Farr's Physics for Medical Imaging (PDF) - Radiation Physics

1 RADIATION PHYSICS Diagnostic imaging employs radiations - X, gamma, radiofrequency and sound - to which the body is partly but not completely tra...

1 RADIATION PHYSICS Diagnostic imaging employs radiations - X, gamma, radiofrequency and sound - to which the body is partly but not completely transparent. IONIZING RADIATION (X-rays and gamma rays) are used most 1.1 STRUCTURE OF THE ATOM Relative mass Relative charge Symbol Nucleons Neutron 1 0 n Proton 1 +1 p Extranuclear Electron 1 -1 e-,β- 1840 Other Positron 1 +1 e+ , β + 1840 Alpha 4 +2 α particle Table 1.1 Some fundamental particles The diameter of the nucleus of an atom is about 5 x 10-15 m. The diameter of the entire atom is about 5 x 10-10 m (100,000 times larger) ∴ Most of an atom is an empty space. Rutherford and Bohr model → an atom is a massive positively charged nucleus sur- rounded by electrons in orbits of specific diameters. NUCLEUS: Has a positive electrical charge, and contains almost all the mass of an atom. Made of several types of particles "NUCLEONS" only protons & neutrons considered. The proton has a positive electric charge numerically equal to the charge of the electron, while the neutron has zero electrical charge. The neutron and proton have about the same mass (1.66 x 10-24 gm), which is approximately 1840 times greater than the mass of an electron. The atomic number of the atoms "Z" = the number of protons in the nucleus → synonymous with element name. The mass number "A" = the total number of protons and neutrons in the nucleus. Gold (Au) has a nucleus with 79 protons (Z = 79) and 118 neutrons (A = 197) All atoms of an element have the same atomic number (Z), but may have different mass numbers (isotopes). ISOTOPES have the same number of protons in the nucleus "same atomic number" but have different numbers of neutrons "different mass numbers". 8 12C refers to a carbon atom with A = 12 & Z = 6 → shortened 12 C "Carbon-12". 6 8 Carbon-14 still has Z = 6 but has two more neutrons → unstable and radioactive. It is called a Radionuclide. 2 ELECTRON ORBITS AND ENERGY LEVELS: Fig. 1.1 Electron shells in a sodium atom. An atom is composed of a central positive nucleus + electrons with negative charges revolving around the nucleus in circular orbits. A neutral atom contains an equal number of protons and electrons. The electron orbits are designated by letters: K, L, M, N, O, and so on. The atomic system allows 2 electrons in the first orbit, 8 in the second, 18 in the third, 32 in the fourth, and 50 in the fifth (2N2). An electron in the K shell is called a K electron. L electrons are in the L shell. ¾ Valence shell: 8 Outermost shell. 8 Concerned with the chemical, thermal, optical & electrical properties of the element. 8 Can't have more than 8 electrons (called 'free electrons'). X-rays involve the inner shells, and radioactivity concerns the nucleus. The diameters of the electronic shells are determined by the nuclear force on the electron, and by the angular momentum and energy of the electron. BINDING ENERGY: The "binding force" of the electron = the attractive force between the positively charged nucleus and the negatively charged electron, that keeps the electrons in the atom. The binding force is inversely proportional to the square of the distance between the nucleus and electron → K electron has a larger binding force than an L electron. Binding energy = the energy expended in completely removing the electron from the atom against the attractive force of the positive nucleus → expressed in electronvolts (eV). 8 Never greater than 100 keV. 8 The binding energy depends on 1. The shell (EK > EL > EM …). 2. The element (↑ Atomic number → ↑ binding energy) For example; In the case of tungsten (W; Z = 74) the binding energies of different shell are EK EL EM 70 11 2 keV In the case of the K shell, the binding energies of different elements are W (Z = 74) I (Z = 53) Mo (Z = 42) Cu (Z = 29) 70 33 20 9 keV 3 An electron cannot have any more or less energy than shell energy, but electron may jump from one energy shell to another "higher or lower" energy shell 8 Electron movement to a lower energy shell results in the emission of energy. 9 Emitted energy = the difference in the binding energy between the two shells. 9 The energy may take the form of an x ray photon. 8 Electron movement to a higher energy e.g. absorption of an x-ray photon. Each atomic energy shells, except K, has SUBSHELLS of slightly different energies Ionisation & Excitation: Ionized atom → if one of its electrons has been completely removed → ion pair "electron + positive ion" Excited atom → if an electron is raised from one shell to a farther one with the absorption of energy → the atom has more energy than normal. When it falls back → energy is re-emitted as a single 'packet' of energy or light photon. 