Baixe The Physics of Radiation Therapy - Faiz M. Khan - 3khan e outras Manuais, Projetos, Pesquisas em PDF para Física, somente na Docsity! Editors: Khan, Faiz M. Title: Physics of Radiation Therapy, The, 3rd Edition Copyright ©2003 Lippincott Williams & Wilkins > Table of Contents > Part I - Abasic Physics > 3 - Production of X-Rays 3 Production of X-Rays X-rays were discovered by Roentgen in 1895 while studying cathode rays (stream of electrons) in a gas discharge tube. He observed that another type of radiation was produced (presumably by the interaction of electrons with the glass walls of the tube) that could be detected outside the tube. This radiation could penetrate opaque substances, produce fluorescence, blacken a photographic plate, and ionize a gas. He named the new radiation x- rays. Following this historic discovery, the nature of x-rays was extensively studied and many other properties were unraveled. Our understanding of their nature was greatly enhanced when they were classified as one form of electromagnetic radiation (section 1.9). 3.1. THE X-RAY TUBE Figure 3.1 is a schematic representation of a conventional x-ray tube. The tube consists of a glass envelope which has been evacuated to high vacuum. At one end is a cathode (negative electrode) and at the other an anode (positive electrode), both hermetically sealed in the tube. The cathode is a tungsten filament which when heated emits electrons, a phenomenon known as thermionic emission. The anode consists of a thick copper rod at the end of which is placed a small piece of tungsten target. When a high voltage is applied between the anode and the cathode, the electrons emitted from the filament are accelerated toward the anode and achieve high velocities before striking the target. The x-rays are produced by the sudden deflection or acceleration of the electron caused by the attractive force of the tungsten nucleus. The physics of x-ray production will be discussed later, in section 3.4. The x-ray beam emerges through a thin glass window in the tube envelope. In some tubes, thin beryllium windows are used to reduce inherent filtration of the x-ray beam. A. The Anode The choice of tungsten as the target material in conventional x-ray tubes is based on the criteria that the target must have high atomic number and high melting point. As will be discussed in section 3.4, the efficiency of x-ray production depends on the atomic number, and for that reason, tungsten with Z = 74 is a good target material. In addition, tungsten, which has a melting point of 3,370°C, is the element of choice for withstanding intense heat produced in the target by the electronic bombardment. Efficient removal of heat from the target is an important requirement for the anode design. This has been achieved in some tubes by conduction of heat through a thick copper anode to the outside of the tube where it is cooled by oil, water, or air. Rotating anodes have also been used in diagnostic x-rays to reduce the temperature of the target at any one spot. The heat generated in the rotating anode is radiated to the oil reservoir surrounding the tube. It should be mentioned that the function of the oil bath surrounding an x-ray tube is to insulate the tube housing from high voltage applied to the tube as well as absorb heat from the anode. Some stationary anodes are hooded by a copper and tungsten shield to prevent stray electrons from striking the walls or other nontarget components of the tube. These are secondary electrons produced from the target when it is being bombarded by the primary electron beam. Whereas copper in the hood absorbs the secondary electrons, the tungsten shield surrounding the copper shield absorbs the unwanted x-rays produced in the copper. An important requirement of the anode design is the optimum size of the target area from which the x-rays are emitted. This area, which is called the focal spot, should be as small as possible for producing sharp radiographic images. However, smaller focal spots generate more heat per unit area of target and, therefore, limit currents and exposure. In therapy tubes, relatively larger focal spots are acceptable since the radiographic image quality is not the overriding concern. The apparent size of the focal spot can be reduced by the principle of line focus, illustrated in Fig. 3.2. The target is mounted on a steeply inclined surface of the anode. The apparent side a is equal to A sin θ, where A is the side of the actual focal spot at an angle θ with respect to the electron beam. Since the other side of the actual focal spot is perpendicular to the electron, its apparent length remains the same as the original. The dimensions of the actual focal spot are chosen so that the apparent focal spot results in an approximate square. Therefore, by making the target angle θ small, side a can be reduced to a desired size. In diagnostic radiology, the target angles are quite small (6–17 degrees) to produce apparent focal spot sizes ranging from 0.1 × 0.1 to 2 × 2 mm. In most therapy tubes, however, the target angle is larger (about 30 degrees) and the apparent focal spot ranges between 5 × 5 to 7 × 7 mm. P.29 FIG. 3.1. Schematic diagram of a therapy x-ray tube with hooded anode. P.30 The alternating voltage applied to the x-ray tube is characterized by the peak voltage and the frequency. For example, if the line voltage is 220 V at 60 cycles/sec, the peak voltage will be 220√2 = 311 V, since the line voltage is normally expressed as the root mean square value. Thus, if this voltage is stepped up by an x-ray transformer of turn ratio 500:1, the resultant peak voltage applied to the x-ray tube will be 220√2 × 500 = 155,564 V = 155.6 kV. Since the anode is positive with respect to the cathode only through half the voltage cycle, the tube current flows through that half of the cycle. During the next half-cycle, the voltage is reversed and the current cannot flow in the reverse direction. Thus the tube current as well as the x-rays will be generated only during the half-cycle when the anode is positive. A machine operating in this manner is called the self-rectified unit. The variation with time of the voltage, tube current, and x-ray intensity1 is illustrated in Fig. 3.4. 3.3. VOLTAGE RECTIFICATION The disadvantage of the self-rectified circuit is that no x-rays are generated during the inverse voltage cycle (when the anode is negative relative to the cathode), and therefore, the output of the machine is relatively low. Another problem arises when the target gets hot and emits electrons by the process of thermionic emission. During the inverse voltage cycle, these electrons will flow from the anode to the cathode and bombard the cathode filament. This can destroy the filament. The problem of tube conduction during inverse voltage can be solved by using voltage rectifiers. Rectifiers placed in series in the high-voltage part of the circuit prevent the tube from conducting during the inverse voltage cycle. The current will flow as usual during the cycle when the anode is positive relative to the cathode. This type of P.32 FIG. 3.4. Graphs illustrating the variation with time of the line voltage, the tube kilovoltage, the tube current, and the x-ray intensity for self- or half-wave rectification. The half-wave rectifier circuit is shown on the right. Rectifier indicates the direction of conventional current (opposite to the flow of electrons). rectification is called half-wave rectification and is illustrated in Fig. 3.4. The high-voltage rectifiers are either valve or solid state type. The valve rectifier is similar in principle to the x- ray tube. The cathode is a tungsten filament and the anode is a metallic plate or cylinder surrounding the filament. The current2 flows only from anode to the cathode but the valve will not conduct during the inverse cycle even if the x-ray target gets hot and emits electrons. A valve rectifier can be replaced by solid state rectifiers. These rectifiers consist of conductors which have been coated with certain semiconducting elements such as selenium, silicon, and germanium. These semiconductors conduct electrons in one direction only and can withstand reverse voltage up to a certain magnitude. Because of their very small size, thousands of these rectifiers can be stacked in series in order to withstand the given inverse voltage. Rectifiers can also be used to provide full-wave rectification. For example, four rectifiers can be arranged in the high-voltage part of the circuit so that the x-ray tube cathode is negative and the anode is positive during both half-cycles of voltage. This is schematically shown in Fig. 3.5. The electronic current flows through the tube via ABCDEFGH when the transformer end A is negative and via HGCDEFBA when A is positive. Thus the electrons flow from the filament to the target during both half-cycles of the transformer voltage. As a result of full-wave rectification, the effective tube current is higher since the current flows during both half-cycles. In addition to rectification, the voltage across the tube may be kept nearly constant by a smoothing condenser (high capacitance) placed across the x-ray tube. Such constant potential circuits are commonly used in x-ray machines for therapy. FIG. 3.5. Graphs illustrating the variation with time of the line voltage, the tube kilovoltage, the tube current, and the x-ray intensity for full-wave rectification. The rectifier circuit is shown on the right. The arrow symbol on the rectifier diagram indicates the direction of conventional current flow (opposite to the flow of electronic current). P.33 3.4. PHYSICS OF X-RAY PRODUCTION There are two different mechanisms by which x-rays are produced. One gives rise to bremsstrahlung x-rays and the other characteristic x-rays. These processes were briefly mentioned earlier (sections 1.5 and 3.1) but now will be presented in greater detail. A. Bremsstrahlung The process of bremsstrahlung (braking radiation) is the result of radiative “collision” (interaction) between a high-speed electron and a nucleus. The electron while passing near a nucleus may be deflected from its path by the