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A MONTE CARLO STUDY OF DOSE DISTRIBUTIONS AND ENERGY IMPARTED IN COMPUTED TOMOGRAPHY DOSIMETRY PHANTOMS BY JAMES VINCENT ATHERTON A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1993 ACKNOWLEDGMENTS The author wishes to extend copious and sincere thanks to his committee chairman, Dr. William Properzio, for his many efforts on the author's behalf. The author also wishes to extend his thanks to his advisor and cochair, Dr. Libby Brateman, for her hard work, support and advice in the development of this project. Many thanks also go to the other committee members, Drs. Hintenlang, Honeyman, and Roessler, for their encouragement and assistance. Additional recognition is due Drs. Roessler and Brateman for rearranging their travel schedules to accommodate the author. The author also wishes to extend his sincere thanks to Dr. Walter Huda for his suggestions and advice. Also, thanks go to the staff of The CancerCare Center and particularly Dr. Eric Rost for the use of the computers and office equipment located there. The author would like to acknowledge the support he received from the CDRH through the assistance of Drs. Orhan Suleiman and Marvin Rosenstein. The author wishes to extend his great thanks to his family for their continued love and encouragement. Finally, the author wishes to extend his most sincere thanks to his wife for her love and support during the course of this project. TABLE OF CONTENTS ACKN OW LED GM ENTS........................................................ ......................... ii LIST O F TA B LE S.................................. ....... ... ....... ................. ..... vi LIST OF FIGURES...................... .. ... ...... ...... ............. .. ..................... ix A B STR A C T ................................ .. ..................... .................................. xiii CHAPTERS 1. INTRODUCTION........................ .. ..... ..... ..................... 1 2. SURVEY OF COMMON CT SCANNER CHARACTERISTICS.................. 13 Introduction..................................................................... ......... ........... 13 Basic Operational Principles........................................... ................... 13 Differences Among CT Scanners from Various Manufacturers............. 15 Sum m ary............. ...... ............................... .................... .................. 27 3. THE MONTE CARLO TECHNIQUE.......................................... 30 Introduction............. ................................................ ................... .. 30 Sampling M ethods............ ......... ................................... ......... 32 Random Number Generation................................................ ............ 37 Data Analysis......................... ...... .. ... .. .......................... 38 4. THE EGS MONTE CARLO SYSTEM.................................. ....... 41 Introduction.................................................................................. ....... 41 EGS Components........................... ....... ... ........................ 43 Summary ......... .................. ............................. 65 5. VERIFICATION OF THE MONTE CARLO MODEL............................... 67 Conservation of Energy.................................................................... ..... 67 In Air Dose Calculation........ ..... ............... ............................. .......... 69 Primary X Ray Transmission Through a Cylinder................... ........... 71 6. DOSE DISTRIBUTIONS AND RELATED DOSIMETRIC QUANTITIES... 74 Introduction....................................................................................... 74 D ose Profiles.................... ................................ ........ ......... .......... 75 Integration of Dose Profiles............................ ................ 79 Photon Energy Variation............... .... .... .................. ...................... 89 Beam Filter V ariation................................................... ....................... 95 Slice Thickness V ariation...................... .......................................... 98 Phantom Size Variation................................ .. ............... 100 Phantom M material Variation............................................ ..................... 100 SA D V ariation.......................................... ...................... 102 Summary............ .... ... .......................... .................. 104 7. ENERGY IMPARTED RESULTS..................................... ........................ 106 Introduction........................................................................................ 106 Photon Energy V ariation.................................................. .................. 106 Beam Filter Variation....................... .... ......... .......... 112 Slice Thickness Variation............................... .. ............... 115 Phantom Size Variation.................................................... .................. 115 Phantom M material Variation................................................................ 115 SAD Variation ........................................................... ................... 119 Phantom Composition and Shape Variation................................. 120 Sum m ary............................................................................................... 128 8. DISCUSSION AND CONCLUSIONS.................................... ................... 130 APPENDICES A. CT MANUFACTURER SURVEY FORM........... ........................................ 141 B. PRIMARY X RAY TRANSMISSION THROUGH A CYLINDER............. 145 C. DESCRIPTION OF MACRO $ELLCYL................................................... 148 D. LISTING OF PERMON1.MOR ................................................................. 156 REFEREN CE S.............................................. ..... .............. ....... .................. 186 BIOGRAPHICAL SKETCH..................................... .. .. .................... 194 LIST OF TABLES Table 11 Comparison of effective dose equivalents for standard exams for three common CT scanners ............................................................................. 6 Table 12: Ratios of the effective dose equivalent to the energy imparted for different exams and scanners......... ...... .... .... .. .......... ............ ........ ............... 9 Table 13. The range of parameters examined in this work............................... 12 Table 21: Half value layers for the GE 9800 scanner as function of detector and kV p................. ............. ................. ...... ........... ......... .. ................. 19 Table 22: Comparison of head CTDI values [mrad./mAs]............................ 28 Table 23: Comparison of body CTDI values [mrad/mAs].......................... 29 Table 51: Illustration of conservation of energy for four separate Monte Carlo runs with an acrylic phantom and no filter with a 65 cm SAD......................... 68 Table 52: Comparison of CTDI values per incident fluence for various energies and acrylic rod diameters............................. .................. ....................... 70 Table 53: Comparison of percentage transmission of primary radiation through acrylic cylinders of various diameters as calculated analytically and with the EGS code..................... ... ................................................ ............ .................. 72 Table 61: C(r,e) as a function of integration limits e and radial position r in a head phantom at 50 keV ......................................................... ........... .... 83 Table 62: Summary of spectra data.......... .................. ................................... 92 Table 63: Comparison of CTDIa. values for the three beam filters used............ 92 Table 71: Energy dispositions for an 8 cm acrylic phantom with no beam filter and a 5 mm slice thicknesses........ ............... ............................. 107 Table 72: Energy dispositions for a 16 cm acrylic phantom with no beam filter and a 5 mm slice thickness.............................................. 108 Table 73: Energy dispositions for an 8 cm acrylic phantom with no beam filter and 5 mm slice thickness for four spectra............................................................ 109 Table 74: Percentage energy dispositions for an 8 cm acrylic phantom with no beam filter and 5 mm slice thickness for four spectra..................................... 109 Table 75: Energy dispositions in an 16 cm acrylic phantom with no beam filter and 5 mm slice thickness for four spectra....................................... ...... ....... 110 Table 76: Percentage energy disposition for four spectra in a 16 cm radius acrylic phantom with no beam filter................................................................... 110 Table 77: Energy dispositions at 50 keV for 8 cm and 16 cm radii acrylic phantoms for a 5 mm slice thickness, for three filter configurations............................ 113 Table 78: Percentage energy dispositions at 50 keV for 8 cm and 16 cm radii acrylic phantoms for a 5 mm slice thickness, for three filter configurations .......... 113 Table 79: Comparison of energy disposition categories of monoenergetic beams with two typical CT spectra on a 16 cm acrylic phantom with the GE beam filter.......................... ....................... ... ................................ 114 Table 710: Percentage comparison of energy disposition categories of monoenergetic beams with two typical CT spectra on a 16 cm acrylic phantom w ith the G E beam filter....................................................... ......................... 114 Table 711: Effect of slice thickness on energy dispositions for 50 keV incident photons on an 8 cm radius acrylic phantom with no filter................................ 116 Table 712: Energy dispositions for acrylic phantoms with indicated radii for 50 keV incident photons and 5 mm slice thickness.................................... ........ 116 Table 713: Variations of the energy dispositions with phantom material in an 8 cm radius phantom ...... .............. .. ...... ................. ................................... 117 Table 714: Variations of energy dispositions with phantom material in a 16 cm radius phantom ......................................... ...................................................... 118 Table 715: Variation of energy dispositions with change in the SAD for 50 keV incident photons and a 5 mm slice thickness ............ ........... ...................... 