1.2 ELECTROMAGNETIC RADIATION Energy traveling across empty space ¾ All EMR travel with velocity (c) of light in vacuo "3 x 108 m\sec". ¾ Named according to the way of production and the special properties they possess. e.g. X-rays (emitted by X-ray tubes) & gamma rays (emitted by radioactive nuclei) have essentially the same properties and differ only in their origin. Quantum aspects: Electromagnetic radiation is a stream of 'packets' or quanta of energy "PHOTONS" traveling in straight lines. Wave aspects: EMR is sinusoidally varying electric & magnetic fields traveling with velocity c when in vacuo. They are transverse waves; with the electric and magnetic field vectors point at right angles to each other and to the direction of travel of the wave. Fig. 1.2 Electromagnetic wave. Field strength versus (a) time and (b) distance. Definitions: Amplitude (A) = the peak field strength. The Period (T) = the time interval between successive crests of the wave. The Wavelength (λ) = the distance between successive crests of the wave. The frequency (f) = the number of crests passing a point in a second. f=1/T Wavelength and frequency are inversely proportional to each other, wavelength x frequency = constant (velocity) 4 The types of radiation are listed in Table 1.2, in order of increasing photon energy, increasing frequency, and decreasing wavelength. Wavelength Frequency Energy Radio waves 30-6 m 10-50 MHz 40-200 neV Infrared 10000-700 nm 30-130 THz 0.12-1.8 eV Visible light 700-400 nm 430-750 THz 1.8-3 eV Ultraviolet 400-100 nm 750-3000 THz 3-12 eV 6 6 X- and gamma 60-2.5 pm 5 x 10 –120 x 10 THz 20-500 keV When the energy is less than 1 keV the radiation is usually described in terms of its frequency, except that visible light → described in wavelength. Only radiations at the ends of the spectrum penetrate the human body sufficiently to be used in imaging → radio waves and X- or gamma rays. N.B. sound is a mechanical wave not an electromagnetic wave (MCQ). PHASE Two objects are said to move in synchronism when their phase difference is constant. The two sine waves in Fig. 1.2a are out of phase. They have the same period or frequency but the dashed curve lags behind the solid curve "i.e. reaching its maximum at a later time". Phase difference = the time interval between their peaks expressed as an angle, lying between 0 and 360°, on a scale which makes the period T correspond to 360°. In single-phase mains supply → the current rises and falls as a single sine wave. In a three-phase supply → the current rises and falls as three sine waves having phase differences of 120°. Wave and quantum theories combined Photon energy is proportional to the frequency. The constant of proportionality is called Planck's constant (h). Thus, E = h f Since frequency is inversely proportional to wavelength, so also is photon energy: E (in keV) = 1.24 / λ (in nm) For example: Blue light λ = 400nm E = 3 eV Typical X- and gamma rays λ = 0.1 nm E = 140 keV Intensity Radiation travels in straight lines "= RAYS" radiating in all directions from a point source. BEAM = a collimated set of rays (Fig. 1.3a). The photon fluence at the point = the number of photons per unit area passing through the cross section in the time. The energy fluence at the point = the total amount of energy "the sum of the energies of all the individual photons" per unit area passing through the cross-section in the time. 5 The energy fluence rate at the point (= beam intensity) is the total amount of energy per unit area passing through the cross-section per unit time (watts per square millimeter). Intensity is proportional to the square of the amplitude (A), see Fig. 1.2. Energy fluence and intensity are not easy to measure directly. Instead, an easier indirect measurement is made: : 'Air kerma' instead of energy fluence. : "Air kerma rate" instead of intensity. INVERSE SQUARE LAW The intensity of the radiation is inversely proportional to the square of the distance from a point source When the distance is changed: New intensity (Old distance)2 = Old intensity (New distance)2 or New air kerma rate (Old distance)2 = Old air kerma rate (New distance)2 ∴ Halving the distance quadruple's the intensity or air kerma rate & doubling the distance reduces them by a factor of 4. N.B. Only the intensity of the x-ray will decrease with distance but the energy of the photons not change. 6 PRODUCTION OF X RAYS X-RAY GENERATORS X-ray generator is the device that supplies electric power to the X-ray tube. Two sources of electrical energy are required and are derived from the alternating current (AC) mains by means of transformers. Figure l.4 shows: 8 The filament heating voltage (about 10 V) and current (about 10 A), → produced by a step-down low-voltage transformer → for heating of the filament. 8 The accelerating voltage (30-150 kV) between the anode and cathode ('high tension', 'kilovoltage', or 'kV'), produced by a high-voltage transformer. → accelerates the current of electrons (typically 0.5-1000 mA) flowing between the anode and cathode ('tube current', 'milliamperage', or 'mA'). The mA is controlled by varying the filament temperature. A small ↑ in filament temperature, voltage, or current → large ↑ in tube current kV & mA can be varied independently in the X-ray set. The anode-cathode voltage = kVp or kV. THE WAVEFORM & RECTIFICATION: Rectification is the process of changing alternating current into direct current. Using an alternative current for X-ray tube → makes electrons moves in one half of the cycle from the cathode to anode, in the other half of cycle the electrons with move in opposite direction → undesirable, because: 1. ↑↑ heating of the filament → ↓↓ lifetime. 2. wouldn't produce useful X-ray. Figure 1.5 depicts the waveforms of 4 types of high-tension voltage supply: 1. Alternating voltage ('self-rectification'). 