%. This is analogous to the use of boundary factors16 to describe the absorbed doses at the field edge. Additional corrections are then applied to this shifted off axis ratio (SOAR) in order to smooth the transition to the cutoff point and to account for the dose reduction by the smaller asymmetric field. The term OAR used below still refers to the off axis ratio at the point of interest in a symmetric field. 5. CFE is for points with SOAR > 0.5 and to the cutoff point of the asymmetrically collimated side and its purpose is to smooth the transition to the cutoff point. Similarly, the 90 cutoff point is 1.5 cm from the geometric field edge of the asymmetrically collimated side. CFE is empirically determined to fit the measured data. CFE = ((AW -W !2-r + (1.5 - AW + W I 2 + r) x SOAR I OAR) 11.5) xCFP2x^SOAR-05) xyfCFC where CFP is the correction factor at the cutoff point on the asymmetrically collimated side given by: CFP = JOPF(3x L)/OPF((2W-2AfV + 3)x L) x yJTMR(d,3x L)/TMR(d,(2W - 2 A W + 3) x L) 6. CFF = (SOAR I OAR) x JCFC x CFP2H0-5-SOAR) for points with SOARs between 0.3 to 0.5. CFF reduces to CFE and CFG for points with SOARs of 0.5 and 0.3, respectively. 7. CFG = (SOAR I OAR) x JCFP x CFC x cFA4x(0-3-SOAR) for points with SOARs between 0.05 to 0.3. CFG reduces to CFF and CFH for points with SOARs of 0.3 and 0.05, respectively. 8. CFH = (SOAR I OAR) x JCFP x CFC x CFA for points with SOAR < 0.05. Again, this is an empirically determined correction factor. The significance of this correction factor is not as critical since the actual value is only a small fraction of the primary absorbed dose at the field center. Note that all the correction factors across the radiation field reduce to unity when the asymmetric field width, AW, equals the symmetric field width, W. The same equations for the various correction factors can then be used for other photon beams of different photon energies, as confirmed by the agreement between the 10 MV calculated and measured dose profiles at all three depths (Fig. 33). As these correction factors are parametrized with beam and position specific parameters, these correction factors are universal and can be applied for 91 J3 E CO -15.0 -10.0 -5.0 0.0 5.0 off axis distance (cm) 10.0 15.0 E -15.0 -10.0 -5.0 0.0 5.0 off axis distance (cm) 10.0 15.0 to E M a 100.0 â€¢ C. J T 80.0 â€¢ '"Xi 60.0 â€¢ T 40.0 -I J *^~ I 1 ^ 0.9- 1 1 1 -15.0 -10.0 -5.0 0.0 5.0 off axis distance (cm) 10.0 15.0 Figure 33. The measured (solid line) and calculated (dashed line) dose profiles are compared for a 10 MV photon beam at depths of 2 (open triangle), 10 (cross) and 25 (open circle) cm and at 100 cm source to axis distance. A 20 x 20 cm2 symmetric field is (A) one-quarter collimated to a 15 x 20 cm2, (B) half collimated to a 10 x 20 cm2 field, and (C) three-quarter collimated to a 5 x 20 cm2 field. Ion chamber readings were normalized to a point at a depth of 2 cm along the collimator axis of the 20 x 20 cm2 symmetric field. 92 most photon energies, asymmetric field sizes, or linacs. Furthermore, these correction factors can be applied to any symmetric profile regardless of whether it represents measured data or is analytically calculated, and thus can be implemented in any dose calculation program. Any additional asymmetric field dose profiles are then measured for quality assurance purposes only. 4.4.2. Implementation of the correction factors as a FORTRAN subroutine The various correction factors from CFA to CFH were implemented as a FORTRAN subroutine into an existing treatment planning program (Appendix 1). The calculated and measured isodose distributions for two asymmetric 10 MV photon beams are shown in Figure 34. Similar results are observed for the same asymmetric fields with a 6 MV photon beam. Good agreement is observed everywhere including the penumbral regions. Additional comparisons of measured and calculated isodose distributions are also made but are not shown here with both 6 and 10 MV photon beams for 12 x 6 cm symmetric fields collimated to 9 x 6 and 6 x 6 cm asymmetric fields, and for 20 x 20 cm symmetric fields collimated to 15 x 20, 10 x 20 and 5 x 20 cm asymmetric fields. Again, this comparison is required for quality assurance only. The measured isodose distributions for a half-collimated 6 MV photon field are compared to the calculated isodose distributions using the correction factors proposed here and the GE Target full calculation option simulating an asymmetric field with blocking and are shown in Figure 35. The calculated isodose distribution based on the proposed correction factors agrees with the measured isodose distribution slightly better than that based 93 A . 10 MV (0 "x < -10-o Figure 34. The measured (dashed line) and calculated (solid line) isodose distributions for a 10 MV photon beam at 100 cm source to surface distance are shown. (A) A 12 x 6 cm2 rectangular field is three-quarter collimated to a 3 x 6 cm2 field, and (B) a 4 x 4 cm2 square field is quarter-collimated to a 3 x 4 cm2 field. The isodose lines were normalized to a point at the asymmetric field center at a d^ of 2.5 cm. The six isodose lines shown are 100, 90, 70, 50, 30, and 10%. 94 Figure 35. The measured and calculated isodose distributions for a 6 MV photon beam at 100 cm source to surface distance are shown. A 20 x 20 cm2 square field is half-collimated to a 10 x 20 cm2 field. The calculated isodose distributions are based on the correction factors proposed here, the full calculation option of the GE Target system and the fast calculation option of the GE Target system. The calculated isodose distributions were normalized to the 90% isodose line of the measured plots at the asymmetric field center. The five isodose lines shown are 90, 70, 50, 30, and 10%. 95 on the GE Target full calculation option, but the main difference is that the computation time required for the Target full calculation option is 5.5 minutes per asymmetric field, as compared to 15 seconds for the in-house system. This is because the Target full calculation option is based on the Cunningham's IRREG algorithm,2 and hence has to separate the primary and the scatter contributions with the scatter contribution determined over 360Â°. As stated the proposed approach does not require the separation of the primary and the scatter, and the dose computation is much more efficient because of the way the scatter contribution is calculated. For example, the Target full calculation option calculates the scatter contribution at every 5Â° interval, hence it will have to calculate for each point the scatter contribution 72 times; whereas, the correction factor proposed here only takes two field size determinations. The only limitation is that the correction factor method works only for asymmetric rectangular and square fields, and will not handle irregular fields as the Target system can. The computation time with the Target fast calculation option is much faster and is comparable with our in-house system, however, the calculated isodose distribution fails to account for the variation of scatter contribution across the asymmetric field (Fig. 35), and is unacceptable for clinical use, especially for conformal therapy.50 Figures 36 (A) and (B) illustrate the calculated isodose distributions of two adjacent half-collimated asymmetric fields for both the 6 and 10 MV photon beams, respectively. The width of the two asymmetric fields equaled the width of the symmetric field, and the combined isodose distributions should be identical to the isodose distribution of the symmetric field. The combined isodose distributions show a slight ripple at the asymmetric field junction, reflecting the limitation of the existing algorithm. These ripples are due to the gradual drop in 96 A. 6 MV Figure 36. The calculated isodose distribution for two adjacent half-collimated beams (solid curve) and a single symmetric field (dashed curve) for (A) a 6 and (B) a 10 MV photon beam are shown. The seven isodose lines shown are 100, 95, 90, 70, 50, 30, and 10%. 97 the calculated absorbed doses at and near the cutoff point of the asymmetric field edge, and the less than perfect smoothing function between the cutoff point and the point at a shifted off axis ratio of 0.5. 4.4.3. Summary In summary, a treatment planning algorithm for asymmetric collimation has been developed and implemented into an in-house treatment planning system. Conceptually, when one of the independent collimators is closed down, the resultant asymmetric field is smaller than the original symmetric field. The difference in absorbed dose between the asymmetric field and the symmetric field is accounted for by the correction factor described here which is a function of the sizes of the asymmetric and symmetric fields, depth of interest, off-axis distance, and more importantly, the distances at the point of interest in relation to the four independent collimators within the asymmetric field and the symmetric field. This correction factor accounts for the variation in scatter across the asymmetric field which resulted in the dose profile resembling that under a wedge. The absorbed doses within the penumbral regions and outside the radiation field are accounted for by some semi-empirically parametrized correction factors. These correction factors are universal, with the equations made up of constants that are beam, field size, and position specific. The resultant dose profiles and isodose distributions have been shown to be in good agreement with measured data for both the 6 and 10 MV photon beams. Because these correction factors rely only on the output factors and the tissue maximum ratios, they can easily be implemented into any existing 98 treatment planning program. There is no need to store either additional sets of asymmetric field profiles or databases. The method also lends itself to asymmetric collimation in both directions. The present algorithm is superior to a commercial system based on the IRREG program (GE Target 2 system) in that the computation time is 20 times faster for the same degree of accuracy, and that, although comparable in time, the fast calculation option of the commercial system fails to produce an acceptable dose distribution. The only limitation of the present system is that it will not account for the dose distribution within an irregular field. 