120 Table 716: Energy dispositions in the anthropomorphic head phantom for the indicated incident energies with no beam filter............................. .................. 122 Table 717: Energy dispositions in the anthropomorphic head phantom with the GE filter for the indicated incident energies............................ ................ 123 Table 718: Energy dispositions in the anthropomorphic body phantom for the indicated incident energies and no beam filter.................................................... 124 Table 719: Energy dispositions in the anthropomorphic body phantom for the indicated incident energies with the GE filter................................................... 125 Table 720: Energy dispositions for four xray spectra on anthropomorphictype phantoms with no filter..................................................................... .................. 127 Table 721: Percentage energy disposition for four xray spectra incident on anthropomorphictype phantoms................................... .............................. ... 127 Table 81: Comparison of the arithmetic average of the central value and 1 cm depth value of the normalized C(r,L/2) ("average") and the normalized mean CTDI (C) for monoenergies and spectra, calculated with no beam filter.......... 132 LIST OF FIGURES Figure 11: Schematic drawing of CT scanner geometry..................................... 1 Figure 31: Discrete probability density function............................................ 34 Figure 32: Discrete cumulative probability distribution............................... 34 Figure 33: top: Continuous probability distribution; bottom: cumulative distribution functions..................... ............... ...................... 35 Figure 34: An illustration of the Rejection Method. Only the random pairs that fall under the curve are accepted................................................ ................... 37 Figure 41: Flow control diagram of the EGS system....................................... 54 Figure 42 Illustration of the geometry described by subroutine HOWFAR in the user code CTMONO with five radial zones and five planar zones...................... 58 Figure 43. Source and phantom configuration for cylindrical phantom............. 60 Figure 44(a): Head Phantom..................... .......................... 64 Figure 44(b): Body Phantom..................................................... ...................... 65 Figure 51: CTDI in air per incident fluence for acrylic rods of various sizes........ 71 Figure 61: Central portion of dose profiles in a 5 mm diameter acrylic rod for a 3 mm slice thickness for the indicated incident photon energies......................... 76 Figure 62: Dose profiles along the central 5 mm in a 5 mm diameter acrylic rod for 80 keV photons and the indicated slice thicknesses.................................. 77 Figure 63: Normalized dose profiles at the center and at 1 cm depth in an 8 cm radius acrylic phantom for 80 keV incident photons and a 5 mm slice thickness... 77 Figure 64: Normalized dose profiles at the center and at 1 cm depth in a 16 cm radius acrylic phantom for 80 keV incident photons and a 5 mm slice thickness... 78 Figure 65: Portion of the dose profile along the positive zaxis at the center of a 16 cm radius acrylic phantom for 80 keV photons and 5 mm slice thickness........ 78 Figure 66: C(r,t), normalized to the CTDIair value, as a function of the integration limit I in an 8 cm radius acrylic phantom at 50 keV for a 10 mm slice thickness..................................................... ........................................ 82 Figure 67: C(r,), normalized to the CTDIair value, as a function of the integration limit e in an 8 cm radius acrylic phantom at 50 keV for a 5 mm slice thickness..................................... ....................... ....................... ................... 82 Figure 68: C(r,e), normalized to the CTDIair value, as a function of the integration limit e in an 8 cm radius acrylic phantom at 50 keV for a 1 mm slice thickness.......................... ................ ....................... .. ............................ 83 Figure 69: C(r,e) values, normalized to the CTDIair value, as a function of the integration limit e in an 8 cm radius acrylic phantom at 50 keV for a 5 mm slice thickness in a 140 cm long phantom................................................................ 86 Figure 610: C(r,e), normalized to the CTDIair value, as a function of the integration limit e in an 8 cm radius acrylic phantom for a 120 kVp spectrum with 5.4 mm HVL, for a 10 mm slice thickness................................................ 86 Figure 611: C(r,t), normalized to the CTDIair value, as a function of the integration limit t in an 16 cm radius acrylic phantom at 50 keV for a 5 mm slice thickness .......................... .............. ............................ .... ...... 88 Figure 612: C(r,e), normalized to the CTDIair value, as a function of the integration limit e in a 16 cm radius acrylic phantom for a 120 kVp spectrum with 5.4 mm HVL, for a 10 mm slice thickness....................................................... 88 Figure 613: C(rL/2) as a function of radial location in the 8 cm radius phantom, normalized to the CTDIair at the same energy, for a 5 mm slice thickness and various incident energies.................................................... 90 Figure 614: C(r,L/2) as a function of radial location in the 16 cm radius phantom, normalized to the CTDIair at the same energy, for a 5 mm slice thickness and various incident energies....................... ............................... 90 Figure 615: Plots of the four spectra used in this work..................................... 92 Figure 616: C(r,L/2) as a function of radial location for four spectra for 5 mm slices in an 8 cm radius acrylic phantom........................ ... ...... ........ 94 Figure 617: C(r,L/2) as a function of radial location for four spectra for 5 mm slices in a 16 cm radius acrylic phantom................................ ... ............ 94 Figure 618: C(r,L/2) as a function of radial location in the acrylic 8 cm radius phantom at 50 keV for a 5 mm slice thickness, and the indicated beam filter........ 96 Figure 619: C(r,L/2) as a function of radial location in the acrylic 16 cm radius phantom at 50 keV for a 5 mm slice thickness and the indicated beam filter....... 96 Figure 620: C(r,L/2) as a function of radial location for the GE filter in a 16 cm acrylic phantom at 63 cm SAD for the 5 mm slice thickness, and various incident beam s........................................................................... ....... ................. ........ 99 Figure 621: C(r,L/2) as a function of slice thickness in a 8 cm radius acrylic phantom at 80 keV ........................................................ .............................. 99 Figure 622: C(rL/2) plotted against relative distance from the center of the phantom for various values of phantom radius R ................................................ 101 Figure 623: C(r,L/2) plotted against radial location for various phantom materials in a 8 cm radius phantom for 50 keV photons and 5 mm slice thickness 101 Figure 624: C(rL/2) plotted against radial location for various phantom material in an 16 cm radius phantom for 50 keV photons and 5 mm slice thickness...................... .. .. ...... ............... .. .. ................ ........................... 103 Figure 625: C(r,L/2) plotted against radial location for various SAD values for a 5 mm slice thickness and 50 keV photons........................................ 103 Figure 71: Percentage energy dispositions for an 8 cm acrylic phantom with no beam filter and a 5 mm slice thickness........................................................... 107 Figure 72: Percentage energy dispositions for an 16 cm acrylic phantom with no beam filter and a 5 mm slice thickness ......................................................... 108 Figure 73: Percentage energy dispositions acrylic phantoms with indicated radii for 50 keV incident photons and 5 mm slice thickness....................................... 116 Figure 74: Percentage variations with phantom material. Data are for an 8 cm radius phantom and 5 mm slice thickness at 50 keV........................................... 117 Figure 75: Percentage variations with phantom material. Data are for a 16 cm radius phantom and 5 mm slice thickness at 50 keV........................................ 118 Figure 76: Percentage energy disposition for the anthropomorphic head phantom for a 5 mm slice and no beam filter........................... ................ 122 Figure 77: Percentage energy disposition for the anthropomorphic body phantom for a 5 mm slice and the GE beam filter............................................... 123 Figure 78: Percentage energy disposition for the anthropomorphic body phantom for a 5 mm slice and no beam filter...................................................... 124 Figure 79: Percentage energy disposition for the anthropomorphic body phantom for a 5 mm slice and the GE beam filter............................................... 125 Figure B : Sourcephantom geometry.............................................................. 145 Figure C1: Geometry of intersection of a vector and an elliptical cylinder........... 148 Figure C2: Geometric possibilities of particle intersecting an elliptical cylinder.... 150 Figure C3: Geometry used to pick incident particle parameters.......................... 