2. Pulsating direct current (DC) ('full wave rectification, single-phase'). 3. 'Constant potential', which is steady DC with a small ripple from a 'three-phase' generator. 4. High frequency which is steady DC with negligible ripple. 7 DIAGNOSTIC X-RAY TUBES X rays are produced by energy conversion when a fast-moving stream of electrons is suddenly decelerated in the "target" anode of an x-ray tube. X-ray tube is made of Pyrex glass encloses vacuum & contain 2 electrodes (diode tube). Electrodes are designed so that electrons produced at cathode (-ve electrode or filament) accelerated by high potential difference toward the anode (+ve electrode or target) Electrons are produced by the heated tungsten filament and accelerated across the tube by the accelerating tube voltage to hit the tungsten target → x rays production. Figure 2-1: The major components of a stationary anode x-ray tube GLASS ENCLOSURE Necessary to seal the two electrodes of the x-ray tube in a vacuum. Vacuum → allow number & speed electrons to be controlled independently. The connecting wires must be sealed into the glass wall of the x-ray tube. Special alloys, having approximately the same coefficients of linear expansion as Pyrex glass, are generally used in x-ray tubes. CATHODE The negative terminal of the x-ray tube. Composition of the cathode: 8 The filament, which is the source of electrons for the x-ray tube. Tungsten wire, 0.2 mm in diameter coiled into a vertical spiral 0.2 cm in diameter and 1 cm in length 8 The connecting wires. 8 A metallic focusing cup. The number (quantity) of x rays produced depends entirely on the number of electrons that flow from the filament to the target (anode) of the tube. The x-ray tube current is measured in milliamperes (1 mA = 0.001 A). & refers to the number of electrons flowing per second from the filament to the target For example, in a given unit of time, a tube current of 200 mA is produced by twice as many electrons as a current of 100 mA, and produces twice as many x rays. Where these electrons come from? → "THERMIONIC EMISSION" Def.: the emission of electrons resulting from the absorption of thermal energy. A pure tungsten filament must be heated to a temperature of at least 2200° C to emit a useful number of electrons (thermions). 8 Tungsten is not as efficient an emitting material as alloys of tungsten, for example. 8 8 But, it is chosen for use in x-ray tubes, because: 1. It can be drawn into a thin wire that is quite strong. 2. Has a high melting point (3370° C). 3. Has little tendency to vaporize. ∴ Tungsten filament has a reasonably long life expectancy. When current flows through tungsten wire → heated → its atoms absorb thermal energy → some of the electrons acquire energy → move small distance from the metal surface → form a small cloud in the vicinity of the filament "the space charge". The electron cloud, produced by thermionic emission, also termed "Edison effect". SATURATION VOLTAGE If the potential applied across the tube is insufficient to cause almost all electrons to be pulled away from the filament when they are emitted → Space Charge Effect: cloud of negative charges tends to prevent other electrons from being emitted from the filament until they have acquired sufficient thermal energy to overcome the force caused by the space charge → limit the number of electrons → limits X-ray tube current. Figure 2-7: Saturation voltage Below the saturation point, The tube current is limited by the space charge effect (space-charge-limited). ↑↑ kV → significant ↑↑ in x-ray tube current although filament heating is the same. Above the saturation voltage, The space charge effect has no influence on the x-ray tube current. The tube current is determined by the number of electrons made available by the heated filament (emission-limited or temperature-limited). ↑↑ kV → very little change in tube current THE AMPERE 8 The unit of electric current. 8 Def.: the "flow" of 1 coulomb of electricity through a conductor in 1 sec. 8 The coulomb = the amount of electric charge carried by 6.25 x 1018 electrons. Therefore, an x-ray tube current of 100 mA (0.1 A) may be considered as the "flow" of 6.25 x 1017 electrons from the cathode to the anode in 1 sec. Electron current across an x-ray tube is in one direction only (always cathode to anode). 9 Cathode focusing cup: 8 Surrounds the filament & maintained at the same negative potential as the filament. So, its electrical forces cause the electron stream to converge onto the target anode in the required size and shape → prevent bombardment of a large area on the anode caused by mutual repulsion of the electrons (Figs. 2-2 and 2-4). 8 The focusing cup is made of nickel. 8 Modern x-ray tubes may be supplied with a single or, more commonly, a double filament (Fig. 2-2). Vaporization of the filament when it is heated: 8 Filament becomes too thin → break up "acts to shorten the life of an x-ray tube". 8 Tungsten is deposited on the inner surface of the glass wall of the x-ray tube → produces bronze-color "sunburn". This tungsten coat has two effects: 1. Filter the x-ray beam. 2. Increases the possibility of arcing between the glass and the electrodes at higher kilovoltage (kVp) values → tube puncture. ANODE: Anodes (positive electrodes) of x-ray tubes are of two types, stationary or rotating. Figure 2-4 Stationary Anode: Consists of a small plate of tungsten "target" embedded in a large mass of copper. Target is 2-3 mm thick, square or rectangular in shape, >1 cm in dimensions. The anode angle is usually 15 to 20°. Tungsten is chosen as the target material for several reasons. 