99 4.5. Asymrnetric Collimation in Both Field Dimensions Here the correction factor proposed by Kwa et al.221 is extended to 2-fold asymmetric collimation where both the upper and the lower collimators are set asymmetrically. The argument that the dose to a point is related to the sum of the dose contributions between the two fields centered at the same point can be extended to the four fields centered at the same point. Figure 37(A) illustrates the four rectangular fields centered at the point P which is a distance r and s away from the mechanical axis in a symmetric field W x L. Figure 37(B) illustrates the four rectangular fields centered at the same point in a 2-fold asymmetric field AW x AL. Using the same formalism used for an asymmetric field in one field dimension23 and discussed in Chapters 4.2 and 4.3, the CF for a 2-fold asymmetric field AW x AL at a point P, a distance r and s away from the collimator axis, would be t JTMi(d,(W+2r) x(2AL-L-2s)) x 7 J V ^ ( r f , ( 2 ^ ^ - ^ - 2 r ) x ( L + 2 5 ) ) x 7 M J ( r f , ( 2 ^ ^ - ^ - 2 r ) x ( 2 ^ L - L - 2 y ) ) | lMR(d, (W+2r)x(L- 2s)) x 1MR(d, (W- 2r) x (L+2s)) x 1Ml(d, (W- 2r)x(L- 2s)) Similar to the approach used in Chapter 4.4.1, the correction factors within the penumbral region and outside the radiation field are parametrized semi-empirically. When the calculation plane that is parallel to the field width and is at least 1.5 cm away from either geometric field edge defining the length, the correction factors are again categorized into eight groups from CFA to CFH (Fig. 32). CF = 100 Figure 37. Illustration of the equivalent field principle for a 2-fold asymmetric field is shown. The absorbed dose at a point P which is a distance r and s away from the central axis is represented by the sum of the absorbed doses at the same point P between the four rectangular fields centered at point P (A) for a symmetric field of W x L and (B) for a smaller asymmetric field of AW x AL. 101 , CFA = Jl-Q-AW,W)* Â» ^ â€¢ ^ - J D < M I ^ - P ^ - t - i ' ) l A" V V 0PF(Wx(L-2s)) TMR(d,Wx(L-2s)) for points with the off-axis ratio (OAR) < 0.3 on the unblocked side. 2. CFB = CFA + (CFC- CFA)(OAR - 0.3) / 0.2 for points with OAR's between 0.3 to 0.5 on the unblocked side. The equation is the same as that in the one-dimensional case (Chapter 4.4.1) except that the actual value would be different since CFA and CFC are different. 3. CFC is used for points with OAR > 0.5 and to the cutoff point 1.5 cm within the field edge on the unblocked side. This is basically the correction factor at the cutoff point for the 2-fold asymmetric field, and is given as: CFC = â€¢i i OPF(3 x (2AL - L - 2s)) x OPF((2AW -3)x(L + 2s)) x OPF((2AW - 3) x (2AL - L - 2s)) OPF(3 x(L- 2s)) x OPF((2W - 3) x (L + 2s)) x OPF((2W - 3) x (L - 2s)) TMR(d,3 x (2AL - L - 2s)) x TMR(d,(2AW - 3) x (L + 2s)) x TMR(d,(2AW - 3) x (2AL - L - 2s)) TMR(d,3 x(L- 2s)) x TMR(d,(2W - 3) x (L + 2s)) x TMR(d,(2W -3)x(L- 2s)) 4. CFD is the 2-fold correction factor given earlier for points within the main radiation field between the two cutoff points 1.5 cm away from the field edges (Eq. 44). CFD= OPF((W+2r) x (2AL -L-2s))x OPF((2A W- W-2r)x(L+2s)) x OPF((2A W- W- 2r) x (2AL -L- 2s)) OPF((W+ 2r) x(L- 2s)) x OPF((W- 2r) x(L+2s)) x OPF((W- 2r) x(L- 2s)) * TMR(d, (W+ 2r) x (2AL -L-2s))x lMR(d, (2 A W- W- 2r) x (L+2s)) x 1Mi(d, (2 A W- W- 2r) x (2AL -L-2s)) TMR(d,(W+ 2r) x(L- 2s)) x TMR(d, (W- 2r)x(L+2s)) x TMR(d, (W- 2r) x(L-2s)) Similarly, for points within the penumbral region of the blocked side and outside the radiation field, the shape of the symmetric field edge is used as the basis upon which the asymmetric field edge calculation is done. The off axis ratio of the symmetric field at the field edge is shifted to the field edge of the asymmetric field (shifted off axis ratio). Additional 102 corrections are then applied to the shifted off axis ratio (SOAR) in order to smooth the transition to the cutoff point and to account for the dose reduction by the smaller asymmetric field. Again the equations are identical to the one-dimensional case with the actual values being different due to the new correction factors, namely, CFA, CFC, CFD and CFP. 5 CFE is for points with SOAR > 0.5 to the cutoff point of the asymmetrically collimated width. CFE = ((AW - W12 - r + (1.5 - AW + W12 + r) x SOAR I OAR) 11.5) xCFP2<SOAR-Â°-5) X yfCFC where CFP is the correction factor for the 2-fold asymmetric field at the cutoff point of the asymmetrically collimated width given by: CFP j OPF((2AW-3)x(2AL-L-2s))xOPF(3x(L + 2s))xOPF(3x(2AL-L-2s)) ~ \ OPF((2AW-3)x(L-2s)) x OPF((2W-2AW+3) x (L + 2s)) x OPF((2W-2AW+3) x (L -2s)) * I ndR(dX2AW-3)x(2AL-L-2s))xTMJ(d,3x(L + 2s))xTAdR(d,3x(2AL-L-2s)) \ 1MR(d,(2AW-3) x (L-2s)) x TMR(d,(2W-2AW+3) x (L + 2s)) x TMR(d,(2W-2AW+3)x(L-2s)) 6. CFF = (SOAR I OAR) x 4CFC x CFP2^5-SOAR) for points with SOAR's between 0.3 to 0.5. 7. CFG = (SOAR I OAR) x JCFP x CFC x CFAW~S0AR) for points with SOAR's between 0.05 to 0.3. 8. CFH = (SOAR I OAR) x JCFP x CFC x CFA for points with SOAR < 0.05. Again, all the correction factors reduce to unity when the asymmetric field width AW and length AL equals the symmetric field width W and length L. The same approach can also be used for dose profiles parallel to L by interchanging the variables between the width and length. Since these correction factors are a function of the position of the point of calculation 103 in relation to the four field edges as represented by the four equivalent fields, they can be readily applied to any three dimensional (3D) symmetric dose profile to obtain a 3D dose representation of an asymmetric field. One merit of this correction method is that the resultant 3D dose representation of an asymmetric field will automatically include the beam hardening effect and the presence of horns in the radiation field if already included in the original 3D dose representation of a symmetric field. Figures 38 and 39 are the measured and calculated dose profiles along the transverse principal plane for both the 6 and 10 MV photon beams, respectively, for various asymmetric fields with the field length one-quarter collimated. Figures 40 and 41 are the measured and calculated dose profiles along the transverse asymmetric field central plane for both the 6 and 10 MV photon beams, respectively, for various asymmetric fields with the field length one-quarter collimated. The asymmetric field central plane is taken at 2.5 cm away from the principal plane for a 20 cm length collimated to 15 cm asymmetric length. The field widths are collimated from a 20 cm width to (A) 15 cm, (B) 10 cm, and (C) 5 cm asymmetric width. For each 2-fold asymmetric field, dose profiles are measured at dmax, 10 and 25 cm depth. Good agreement is observed between the measured and calculated dose profiles at all three depths for both photon energies. Both the measured and calculated dose profiles are not smooth and the ripples do not match perfectly between the two profiles. This is because of the machine output fluctuation during measurements between the symmetric fields upon which the calculated asymmetric field profiles are based and the asymmetric fields. The differences between the calculated and measured ionization unit at each point were expressed as a percentage of the ionization unit measured at dmax and at the asymmetric 104 - 6 - 3 0 3 o f f a x i s d i s t a n c e ( c m ) - 3 0 3 6 o f f a x i s d i s t a n c e ( c m ) o f f a x i s d i s t a n c e ( c m ) Figure 38. The measured (solid line) and calculated (dashed line) dose profiles along the principal plane parallel to the field width at dmax (open triangle), 10 (cross) and 25 (open circle) cm depths and at 100 cm source to axis distance are compared for a 6 MV photon beam. A 20 x 20 cm2 symmetric field is (A) one-quarter collimated in both dimensions to a 15 x 15 cm2 2-fold asymmetric field. The field width is further collimated to (B) a 10 x 15 and (C) a 5 x 15 cm2 2-fold asymmetric fields. Ion chamber readings were normalized to a point at a depth of 1.5 cm along the collimator axis of the 20 x 20 cm2 symmetric field. 105 2 Â£ o c -1 8 -1 5 -1 2 - 9 - 6 - 3 0 3 6 9 1 2 1 5 1 8 o f f a x i s d i s t a n c e ( c m ) o f f a x i s d i s t a n c e ( c m ) o f f a x i s d i s t a n c e ( c m ) Figure 39. The measured (solid line) and calculated (dashed line) dose profiles along the principal plane parallel to the field width at d^x (open triangle), 10 (cross) and 25 (open circle) cm depths and at 100 cm source to axis distance are compared for a 10 MV photon beam. A 20 x 20 cm2 symmetric field is (A) one-quarter collimated in both dimensions to a 15 x 15 cm2 2-fold asymmetric field. The field width is further collimated to (B) a 10 x 15 and (C) a 5 x 15 cm2 2-fold asymmetric fields. Ion chamber readings were normalized to a point at a depth of 2.5 cm along the collimator axis of the 20 x 20 cm2 symmetric field. 106 -3 0 3 6 o f f a x i s d i s t a n c e ( c m ) -1 8 - 1 5 -1 2 - 9 -6 -3 0 3 6 9 1 2 1 5 1 8 o f f a x i s d i s t a n c e ( c m ) 1 0 0 + o f f a x i s d i s t a n c e ( c m ) Figure 40. The measured (solid line) and calculated (dashed line) dose profiles along the asymmetric central plane (2.5 cm away from the principal plane) parallel to the field width at dmax (open triangle), 10 (cross) and 25 (open circle) cm depths and at 100 cm source to axis distance are compared for a 6 MV photon beam. A 20 x 20 cm2 symmetric field is (A) one-quarter collimated in both dimensions to a 15 x 15 cm2 2-fold asymmetric field. The field width is further collimated to (B) a 10 x 15 and (C) a 5 x 15 cm2 2-fold asymmetric fields. Ion chamber readings were normalized to a point at a depth of 1.5 cm along the collimator axis of the 20 x 20 cm2 symmetric field. 107 â€¢ 1 8 - 1 5 - 1 2 - 9 o f f a x i s d i s t a n c e ( c m ) Figure 41. The measured (solid line) and calculated (dashed line) dose profiles along the asymmetric central plane (2.5 cm away from the principal plane) parallel to the field width at dmax (open triangle), 10 (cross) and 25 (open circle) cm depths and at 100 cm source to axis distance are compared for a 10 MV photon beam. A 20 x 20 cm2 symmetric field is (A) one-quarter collimated in both dimensions to a 15 x 15 cm2 2-fold asymmetric field. The field width is further collimated to (B) a 10 x 15 and (C) a 5 x 15 cm2 2-fold asymmetric fields. Ion chamber readings were normalized to a point at a depth of 2.5 cm along the collimator axis of the 20 x 20 cm2 symmetric field. 108 field center and are shown in Table 8. The percentage dose differences shown are averaged over dose points 1.5 cm from the field edges defining the field width and their respective standard deviations are summarized. Most of the average percentage dose differences are within half a percent and are less than the standard deviation. The discrepancy is largest at greater depths (25 cm depth) and with heavily collimated asymmetric fields (three-quarter collimated field width). Figure 42 shows the measured and calculated dose profiles for a 6 MV half-collimated asymmetric field in both field dimensions. Such an asymmetric field is often used in the treatment of isocentric three-field breast technique.52"54 The calculation plane is at the asymmetric central plane, which is parallel to the field width and is 10 cm away from the principal plane. Results similar to other asymmetric field results are observed, with the largest discrepancy occurring at 25 cm depth (Table 8). 