151 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy A MONTE CARLO STUDY OF DOSE DISTRIBUTIONS AND ENERGY IMPARTED IN COMPUTED TOMOGRAPHY DOSIMETRY PHANTOMS by James Vincent Atherton August 1993 Chairman: William Properzio, Ph.D. Cochairman: Libby Brateman, Ph.D. Major Department: Nuclear Engineering Sciences The EGS4 Monte Carlo system was used to study the factors that affect dose distributions and the energy imparted to dosimetry phantoms in computed tomography (CT). The energy imparted is a useful quantity since it is directly correlated with the stochastic risk to the patient. Also, since the energy imparted per slice is independent of both the precise anatomic location of the scanned slice and the total number of slices imaged, the total energy imparted from an exam can be easily found. The parameters that were investigated were incident energy, beam shaping filter, slice thickness, phantom size, phantom composition, and sourcetoaxisdistance (SAD). These parameters were evaluated for irradiation by both monoenergetic xray beams and typical xray spectra incident upon acrylic cylinders modeled on standardized Computed Tomography Dose Index (CTDI) phantoms. In addition, two phantoms similar to the anthropomorphic phantoms used in previous Monte Carlo investigations of patient dosimetry were studied, and the results obtained from these phantoms were compared to those obtained from the CTDI phantoms. In all cases the results obtained were normalized to the dose to acrylic determined "inair" at the isocenter of the scanner in the absence of any other phantom. The results quantitatively demonstrate the effects of modifying key CT parameters on energy deposition patterns in CT dosimetry phantoms. Also, a method is presented that allows estimation of the total energy imparted per slice to a CTDI phantom. In general, the factors most affecting the quantitative values of energy deposited in CT dosimetry phantoms are beam filtration, the size and composition of the object being scanned, and the incident energy. The results also suggest that the energy imparted is only moderately dependent on the characteristics of the incident xray spectrum. The results of this work may be used as a basis for estimating the energy imparted to a phantom or a patient for nonstandard or newly developed CT exams or scanners. The values of the energy imparted may also be used to estimate other quantities such as the effective dose. These estimates may then be used as indices of stochastic risk for comparisons between scanners or imaging modalities, exam optimization, or for populationbased studies of radiation detriment. CHAPTER 1 INTRODUCTION Computerized tomography (CT) is unlike any other radiological imaging method in that an xray beam, tightly collimated in one dimension, is revolved about an object and produces a complex threedimensional pattern of energy deposition. The energy distribution is a function of the xray spectrum, the xray beam filtration, collimation, and the nature of the object scanned. A schematic drawing of the basic geometry of CT scanners is shown in Fig. 11. Since the clinical introduction of CT in the early 1970s, dosimetric investigations have generally followed one of two tracks. One track has been the specification of radiation doses to exact locations in patients and phantoms. The other track has been the evaluation of total radiation risk to the patient from CT exams. The risk has generally been assessed in one of two ways: organbyorgan dose determination; or by estimation of the total energy imparted to the patient. xray source direction of source motion Figure 11: Schematic drawing of CT geometry. Initial investigations of radiation dose in CT followed the first track, reporting doses to specific points or groups of points in phantoms. Horsley and Peters (1976) reported on the dose to the skull from multiple scans from an EMI scanner as measured in a Rando phantom. Dixon and Eckstrand (1978) used a film dosimetry system to measure surface dose in a 19 cm diameter water phantom for both single and multiple slices. McCullough and Payne (1978) used thermoluminescent dosimeters (TLD) to measure surface dose for single and multiple scans in circular and elliptical acrylic phantoms. Shope et al. (1982) used TLD to measure point doses for single and multiple scans in both cylindrical and anthropomorphic phantoms in scanners from ten manufacturers. They presented surface and center doses for the cylindrical phantom and the maximum dose measured in the anthropomorphic phantom. Fearon and Vucich (1985) measured surface doses in pediatric patients for several standard exams and compared the results to inphantom measured values. Storrs and Byrd (1988) measured the dose to the lens of the eye for pediatric patients. There have been several studies of fetal or intrauterine dose from CT (Wagner, et al. 1986, Guidozzi et al. 1987, Felmlee et al. 1990). In 1981 Shope et al. proposed the Computed Tomography Dose Index (CTDI) as a dose descriptor in CT. The CTDI is measured in cylindrical acrylic phantoms that are in tended to approximate the size and shape of a patient's head and body. The CTDI, as defined by the United States Food and Drug Administration (FDA), is given by: +7T CTDI = T (z)dz (11) 7T where n is the number of scans per slice, D(z) is the dose profile for a single scan along a line perpendicular to the scanned slice, and T is the nominal slice thickness (FDA 1985). The CTDI is given in units of absorbed dose to acrylic for a specific depth in one of the two cylindrical phantoms. The CTDI is meant to approximate the dose at the depth of measurement for a point in middle of fourteen contiguous scans. The CTDI is measured the center of the phantom and at one centimeter depth from the surface. The FDA has mandated that CT manufacturers supply users with CTDI values for a particular CT scanner model for the range of tube potentials, tube currents, scan times, slice thicknesses, and gantry angles likely to be used clinically. The FDA requirement has had the effect of making the CTDI a standardized dose descriptor. Apart from its use as a dose estimator, the CTDI can be employed for intercomparisons among scanners, and as an acceptance testing and quality control check. The CTDI is specified by the FDA to be given for two depths and with integration limits that are a function of the nominal slice thickness.' It should be noted that the FDA specifies only a minimum phantom length of 14 cm for CTDI measurements, and the phantoms commercially available are 16 cm long.2 Note that the line integral of the dose can be calculated at any depth in the phantom and with any integration limits (up to the size of the phantom, of course). Viewed in this light, the CTDI as specified by the FDA is a special case of a "family" of CTDI's. Part of this work investigates these different classes of CTDI's and their relationship to the FDA's definition. A new, more generalized dose index is defined, and its relation to the total energy deposited is demonstrated. The second main track of dosimetric investigations in CT have endeavored to evaluate the total radiation risk to the patient undergoing an examination. For doses of less than 1 Gy, the total risk to the patient is considered to be the sum of the risks associated with the individual irradiated organs (ICRP 1977). In diagnostic radiology the main concern is with stochastic effects, e.g., carcinogenesis, genetic injury, and concepts injury (ICRP 1986). Although doses from CT scans are greater than in conventional radiography, the doses are below the threshold for deterministic effects such as lens opacification or skin erythema (ICRP 1990). The method of estimating risk by using the weighted sum of the doses to individual organs is the basis of the Effective Dose Equivalent HE (ICRP 1977) and the Effective Dose E (ICRP 1990) quantities. The 1 Spokas (1982) has pointed out a weakness with the definition of the CTDI in that it combines a dose measurement with an imaging parameter that is not measured. He suggested an alternate descriptor of CT performance, the effective width w, but the CTDI remains to be the most widely used CT dose descriptor. 2 Nuclear Associates, Carle Place, NY 11514 weighting values used in calculation of E were intended to take into account the risk of fatal cancer induction, the risk and the severity of nonfatal cancer induction, the probability of severe hereditary effects, and the relative length of life lost for general populations. The effective dose E is given by E =wTHT T where HT is the equivalent dose in organ or tissue T and wT is the weighting factor for tissue T. The tissue weighting factor represents the relative contribution from tissue or organ T to the overall stochastic effects from uniform irradiation of the whole body. To ensure that a uniform equivalent dose is numerically equal to a uniform equivalent dose over the whole body, the sum of tissue weighting factors is one (ICRP 1990). The values ofE and HE are given in units of Sv and are numerically equal to the absorbed dose in Gy, because the radiation weighting factor wR (formerly the quality factor Q) is unity for photons.3 The calculation of HE is similar to that for E, but different risk estimates (hence different weighting factors) and fewer organs are used in the calculation. The risk estimates used in the determination of the weighting factors for the effective dose equivalent are based on an occupationally exposed population. The effective dose equivalent and its successor the effective dose are both intended as a method to assess nonuniform irradiations for use in radiation protection. The weighting factors used in the calculation of HE are based on radiation risk estimates for radiation workers, but the factors used in the calculation of E are based on risk estimates for whole populations (ICRP 1990). The effective dose equivalent (and to some extent the effective dose) have been used as a gauge in establishing radiation risks to patients in diagnostic radiology. In the case of the effective dose equivalent, the patient population has different demographics and presumably different risk factors than do radiation 3 As given in ICRP 60, HT = wRDTR where DTR is the absorbed dose averaged over organ or tissue R T from radiation R, and wR is the radiation weighting factor. workers. In spite of this limitation, the effective dose equivalent continues to be used as a yardstick in comparing patient doses in diagnostic radiology (Shrimpton et al. 1991, Jones et al. 1991, Le Heron 1992). The use of the effective dose equivalent as an absolute indicator of patient risk may not be as appropriate as the use of the effective dose, but it does provide an objective method of comparison of differing irradiation conditions. One aim of this project is the development of a method allowing estimation ofHE or E in CT, based on the estimation of energy imparted values. Organ dose assessment in CT has generally followed two approaches: measurement in anthropomorphic phantoms, and Monte Carlobased calculations in idealized math ematical phantoms. In general, physical measurement in an anthropomorphic phantom has the advantage using of a realistic phantom but tends to be a very laborintensive process. Monte Carlo simulation can be used to study a wide range of irradiation configurations, but it has the disadvantage of being computationally demanding and time intensive. Huda and Sandison (1985) used TLD to measure organ dose from an EMI scanner in a Rando phantom and presented risk estimates for standard exams, based on the ICRP risk estimates for radiation workers. Huda and Sandison (1986) also published effective dose equivalents based on the EMI scanner measurements. Fearon and Vucich (1985) measured organ doses in a pediatric anthropomorphic phantom, although they presented neither HE values nor risk estimates. In 1989 Huda et al. extrapolated the EMI measurements to other models of CT scanners and presented HE values for standard exams. Nishizawa et al. (1991) measured organ doses in a Rando phantom for a wide range of CT scanners used in Japan. They similarly determined the effective dose equivalents for standard exams for selected CT scanners. There have been two significant studies using mathematical modeling for organ dose assessment. In 1985 Drexler et al. published organ dose tables calculated by using Monte Carlo simulation for standardized CT exams. These tables provide doses to a number of organs in mathematically modeled male and female phantoms. The CT geometry was based on that of a Siemens Somatom scanner. Faulkner and Moores (1987) used the Drexler data to provide organ dose estimates for three different types of CT scanners. Panzer et al. (1989) have also used the Drexler data to estimate organ doses, based on a survey of 122 facilities in the former West Germany. Neither Faulkner and Moores nor Panzer et al. presented effective dose equivalent values for standard exams. Recently, Shrimpton et al. (1991) and Jones et al. (1991) of the National Radiation Protection Board (NRPB) in the United Kingdom published organ dose tables for a range of CT scanners and standard exams. The NRPB results were obtained using Monte Carlo simulation on a mathematical anthropomorphic phantom. Values of HE and E were included with the organ dose values presented. Comparison of results from the organdose studies listed above shows a wide variation in the results, even when comparing the same type of scanner for the same type of exam. A comparison of findings from various authors is given in Table 11, which lists effective dose equivalent values for four standard exams for the scanners which the studies had in common. It is seen that the values of the effective dose equivalent for the same exam and the same machine can vary by more than a factor of two. These variations seem to be mainly due to three reasons: differences in the clinical protocol of "standard" exams; differences in the treatment of the nonspecified "remainder" tissues; and the Table 11: Comparison of effective dose equivalents for standard exams for three common CT scanners. Effective dose equivalent in mSv by scanner Scanner: GE 9800 Siemens DRH Siemens DRG _study* Exam A B C A C B(male) (female) C Head 1.9 4.3 2.3 2.5 2.6 Chest 15.7 7.7 9.0 16.0 5.8 6.5 6.5 5.3 Abdomen 6.3 10.3 9.5 8.1 2.6 2.7 7.0 Pelvis 6.7 11.0 13.4 7.9 6.2 12.5 5.5 * Data are from Huda et al. (1989) abbreviated A; Nishizawa et al. (1991) abbreviated B; and Shrimpton et al. (1991) abbreviated C. differences between TLD measurements in physical phantoms and mathematical modeling. Thus, even with standardized measurement techniques and standard phantoms, estimation of organ dose and patient risk provides inconsistent and widely varying results. Further more, organ dose assessment is difficult to perform. One must either use a large number of small dosimeters placed in an anthropomorphic phantom, or one must employ a mathematical model which must be constructed and tested for accuracy. Moreover, in order to study different examinations and exposure geometries, multiple measurements must be performed. Organ dose studies therefore tend to be labor and time intensive and usually provide results for only a limited number of examination types or exposure geometries. Another method of assessing the radiation risk to the patient has been through estimation of the total energy deposited or imparted to the patient from an exam. As the studies cited below indicate, the energy imparted to the patient (formerly "integral dose") has been shown to be a useful estimator of stochastic risk in diagnostic radiology. The use of the energy imparted to a patient as a risk estimator assumes a homogeneous mix of radiosensitive and radioresistant tissues within the body (Wall et al. 1988). This method is both simpler and cruder than organ dose estimation, and several arguments can be made for its use. The energy imparted is a physical quantity and is independent of organ weighting factors. These weighting factors are based on risk estimates which in turn are subjectivelyjudged and subject to change following developments in the knowledge of radiobiology (Greening 1986). They are subjective values and are not a physical quantity. Also, organ dose determinations, as demonstrated above, vary widely in their results and ignore interpatient variations in organ dimensions and positioning (Harrison 1983). Concerning the efficacy of using energy imparted as a risk indicator, Wall et al. (1988, p. 8) state: ...the distribution of sensitive organs within the trunk may in many circumstances be sufficiently uniform for the errors involved in this approach to be no greater than those associated with using a suitable combination of specific organ doses and weighting factors to express the overall risk. They conclude (p.55): The reasonable degree of correlation that is evident between energy imparted and health detriment for a wide range of xray examinations suggests that in appropriate circumstances it [the energy imparted] can represent a useful practical quantity for estimating the risk to patients. The studies below show that the energy imparted can be used outright as an indicator of patient risk, or it can be used to estimate other risk indicators. Bengtsson et al. (1978) used the energy imparted as a basis for risk estimates for conventional radiographic examinations. They based their estimates on the risk coefficient 1.65x 102 Sv' for radiation workers (ICRP 1977) and identified a risk of 2.0x 104 J1, which corresponds to a ratio of 12.1 mSv/J. Southon (1980) reported values for energy imparted in comparisons of six different CT scanners but did not present any explicit risk estimates corresponding to the energy imparted values. Shrimpton (1985) studied the relationship between the energy imparted and the effective dose equivalent in common radiographic examinations and found a linear relationship (within a factor of two) between the two of 13.8 mSv/J. Le Heron (1992) claimed "good agreement" between the energy imparted and the effective dose in conventional radiography, although he did not present any values. He based his work on the NRPB organ dose data (Jones and Wall 1986). Alm Carlsson and Carlsson (1986) discussed the merits of using a quantity called the mean absorbed dose D, given as D = s/M, where e is the total energy imparted and Mis the mass of the patient. In a homogeneous wholebody exposure, the ratio of HE/D would be 1.0 Sv/Gy, which corresponds to a HE/8 ratio of 14.3 mSv/J for a 70 kg patient or phantom. The authors analyzed studies of patient dose in radiology (Laws and Rosenstein 1978, Rosenstein 1982, Huda 1984, and Stentstrom et al. 1986) and concluded that in all cases, the ratios HE/D were in the range of 0.44 Sv/Gy to 2.8 Sv/Gy with a mean near 1.0 Sv/Gy. For a 70 kg patient or phantom, these values represent HE/E Table 12: Ratios of the effective dose equivalent to the energy imparted for different exams and scanners. H/ __ratios in mSv/J Exam type EMI 5005 GE 9800 Siemens DRH Head 10.5 16.9 16.5 Chest 28.1 19.5 21.5 Abdomen 14.2 23.5 21.5 Pelvis 17.8 29.4 24.1 The values shown for the EMI scanner are based on data from Huda (1984) and Huda and Sandison (1986). The data for the GE and Siemens scanners are from a private communication from Dr. P.C. Shrimpton of the NRPB. ratios of 6.3 mSv/Jto 40 mSv/J with a mean near 14.3 mSv/J. The radiological studies included in this assessment all involved examinations of the head and trunk. In the specific area of CT imaging, Huda (1984) investigated the relationship between energy imparted and risk for four standard exams in CT. The risk estimates were based on those of the ICRP (ICRP 1977). He based his conclusions on measurements made in an anthropomorphic phantom scanned in an EMI 5005 scanner. The results were also used to calculate HE values for the exams (Huda and Sandison 1986). The ratios of HEf/ based on these two works are shown in Table 12. Also included in Table 12 are values of HE/e for the GE9800 and Siemens DRH, obtained from Dr. P.C. Shrimpton of the NRPB Medical Dosimetry Group in the United Kingdom. The GE and Siemens data are based on the NRPB CT organ dose study (Shrimpton et al. 1991 and Jones et al. 1991). The values for the GE and Siemens units are based on the same scan protocols (mAs, slice width, number of slices) as used in the EMI exams. The values of HE/ shown in Table 12 are in the range of HE/e values derived from the Aim Carlsson and Carlsson data, although somewhat larger. The data for the two more modem scanners are quite consistent. These data show how energy imparted values may be employed to estimate the effective dose equivalent for given irradiation conditions. By combining the data in Table 12 with values of the energy imparted in the different anatomic regions, it should be possible to make estimates of the effective dose equivalent for a wide variety of possible exposure conditions. The overall goal of this project is provision of the fundamental knowledge necessary for the development of a method allowing a simple and convenient way of estimating the energy imparted per CT slice. Values of the energy imparted may then be used as an index of stochastic risk. The organ dose studies cited above provide data for only a limited number of exam types and scanner types. A more generalized method, employable by clinical medical physicists without access to specialized and costly dosimetry systems, would provide a way of estimating a riskbased index for nonstandard or newly established exams or CT scanners. The energy imparted per CT slice has the advantage of being independent of both the number of slices and the exact anatomic location of each slice. Energy imparted values and subsequent risk estimates can be used for exam optimization, intercomparisons between different imaging modalities, and population based studies of detriment. The basis of this project is the assumption that the energy imparted can be used as an index of the stochastic risk to a patient. This assumption is clearly justified on the basis of the works cited above. Furthermore, Carlsson and Aim Carlsson (1990) have stated that, for risk estimates, only crude dosimetry is necessary. The wide availability and use of CTDI phantoms make them an attractive object to study. However, the question of how closely CTDI phantoms model