1. It has a high atomic number (74) → more efficient for the production of x rays. 2. Withstand the high temperature produced "high melting point = 3370° C". 3. Reasonably good for the absorption & rapid dissipation of heat. However, it cannot withstand the heat of repeated exposures → the massive copper anode acts to ↑↑ the total thermal capacity of anode and to speed its rate of cooling. The actual size of the tungsten target > the area bombarded by the electron stream (Fig. 2-4) because copper has a relatively low melting point (1070° C) → the heat produced could melt the copper in the immediate vicinity of the target. Tungsten and copper have different expansion coefficient on heating → needs 10 satisfactory bonding otherwise the tungsten target would peel away from copper anode. 2.7.2 ROTATING ANODE TUBE Rotating anode is used to produce x-ray tubes capable of withstanding the heat generated by large exposures. The anode assembly, seen in cross-section, consists of: 9 An anode disk, 7-10 cm or more in diameter. 9 A thin molybdenum stem. 9 A blackened copper rotor "part of the induction motor which rotates the target stem". 9 Bearings, lubricated with a soft metal such as silver. 9 An axle, sealed into the glass envelope, which supports the target assembly. Figure 2-6: The rotating anode x-ray tube The anode of a rotating anode tube consists of a large disc of tungsten or an alloy of tungsten "tungsten-rhenium alloy" → better thermal characteristics than pure tungsten and does not roughen with use as quickly. Typical disc diameters measure 75, 100, or 125 mm. The diameter of the tungsten disc determines the total length of the target track→ affects the maximum permissible loading of the anode. The anode rotates at a speed of about 3600 revolutions per minute (rpm) using single- phase mains supply. Any area of the tungsten disc is found opposite the electron stream only once every 1/60 sec & during the remainder of the time heat generated during the exposure can be dissipated. High-speed anodes are energized with three-phase mains & rotate at about 9000-17000 rpm. The tungsten disc has a beveled edge. The angle of the bevel may vary from 6 to 20°. The bevel is used to take advantage of the line focus principle. The purpose of the rotating anode is to spread the heat produced during an exposure over a large area of the anode while the apparent or effective focal spot size has remained the same. 11 To make the anode rotate, some mechanical problems must be overcome: Power to the rotating anode → Stator coils. Lack of durable bearings → Metallic lubricants e.g. silver. Heat dissipation → Molybdenum stem. Inertia → short stem, using 2 sets of bearings & ↓ anode weight by using an anode made of molybdenum (lighter than tungsten) + target made of tungsten-rhenium alloy. Roughening & pitting of anode surface, which ↑↑ target scatter & X-ray absorption in target itself → target made of tungsten-rhenium alloy, anode discs with grooves on the target surface & coating the back of anode disc with black substance e.g. carbon. How the anode cools 8 Heat produced on the focal track → conducted quickly and stored temporarily in the anode disk → transferred by radiation to the insulating oil → stored temporarily then transferred by convection to the housing → lost by radiation and by fan-assisted convection through the surrounding air. 8 The molybdenum stem is sufficiently long and narrow to control the amount of heat that is conducted to the rotor → so that it is not in danger of overheating. Heat radiation is promoted by blackening the anode assembly. High-powered tubes used in CT & angiography pump the oil through external heat exchanger GRID-CONTROLLED X-RAY TUBES Conventional x-ray tubes contain two electrodes (cathode and anode). The grid-controlled tube has a 3rd electrode → control the flow of electrons from the filament to the target. The third electrode is the focusing cup that surrounds the filament. In conventional x-ray tubes a focusing cup is electrically connected to the filament. In the grid-controlled tube, the focusing cup is electrically negative relative to the filament ‫اكثر سلبيه‬. 8 The voltage across the filament-grid produces an electric field along the path of the electron beam → pushes the electrons even closer together. 