109 Table 8. The average percentage dose difference between the calculated and measured dose values for points within the radiation field and 1.5 cm away from the field edges along the asymmetric central plane and the principal plane parallel to the field width are shown. The asymmetric field central planes are 2.5 and 10 cm away from the principal plane for asymmetric fields one-quarter and one-half collimated lengthwise, respectively. Shown here are data for a 20 x 20 cm2 square field collimated to 15 x 15, io x 15 and 5 x 15 cm2 asymmetric fields for both the 6 and 10 MV photon beams, and for a 6 MV 20 x 40 cm2 rectangular field collimated to a 10 x 20 cm2 asymmetric field. For each field, the dose profiles were measured at three depths, namely, depth of maximum dose (dmax), 10 and 25 cm. photon 2-fold Ave. dose difference and standard deviation along the profile (%) energy asymmetric 2.5 cm from principal plane principal plane (MV) field dmax 10 cm 25 cm dmax 10 cm 25 cm 15x15 - 0 . 3 Â± 0 . 5 0 . 1 Â± 0 . 7 0 . 3 Â± 0 . 8 - 0 . 6 Â± 0 . 5 0 . 0 Â± 0 . 5 0 . 2 Â± 0 . 7 6 10x15 - 0 . 3 Â± 0 . 6 0 . 4 Â± 0 . 6 0 . 4 Â± 0 . 8 0 . 1 Â± 0 . 7 0 . 3 Â± 0 . 6 0 . 4 Â± 0 . 7 5x15 0 . 0 Â± 0 . 5 0 . 0 Â± 0 . 2 1 .5Â±0.2 0 . 0 Â± 0 . 5 0 . 9 Â± 0 . 6 1 .5Â±1.1 15x15 - 0 . 3 Â± 0 . 7 0 . 0 Â± 0 . 6 0 . 5 Â± 0 . 6 0 .6Â±1 .3 0 . 1 Â± 0 . 7 0 . 6 Â± 0 . 9 10 10x15 - 0 . 4 Â± 0 . 6 0 . 5 Â± 0 . 6 0 .5Â±0 .5 0 . 0 Â± 0 . 6 0 . 3 Â± 0 . 8 0 . 7 Â± 0 . 6 5x15 0 . 6 Â± 1 . 4 1 .5Â±0.4 2 . 2 Â± 0 . 6 0 .3Â±0 .3 0 . 8 Â± 0 . 4 l.ldb0.7 10 cm from principal plane 6 10x20 0 . 2 Â± 0 . 6 1 .0Â±0.4 2 . 6 Â± 0 . 8 110 Figure 42. The measured (solid line) and calculated (dashed line) dose profiles of a 20 x 40 cm2 symmetric field collimated in both dimensions to a 10 x 20 cm2 2-fold asymmetric field along the asymmetric central plane (10 cm away from the principal plane) parallel to the field width at dm a x (triangle), 10 (cross) and 25 (circle) cm depths and at 100 cm source to axis distance are compared for a 6 MV photon beam. Ion chamber readings were normalized to a point at a depth of 1.5 cm along the collimator axis of the 20 x 40 cm2 symmetric field. I l l 5. CLINICAL USE OF ASYMMETRIC COLLIMATORS To produce irregular radiation fields or shield certain parts of a field, Cerrobend or lead blocks of 7 cm thickness are inserted on a tray in the head of the linac. Asymmetric collimators can be used as a replacement for Cerrobend or lead blocks when the block has a straight parallel edge with the treatment field. Stern et. al.1 have demonstrated and commented on the application and the usefulness of asymmetric collimation. However, the full potential of asymmetric collimation can only be realized with a proper dose calculation algorithm. With the limited availability of a proper treatment planning algorithm for asymmetric fields, there are only limited reports on the use of asymmetric collimators either with static or rotational fields.52"58 Various treatment techniques with asymmetric collimation in one field dimension are described here and the resultant dose distributions in the central plane are illustrated. The purpose is to demonstrate the dosimetric effect of asymmetric collimation and to illustrate some of the potential uses and advantages of asymmetric collimation.58 5.1. An Overview Some clinical uses of asymmetric collimation are as follows: 1. Coned-down or boost fields with asymmetric collimation The use of asymmetric collimation is well suited for treatments where a patient is treated with a coned-down or a small boost field placed over the same area as a larger field.1 In 112 this situation, the same center can be used for both the large field and the coned-down or boost field. Each individual jaw can be closed down to match the coned-down or boost field. This simple setup avoids re-simulating the patient to determine the coned-down or boost field center. Subsequently, there is no need to mark a new center on the patient. Blocks, if any, can still be used since the treatment center remains the same. All these result in less patient setup confusion and fewer errors. 2. Half-collimated asymmetric fields The use of half-beam or half-collimated asymmetric fields has found many clinical uses. The use of two half-beams adjacent to each other eliminates the problem of matching two divergent fields which produce hot and cold spots in the dose distribution.1 Another use of a half-collimated asymmetric field is to avoid irradiating critical organs or tissues on the contralateral side by an exit beam because of beam divergence.58 For such a half-beam setup, the collimator axis is centered right next to the critical organ and the collimator leaf over the critical organ is closed down to the collimator axis resulting in a beam edge tangent to the critical organ. An example of the use of half-beam tangential breast irradiation will be discussed in a later section. 3. Conformal therapy with asymmetric collimation In conformal radiotherapy the high dose region is maximized around the tumor with minimal dose to surrounding tissues. With the convenience of using the asymmetric collimators and the availability of a proper treatment planning algorithm for asymmetric 113 fields, novel treatment techniques with multiple stationary or rotational asymmetric fields can be planned. Some of these techniques using multiple stationary fields58 will be described here and a specific head and neck technique with rotational asymmetric fields will be discussed in a later section. Figure 43(A) and (B) illustrate two different treatment plans for the treatment of a nasopharyngeal cancer. The dose distributions in the central plane are shown with retrostyloid tumor extension represented as the dotted region. No inhomogeneity correction is applied to bone or air cavity as this is not typically done for bone and small air cavities less than 1 cm in diameter. For the first plan with asymmetric fields (Fig. 43A), a total of nine fields in five ports are used. Three fields are incident from the anterior port (Port #1), one open ( 9 x 9 cm2) and two asymmetric fields (3.5 x 9 and 2.5 x 9 cm2). Each of the slightly angled lateral fields (Port #2 and #3) has a 45Â° wedge and is half-collimated to 6.5 x 9 cm2. Each of two posterior-oblique ports (Port #4 and #5) consists of two asymmetric fields. Port #4, Field #1 and #2 are 12 x 9 cm2 fields collimated to a 5.5 x 9 and a 8 x 9 Cm2 field, respectively. Port #5, Field #1 and #2 are 12 x 9 cm2 fields collimated to 5 x 9 and 8.5 x 9 cm2, respectively. A 45Â° wedge is used on each of the four posterior-oblique fields. As illustrated by the heavy dashed line in Figure 43(A), the calculated 9 0 % isodose line covers the concavely shaped planning target volume59 as desired. There is a rapid fall-off of dose adjacent to the planning target volume (PTV) near a critical structure such as the brain stem. The brain stem which is just behind the bony structure and at the brain's midline (dark shaded region) receives a maximum dose of less than 7 0 % . On the other hand, Figure 43(B) shows the same central 114 Port #1 Field #1 P Figure 43. Comparison of treatment plans for a concavely shaped planning target volume (dotted pattern) typical of nasopharyngeal cancer with retrostyloid tumor extension using (A) a multiple asymmetric fields technique and (B) a conventional three-field technique. The skull is outlined as a dark shaded region with the brain stem just behind the skull overlaying the isocenter in (A). The prescribed dose is specified at point C in (A) and at the isocenter in (B). 115 plane but with a conventional three-field technique involving an anterior port (Port #1) and two slightly angled lateral fields (Port #2 and #3). In order to cover the most posterior part of the planning target volume, the lateral fields (Port #2 and #3) irradiate part of the brain stem with full dose (100% of prescribed dose) thus exceeding brain stem dose tolerance. Another example is the treatment of a complex L-shaped planning target volume as illustrated in Figure 44. Again no inhomogeneity correction is applied. The plan consists of three ports and four fields using asymmetric collimation. Incident from the anterior port (Port #1) are one open (Field #1: 9.5 x 0 cm2 field with a 15Â° wedge ) and one asymmetric field (Field #2: 9.5 x 10 collimated to a 6.5 x io cm2 field with a 30Â° wedge). Both Port #2 and #3 have a 9 x 10 cm2 field with a 60Â° and 45Â° wedge, respectively. Again, the treated volume (area covered by the 90% isodose line) encompasses the planning target volume tightly. 116 Port #1 P Figure 44. A treatment plan for an L-shaped planning target volume (dotted pattern) typical of nasopharyngeal cancer. The prescribed dose is specified at the isocenter. The spine which is just adjacent to the planning target volume is outlined. 117 5.2. Half-Collimated Asymmetric Breast Treatment Technique The conventional breast treatment technique uses two tangential opposed beams. For each field setup, the isocenter is first aligned at the center of the posterior edge of the treatment field (the medial or lateral mark in Fig. 45A). The gantry is then rotated until the backpointer laser coincides with the posterior edge of the treatment field on the contra-lateral side. The gantry is then tilted by the arctangent of half width/SAD and the couch is lowered so that the posterior edge of the light field matches the posterior edge of the treatment field (Fig. 45B). The setup will be simpler if half of the treatment field is blocked or collimated on the patient side since there will be no need to lower the gantry angle nor the couch (Fig. 46). The use of half-blocks made of Cerrobend or lead have been suggested,60"64 but asymmetric collimation would be preferred.52"55 With the use of asymmetric collimators, there is no need to carry the heavy Cerrobend block around. The patient's underlying lung tissues would receive less dose since the transmission through the collimator is less than 0.5% vs. 5% for a 7.5 cm thick Cerrobend block. This new treatment technique has been developed and implemented at our institution.65 The new technique is found to be faster and simpler to set up as illustrated in Figure 46. The only disadvantage is that it is heavier to carry a thicker wedge which is often required by the plan (45Â° wedge with the asymmetric field technique in Fig. 47B but 30Â° wedge with the tangential opposed beam in Fig. 47A). Because of the wedge effect of asymmetric collimation (as discussed in Ch. 4.3.2), the thicker wedge is needed to compensate for the wedge effect of an asymmetric field, i.e., the reduced scatter dose contribution near the 118 Figure 45. Schematic illustrating the set-up of the conventional tangential breast treatment with gantry tilt. 119 (D gantry rotation couch Figure 46. Schematic illustrating the source to skin distance (SSD) set-up of the half-collimated asymmetric field breast treatment. 