actual patients or anthropomorphic phantoms has not yet been determined. This work therefore studies the factors that determine how much energy is deposited in both CTDI and anthropomorphic phantoms and the patterns of that energy deposition. Quantified estimates of the energy imparted to anthropomorphic phantoms are compared to the energy deposited in CTDI phantoms. This study uses the EGS Monte Carlo system to investigate patterns of energy deposition in phantoms (Nelson et al. 1985). The influence of beam energy, beam filtration, phantom size, phantom composition, sourcetoaxis distance (SAD), and slice thickness on the pattern of energy distribution is systematically determined. The variables studied are listed in Table 13. Each of the parameters was varied over the stated range with the remaining variables held constant at their default value. For each run (i.e., a series of Monte Carlo simulations with identical initial parameters), the energy deposition pattern is found as a function of radial and longitudinal position within the phantom. The dose to each position is calculated, as are line integrals of the dose. The doses as well as the energies deposited in regions of the phantom are normalized to the dose measured in a small acrylic rod placed at the isocenter of the hypothetical scanner. In addition, the Monte Carlo method allows labeling of photons so as to differentiate between scattered and primary contributions to any quantity of interest, therefore allowing identification of scattered and primary components of the energy deposited and of the energy exiting the phantom. Calculations performed in this manner allow the study of the nature of the dose distributions in a way that is not practical by physical measurement. The CTDI is investigated as a function of radius and as a function of the integration limits. The relationship between the CTDI and the energy imparted is studied for the range of irradiation conditions considered. The first step in this project was to determine the ranges of variation of the important characteristics of CT scanners. Although this study uses a simplified model of CT scanners, it is desirable to base the mathematical model on realistic geometries and characteristics. Results from the study are then more pertinent to clinical situations. To accomplish this goal, a survey form was mailed to several CT manufacturers that asked for descriptions of their scanners. The results provided a good overview of the characteristics of common CT scanners in clinical use. The results from the survey were used in determining both the range of values and the default values of the important scanner characteristics in the Monte Carlo calculations. Table 13: The range of parameters examined in this work. Parameter default Range investigated Beam Energy 50 keV 40, 50, 60, 80, 100, 120, 140 keV, typical spectra Beam Filter none none, perfect4, GE9800 Slice Thickness 5 mm 1, 2, 3, 5, 10 mm Phantom Material acrylic acrylic, water, bone, fat, lung, muscle5 Phantom Radius 8, 16 cm 6, 8, 10, 12, 14, 16, 20 cm SAD 65 cm 50, 65, 80 cm Phantom Type CTDI CTDI, anthropomorphicanalog This dissertation is organized in the following way. The results from the CT manufacturer survey are presented in Chapter 2. Chapter 3 provides a background of the past uses of Monte Carlo simulation in diagnostic radiological physics and describes the basic techniques of Monte Carlo simulation. The EGS system, along with the details of the models used in this work, are presented in Chapter 4. The accuracy of the Monte Carlo model is verified in Chapter 5. Chapter 6 introduces a new quantity, the Generalized CTDI (GCTDI), and presents the results concerning dose deposition patterns, the relationship of the energy imparted to the GCTDI, and the variation of the GCTDI as a function of the variables in Table 12. The results concerning the energy imparted to phantoms are presented in Chapter 7. Chapter 8 discusses the results and presents conclusions concerning the entire study. 4 A perfect filter is constructed such that the total path length for any ray emerging from the xray source within the fan beam is constant. For a right cylindrical cylinder of radius R with long axis normal to the scan plane, the filter thickness t is found from 2R = t + L where L is the path length through the cylinder. 5 In this category the phantoms are assumed to be of the same dimensions as the CTDI phantoms but comprised of the different materials listed. The material data were obtained from ICRU Report No. 44 (ICRU 1989). CHAPTER 2 SURVEY OF COMMON CT SCANNER CHARACTERISTICS Introduction The first step in this project was to determine the ranges of variation of the characteristics of CT scanners. This study uses a simplified mathematical model of CT scanners which is based on realistic geometries and characteristics. A survey form was mailed to several CT manufacturers which asked for descriptions of their scanners. The results provided a good overview of the characteristics of common CT scanners in clinical use. The results from the survey were used in determining the both the range of values studied and the default values of the scanner characteristics. Basic Operational Principles Computed tomography was introduced to the radiology community in the early 1970s. The modality's explosive growth is illustrated by the fact that approximately 2.2 million CT studies were performed in hospitals in 1980, only seven to eight years after the first commercial CT units became available (Bunge and Herman 1987). CT is now considered an essential element in radiological imaging. In a computed tomography examination, the patient is exposed to a highly collimated beam of x rays at a number of angular increments. The transmitted x rays are absorbed by a series of detectors, and the data from these projections are used to create a twodimensional map of linear attenuation coefficients, i.e., an image. The configuration of xray tube, xray detectors, and the manner in which these elements are moved, has changed through several socalled "generations." The first CT scanner, introduced by Hounsfield (1973), had a single detector and a pencil xray beam, which moved in a translaterotate manner, i.e., the detector and xray tube translated along a line parallel to the image plane acquiring data. The tube and detector were then rotated one degree, and the process repeated. To overcome the problems of slow scan times and poor resolution, a second generation was devised with multiple detectors and a small fan shaped xray beam. The second generation retained the original translaterotate motion. In the third generation of CT scanners, the translate motion of the tube and detectors was replaced with a rotateonly motion. A broad fanshaped xray beam is used with several hundred detectors, and the entire tubedetector system rotates around the machine's isocenter. The fourth generation CT scanner has stationary detectors, and only the xray tube rotates around the patient. Recently a new type of CT scanner has been developed by Imatron.' In these scanners, the patient lies on a large evacuated chamber. An electron beam is scanned across a series of small tungsten targets lining the interior of the evacuated chamber. These targets act like the anode in a standard xray tube and produce x rays which are collimated, transverse the patient, and are detected by an array of detectors. Both the tungsten targets and the array of detectors cover an arc of 2100. These machines have the advantage of fast (50 100 ms) scan times but have slightly poorer image quality than conventional CT scanners. The following manufacturers provided information regarding their scanners: Elscint2, Picker3, Siemens4, and General Electric5 (GE). Elscint supplied data concerning four of their scanners, all third generation. Picker provided information on four of their 1 Imatron, Inc., San Francisco CA 94080. 2 Elscint Ltd., Haifa, Israel 3 Picker International Inc., Highland Heights, OH 44143 4 Siemens Medical Systems Inc., Iselin, NJ 08830 5 GE Medical Systems, Milwaukee, WI 53201 fourth generation models. Siemens supplied data for three of their scanners, which are all third generation. GE provided data for two versions of the same model scanner. Differences Among CT Scanners From Various Manufacturers This section outlines the differences and similarities among scanners from different manufacturers. A questionnaire was designed to allow comparisons among scanners in physical construction, radiologic technique factors available, and reported CTDI. A copy of this questionnaire is presented in Appendix A. The questionnaire was sent to the major manufacturers of CT scanners. This questionnaire is the primary source of the information presented in this chapter; however, not all manufacturers complied with the request for complete information. The data provided are given in this section. One manufacturer did not return the questionnaire; and one supplied the data requested, with the exception of a description of their beamshaping filter. These missing data are described below. The sections below describe the features of the various CT scanners provided by the manufacturers. Two tables summarize the CTDI data at the end of the section. (Note that the electrical potential across the xray tube is abbreviated as "kVp", the current through the xray tube is represented by "mA", and the product of the exposure time and the tube current is abbreviated as "mAs".) ELSCINT EXEL 2400 Elite/2400E Radiologic technique factors available: Four peak tube potentials are available: (100, 120, 130, and 140 kVp); however, Elscint recommends that only 120 and 140 kVp be used routinely. The tube currents available are 50, 100, 120, 150, and 200 mA, and the scan times available are 0.5, 1, 2, 4, and 8 s, with 1 to 4 s routinely used. The generator is 3phase with continuouslysupplied voltage. Tube characteristics: There are two focal spots of nominal sizes 1.5 mm x 1.4 mm and 0.8 mm x 1.4 mm. The manufacturer specified neither the criteria used for focal spot size selection nor the orientation of focal spot sizes with respect to the anodecathode axis. The anode angle is 70, and the anode is constructed of tungstenongraphite composite. Geometry: The four slice thicknesses available (1.2, 2.5, 5, and 10 mm) are specified at the isocenter. The fan beam arc is 220. The sourcetoisocenter distance is 63 cm, and the isocentertodetector distance is 46 cm. The scanner is thirdgeneration with three scan angles (2020, 3600, 3820) available, although 3600 and 3820 are routinely used. The beam is oriented such that heel effect intensity variation is