action of Coulomb forces of attraction and lose energy as bremsstrahlung, a phenomenon predicted by Maxwell's general theory of electromagnetic radiation. According to this theory, energy is propagated through space by electromagnetic fields. As the electron, with its associated electromagnetic field, passes in the vicinity of a nucleus, it suffers a sudden deflection and acceleration. As a result, a part or all of its energy is dissociated from it and propagates in space as electromagnetic radiation. The mechanism of bremsstrahlung production is illustrated in Fig. 3.6. Since an electron may have one or more bremsstrahlung interactions in the material and an interaction may result in partial or complete loss of electron energy, the resulting bremsstrahlung photon may have any energy up to the initial energy of the electron. Also, the direction of emission of bremsstrahlung photons depends on the energy of the incident electrons (Fig. 3.7). At electron energies below about 100 keV, x-rays are emitted more or less equally in all directions. As the kinetic energy of the electrons increases, the direction of x-ray emission becomes increasingly forward. Therefore, transmission-type targets are used in megavoltage x-ray tubes (accelerators) in which the electrons bombard the target from one side and the x-ray beam is obtained on the other side. In the low voltage x-ray tubes, it is technically advantageous to obtain the x-ray beam on the same side of the target, i.e., at 90 degrees with respect to the electron beam direction. The energy loss per atom by electrons depends on the square of the atomic number (Z2). Thus the probability of bremsstrahlung production varies with Z2 of the target material. However the efficiency of x-ray production P.34 FIG. 3.6. Illustration of bremsstrahlung process. FIG. 3.9. Spectral distribution of x-rays calculated for a thick tungsten target using Equation 3.1. Dotted curves are for no filtration and the solid curves are for a filtration of 1-mm aluminum. (Redrawn from Johns HE, Cunningham JR. The physics of radiology, 3rd ed. Springfield, IL: Charles C Thomas, 1969, with permission.) TABLE 3.1. PRINCIPAL CHARACTERISTIC X-RAY ENERGIES FOR TUNGSTEN Series Lines Transition Energy (keV) K Series Kβ2 NIII – K 69.09 Kβ1 MIII – K 67.23 Kα1 LIII – K 59.31 Kα2 LII – K 57.97 L Series Lγ1 NIV – LII 11.28 Lβ2 NV – LIII 9.96 The purpose of the added filtration is to enrich the beam with higher-energy photons by absorbing the lower- energy components of the spectrum. As the filtration is increased, the transmitted beam hardens, i.e., it achieves higher average energy and therefore greater penetrating power. Thus the addition of filtration is one way of improving the penetrating power of the beam. The other method, of course, is by increasing the voltage across the tube. Since the total intensity of the beam (area under the curves in Fig. 3.9) decreases with increasing filtration and increases with voltage, a proper combination of voltage and filtration is required to achieve desired hardening of the beam as well as acceptable intensity. The shape of the x-ray energy spectrum is the result of the alternating voltage applied to the tube, multiple bremsstrahlung interactions within the target and filtration in the beam. However, even if the x-ray tube were to be energized with a constant potential, the x-ray beam would still be heterogeneous in energy because of the multiple bremsstrahlung processes that result in different energy photons. Because of the x-ray beam having a spectral distribution of energies, which depends on voltage as well as filtration, it is difficult to characterize the beam quality in terms of energy, penetrating power, or degree of beam hardening. A rule of thumb is often used which states that the average x-ray energy is approximately one-third of the maximum energy or kVp. Of course, the one-third rule is a rough approximation since filtration significantly alters the average energy. Another quantity, known as half-value layer, has been defined to describe the quality of an x-ray beam. This topic is discussed in detail in Chapter 7. Lβ1 MIV – LII 9.67 LαI MV – LIII 8.40 Lα2 MIV – LIII 8.33 Data from U.S. Department of Health, Education, and Welfare. Radiological health handbook. Rev. ed. Washington, DC: U.S. Government Printing Office, 1970. TABLE 3.2. CRITICAL ABSORPTION ENERGIES (keV) Level Element H C O Al Ca Cu Sn I Ba W Z 1 6 8 13 20 29 50 53 56 74 K 0.0136 0.283 0.531 1.559 4.038 8.980 29.190 33.164 37.41 69.508 3.6. OPERATING CHARACTERISTICS In this section, the relationships between x-ray output, filament current, tube current, and tube voltage are briefly discussed. L 0.087 0.399 1.100 4.464 5.190 5.995 12.090 Data from U.S. Department of Health, Education, and Welfare. Radiological health handbook. Rev. ed. Washington, DC: Printing Office, 1970. FIG. 3.10. Illustration of typical operating characteristics. Plots of relative exposure rate versus a, filament current at a given kVp; b, tube current at a given kVp; and c, tube voltage at a given tube current. P.37