120 Â© isocentre 104% 100% 90% 50% Figure 47. The dose distributions for breast irradiation with two tangential opposed beams using (A) the conventional and (B) the half-collimated asymmetric field technique. 121 asymmetric field edge. Another drawback is that with the half-collimated asymmetric fields, the maximum treatment width is limited to 10 cm since the 45Â° wedge used is limited to a 20 cm-wide field. An isocentric breast technique has also been implemented at our institution (Fig. 48).65 This isocentric breast technique is most suited for three or four field breast irradiation whereby both the width and length are half-collimated to match the anterior supraclavicular field and the tangential breast fields.52"55 With the isocentric technique, the patient is first leveled with a slant board so no collimator swivel is required. The patient is then set to 100 cm source to skin distance (SSD) at the medial mark (Step 1 of Fig. 48B). The gantry is then rotated by an angle 0 so as to align the medial and lateral marks along the same axis (Step 2 of Fig. 48B). The separation (sep) between the medial and lateral marks is measured. The couch is then re-positioned to the true isocenter by both the translation and elevation of the couch, i.e., translation = (sep/2) x sin 0, and elevation = (sep/2) x cos 0 (Step 3 of Fig. 48B). Finally, the posterior half of the field is asymmetrically collimated (Step 4 of Fig. 48B). 122 Â©gantry rotation slant board Figure 48. Schematic illustrating the isocentric source to axis distance (SAD) set-up of the half-collimated asymmetric field breast treatment. 123 5.3. Head and Neck Conformal Therapy The clinical presentation of squamous cell carcinoma of the head and neck with metastatic involvement of the posterior cervical lymphatics often represents a difficult radiation treatment planning problem for the treating radiation oncologist. If the planning target volume includes bilateral cervical lymph nodes, it will necessarily take on a U-shape, wrapping around the spinal cord. Some authors have suggested a fixed or synchronously movable spinal cord block with isocentric rotational therapy.66"69 A more common solution was proposed by Tapley70 and is described in many radiotherapy textbooks. This consisted of the use of a pair of lateral opposed photon fields to encompass the primary tumor and nodes at risk. The posterior neck region was then blocked to spare the underlying spinal cord and the posterior lymphatics were boosted with direct electron fields. This is the standard technique at our institution. However, limitations exist with the standard technique. An asymmetric arc technique is proposed as an alternative. The two techniques are compared by studying the calculated dose distributions as planned with a head phantom .and with actual patients. With the head phantom, thermoluminescent dosimeters (TLDs) are placed at discrete points to measure and verify the absorbed dose calculated. Additionally, the dose calculations of the arced asymmetric fields are compared between a commercial system and the asymmetric field algorithm proposed here. For the standard technique, a typical set-up consists of, initially, two large parallel opposed pair fields at 100 cm source to axis distance (SAD). For the head phantom used 124 which is made up of 5 mm sliced prestwood, the field size was arbitrarily taken as 10 x 10 cm2 (Field A of Fig. 49A). The prescribed dose was 2.4 Gy * 13 fractions (31.2 Gy) to the isocenter. The second phase consisted of blocked photon portals using 7.5 cm thick Cerrobend to block the posterior field at a distance 1 cm anterior to the spinal cord (Field B of Fig. 49A). For these fields, 2.4 Gy * 12 fractions (28.8 Gy) were prescribed to the isocenter. Finally, the posterior neck was then treated with an electron field of 12 MeV, 3.5 x 10 cm2, which was positioned to match the posterior border of the photon field (Field C of Fig. 49 A). For these fields, 2.4 Gy * 12 fractions were prescribed to dmax (2.8 cm), at a treating distance of 100 cm source to surface distance (SSD). Figure 49(A) illustrates the calculated isodose distribution as planned with the GE Target system along the central plane of a prestwood head phantom. Some of the dose * points have been verified with TLD measurements which are recorded in Table 9. As demonstrated in Figure 49(A), there will be potential overdosage and underdosage at the electron-photon junction, as seen by the unacceptable maximum dose, Dm a x, of 110% and the constriction of the 90% isodose curve on the treated volume. A similar value of Dm a x was also observed by Sidhu and Smith71 with blocked Cobalt 60 fields and extended SSD electron beams. Reisinger et al.12 have addressed the potential of underdosing in patients with cervical adenopathy and advanced head and neck cancer using the standard technique. Their retrospective review of 24 patients with primary head and neck cancers and N1-N3 cervical adenopathy demonstrated that 11/12 patients with Nl disease had adequate treatment using the standard technique, whereas in 11/12 patients with N2 or N3 disease the technique failed to adequately cover disease. If adequate electron energy had 125 (A) a standard technique Figure 49. The dose distributions in the central plane of a prestwood head phantom for (A) a standard technique and (B) an alternative technique. The standard technique consists of large lateral photon portals, blocked photon portals and posterior electron fields. The alternative technique consists of asymmetric arcs and large wedged lateral portals. 126 Table 9. TLD verification of doses received with the standard technique at discrete points in a prestwood head phantom is shown. TLD measurements are expressed as a mean of six measurements, for each of three separate radiation fields with standard deviation. The measured doses are the sum of the TLD measurements with the photon field and with the electron field separately. For each measurement, the TLD are calibrated with known doses of the same radiation quality. ANT = anterior, POST = posterior. Point no. (Fig. 49A) Location of points of interest Absorbed dose (Gy) Calculated Measured P Isocenter 60 60 Â±3 1 Tumor 61 60 + 3 2 Node POST 61 64 + 1 3 Cord ANT 37 45 + 3 4 Cord POST 43 48 Â±2 127 been utilized, then 75% of these patients would have received doses exceeding spinal cord tolerance. The problems of a discontinuously treated volume and dose inhomogeneities in the treated volume for abutting photon and electron junctions have previously been discussed by Olch et al.n They demonstrate that overlapping of the fields may reduce the potential for underdosage but at the expense of an increased maximum dose. The dose calculations of mixed photon and electron beams are very time consuming and not practical. For instances as discussed in Chapter 4.4.2, the GE Target full calculation option took 5.5 minutes to calculate a blocked field. If both open and wedged parallel opposed pairs are blocked, the computation time for one trial will be at least 22 minutes. Since the commercial system will recalculate the whole plan with each step, such as, to plot the treatment plan and to calculate the monitor units, the total calculation time can easily be over an hour even for just one trial in planning. Without proper treatment planning, considerable uncertainty exists regarding coverage of planning target volume, homogeneity and spinal cord dose. The standard technique may fail either due to insufficient depth dose penetration and a potential overdose of the spinal cord because of the choice of electron energy, or due to inadequate coverage of the planning target volume at the junction of radiation fields. An alternative technique, which is fairly simple, is proposed here. The treatment technique consists of a pair of rotational arcs with asymmetrically collimated fields, and a lateral or oblique pair of beams (Fig. 49B).74 The treatment plan is carried out with our in-house treatment planning system using the proposed asymmetric field algorithm. To verify the algorithm for arced asymmetric field, the calculated isodose distribution for a 128 single arced asymmetric field has been compared with that calculated based on the GE Target full calculation option (Fig. 50). Good agreement is observed between the two systems when the treatment plan is carried out with the arced, asymmetric field rotating counterclockwise (Fig. 50A). However when running the opposite arced field, the GE Target system gives incorrect dose distribution with dose above 60 cGy (Fig. 5OB). This is because the commercial system incorrectly uses the wrong wedge orientation during calculation with a combination of rotational wedged and blocked fields.75 Thus, the proposed asymmetric field algorithm is used to calculate the dose distribution for the alternative technique and the dose calculation is then confirmed with TLD measurements using the same head phantom as in Figure 49(A). For the alternative technique setup, an isocenter is chosen to lie within the spinal cord. For the arced fields, an asymmetric collimator is brought across the midline to shield the spinal cord, the dimension depending upon the proximity of the planning target volume to the spinal cord. The spinal cord thus receives only scatter dose contribution from the arced fields. The arced field size is chosen to cover the planning target volume anteriorly. The two arced fields overlap each other with typical start and stop angles of 280Â° and 60Â° respectively for the right arc, and 300Â° and 80Â° respectively for the left arc. For the treatment plan utilizing the head phantom, start and stop angles as described above were used, with the field size of 16 * 10 cm2 collimated to 7 x 10 cm2 (Field B of Fig. 49B). By themselves, these arcs will produce a U-shaped treated volume, but by virtue of treating anterior structures preferentially, an unavoidable dose gradient is produced, similar to the treatment plans of Grimard et al.51 The addition of two wedged lateral 129 Figure 50. The dose distribution for a single arced