8 If the voltage is large enough → the tube current may be completely pinched off "act like a on & off switch for the tube current → used in cinefluorography". TUBE SHIELDING AND HIGH-VOLTAGE CABLES X-rays are emitted with equal intensity in every direction from the target. In addition, the x rays are scattered in all directions following collisions with various structures in and around the tube. The tube housing is lined with lead except a plastic window through which useful X-ray beam emerges → absorb 1ry and 2ry x-rays that would otherwise produce a high intensity of radiation around the tube → needless exposure of patients and personnel + excessive film fogging. The effectiveness of the tube housing in limiting leakage radiation must meet the specifications listed in The National Council of Radiation Protection and Measurements Report No. 49, which states that: "The leakage radiation measured at a distance of 1 meter from the source shall not exceed 100 mR in 1 hour when the tube is operated at its 12 maximum current & maximum tube potential". Another function of the tube housing "Mineral oil around the tube" → provide shielding for the high voltages & prevent short- circuiting between the grounding wires and the tube. Other aspects of tube and generator design 8 The glass insert is immersed in oil → 1) convects heat away from the tube & 2) act as an electrical insulator for tube. 8 The high tension and filament transformers are contained in oil-filled earthed metal tank and connected to the tube housing by a pair of highly insulated flexible cables. 8 Dental X-ray tube: low-powered - small - stationary anode tube. 2.7 LIMITATIONS OF THE X-RAY TUBE There are two important limiting factors in imaging with X-rays: 1. The dose of radiation delivered to the patient, and 2. The heat which inevitably accompanies the production of X-rays. If heat accumulate in X-ray tube → shorten or damage the tube. 2.7.1 LINE FOCUS PRINCIPLE The actual focal spot is the area of the tungsten target bombarded by electrons from the cathode→ the area over which heat is produced and which determines the tube rating (see Section 2.7.3). The size and shape of the focal spot are determined by the size and shape of the electron stream when it hits the anode. The size and shape of the electron stream are determined by 1) the dimensions of the filament tungsten wire coil, 2) the construction of the focusing cup "also called electron lens", and 3) the position of the filament in the focusing cup. The problems posed by 1) The need for a large focal spot to allow greater heat loading. 2) The conflicting need for a small focal area to produce good radiographic detail, as larger focal area will lead to blurring of the image "geometrical blurring". The line focus principle (Figure 2-3) → the surface of target is inclined so that it forms an angle with the plane ⊥ to incident beam. The target anode angle = 6 - 20°. If it is 17° and the effective focal spot is 1 x 1 mm, the actual focal spot must be 4x1 mm. 13 This angulation makes the effective 'or apparent' focal spot BC foreshortened & is considerably smaller than that of the actual focal spot & is square in shape. This makes the focal spot blurring small and fixed whatever the orientation of a structure. The effective focal spot varies across the film → elongated from the cathode side of the film & contracted from the anode side. Angle θ → the angle between the central ray and the target face The size of the projected focal spot is directly related to the sine of the angle of the anode. ∴ The smaller the angle of the anode, the smaller the apparent focal spot TAKE CARE: The steeper the target for the same actual focal spot and target heat rating → the smaller the effective focal spot. The steeper the target for the same effective focal spot → the larger the actual focal spot and target heat rating. The steeper the target → the narrower the useful X-ray beam and the smaller the field covered. Some newer 0.3-mm focal spot tubes may use an anode angle of only 6°. Ë There is a limit to which the anode angle can be decreased as dictated by the heel effect (the point of anode cutoff). MCQ: For general diagnostic radiography done at a 40-inches focus-film distance (1 m), the anode angle is usually no smaller than 15°. Focal spot size is expressed in terms of the apparent or projected focal spot; sizes of 0.3, 0.6, 1.0, and 1.2 mm are commonly employed. Usually, an X-ray tube has two filaments and two focal spots of different sizes which are selected from the control panel. The smaller focal spot is selected where small fields are needed & for better resolution "in mammography and in cineradiography with a small field image intensifier" and the larger one for thicker parts of the body where a greater intensity of X-rays is needed "in general radiography using large films" (Table 2.1). Table 2.1 Typical effective focal sizes (mm) Macromammography 0.1 Mammography 0.3 Macroradiography 0.3 Radiography 0.6-1.2 Fluoroscopy 0.6 MCQ X-ray output DOES NOT depend on focal size, only sharpness and effective field of view do. MEASUREMENT OF THE EFFECTIVE FOCAL SPOT There are two principal methods of measuring the effective focal spot. 14 'PINHOLE CAMERA': This consists of a hole drilled in a disk of heavy metal, such as gold, incorporated in a lead sheet. Must be positioned half way between the focal spot and the film. The pinhole is may be positioned closer to the tube anode than to the cassette → magnified image of the effective focal spot → knowing the magnification enables the true size of the effective focal spot to be calculated. It is important to align the pinhole to central beam of the X-ray tube accurately. The pinhole must be several times smaller than the focal spot (e.g. pinhole of 0.03 mm for focal spots below 1mm, and 0.08 mm for focal spots from 1 to 2.5 mm). Although X-rays diverge in all directions from each point on the target, only one of them passes through the pinhole, and it produces a dot of blackening on the film. Notice the following: Pinhole size of 0.03mm is very small, so special equipments are needed for accurate measurement. Intensity is more towards periphery of the focal spot (edge band distribution → commonest pattern, though undesired). The resulting image (Fig. 2.12b) shows: a. The size & shape of the effective focal spot. b. Density pattern represents intensity distribution & any lack of uniformity is shown. c. Reveals any extra-focal X-radiation "which degrades image. STAR TEST TOOL: This technique is used in measuring focal spots less than 0.3 mm A 'star test' tool comprises a number of tapered 'spokes' of lead mounted on a Perspex disk (Figure). This is mounted partway between the film and the tube (not in contact with film). 