not present in the scan plane. The gantry tilt angles were not supplied. Filtration: The inherent filtration is equivalent to 1.1 mm Al equivalent at 100 kVp. The unit has both a flat, fixed, added filter and a shaped compensating filter, the details of which are proprietary. The couch attenuation is equivalent to 1.4 mm Al (the kVp was not specified). CTDI: The CTDI for the head phantom using the recommended head technique (120 kVp, 300 mAs, 10 mm) is 3.9 cGy (13.0 mrad/mAs) in the center and 4.6 cGy (15.3 mrad/mAs) in the 12 o'clock (maximum value) position. For the body phantom and technique, the CTDI is 1.7 cGy (5.4 mrad/mAs) in the center and 3.6 cGy (11.4 mrad/mAs) at 12 o'clock (140 kVp, 315 mAs, 10 mm). Elscint has provided CTDI slice width and voltage dependence data. The maximum deviation from the specified CTDI values is 20%. ELSCINT 2400 Radiologic technique factors available: Four peak tube potentials are available (100, 120, 130, and 140 kVp); however, Elscint recommends that only 120 and 140 kVp be used routinely. The tube currents available are 50, 100, 120, 150, and 200 mA, and the scan times available are 0.5, 1, 2, 4, and 8 seconds, with 1 to 4 s routinely used. The generator is 3phase with continuouslysupplied voltage. Tube characteristics: There are two focal spots of nominal sizes 1.5 mm x 1.7 mm and 0.8 mm x 1.7 mm. The anode angle is presently 100 (although it will be changed to 70 in the near future, according to the manufacturer), and the anode is constructed of tungsten on graphite composite. Again, neither the orientation of the focal spots nor the criteria used for focal spot size selection were specified. Geometry: The four slice thicknesses available (1.2, 2.5, 5 and 10 mm) are specified at the isocenter. The fan beam arc is 220. The sourcetoisocenter distance is 63 cm, and the isocentertodetector distance is 46 cm. The scanner is thirdgeneration with three scan angles (2020, 3600, 3820) available, although 360 and 3820 are routinely used. The beam is oriented such that heel effect intensity variation is not present in the scan plane. The gantry tilt angles were not supplied. Filtration: The inherent filtration is 1.1 mm Al equivalent at 100 kVp. The unit has both a flat, fixed, added filter and a shaped compensating filter, the details of which are proprietary. The couch attenuation is 1.4 mm Al equivalent (at an unspecified kVp). CTDI: The CTDI for the head phantom using the recommended head technique (120 kVp, 300 mAs, 10 mm) is 3.8 cGy (12.7 mrad/mAs) in the center and 4.5 cGy (15 mrad/mAs) in the 12 o'clock (maximum value) position. For the body phantom and technique (140 kVp, 310 mAs, 10 mm), the CTDI is 1.6 cGy (5.2 mrad/mAs) in the center and 3.5 cGy (11.3 mrad/mAs) at 12 o'clock. Elscint has provided CTDI slicewidth and voltage dependence data. The maximum deviation from the specified CTDI values is 20%. ELSCINT 1800 Radiologic technique factors available: Four peak tube potentials are available (100, 120, 130, and 140 kVp); however, Elscint recommends that only 120 and 140 kVp be used routinely. The tube currents available are 50, 100, 120, 150, and 200 mA, and the scan times available are 0.5, 1, 2, 4, and 8 s, with 1 to 4 s routinely used. The generator is 3phase with continuouslysupplied voltage. Tube characteristics: The nominal focal spot size is 1.5 mm x 17 mm. The anode angle is 100, and the anode is constructed of tungstenongraphite composite. Geometry: The three slice thicknesses available (2, 5, and 10 mm) are all specified at the isocenter. The fan beam arc is 220. The sourcetoisocenter distance is 63 cm, and the isocenter todetectordistance is 46 cm. The scanner is thirdgeneration, with three scan angles (2020, 3600, 3820) available, although 3600 and 3820 are routinely used. The beam is oriented such that heel effect intensity variation is not present in the scan plane. The gantry tilt angles were not supplied. Filtration: The inherent filtration is equivalent to 1.1 mm Al at 100 kVp. The unit has both a flat, fixed, added filter and a shaped compensating filter, the details of which are proprietary. The couch attenuation is 1.4 mm Al equivalent at an unspecified kVp. CTDI: The CTDI for the head phantom using the recommended head technique (120 kVp, 300 mAs, 10 mm) is 3.1 cGy (10.3 mrad/mAs) in the center and 3.6 cGy (12.0 mrad/mAs) in the 12 o'clock (maximum value) position. For the body phantom and technique (140 kVp, 310 mAs, 10 mm), the CTDI is 1.3 (4.2 mrad/mAs) cGy in the center and 3.1 cGy (10 mrad/mAs) at 12 o'clock. Elscint has provided CTDI slicewidth and voltage dependence data. The maximum deviation from the specified CTDI values is 20%. GENERAL ELECTRIC 9800 The GE 9800 CT scanner is available with two different detector systems. The older version, with xenon detectors, has several different characteristics from the newer version, with "HiLight" (solid state) detectors. These differences are noted where appropriate. Three peak tube potentials available (80, 120, and 140 kVp); GE recommends 120 kVp for routine use. The tube currents available are 10, 20, 40, 70, 100, 120, 170, 200, 240, and 300 mA, and the scan times available are 2, 3, 4, and 8 s. The generator is 3 phase with continuouslysupplied voltage. Tube characteristics: The nominal focal spot size is 0.9 mm x 0.7 mm. The anode angle is 70, and the anode is constructed of tungsten and rhenium on a titaniumzirconium molybdenum substrate. Geometry: The 9800 series are third generation scanners. The four slice thicknesses available are 1.5, 3, 5, and 10 mm, all specified at the isocenter. The fan beam arc is 45. The beam is oriented such that heel effect intensity variation is not present in the scan plane. The sourcetoisocenter distance is 63 cm, and the isocentertodetector distance is 47 cm. The gantry can tilt 200. Filtration: The inherent filtration of the x ray tubes were not explicitly listed. However, the values of the halfvalue layers of the central rays are listed in Table 21 below. CTDI: The CTDI of the 9800 varies with the type of detector. Solid State: The CTDI for the head phantom using the recommended head technique (120 kVp, 340 mAs, 10 mm) is 4.0 cGy (11.8 mrad/mAs) in the center and also 4.0 cGy (11.8 mrad/mAs) at 1 cm depth. For the body phantom and technique (120 kVp, 340 mAs, 10 mm), the CTDI is 1.1 cGy (3.2 mrad/mAs) in the center and 2.0 cGy (5.9 mrad/mAs) at 1 cm depth. Xenon: The CTDI for the head phantom using the recommended head technique (120 kVp, 340 mAs, 10 mm) is 5.0 cGy (14.7 mrad/mAs) in the center and 4.8 cGy (14.1 mrad/mAs) at 1 cm depth. For the body phantom and technique (120 kVp, 340 mAs, 10 Table 21: Half value layers for the GE 9800 scanner as function of detector and kVp. Detectors 80 kVp 120 kVp 140 kVp _mm All [mm All mm All Solid State 3.9 6.2 7.1 Xenon 3.6 5.0 6.0 mm), the CTDI is 1.4 cGy (4.1 mrad/mAs) in the center and 2.5 cGy (7.4 mrad/mAs) at 1 cm depth. GE provided CTDI slicewidth and voltage dependence data, although the maximum variation of the CTDI values were not provided. PICKER 1200 SX Radiologic technique factors available: The peak tube potentials available cover the range from 100 to 140 kVp in 5 kVp steps. The tube currents range from 5 to 200 mA in 15 mA increments, and the scan times available are 1 to 20 s. The generator waveform is highfrequency; the frequency was not provided. Tube characteristics: The two nominal focal spot sizes are 0.5 mm x 1.65 mm and 0.9 mm x 2.4 mm. The orientations of the focal spots with respect to the scan plane were not indicated. The anode angle is 120, and the anode is constructed of a tungstenrhenium track on molybdenum. Geometry: The slice thicknesses available range from 1 to 10 mm in 1 mm increments at the isocenter. The fan beam arc is 240 for head scans and 48 for body scans. The sourcetoisocenter distance is 64 cm, and the isocentertodetector distance is 85 cm. The scanner is fourthgeneration with three scan angles (2200, 360, 3980) available, although only 3600 is routinely used. The beam is oriented such that heel effect intensity variation is not present in the scan plane. The gantry can tilt 200. Filtration: The inherent filtration is 3 mm Al equivalent at 100 kVp. The unit has both a flat, fixed, added filter and a shaped compensating filter, the details of which are proprietary and not disclosed. The couch attenuation is 0.8 mm Al equivalent at an unspecified kVp. CTDI: The CTDI for the head phantom using the recommended head technique (130 kVp, 240 mAs, 10 mm) is 3.7 cGy (15.4 mrad/mAs) in the center position and 4.1 cGy (17.1 mrad/mAs) at 1 cm depth. For the body phantom and technique (130 kVp, 240 mAs, 10 mm), the CTDI is 1.5 cGy (6.3 mrad/mAs) in the center and 4.2 cGy (17.5 mrad/mAs) at 1 cm. Picker has provided CTDI slicewidth, voltage dependence, slice thickness, added filtration and scan angle dependence data. The maximum deviation from the specified CTDI values is 15%. PICKER 10 Premier Radiologic technique factors available: The only peak tube potential available is 130 kVp. The tube currents available are 20, 45, 65, 85, 105, and 125 mA, and the scan times available are 2 and 4 s. The solidstate, highfrequency generator is mounted on a rotating frame. Tube characteristics: The nominal focal spot size is 0.9 mm x 2.0 mm. The anode angle is 120, and the anode is constructed with a tungstenrhenium track on molybdenum. Geometry: The slice thicknesses available are: 2, 5, and 10 mm, all specified at the isocenter. The fan beam arc is 480. The sourcetoisocenter distance is 64 cm, and the isocentertodetector distance is 85 cm. The scanner is fourthgeneration with two scan angles (3600 and 3790) available, although 3600 is routinely used. The beam is oriented such that heel effect intensity variation is not present in the scan plane. The gantry can tilt 300. Filtration: The inherent filtration was specified to be 3 to 4 mm Al equivalent at 130 kVp. The unit has both a flat, fixed, added filter and a shaped compensating filter, the details of which are proprietary and not disclosed. The couch attenuation is 0.8 mm Al equivalent at an unspecified kVp. CTDI: The CTDI for the head phantom using the recommended head technique (130 kVp, 260 mAs, 10 mm) is 4.2 cGy (16.2 mrad/mAs) in the center position and 3.9 cGy (15.0 mrad/mAs) in the 12 o'clock position. For the body phantom and technique (130 kVp, 260 mAs, 10 mm) the CTDI is 1.6 cGy (6.2 mrad/mAs) in the center and 3.5 cGy (13.5 mrad/mAs) at 12 o'clock. Picker has provided CTDI slicewidth, voltage dependence, slice thickness, added filtration and scan angle dependence data. The maximum deviation from the specified CTDI values is 