asymmetric field in a circular phantom as calculated with the proposed asymmetric field algorithm (solid line) and with the GE Target system (dashed line). (A) The single arc rotates counterclockwise from a gantry angle of 40Â° to 320Â°, with the thick end of the wedge positioned anteriorily and with the posterior asymmetric collimator set 1.5 cm past the isocenter. (B) The single arc rotates clockwise from a gantry angle of 320Â° to 40Â°, with the thick end of the wedge positioned anteriorily and with the posterior asymmetric collimator set 1.5 cm past the isocenter. Units are in cGy. 130 portals which treats the entire planning target volume including the spinal cord will restrict the treated volume and, by choosing the appropriate wedge filter (thick end anterior), will compensate for the dose gradient produced by the asymmetric arcs. The isocenter continues to be the same. Field sizes for the treatment plan using the head phantom were 16x10 cm2, collimated asymmetrically to a 10 * 10 cm2 field size. Wedge filters of 45Â° have been used for irradiation of the head phantom, thick end placed anteriorly. Approximately equal contributions are given from the lateral pair and the arced pair, the amount being dependent upon the balance between homogeneity and increasing spinal cord dose. An increase in the contribution of the lateral pair will naturally increase the dose to the spinal cord. Above all, the isodose distribution for the alternative technique as planned with the proposed asymmetric field algorithm is much more uniform than for the standard technique (Fig. 49). The 90% isodose curve of the alternative technique does not constrict, and the maximum dose is merely 102% (Fig. 49B). Furthermore, the calculated and measured spinal cord doses are generally lower for the alternative technique than the standard technique (Tables 10 and 9, respectively). Table 10 also shows that the calculated values for the alternative technique using the proposed asymmetric field algorithm were on average within 1 Gy of the TLD measured values. The standard deviation for the measured values is on average 5%. Figures 51(A) and 51(B) illustrate the isodose distributions of a patient's neck using the standard technique and the alternative technique, respectively. Cord dose is lower with the standard technique but the typical use of the 12 MeV electron beam does not provide enough penetration of the 90% isodose as the alternative technique. With the 131 Table 10. TLD verification of doses calculated using the in-house treatment planning system with the alternative technique at discrete points in a prestwood head phantom is shown. TLD measurements are reported as a mean of six readings with standard deviations. ANT = anterior, POST = posterior. Point no. (Fig. 49B) Location of points of interest Absorbed dose (Gy) Calculated Measured 1 Tumor mid-line POST 59 60 + 3 2 Tumor mid-line ANT 61 59 + 3 3 Tumor Right 61 61+2 4 Node ANT 61 59 + 3 5 Node POST 60 60 + 4 6 Cord ANT 34 34 + 2 7 Cord POST 34 33+3 8 Cord Penumbra 52 53+2 132 (A) a standard technique (B) an alternative technique Figure 51. The dose distributions for (A) a standard technique and (B) an alternative technique along the mid-plane of a patient's neck are shown. The standard technique consists of large lateral photon portals, blocked photon portals and posterior electron fields. The alternative technique consists of asymmetric arcs and large wedged lateral portals. 133 alternative technique, the planning target volume can extend superiorly as far as the nasopharynx at which point the brain and orbital structures will constitute the dose-limiting tissues. Remarkably, tissue which is anterior to the lateral portals can be spared to 30% of the prescribed dose and in addition, the external contour changes the isodose distribution very little (Fig. 52). If the planning target volume and thereby the treatment length extends to the shoulder level, the lateral pair, in particular, will radiate the shoulder region unnecessarily. With the combined photon and electron technique, this is often circumvented by turning the couch at a slight angle so that the photon fields miss the shoulder. With the asymmetric arc technique, this is not possible. One solution would be to add a separate supraclavicular field. Alternatively, the lateral pair can be angled at an oblique angle, so as to spare the shoulder (Fig. 53). With the proper selection of the start and stop angles for the arced fields, minimal dose will be delivered to the shoulder. Sometimes, the maximum dose at the inferior plane can be as high as 110% due to the smaller cross-section at this level (Fig. 53). In such a case, individual compensators, superior and inferior wedging or partial asymmetric collimation on the posterior length will be required. In general, the shapes of the treated volume are similar along the treatment length. With the asymmetric arc technique, conformal radiotherapy is achievable with a constant cross-sectional treated volume along the treatment length. 134 Figure 52. The dose distribution of the same patient using the same alternative technique at a plane 5 cm superiorly is shown. 135 Figure 53. The dose distribution of the same patient is shown at a plane 5 cm inferiorly using the alternative technique but with the large lateral pair angled at an oblique angle so as to avoid the shoulder. 136 6. CONCLUSIONS To summarize, the dosimetric characteristics of asymmetric x-ray fields have been investigated. In particular, the effect of asymmetric collimation on the output factors has been analyzed. Based on the physical attributes of an asymmetric field, a correction factor has been proposed. This correction factor uses the ratio of the equivalent field contribution between the asymmetric and symmetric fields. With the use of collimator-specific correction factors, these correction factors are shown to account for the collimator backscatter effect on the output factors of asymmetric fields. Unlike other algorithms that are based on some form of beam modeling technique, this correction factor is a mathematical expression to account for the dose reduction when a corresponding symmetric field is collimated asymmetrically to a smaller asymmetric field. With this approach, the correction factor thus can be applied to a wide range of asymmetric fields, photon energies, and linacs without the need of additional measurements or new sets of databases for asymmetric fields. At present, some semi-empirically parametrized correction factors are needed to represent the absorbed dose in the penumbral regions and outside the radiation field. Since the equations for these correction factors are based on radiation beam and position-specific parameters, such as AW, W, L, d, r, OPF, TMR, etc., again they can be used for a wide range of asymmetric fields, photon energies, and linacs once they have been confirmed. Any further measurements are required for quality assurance and testing of the calculation only. There is no need to store any asymmetric field profiles or new sets of databases. The implementation of the correction factors into 137 an existing treatment planning system is simple and straightforward, since the only machine parameters required are the output factors and tissue maximum ratios for symmetric fields which are readily available. The correction factors can be implemented as a FORTRAN subroutine. The accuracy of this calculation method has been confirmed with measured depth dose profiles and isodose distributions for various asymmetric fields, and for both the 6 and 10 MV photon beams. The computation time is found to be 20 times faster than a commercial treatment planning system based on the IRREG field calculation method. This algorithm not only satisfies two qualities of a desired treatment planning algorithm, namely, minimal effort required for the implementation and fast computation time, it also has an additional advantage in that it can be readily implemented into any existing treatment planning system. These correction factors are extended to 2-fold asymmetric fields whereby both the field width and length are collimated asymmetrically. The 2-fold asymmetric field correction factors proposed in Ch. 4.5 have recently been implemented into our in-house treatment planning system. The scatter reduction and thereby the absorbed dose at any points and at any depths along either the principal plane or any offset planes can now be calculated for asymmetric fields collimated asymmetrically either in the field width, length or both. In addition, the algorithm has also been used clinically for the asymmetric field calculation of a 4MV Varian linac (Varian Associates, Palo Alto, CA) and a 4MV Philips linac (Elekta Oncology Systems, Inc., formerly Philips Medical Systems, Shelton, CT) with no additional measurement or modification to the algorithm required, thus confirming its universality in being applicable to a wide range of photon energies and linacs. 138 Some of the clinical uses of asymmetric fields are outlined. In particular, the wedge effect of an asymmetric field is discussed and its implication in treatment plan optimization is demonstrated. For proper treatment plan optimization, it is important to have an algorithm that can account for the dose variation across the asymmetric field. The set-ups for half-collimated asymmetric field breast treatment techniques are described and the necessary equations for the positioning of the isocenter with the isocentric breast technique are devised. Using the proposed asymmetric field algorithm in treatment planning, the potential use of asymmetric fields in conformal therapy is demonstrated. Several treatment plans with asymmetric fields are shown. The proposed arced asymmetric field technique in head and neck radiotherapy is much superior to the standard technique with mixed photon and electron beams. The dose distribution with the alternative technique shows that the treated volume follows the shape of the planning target volume with no excessive maximum dose or cold spots. The dose calculations have been verified with thermoluminescent dosimeter measurements in a body phantom for both the standard technique and the alternative technique. Over the past four years, more than 30 head and neck patients have been treated with the arced asymmetric field technique with positive response and no acute complications observed. 139 BIBLIOGRAPHY 1. R. L. Stern, S. A. Rosenthal, E. C. Doggett, J. K. Mangat, T. L. Phillips, and J. K. Ryu, "Applications of asymmetric collimation on linear accelerators," Med. Dosimetry 20(2), 95-98 (1995). 2. J. R. Cunningham, P. N. Shrivastava, and J. M. Williamson, "Program IRREG-calculation of dose from irregularly shaped radiation beams," Comput. Programs. Biomed. 