15 Exposure produces a magnified and unsharp image of the star (Fig. 2.13b), shows following features: 1. RING OF BLURRING → Diameter of ring is used to calculate the effective focal spot size. 2. Outside this ring a sharp NEGATIVE image is produced. 3. Paradoxically, inside the ring there is a POSITIVE and sharp image of the spokes. Fig. 2.13: Measurement of the effective focal spot with a 'star test' tool, (a) The star test tool, (b) Image with a blurring diameter Blooming 9 Blooming = unwanted increase in focal spot size which occurs when the tube is operated at high milliamperage. 9 Occurs because the negative charge of the focusing cup is less effective, so electrons emitted from the filament are not well focused in a regular beam → hit a larger area > actual focal spot. 9 It occurs particularly at low kV values and with small focal spots. Regarding focal spot: The focal spot size can limit the spatial resolution "geometric unsharpness", depends on the location of the object in the source-to-detector direction. The resolution impact of the focal spot increases with geometric magnification, i.e. increasing distance between the object and the film or detector if FFD is fixed. Thus, a small focal spot is desired in order to optimize spatial resolution. The focal spot size also sets the upper limit on X-ray tube current or output rate (heat loading). If an X-ray tube is operating at its instantaneous power limit, decreasing the size of the focal spot will require a decrease in the tube current (radiation output). ∴ There is a trade-off between spatial resolution due to the size of the focal spot & image noise in a fixed exposure time due to the decreased X-ray intensity and imaging time. 2.7.4 UNIFORMITY OF THE X-RAY BEAM The useful X-ray beam is taken in a direction perpendicular to the electron stream "at right angles to the tube axis from the center of the focal spot ". (B in Fig. 2.15). → It is usually pointed toward the center of the area of interest in the body. S Toward the anode edge of the field, the beam A is cut off by the face of the target. Toward the cathode edge, the beam C is cut-off by the edge aperture in the lead shield. S Thus, the X-ray field is made symmetrical around the central ray B, → A and C are the limits of the useful beam. In fact the useful beam is narrower than suggested because of THE HEEL EFFECT. 16 Fig. 2.15 Heel effect. THE HEEL EFFECT The intensity of the x-ray beam that leaves the x-ray tube is not uniform but depends on the angle at which the x rays are emitted from the focal spot. Mechanism: 9 Electrons penetrate a few micrometers into the target before being stopped by a nucleus → so; the X-rays produced are attenuated and filtered by the target material on their way out. 9 X-rays traveling toward the anode edge of the field have more target material to cross → ∴attenuated more than those traveling toward the cathode edge → the intensity of the beam decreases toward the anode end of the fields (Less importantly, the HVL increases because of the filtration effect). Factors affecting the heel effect: 1. Anode angle: the steeper the target → ↑↑ heel effect. 2. FFD: ↑↑ FFD → ↓↓ heel effect "with fixed film size". 3. Film size: ↓↓ film size → ↓↓ heel effect "with fixed FFD". 4. Roughening of the target surface → ↓↓ X-rays output & ↑↑ the heel effect. In radiographs of body parts of different thicknesses → the thicker parts should be placed toward the cathode (filament) side of the x-ray tube. e.g. AP film of the thoracic spine → anode end over the upper thoracic spine where the body is less thick & the cathode end of the tube is over the lower thoracic spine where thicker body structures will receive the increased exposure. 2.7.3 HEAT RATING The heat loading of an X-ray tube (calculated in joules) = kV x mAs for a constant potential (three phase). = 0.7 x kV x mAs for a pulsating single-phase generator. 17 Single radiographic exposure In order to 'freeze' and display movement, individual exposures should be as short as the heating of the X-ray tube permits. The allowable mAs at a particular kV increase as the exposure time is lengthened (MCQ). Any combination of kV, mA, and exposure time should be such that, at end of the exposure, the temperature of the anode does not exceed its safe value, i.e. there should be no risk of the target melting, vaporizing or roughening. The rating is usually stated as the allowable mA, and this: 9 Decreases as the exposure time is increased. 9 Decreases as the kV is increased. 9 Increases with the effective focal spot size (because increase effective focal spot means increase actual focal spot for a fixed anode angle)…and, Increases with smaller target angles for a fixed effective focal spot, (Drawing above explain it, because the actual focal spot then larger). 