15%. PICKER IQ and IQ T/C Radiologic technique factors available: The only peak tube potential available is 130 kVp. The tube currents are 20, 45, 65, 85, 105, and 125 mA, and the scan times available are 2 and 4 s. The solidstate, highfrequency generator is mounted on a rotating frame. Tube characteristics: The nominal focal spot size is 0.9 mm x 2.0 mm. The anode angle is 13.5, and the anode is constructed with a tungstenrhenium track on molybdenum. Geometry: The slice thicknesses available are 2, 5, and 10 mm, all specified at the isocenter. The fan beam arc is 480. The sourcetoisocenter distance is 64 cm, and the isocentertodetector distance is 85 cm. The scanner is fourthgeneration with two scan angles (3600 and 3790) available, although 3600 is routinely used. The beam is oriented such that heel effect intensity variation is not present in the scan plane. The gantry can tilt 300. Filtration: The inherent filtration was specified as 3 to 4 mm Al equivalent at 130 kVp. The unit has both a flat, fixed, added filter and a shaped compensating filter, the details of which are proprietary and were not disclosed. The couch attenuation is 0.8 mm Al equivalent at an unspecified kVp. CTDI: The CTDI for the head phantom using the recommended head technique (130 kVp, 260 mAs, 10 mm) is 4.7 cGy (18.1 mrad/mAs) in the center position and 4.4 cGy (16.9 mrad/mAs) in the 12 o'clock position. For the body phantom and technique (130 kVp, 260 mAs, 10 mm), the CTDI is 1.7 cGy (6.5 mrad/mAs) in the center and 3.9 cGy (15.0 mrad/mAs) at 9 o'clock. Picker provides CTDI slicewidth, voltage dependence, slice thickness, added filtration and scan angle dependence data. The maximum deviation from the specified CTDI values is 15%. PICKER PQ2000 Radiologic technique factors available: The peak tube potentials available are 80, 100, 120, 130, and 140 kVp. The tube currents are 30, 50, 65, 100, 125, 150, 175 and 200 mA, and the scan times available are 1, 1.5, 2, 3, and 4 s. The solidstate, high frequency generator is mounted on a rotating frame. Tube characteristics: There two nominal focal spot sizes are 0.9 mm x 2.4 mm and 0.6 mm x 1.65 mm. The anode angle is 12.50, and the anode is constructed with a tungstenrhenium track on molybdenum. Geometry: The slice thicknesses available are 1.5, 2, 3, 4, 5, 8, and 10 mm, at the isocenter. The fan beam arc is 44. The sourcetoisocenter distance is 64 cm, and the isocentertodetector distance is 85 cm. The scanner is fourthgeneration with a scan angle of 3600. The beam is oriented such that heel effect intensity variation is not present in the scan plane. The gantry can tilt 30. Filtration: The inherent filtration is 3 mm Al equivalent at 100 kVp. The unit has both a flat, fixed, added filter and a shaped compensating filter, the details of which are proprietary and were not disclosed. The couch attenuation is 0.8 mm Al equivalent at an unspecified kVp. CTDI: Picker has indicated that the CTDI report for the PQ2000 is not complete but that the CTDI values can be expected to be similar to those for the IQ. The CTDI for the head phantom using the recommended head technique (130 kVp, 250 mAs, 10 mm) is 4.7 cGy (18.8 mrad/mAs) in the center position and 4.4 cGy (17.6 mrad/mAs) in the 12 o'clock position. For the body phantom and technique (130 kVp, 250 mAs, 10 mm), the CTDI is 1.7 cGy (6.8 mrad/mAs) in the center and 3.9 cGy (15.6 mrad/mAs) at 9 o'clock. Picker has provided CTDI slicewidth, voltage dependence, slice thickness, added filtration and scan angle dependence data. The maximum deviation from the specified CTDI values is 15%. SIEMENS Somatom PLUS Radiologic technique factors available: The peak tube potentials available are 80, 120, and 137 kVp. The tube currents available are 70 to 300 mA (the increments were not specified), and the scan times available are 0.7, 1, 2, 3, 4, 5, and 6 s. The generator has a highfrequency waveform. Tube characteristics: The nominal focal spot size is 1.1 mm x 1.8 mm. The anode angle is 100, and the anode is tungstenongraphite. Geometry: The slice thicknesses available are 1 through 10 mm in 1 mm increments, specified at the isocenter. The fan beam arc is 420. The sourcetoisocenter distance is 70 cm, and the isocentertodetector distance was not supplied. The scanner is thirdgeneration with two scan angles (3600 and 2400) available, although 3600 is routinely used. The beam is oriented such that heel effect intensity variation is not present in the scan plane. The gantry can tilt 250. Filtration: The inherent filtration is 2.5 mm Al equivalent at 120 kVp. The unit has only a flat, fixed, added filter, which is 0.2 mm Cu. The couch attenuation is 1.2 mm Al equivalent at an unspecified kVp. CTDI: The CTDI for the head phantom using the recommended head technique (120 kVp, 500 mAs, 10 mm) is 3.9 cGy (7.7 mrad/mAs) in the center position and 5.0 cGy (9.9 mrad/mAs) at the 1 cmdepth position. For the body phantom and technique (120 kVp, 290 mAs, 10 mm), the CTDI is 1.2 cGy (4.1 mrad/mAs) in the center and 2.8 cGy (9.6 mrad/mAs) at 1 cm depth. Siemens provides CTDI slicewidth, voltage dependence, slice thickness, and scan angle dependence data. The expected variations in CTDI values are given as 15%. SIEMENS Somatom HiO Radiologic technique factors available: The peak tube potentials available are 85, and 133 kVp. The tube currents are 70 to 225 mA (the increment was not specified), and the scan times available are 1.3, 2, 2.7, 4, and 8 s. The generator has a highfrequency waveform. Tube characteristics: The nominal focal spot size is 1.8 mm x 1.8 mm. The anode angle is 100, and the anode is tungstenongraphite. Geometry: The slice thicknesses available are 1 through 10 mm (the increment was not specified) at the isocenter. The fan beam arc is 420. The sourcetoisocenter distance is 70 cm, and the isocentertodetector distance was not supplied. The scanner is third generation with two scan angles (3600 and 2400) available, although 3600 is routinely used. The beam is oriented such that heel effect intensity variation is not present in the scan plane. The gantry can tilt 250. Filtration: inherent filtration is 2.5 mm Al equivalent at 120 kVp. The unit has only a flat, fixed, added filter, which is 0.1 mm Cu. The couch attenuation is 1.2 mm Al equivalent at an unspecified kVp. CTDI: The CTDI for the head phantom using the recommended head technique (133 kVp, 350 mAs, 5 mm) is 4.1 cGy (11.7 mrad/mAs) in the center position and 5.3 cGy (15.1 mrad/mAs) at the 1 cmdepth position. For the body phantom and technique (133 kVp, 225 mAs, 10 mm), the CTDI is 1.2 cGy (5.2 mrad/mAs) in the center and 2.4 cGy (10.7 mrad/mAs) at 1 cm depth. Siemens provides CTDI slicewidth, voltage dependence, slice thickness, and scan angle dependence data. The expected variations in CTDI values are given as 15%. SIEMENS Somatom CRX Radiologic technique factors available: The only peak tube potential available is 125 kVp. Neither the tube currents nor the scan times were provided. The highfrequency generator pulses the tube potential at a frequency of 360 pulses per second. Tube characteristics: The nominal focal spot size is: 1.6 mm x 1.6 mm. The anode angle is 10, and the anode is tungstenongraphite. Geometry: The slice thicknesses available are 2, 4, and 8 mm, specified at the isocenter. The fan beam arc is 32. The sourcetoisocenter distance is 70 cm, and the isocentertodetector distance was not supplied. The scanner is thirdgeneration with a scan angle of 3600. The beam is oriented such that heel effect intensity variation is not present in the scan plane. The gantry can tilt 250. Filtration: The inherent filtration is 2.2 mm Al equivalent at 125 kVp. The unit has only a flat, fixed, added filter, which is 0.2 mm Cu. The couch attenuation is 1.2 mm Al equivalent at an unspecified kVp. CTDI: Only the surface CTDI values were supplied by Siemens. The CTDI for the standard head technique (125 kVp, 550 mAs, 8 mm) is 4.7 cGy (8.6 mrad/mAs). The CTDI for body scans is 2.6 cGy (8.0 mrad/mAs) using the standard technique (125 kVp, 330 mAs, 8 mm). Data Not Obtained Below is the list of data not provided by the manufacturers. PHILIPS: All Models Philips has not returned the questionnaire. PICKER: All Models Picker has returned the questionnaire but has refused to provide the construction details of their shaped compensating filter(s). SIEMENS: Somatom CRX Neither the available tube currents nor scan times were supplied. Summary The CT system information above may be summarized as follows. According to the manufacturers' recommendations, most scanners use 3600 rotation of the tube, continuous voltage supply, and very similar peak tube voltages. In addition, the sourcetoisocenter distances are similar (between 63 and 70 cm) as well; this indicates the xray output for different scanners (specified at a given distance) would depend primarily on the filtration present. The major difference among the scanners is the type of xray beam filtration, i.e., the presence or absence of a beamshaping filter. The presence of a shaped compensating filter is expected to produce a more homogeneous depthdose distribution pattern in the phantom than the use of a flat filter because of the preferential filtering of the beam near the periphery of the phantom. The variation in depth dose distributions can be seen from inspection of the ratios of the CTDI at the central position to the CTDI at the 1 cm depth position. Table 22 below lists the CTDI for typical exams as a function ofmrad per mAs for the head exam in the center of the phantom and at 1 cm depth.6 Table 23 lists the CTDI for body exams as function ofmrad per mAs as measured in the center and at 1 cm depth. Note that the mrad/mAs values are listed for the manufacturerrecommended technique. The headCTDI data in Table 22 show that the Picker units, all fourth generation scanners, produce larger CTDI values than do the other units which are all third generation scanners. Also, the effects of the shapes and materials of the beamshaping filters are readily observed. The Siemens units have only a fixed, flat filter, and the ratios of the centraltoperipheral CTDI values are smaller than for any other manufacturer's scanner. This situation is contrasted with the GE 9800series the ratio of the CTDI values is almost unity. The ratios for the Picker units are also close to one with the exception of the 1200SX. The 1200SX presumably has a beamshaping filter of a 6 The unit mrad/mAs, while a nonSI unit, is commonly used in clinical medical physics and for convenience will be used here. different design than do the other Picker units. The Elscint units have ratios between the values of