2, 192-199 (1972). 3. American Association of Physicists in Medicine Task Group (AAPM TG) 21, "A protocol for the determination of absorbed dose from high-energy photon and electron beams," Med. Phys. 10(6), 741-771 (1983). 4. R. O. Kornelsen and M. E. J. Young, "Empirical equations for the representation of depth dose data for computerized treatment planning," Brit. J. Radiol. 48, 739-748 (1975). 5. R. Clarkson, "A note on depth doses in fields of irregular shape," Brit. J. Radiol. 14, 265-268 (1941). 6. P. F. B. Klemp, A. M. Perry, B. Hedland-Thomas, S. Stevenson, and D. Zucaro, "Commissioning of a linear accelerator with independent jaws: computerised data collection and transfer to a planning computer," Phys. Med. Biol. 33(7), 865-871 (1988). 7. P. Cadman, "A dosimetric investigation of scatter conditions for dual asymmetric collimators in open fields," Med. Phys. 22(4), 457-463 (1995). 8. J. R. Palta, K. M. Ayyangar, and N. Suntharalingam, "Dosimetric characteristics of a 6 MV photon beam from a linear accelerator with asymmetric collimator jaws," Int. J. Radiat. Oncol. Biol. Phys. 14(2), 383-387 (1988). 9. M. Tenhunen and T. Lahtinen, "Relative output factors of asymmetric megavoltage beams," Radiother. Oncol. 32(3), 226-231 (1994). 10. B. Murray, B. McClean, and C. Field, "Output factors for fields defined by four independent collimators," Med. Phys. 22(3), 285-290 (1995). 11. I. Rosenberg, J. C. H. Chu, and V. Saxena, "Calculation of monitor units for a linear accelerator with asymmetric jaws," Med. Phys. 22(1), 55-61 (1995). 12. G. Marinello and A. Dutreix, "A general method to perform dose calculations along the axis of symmetrical and asymmetrical photon beams," Med. Phys. 19(2), 275-281 (1992). 140 13. F. M. Khan, B. J. Gerbi, and F. C. Deibel, "Dosimetry of asymmetric x-ray collimators," Med. Phys. 13(6), 936-941 (1986). 14. M. K. Woo, A. Fung, and P. O'Brien, "Treatment planning for asymmetric jaws on a commercial TP system," Med. Phys. 19(5), 1273-1275 (1992). 15. C. S. Chui, R. Mohan, and D. Fontenla, "Dose computations for asymmetric fields defined by independent jaws," Med. Phys. 15(1), 92-95 (1988). 16. C. S. Chui and R. Mohan, "Off-center ratios for three-dimensional dose calculations," Med. Phys. 13(3), 409-412 (1986). 17. D. D. Loshek and K. A. Keller, "Beam profile generator for asymmetric fields," Med. Phys. 15(4), 604-610 (1988). 18. S. J. Thomas and R. L. Thomas, "A beam generation algorithm for linear accelerators with independent collimators," Phys. Med. Biol. 35(3), 325-332 (1990). 19. D. D. Loshek and T. T. Parker, "Dose calculation in static or dynamic off-axis fields," Med. Phys. 21(3), 401-410 (1994). 20. P. Cadman, "Using the field edge correction (FEC) method to generate accurate POCRs and OCRs for asymmetric fields," Med. Phys. 23(3), 353-356 (1996). 21. P. Storchi and E. Woudstra, "Calculation models for determining the absorbed dose in water phantoms in off-axis planes of rectangular fields of open and wedged photon beams," Phys. Med. Biol. 40(4), 511-527 (1995). 22. M. J. Day, "A note on the calculation of dose in x-ray fields," Brit. J. Radiol. 23(270), 368-369 (1950). 23. W. Kwa, R. O. Kornelsen, R. W. Harrison, and E. El-Khatib, "Dosimetry of asymmetric x-rays fields," Med. Phys. 21(10), 1599-1604 (1994). 24. J. K. Haywood, C. K. Bomford, and J. A. Hatton, "A less empirical method of representing megavoltage beams for use in rapid radiotherapy dose calculations," Brit. J. Radiol. 52(621), 709-718 (1979). 25. W. Kwa and E. El-Khatib, "To the editors: The dosimetric effects of asymmetric megavoltage beams," Radiother. Oncol. 35(2),162-163 (1995). 26. M. Tenhunen and T. Lahtinen, "Response to W. Kwa and E. El-Khatib," Radiother. Oncol. 35(2), 164-165 (1995). 141 27. M. S. Patterson and P. C. Shragge, "Characteristics of an 18 MV photon beam from a Therac 20 Medical Linear Accelerator," Med. Phys. 8(3), 312-318 (1981). 28. K. R. Kase and G. K. Svensson, "Head scatter data for several linear accelerators (4-18 MV)," Med. Phys. 13(4), 530-532 (1986). 29. N. C. Ikoro, D. A. Johnson, and P. P. Antich, "Characteristics of the 6-MV photon beam produced by a dual energy linear accelerator," Med. Phys. 14(1), 93-97 (1987). 30. D. A. Johnson, N. C. Ikoro, C. H. Chang, E. C. Scarbrough, and P. P. Antich, "Properties of the 18-MeV photon beam from a dual energy linear accelerator," Med. Phys. 14(6), 1071-1078 (1987). 31. M. Tatcher and B. E. Bjarngard, "Head-scatter factors in rectangular photon fields," Med. Phys. 20(1), 205-206, (1993). 32. P. Vadash and B. Bjarngard, "An equivalent-square formula for head-scatter factors," Med. Phys. 20(3), 733-734 (1993). 33. M. K. Yu, B. Murray, and R. Sloboda, "Parametrization of head-scatter factors for rectangular photon fields using an equivalent square formalism," Med. Phys. 22(8), 1329-1332(1995). 34. D. A. Jaffray, J. J. Battista, A. Fenster, and P. Munro, "X-ray sources of medical linear accelerators: Focal and extra-focal radiation," Med. Phys. 20(5), 1417-1427 (1993). 35. M. B. Sharpe, D. A. Jaffray, J. J. Battista, and P. Munro, "Extrafocal radiation: A unified approach to the prediction of beam penumbra and output factors for megavoltage x-ray beams," Med. Phys. 22(12), 2065-2074 (1995). 36. E. L. Chaney and T. J. Cullip, "A Monte Carlo study of accelerator head scatter," Med. Phys. 21(9), 1383-1390 (1994). 37. A. Ahnesjo, "Collimator scatter in photon therapy beams," Med. Phys. 22(3), 267-278 (1995). 38. M. K. Yu and R. Sloboda, "Analytical representation of head scatter factors for shaped photon beams using a two-component x-ray source model," Med. Phys. 23(6), 973-984 (1996). 39. P. B. Dunscombe and J. M. Nieminen, "On the field-size dependence of relative output from a linear accelerator," Med. Phys. 19(6), 1441-1444 (1992). 142 40. A. Ahnesjo, T. Knoos, and A. Montelius, "Application of the convolution method for calculation of output factors for therapy photon beams," Med. Phys. 19(2), 295-301 (1992) . 41. G. Luxton and M. A. Astrahan, "Characteristics of the high-energy photon beam of a 25-MeV accelerator," Med. Phys. 15(1), 82-87 (1988). 42. G. Luxton and M. A. Astrahan, "Output factor constituents of a high-energy photon beam," Med. Phys. 15(1), 88-91 (1988). 43. H. Kubo and K. K. Lo, "Measurements of backscattered radiation from Therac-20 collimator and trimmer jaws into beam monitor chamber," Med. Phys. 16(2), 292-294 (1989). 44. H. Kubo, "Telescopic measurements of backscattered radiation from secondary collimator jaws to a beam monitor chamber using a pair of slits," Med. Phys. 16(2), 295-298 (1989). 45. C. Duzenli, B. McClean, and C. Field, "Backscatter into the beam monitor chamber: Implications for dosimetry of asymmetric collimators," Med. Phys. 20(2), 363-367 (1993) . 46. M. K. Yu, R. S. Sloboda, and F. Mansour, "Measurement of photon beam backscatter from collimators to the beam monitor chamber using target-current-pulse-counting and telescope techniques," Phys. Med. Biol. 41(7), 1107-1117 (1996). 47. P. H. Huang, J. Chu, and B. E. Bjarngard, "The effect of collimator backscatter radiation on photon output of linear accelerators," Med. Phys. 14(2), 268-269 (1987). 48. D. L. Watts and G. S. Ibbott, "Measurement of beam current and evaluation of scatter production in an 18-MeV accelerator," Med. Phys. 14(4), 662-664 (1987). 49. J. W. Scrimger, "Backscatter from high atomic number materials in high energy photon beams," Radiol. 124, 815-817 (1977). 50. W. Kwa and E. El-Khatib, "The dosimetric characteristics and clinical implementation of asymmetric x-ray beams," in Proceedings of the Canadian College of Physicists in Medicine (CCPM) and the Canadian Organization of Medical Physicists (COMP), (Montreal, P.Q., June 4-7, 1995), pp. 71-72. 51. J. P. Gibbons and F. M. Khan, "Calculation of dose in asymmetric photon fields," Med. Phys. 22(9), 1451-1457 (1995). 143 52. U. F. Rosenow, E. S. Valentine, and L. W. Davis, "A technique for treating local breast cancer using a single set-up point and asymmetric collimation," Int. J. Radiat. Oncol. Biol. Phys. 19(1), 183-188 (1990). 53. E. E. Klein, M. Taylor, M. Michaletz-Lorenz, D. Zoeller, and W. Umfleet, "A mono-isocentric technique for breast and regional nodal therapy using dual asymmetric jaws," Int. J. Radiat. Oncol. Biol. Phys. 28(3), 753-760 (1994). 54. C. Li, E. W. Torigoe, A. Dunning, F. Halberg, and R. Evans, "Three-field breast irradiation technique using tangential quarter fields," Med. Dosimetry 19(2), 107-110 (1994). 55. M. G. Marshall, "Three-field isocentric breast irradiation using asymmetric jaws and a tilt board," Radiother. and Oncol. 28(3), 228-232 (1993). 56. J. R. Palta, K. M. Ayyanger, N. Suntharalingam, and L. Tupchong, "Asymmetric field arc rotations," Brit. J. Radiol. 62 (742), 927-931 (1989). 57. L. Grimard, J. Szanto, A. Girard, M. Howard, L. Eapen, and L. Gerig, "Asymmetric arc technique for posterior pharyngeal wall and retropharyngeal space tumors," Int. J. Radiat. Oncol. Biol. Phys. 31(3), 611-615 (1995). 58. W. Kwa, V. Tsang, R. N. Fairey, S. M. Jackson, E. El-Khatib, R. W. Harrison, and S. Kristensen, "Clinical use of asymmetric collimators," Int. J. Radiat. Oncol. Biol. Phys. 37(3), 705-710 (1997). 59. ICRU Report 50, "Prescribing, Recording, and Reporting Photon Beam Therapy," (International Commission on Radiation Units and Measurements, Bethesda, Maryland, 1993). 60. E. B. Podgorsak, M. Gosselin, M. Pla, T. H. Kim, and C. R. Freeman, "A simple isocentric technique for irradiation of the breast, chest wall and peripheral lymphatics," Br. J. Radiol. 57(673), 57-63 (1984). 61. G. Conte, O. Nascimben, G. Turcato, R. Polico, M. B: Idi, L. M. Belleri, F. Bergoglio, F. Simonato, L. Stea, F. Bugin, and N. Bortot, "Three-field isocentric technique for breast irradiation using individualized shielding blocks," Int. J. Radiat. Oncol. Biol. Phys. 14(6), 1299-1305 (1988). 62. W. F. Hartsell, A. K. Murthy, K. D. Kiel, M. Kao, and F. R. Hendrickson, "Technique for breast irradiation using custom blocks conforming to the chest wall contour," Int. J. Radiat. Oncol. Biol. Phys. 19(1), 189-195 (1990). 144 63. R. L. Siddon, G. L. Tonnesen, and G. K. Svensson, "Three-field technique for breast treatment using a rotatable half-beam block," Int. J. Radiat. Oncol. Biol. Phys. 7(10), 1473-1477(1981). 64. G. K. Svennson, B. E. Bjarngard, R. D. Larsen, and M. B. Levene, "A modified three-field technique for breast treatment. Int. J. Radiat. Oncol. Biol. Phys. 6(6), 689-694, (1980). 65. W. Kwa, S. Kristensen, and E. El-Khatib, "Clinical use and the dosimetry of half-collimated asymmetric x-ray fields in tangential breast treatment," presented at the Western Canadian Physicists and Technologists (WESCAN), Victoria, B.C., 1995. 