9 Is greater for a rotating than a stationary anode. 9 Is greater for a 10 cm disk than a 7 cm disk. 9 Is greater for a high-speed anode. 9 Is greater for a three-phase constant potential than for a single-phase pulsating potential - because the former produces heat more evenly throughout the exposure. The foregoing information is stored on a microprocessor in the control circuit which prevents any exposure being made which would exceed the rating of the tube. Repeated radiographic exposures To display movement, e.g. angio- or cineradiography, a rapid series of exposures is made. Each exposure must be sufficiently short & within the rating of the focal area. For repeated exposures → depends also on the ability of the anode assembly and the oil to accumulate heat → both not allowed to exceed its maximum safe temperature. The rapidity with which a series of such exposures can be made depends on: a) ‫ س عة التخ زين‬The maximum amount of heat that can be temporarily stored in the anode in particular & the tube housing as a whole; and b) ‫ سرعة التوزيع‬The rate at which they lose heat by cooling. The heat storage capacity of the anode may be increased by soldering to the back of the tungsten plate a disk of molybdenum and/or solid graphite (both have a higher heat capacity per unit mass than tungsten). Microprocessor in control circuit calculates the max. total number of exposures allowed. If the anode heat capacity (typically 0.2 MJ) has been reached → need at least 15 min to cool down completely; & the entire assembly (typical heat capacity 1.0 MJ) may need an hour. 18 Continuous operation: fluoroscopy Heat must be removed at the same rate as it's produced from the housing "not allowed to accumulate in the oil". ∴ The rating depends only on the cooling rate (and whether or not the fan is on) and NOT at all on the focal spot size or the type of generator. In fluoroscopy the anode is stationary or rotating at reduced speed, to ↓ bearing wear. Other ratings: Maximum kV also depends on the insulation of the tube, cables, etc. Maximum mA → is low at a low kV than at a high kV (d.t. 'space charge effect'). N.B. allowable mA (tube rating) is low at high kV. 2.7.5 QUALITY ASSURANCE OF EXPOSURE PARAMETERS ∼ At installation; each X-ray tube and generator should be checked for compliance to a certain specification. ∼ X-ray generators need to be checked periodically → for exposure parameters (e.g. kV and mAs), and tube parameters (e.g. focal spot and filtration). More details in Section 3.8 Focal spot and filtration Focal spot should be measured at installation. If the HVL and the kV measured carefully → the total filtration can be deduced from a set of published graphs. Kilovoltage and output The kV can either be measured: 9 Directly (invasively) by potential divider applied across the high tension leads 9 Indirectly (non-invasively) by a penetrameter method. A calibrated electronic penetrameter is placed in the beam → compares the differentially filtered response of detectors contained within it → gives equivalent kV. The tube output → measured by a dosemeter, often an ionization chamber. For constant mAs, the output is a function of kVX. "X ≈ 2". For a constant kV, the output is a linear function of mA and exposure time. Field definition and uniformity The size of the X-ray field is delineated using lead diaphragms + a light beam incorporated in overcouch tube. Regular checks should be made to ensure that: a. The light beam and field outline match. b. The center of the field, on the cross wires of the light beam diaphragm, coincides with the center of the X-ray field. The extent of the heel effect and field non uniformity can be measured by exposing a large, plain film and measuring the density differences across the field. 19 PROCESSES OCCURRING IN THE TARGET OF AN X-RAY TUBE Each electron arrives at the surface of the target with a kinetic energy (in kiloelectronvolts "keV") = the kV between the anode and cathode. INTERACTION WITH THE K-SHELL: LINE SPECTRUM, CHARACTERISTIC RADIATION 8 Electron (a) from the filament collides with an electron (b) in the K-shell of an atom → ejected from the atom, provided that the energy of the bombarding electron is greater than the binding energy of the shell. 8 The remaining energy is shared between the initial electron & the ejected electron → both leave the atom 8 The hole created in the K-shell is most likely to be filled by an electron (c) falling from the L-shell → emission of a single X-ray photon (d) of energy equal to the difference in the binding energies of the two shells, EK - EL. The photon is referred to as Kα radiation. Fig. 1.6 Production of characteristic radiation. 8 Alternatively, but less likely, the hole may be filled by an electron falling from the M-shell → emission of a single X-ray photon of energy EK - KM. (Kβ radiation) In the case of the usual target material, Tungsten "W" (Z = 74), EK = 70 keV, EL = 12 keV, and EM = 2 keV. ∴ Kα radiation has photon energy of 58 keV & Kβ radiation has photon energy of 68 keV. The x-ray photon energy is a "characteristic" of the K shell of a tungsten atom regardless of the energy of the electron that ejected the K-shell electron 20 L-radiation → if hole created in the L-shell is filled by an electron from farther shell. Even in the case of tungsten, L-radiation photons have only energy = 10 keV → insufficient to leave the X-ray tube assembly "no part in radiology". Characteristic X-ray photons have discrete photon energies → line spectrum. In the case of another target material, Molybdenum (Z = 42), EK = 20 KeV, EL = 2.5 keV ∴ Kα radiation has a photon energy of 17.5 keV & Kβ radiation has a photon energy of 20 keV. ∴ The energy of the K-radiation photons: 1. Increases → with ↑ atomic number of the target. 