the Siemens units and the GE and Picker units, demonstrating the effects of differences in the filter designs. The bodyCTDI data in Table 23 show that the fourth generation Picker scanners also produce larger CTDI values than do the third generation scanners. In general, the effect of the beamshaping filter is reduced. All of the units, including the Siemens scanners with no beamshaping filter, have centraltoperipheral CTDI ratios of approximately 0.35 to 0.55. The Picker 1200SX has smaller ratio than the other Picker units do, again illustrating a probable difference in beamfiltration. Table 22: Comparison of head CTDI values [mrad/mAs]. manufacturer's recommended technique. Manufacturer/Model Center 1 cm Ratiot Elscint Exel 2400 Elite/E 13.0 15.3 0.85 2400 12.7 15.0 0.85 1800 10.3 12.0 0.86 General Electric 9800 Xenon 14.7 14.1 1.04 9800 Hilight 11.8 11.8 1.00 Picker 1200SX 15.4 17.1 0.90 IQ Premier 16.2 15.0 1.08 IQ, IQ T/C 18.1 16.9 1.07 PQ2000 18.8 17.6 1.07 Siemens Somatom Plus 7.7 9.9 0.78 * Somatom HiQ 11.7 15.1 0.78* Somatom CRX ** 8.6 $ CTDI at center + CTDI at 1 cm depth 5 mm slice thickness ** not supplied Values are derived from the Table 23: Comparison of body CTDI values [mrad/mAs]. Values are derived from the manufacturer's recommended technique. Manufacturer/Model Center 1 cm Ratiol Elscint Exel 2400 Elite/E 5.4 11.4 0.47 2400 5.2 11.3 0.46 1800 4.2 10.0 0.42 General Electric 9800 Xenon 4.1 7.4 0.55 9800 Hiliht 3.2 5.9 0.54 Picker 1200SX 6.3 17.5 0.36 IQ Premier 6.2 13.5 0.46 IQ, IQ T/C 6.5 15.0 0.43 PQ2000 6.8 15.0 0.45 Siemens Somatom Plus 4.1 9.6 0.43 Somatom HiQ 5.2 10.7 0.49 Somatom CRX ** 8.0 $ CTDI at center + CTDI at 1 cm depth ** not supplied CHAPTER 3 THE MONTE CARLO TECHNIQUE Introduction The Monte Carlo method is a calculational technique that utilizes random sampling to solve problems numerically that may be difficult or impossible to solve analytically. Radiation transport is simulated in the Monte Carlo technique by following individual particles on a "random walk" through given geometries and media. The term particle, as used here, refers to either photons or electrons. Random numbers are used to sample the probability distributions that describe particle behavior. By recording events of interest that occur during a large number of these random histories, one may accumulate average values for the events or quantities of interest (Cashwell and Everett 1959). In contrast to analytic methods, Monte Carlo simulation can use realistic cross sections, model realistic beam conditions, and model complex geometries (Chilton et al. 1984). The price paid for using the method is lengthy calculational times. Monte Carlo simulation can also assess quantities that cannot be physically measured, e.g., the percentage of dose contributed by Compton interaction recoil electrons (Ito 1988). The Monte Carlo method has been used in the studies of nuclear medicine physics, radiation oncology physics, diagnostic radiological physics, and in radiation protection. Use of the method has increased greatly with the advent of small, powerful computers and the availability of several generalpurpose Monte Carlo codes to the medical physics community (Andreo 1991). As an illustration of the explosive growth the method has seen in the field of radiological physics, consider the following. A review of uses of the method by Raeside in 1976 had 86 references. In 1991 Andreo reviewed work in the field since the Raeside paper and had 299 references in a list ten pages long (!). In the field of diagnostic radiological physics the Monte Carlo method has been used to study both dosimetry and imaging. Dosimetry studies have investigated dose deposition in individual organs from specific radiographic examinations and in anthro pomorphic phantoms. The absorbed dose from chest radiography was estimated using Monte Carlo methods by Koblinger and Zarind (1973). Doi and Chan (1980) used the method to evaluate absorbed dose in film/screen mammography. Morin produced a Monte Carlo model of a CT scanner in 1980 to investigate artifact removal but did not consider patient dose. Dance (1984) used the method to calculate integral dose (energy imparted) in xeromammography. Patient dose from dental radiography was estimated by Gibbs et al. (1984) using a method described by Pujol and Gibbs (1982). In 1983 Beck et al. published a work describing a Monte Carlo model for estimating integral dose in CT examinations. The method used by Beck et al. was based on a simple elliptical, homogeneous phantom and estimated integral dose to large volumes of the phantom. They did not, however, do any direct measurements in a phantom to verify their calculation, and did not take into account fan beam intensity variations. Several investigations have used Monte Carlo methods to estimate organ doses in anthropomorphic phantoms from a wide range of diagnostic radiological procedures. Rosenstein (1976) reported on the use of the Medical Internal Radiation Dose (MIRD) phantom to calculate organ doses from simple radiographic exams. The phantom used simple mathematical expressions to model the shapes and sizes of various internal organs. In 1985 Jones and Wall of the NRPB in the United Kingdom published a study that was similar to Rosenstein's in method. They used the MIRD phantom with modifications suggested by Christy (1980), e.g., breasts were incorporated. The results of the study were similar to Rosenstein's, although some differences occurred and were attributed to differences in xray spectra and phantom geometry. Kramer et al. (1982) at the Gesellschaft fir Strahlenund Umweltforschung (GSF) in Germany produced patient organ dose data based on Monte Carlo simulations with male and female anthropomorphic phantoms (ADAM and EVA), similar to the MIRD phantom. In 1985 Drexler et al. produced a set of tables which allow estimation of organ dose based on calculations with the ADAM and EVA phantoms. The results for simple radiographic exams are similar to those of Rosenstein's and Jones and Wall. In addition, organ dose data for CT were included for pelvis, liver, lung, and head exams. These data were described in Chapter 1. The NRPB study (Jones et al. 1990, Shrimpton et al. 1990) of CT organ doses lists organ doses for a range of standard examinations and CT scanners. Sampling Methods In the Monte Carlo method of numerical analysis, statistical results are obtained by sampling appropriate probability distributions. The general methods with which probability distributions are sampled are described in this chapter. The next chapter describes the specific probability distributions and the sampling methods used in the EGS Monte Carlo system, which is a general purpose, public domain code. The following treatment is based on that of Carter and Cashwell (1975) and Chan (1981). Monte Carlo simulation constructs a set of random samples {xi} based on a set of random numbers (r,} that are uniformly distributed on the unit interval. The samples {xi) are distributed according to a probability density function, or PDF, p(x) such that: p(x) dx = the probability that any x, will lie between x and x+dr. We may also define the cumulative distribution function, or CDF, P(x) in terms of p(x): P(x)= p(y)dy (31) O which is the sum of probabilities of x, falling inside each infinitesimal interval between oo and x. Because the probabilities of mutually exclusive events are additive, P(x) is interpreted as the probability that any given x, is less than x. The function P(x) is non decreasing in x, because p(x)>O for all x. The probability integrated along all possible outcomes is unity. The properties of probability distribution functions and cumulative distribution functions are used in the three sampling methods described below. Inversion Method of Sampling Assume that a given series of events E,, E2,..., E, are mutually exclusive and have probabilities pl, p2,..., p, such that Ep, = 1. Such a series of events may be the type of interaction a photon undergoes the occurrence of a photoelectric absorption, for instance, precludes the occurrence of any other type of interaction. If a random number C, uniformly distributed on the unit interval, is selected such that Pl + P2+..+Pi1 <+P, +..+Pi then the random number C uniquely determines the event E,. Next, a probability density function p(x) can be constructed such that p(x) = p,, with the understanding that x is mapped on the interval 0 < x < n to the events E, ... E,, and that event E, is determined from (i1) < x If the PDF is normalized, the sum of the rectangular areas must be unity. We next define a cumulative distribution function P(x) which is written as P(x) fp(x')dx' (0 and shown in Fig. 32. Obviously P(0) = 0 and P(n) = 1. Also, since P(i) =p, + ... + i, the term P(x) can be interpreted as Pr{( < x}, i.e., the probability that any randomly selected value ofx is less than a given x. Furthermore, if a random number CE [0,1] is selected and the equation = P(x)= p(y)dy (33) 0 1 2 Figure 31: Discrete probability density function. 1 2 n1 Figure 32: Discrete cumulative probability distribution. p(x) 0 E p =1 n P1 P, P, o E, E, is solved for x, x will fall on the interval (i 1) < x < i with frequency p,, thereby determining a value for i and thus determining event E,. The discrete case can be extended to the continuous case (see Figure 33) by making the step size ofp(x) arbitrarily small. If Ax is an infinitesimally small increment of x, and x is given in the range [x,x+Ax], then the CDF is given by definition. That is, as Ax approaches zero, the probability that x falls between x and x+Ax is approximated by P(x + A) P(x) = dP(x) A dr (34) = p(x)Ax. If C is a random number and ifp(x) is defined over the interval a < x = P(x)= p(y)dy (35) a determines x as a function of x representing a random sample of the function p(x). P (x) I I I I x a x x+Ax b P (x + x)  P (x)   I I o x a x x+Ax b Figure 33: top: Continuous probability distribution; bottom: cumulative distribution functions. Rejection Method of Sampling The rejection method was first described by Kahn (1950). The method is used in situations in which the probability distribution function p(x) is bounded and calculable. If p(x) is defined on an interval [a,b] and Mis the maximum value offx) on the interval [a,b], then the function p*(x) can be defined such that p*(x)=p(x)/M. (36) Next, two random numbers, C, and C2 are generated, and x*, a possible value for x, is computed from x* = a + Cl(b a). If 2
the process is repeated. A rigorous proof of the rejection method is given by Spanier and
by Evans (1955). As discussed above, the electron energy is assumed to be absorbed at 