66. B. S. Proimos, "Synchronous protection and field shaping in cyclotherapy, "Radiol. 77,591-599(1961). 67. J. A. Rawlinson and J. R. Cunningham, "An examination of synchronous shielding in 6 0Co rotational therapy," Radiol. 102, 667-671 (1972). 68: V. Thambi, P. J. Pedapatti, A. Murthy, and P. K. Kartha, "A radiotherapy technique for thyroid cancer," Int. J. Radiat. Oncol. Biol. Phys. 6(2), 239-243 (1980). 69. J. G. Trump, K. A. Wright, M. I. Smedal, and F. A. Salzman, "Synchronous field shaping and protection in 2-million-volt rotational therapy," Radiol. 76, 275, (1961). 70. N. D. Tapley, "Clinical experience with electron beams," in High-Energy Photons and Electrons: Clinical Applications in Cancer Management, ed. S. Kramer, N. Suntharalingam, and G. Zinninger, (John Wiley & Sons, New York, NY, 1976) pp. 170-195. 71. N. P. S. Sidhu and C. J. Smith, "Dosimetric effects of matching electron fields with cobalt 60 fields in the management of head and neck cancer," Med. Dosimetry 20(1), 19-24 (1995). 72. S. A. Reisinger, K. Ayyangar, A. Flanders, J. Sweet, and M. Mohiuddin, "Potential underdosing with the use of electron-beam therapy in patients with cervical adenopathy and advanced head and neck cancer," Med. Dosimetry 19(2), 97-101 (1994). 73. A. Olch, J. Bellotti, M. Wollin, and A. R. Kagan, "External beam electron therapy: pitfalls in treatment planning and deliverance," in The Role of High Energy Electrons in the Treatment of Cancer, eds. J. M. Vaeth and J. L. Meyer, Front. Radiat. Ther. Oncol. 25, 64-79. (Karger, Basel, Switzerland, 1991). 74. W. Kwa, H. Joe, S. M. Jackson, J. Hay, R. W. Harrison, and E. El-Khatib, "Head and neck: A radiotherapy technique with a combination of fixed and arced asymmetric 145 fields," in Proceedings of the Canadian College of Physicists in Medicine (CCPM) and the Canadian Organization of Medical Physicists (COMP), (Vancouver, B.C., June 20-22, 1996), pp. 304-305. Notice: Safety Advisory to all users of Target 2 and Target Series 2, June 20th, 1995 (GE Medical Systems, Milwaukee, WI.). 146 APPENDIX 1: AsymCorrFactor- a FORTRAN subroutine for the asymmetric field treatment planning algorithm This computer algorithm in Fortran permits calculation of absorbed dose under an asymmetric field. Subroutine AsymCorrFactor(RedOffAx,Depth,iBeam,OpenOAR,CF) Character SCCS*80 Data SCCS/'%W% %G%7 C Calculate a Correction Factor for an asymmetrically-blocked field. C RedOffAx = Reduced off-axis distance of the calculation point (= +1/-1 at field edge). C Depth = Actual depth of the point. C iBeam = port number. C OpenOAR = OAR for an open field. C CF = Correction Factor (returned) Implicit Undefined (A-Z) Include TSCOMTR' C Parameters passed to this routine: Integer iBeam RealRedOffAx,Depth,OpenWidth,BlockedWidth,OpenOAR,CF C Functions used: Real OAR C Local variables: Real OpenWidth,BlockedWidth,AbsBlockedWidth RealK,y,yl,y2,yPrime,SOT,CFN,CFP,OARprime,OffAx Logical PrtOut Data PrtOut/. True./ Integer PrtCount,MaxPrtCount,AsymOut Common/AsymCom/PrtCount Data PrtCount/0/MaxPrtCount/100/AsymOut/13/ OpenWidth = W(iBeam) OffAx = RedOffAx*OpenWidth/2.0 BlockedWidth = AsymBlock(iBeam) AbsBlockedWidth = Abs(BlockedWidth) If(PrtCount.eq.O) Open(AsymOut;FILE='ASYM.NCPY') PrtCount = PrtCount +1 147 If (PrtCount.gt.MaxPrtCount) Then Close(AsymOut) PrtOut = .False. Endlf If (PrtOut) Write(AsymOut,100) OffAx,Depth,iBeam,OpenOAR 100 Format(/'Enter AsymCorrFactor, OffAx=',G14.7,' Depth=',G14.7,' iBeam=',I4,' OpenOAR=',G14.7) C Check that it is really asymmetric. If (AbsBlockedWidth .ge. OpenWidth) Then CF=1.0 Return Endlf C A negative BlockedWidth means left side is narrower than right, C so do a left-right swap. If (BlockedWidth.gt.0.0) Then y = OffAx Else y = -OffAx Endlf y2 = -OpenWidth/2.0 yl = AbsBlockedWidth + y2 K = SqrtQ.O - ((OpenWidth-AbsBlockedWidth)/OpenWidth)**2) If(y .le. (yl - 1.5)) Then C If (OpenOAR.lt.0.3) Then Case#l: K = CFA CF = K C Elself (OpenOAR.lt.0.5) Then Case #2: CFB CFN = SOT(y2+1.5,Depth,OpenWidth,AbsBlockedWidth,iBeam) CF = K + (OpenOAR - 0.3)*(CFN - KV0.2 Else If(y .le. (y2+1.5)) Then C Case #3: CFC CF = SOT(y2+1.5,Depth,OpenWidth,AbsBlockedWidth,iBeam) C Else Case #4: CFD CF = SOT(y,Depth,OpenWidth,AbsBlockedWidth,iBeam) Endlf Endlf Else 148 s CFP = SOT(yl-1.5,Depth,OpenWidth,AbsBlockedWidth,iBeam) CFN = SOT(y2+1.5,Depth,OpenWidth,AbsBlockedWidth,iBeam) yPrime = y2-y + yl OARprime = OAR(2.0*yPrime/W(iBeam)) If (OARprime.lt.0.05) Then C Case #8: CFH CF = K*OARprime*Sqrt(CFP*CFN)/OpenOAR Elseif (OARprime.le.0.3) Then C Case #7: CFG CF = (OARprime/OpenOAR)*Sqrt(CFP*CFN)*K**((0.3 - OARprime)*4.0) Elseif (OARprime.le.0.5) Then C Case #6: CFF CF = (OARprime/OpenOAR)*Sqrt(CFN)*CFP**((0.5 - OARprime)*2.5) Else C Case #5: CFE CF = ((AbsBlockedWidth - OpenWidth/2.0 - y + (1.5 - AbsBlockedWidth + OpenWidth/2.0 + y)*(OARprime/OpenOAR))/1.5*Sqrt(CFN)* CFP**(2.0*(OARprime-0.5)) Endlf Endlf Return End Real Function SOT(y,Depth,WOpen,WBlocked,iBeam) Implicit Undefined (A-Z) Include TSCOM.ER' C Parameters: Integer iBeam Real y,Depth,WOpen,WBlocked C Functions: Real VarianOPF,RadEq C Local variables: Real Length, WOI^WBR,Refn,Reff2,RlJMRlJMR2 Length = B(iBeam) WBR = 2.0*(Wblocked - y) - Wopen Reffl = RadEq(WBR,Length) WOR = Wopen - 2.0*y Reff2 = RadEq(WOR,Length) 149 RI = VarianOPF(LiMeV,WBR,Length)/VarianOPF(LiMeV,WOR,Length) If (LiMeV.eq.6) Then Call TMRVar6(Reffl,Depth,TMRl) Call TMRVar6(Reff2,Depth,TMR2) Elseif (LiMeV.eq. 10) Then Call TMRVarlO(Reffl,Depth,TMRl) Call TMRVarlO(Reff2,Depth,TMR2) Else Write(*,*) 'Invalid energy in Function OT: ',LiMeV Call ICQuit Endlf SOT = Sqrt(Rl *TMR1/TMR2) Return End APPENDIX 2: Glossary of Terms Absorbed dose is a measure of the energy absorbed by material by the interaction of radiation. It is defined as energy per unit mass of material. The present SI unit of dose is the Gray (Gy) and is specified as 1 Gy = 1 J/kg. A subunit, centigray (cGy), is equivalent to the old unit, the rad. Arc therapy or rotation therapy is a radiotherapy treatment technique in which the radiation source moves in a circular arc during irradiation with the patient located on the axis of this rotation. Asymmetric collimator refers to a pair of field-defining jaws or collimators that can be set independently of each other resulting in an asymmetric field. Asymmetric field is an off-set radiation field whereby the central axis or beam axis of the radiation field does not coincide with the collimator axis as the opposite pair of collimators no longer are equidistant from the collimator axis (see also symmetric field). Attenuation coefficient is a coefficient expressing the fractional change of absorbed dose with respect to attenuator thickness. 151 Backpointer is a device that is used to identify the point of the radiation beam exit from the patient. Backscatter radiation is radiation that is deflected by an irradiated medium in the path of the beam at such an angle that the deflected rays pass backward into the path of the original beam. Beam axis or central axis of a radiation beam is a line passing through the center of the radiation source and the center of the final beam defining collimator. Beam flattening filter is a filter or attenuator designed to make the energy fluence rate or absorbed dose rate reasonably constant across a beam at a chosen depth. Beam monitor chamber is an ionization chamber placed upstream from the field-defining collimators in the linac head to monitor the radiation output and symmetry of the linac. Body phantom is a phantom made in the shape of a human body or part of it where the various tissues have been simulated in density, size, shape, position, and with respect to radiation interaction. Bremsstrahlung radiation consists of x-rays produced from deceleration of electrons when the electrons strike a target. 152 Build-up depth or region refers to the initial increase in absorbed dose with depth below the surface in material irradiated by a photon beam (see also electronic equilibrium). Cerrobend is a low melting point lead alloy used to form irregular shaped attenuating materials so as to define an irregular shaped radiation field by blocking area under the Cerrobend blocks. Collimator is a set of diaphragms or shielding materials made of heavy metals designed to define the dimensions of a radiation beam. Collimator axis is the axis of the collimator rotation. When the field-defining collimator is set symmetrically, the collimator axis coincides with the beam axis. Compensator is an attenuating material placed in the treatment beam to compensate for unevenness of body contour. Computed tomography (CT) is the reconstruction of images from radiographic signals to form cross-sectional images along the transverse planes of the patient. The images are useful for both diagnosis and treatment planning, providing density and outline of the structures inside the patient. 153 Critical structures are normal tissues or organs that might affect the patient's quality of life or might result in complications upon irradiation beyond certain tolerance doses, e.g. eyes, spinal cord, etc. Depth is the distance measured from the irradiated surface to the point of interest. Depth of maximum dose or ionization (dmai) is the depth at which maximum dose occurs. This distance will vary with the radiation quality of the radiation beam and to some extent with field size and source to surface distance. Depth dose is the relationship between dose at any depth from a beam of radiation compared with the dose at the entrance or at some reference depth from that beam, and is usually expressed as a percentage. Depth Dose profile is a graph of absorbed dose versus lateral position in a cross sectional plane. Normally the profile is measured in a water phantom along a principal plane. Dose distribution is a representation of the variation of absorbed dose with position usually along a cross-sectional plane of an irradiated object. 154 Dose tolerance is the absorbed dose level to normal tissue in which adverse reaction, such as blindness to eye, damage to spinal cord or brain stem, will occur if the dose delivered exceeds this level. Dosimeter is an instrument for measuring ionizing radiation. Dosimetry is the measurement of radiation dose using appropriately calibrated detectors. Effective atomic number is the assigned atomic number to a compound that has the same absorption properties as an element with the same atomic number. Electronic equilibrium describes the build-up of moving electrons set in motion by interacting photons until a maximum fluence rate has been reached where as many electrons are coming in as are leaving (see also build-up depth or region). Equivalent field is defined as that standard (i.e., circular or square) field which has the same central axis depth dose characteristics as the given non-standard field (i.e., irregular or rectangular). Field light is a light system that illuminates an area of the patient's body identifying the area of radiation beam entry. 155 Ionization chamber is an absorbed dose measuring device that contains a small cavity filled with air which has the capability of collecting the ionic charge which is liberated during irradiation. Isocenter is the point of intersection of the axes of the gantry, collimator and turntable rotations. Isocentric technique or fixed SAD technique is a radiotherapy treatment technique in which a chosen point in the target volume is placed at the isocenter with beams all centered at the isocenter. Isodose chart is a graphical map of the radiation dose distribution in an irradiated medium in which all points with identical doses are connected by contour lines. Isodose curve is a line usually in a plane along which the absorbed dose is constant. Linear accelerator (linac) is a radiation emitting device that uses microwave energy to accelerate electrons to high energies. Its use is to aim a beam of photons or electrons at the target volume of the patient from some distance away. Maximum dose (Dm s u) is a term proposed by the ICRU representing the highest dose within the patient provided this dose covers a minimum area of 2 cm2.59 156 Monitor unit (MU) is the readout displayed by the linac to represent the amount of radiation received by the patient as measured at the linac head. Output is a measure of the radiation beam produced by a radiotherapy treatment unit. It is usually stated as the absorbed dose rate at a reference point under a closely defined set of conditions. Penumbra is the region at the edge of a radiation beam over which the dose rate changes rapidly as a function of distance from the beam axis. Phantom is a volume of tissue-equivalent material used for absorbed dose measurements (see also Body Phantom). Photon beam is the region of space traversed by photons from the source. Its edges are determined by the collimator, its cross-section perpendicular to the beam axis at a specified distance from the source is the radiation field size, and its direction is that of photon travel. Planning target volume (PTV) is a term proposed by the ICRU to define a treatment volume for dose planning. It includes a margin around the clinical target volume (CTV) to ensure that the CTV receives the prescribed dose so as to account for any organ motion, anatomical changes or setup uncertainties. The CTV is a volume that includes the gross tumor volume 157 (GTV) plus a margin to encompass possible tumor extremities or local subclinical tumor spread, whereas the GTV is the gross extent of the malignancy.59 Primary radiation is the photons incident directly from the target or source of radiation to a phantom without being scattered from other components in the linac head or from within the phantom. Principal plane is normally a transverse plane of an irradiated medium. Quality assurance of a treatment planning algorithm involves extensive measurement of a wide range of radiation fields so as to compare to calculation based on the treatment planning algorithm. Radiation field is a plane section of a beam perpendicular to the beam axis. The field is therefore two dimensional whereas the beam is three dimensional. Usually the dimensions of a radiation field are represented by the width and length, W x L, of the plane section at a source to axis distance of 100 cm. Simulation is a process in which the treatment setup of a patient is established with a simulator to verify the treatment center, and the locations of critical structures and treatment volume. A simulator is a diagnostic x-ray machine that has the same features of a linac, such 158 as the same isocentric rotation of the gantry, collimator and couch, and similar field defining collimators, but provides superior x-ray images for treatment setup verification. Source to axis distance (SAD) is the distance measured along the beam axis, from the radiation source to the isocenter. Source to surface distance or source to skin distance (SSD) is the distance measured along the beam axis, from the radiation source to the surface of the irradiated object. Symmetric field is a radiation field with the opposite pair of collimators being the same distance from the collimator axis and hence the radiation field central axis or beam axis coincides with the collimator axis. Target volume is a volume in the patient to which it is desired to deliver a specified dose. Thermoluminescence dosimeters (TLD) are crystals that exhibit the phenomenon of thermoluminescence. When they are irradiated with ionizing radiation, the energy absorbed is stored in the crystal lattice. Some of this energy is emitted as visible light when the crystal is heated and the amount of light emitted is proportional to the energy absorbed. Thermoluminescence dosimetry is the use of thermoluminescence dosimeters such as lithium fluoride (LiF) to measure absorbed dose within an irradiated medium. 159 Treated volume is the volume enclosed by an isodose line in which the dose is greater than the desired tumoricidal dose. Upper and lower collimators are sets of shielding blocks or jaws in which the upper and lower collimators are perpendicular to each other to define a useful radiation beam of square or rectangular shape. Water or tissue equivalent materials are materials that have similar radiation properties as that of water or tissue, respectively. Wedge filter is an attenuating material of graduated thickness inserted into the beam which causes a progressive decrease in the dose rate across the whole beam. 160
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Asymmetric collimation : dosimetric characteristics, treatment planning algorithm, and clinical applications Kwa, William 1998
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Title | Asymmetric collimation : dosimetric characteristics, treatment planning algorithm, and clinical applications |
Creator |
Kwa, William |
Date Issued | 1998 |
Description | Asymmetric collimation of photon beams produces non-trivial alterations in absolute output, depth dose and beam profile. The full potential of asymmetric collimation can only be realized with a proper treatment planning algorithm specific for asymmetric collimation. In this thesis the dosimetric characteristics of asymmetric fields are investigated and a new computation method for the dosimetry of asymmetric fields is described and implemented into an existing treatment planning algorithm. Based on this asymmetric field treatment planning algorithm, the clinical use of asymmetric fields in cancer treatment is investigated, and new treatment techniques for conformal therapy are developed. Dose calculation is verified with thermoluminescent dosimeters in a body phantom. An asymmetric field is referred to as an off-set radiation field whereby the central axis of the radiation field does not coincide with the collimator axis as the opposite pair of collimators no longer are equidistant from the collimator axis. Here, the corresponding symmetric field is a radiation field centered at the collimator axis with the opposite pair of collimators set equidistant from the collimator axis and to the largest asymmetric collimator setting. Usually the dose distribution in an asymmetric field is represented by some form of beam modeling. In this thesis, an analytical approach is proposed to account for the dose reduction when a corresponding symmetric field is collimated asymmetrically to a smaller asymmetric field. This is represented by a correction factor that uses the ratio of the equivalent field dose contributions between the asymmetric and symmetric fields. The same equation used in the expression of the correction factor can be used for a wide range of asymmetric field sizes, photon energies and linear accelerators. This correction factor will account for the reduction in scatter contributions within an asymmetric field, resulting in the dose profile of an asymmetric field resembling that of a wedged field. The output factors of some linear accelerators are dependent on the collimator settings and whether the upper or lower collimators are used to set the narrower dimension of a radiation field. In addition to this collimator exchange effect for symmetric fields, asymmetric fields are also found to exhibit some asymmetric collimator backscatter effect. The proposed correction factor is extended to account for these effects. A set of correction factors determined semi-empirically to account for the dose reduction in the penumbral region and outside the radiated field is established. Since these correction factors rely only on the output factors and the tissue maximum ratios, they can easily be implemented into an existing treatment planning system. There is no need to store either additional sets of asymmetric field profiles or databases for the implementation of these correction factors into an existing in-house treatment planning system. With this asymmetric field algorithm, the computation time is found to be 20 times faster than a commercial system. This computation method can also be generalized to the dose representation of a two-fold asymmetric field whereby both the field width and length are set asymmetrically, and the calculations are not limited to points lying on one of the principal planes. The dosimetric consequences of asymmetric fields on the dose delivery in clinical situations are investigated. Examples of the clinical use of asymmetric fields are given and the potential use of asymmetric fields in conformal therapy is demonstrated. An alternative head and neck conformal therapy is described, and the treatment plan is compared to the conventional technique. The dose distributions calculated for the standard and alternative techniques are confirmed with thermoluminescent dosimeters in a body phantom at selected dose points. |
Extent | 6736857 bytes |
Genre |
Thesis/Dissertation |
Type |
Text |
FileFormat | application/pdf |
Language | eng |
Date Available | 2009-05-28 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0085493 |
URI | http://hdl.handle.net/2429/8435 |
Degree |
Doctor of Philosophy - PhD |
Program |
Physics |
Affiliation |
Science, Faculty of Physics and Astronomy, Department of |
Degree Grantor | University of British Columbia |
GraduationDate | 1998-05 |
Campus |
UBCV |
Scholarly Level | Graduate |
AggregatedSourceRepository | DSpace |
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