2. It is characteristic of the target material. 3. Not affected by the tube voltage, except that: A K-electron cannot be ejected if the peak tube voltage is less than EK. The rate of production of the characteristic radiation increases as the kV is increased above this value. Contribution of characteristic radiation to the total production of x rays? 1. Below 70 kVp → no K-shell characteristic radiation. 2. Between 80 and 150 kVp → K-shell characteristic radiation contributes about 10% (80 kVp) to 28% (150 kVp) of the useful x-ray beam. 3. Above 150 kVp the contribution of characteristic radiation decreases, and it becomes negligible above 300 kVp. INTERACTION WITH THE NUCLEUS: BREMSSTRAHLUNG, CONTINUOUS SPECTRUM When an electron penetrates K shell & passes near the nucleus of a tungsten atom → the +ve charge of the nucleus acts on the -ve charge of the electron. ∴ The electron is deflected from its original direction & slowed down The kinetic energy lost by the electron is emitted directly in the form of a photon of radiation called general radiation or bremsstrahlung ("braking radiation" in German) Except in mammography, 80% or more of the X-rays emitted by a diagnostic X-ray tube are bremsstrahlung. Most electrons that strike the target: Make interactions with a number of atoms & loses only part of its energy at each interaction which appear in the form of radiation. Penetrate many atomic layers before giving up all their energy; therefore, not all x- rays are produced on the surface of the target. Occasionally, the electron will collide head-on with a nucleus → single photon of energy = kVp. "the largest photon energy that can be produced at this kilovoltage" 21 Most of the radiation will have little energy, and will appear as heat "over 99% of all reactions" + few x rays will appear. The energy of a photon of radiation is related to the kinetic energy (keV) of the electron, which is related to the potential difference (kVp) across the x-ray tube. Remember, Energy of photon of radiation is inversely related to wavelength. In case of a head-on collision between the electron and nucleus. All the energy of the electron is given to the resulting x-ray photon. The minimum wavelength (in angstroms) of this x-ray photon can be calculated: λmin = 12.4 / kVp For example, 0.124 Å is the shortest wavelength (highest energy) x-ray photon that can be produced with an x-ray tube potential of 100 kVp. Most of the x rays produced will have wavelengths longer than 0.124 Å. Figure 2-14 is a graph of continuous spectrum of the wavelengths of x rays. Notice that: 1. There is well defined minimum wavelength (λmin) → depend on the kVp. 2. The x-ray beam contains all wavelengths of x rays longer than λmin. 3. Filters are used to remove the long wavelength from the beam. Conclusion, Ð The highest energy x-ray photon leaving the x-ray tube depends on the kVp. Ð The lowest energy x-ray photon leaving the x-ray tube depends on the filtration. X-RAY SPECTRUM: Figure 1.8 plots the relative number of photons having each photon energy (in keV) The bremsstrahlung forms a continuous spectrum (a). The maximum photon energy (kiloelectronvolts) is equivalent to the kVp. If peak kV > K-shell binding energy, characteristic X- rays are also produced. They are shown at (c) in Fig. 1.8 as lines superimposed on the continuous spectrum. The dashed line (b) shows the spectrum of bremsstrahlung of low-energy which is absorbed by the target itself & the glass wall of the tube "FILTRATION". ∴ There is low-energy cut-off, at about 20 keV (depends on the filtration added to the tube), as well as a maximum energy (depends only on the kV). The area of the spectrum represents the total output of all X-ray photons emitted. 22 The average or effective energy of the continuous spectrum = 1/3 to 1/2 of the kVp. Thus, an X-ray tube operated at 90 kVp can be thought of as emitting, effectively, 45 keV X-rays. Figure 1.9 compares the spectrum from a tube with a tungsten target, operating at three different kV values. As the tube voltage is increased → both the width and height of the spectrum increase → the area increases → ∴ the output of X-rays increases, which is proportional to kV2. The intensity of X-rays emitted is proportional to kV2 x mA. The efficiency of X-ray production is the ratio X-ray output electrical power supplied & the efficiency a. Increases with the kV. b. Is greater, the higher the atomic number of the target. CONTROLLING THE X-RAY SPECTRUM INTENSITY OF X-RAY BEAMS Intensity of x-ray beam = no. of photons in the beam X the energy of each photon The intensity is commonly measured in roentgens / minute (R/min, or C/kg) X-ray beam intensity varies with kilovoltage, tube current, target material & filtration. 9 The quantity (number) of the x rays generated is proportional to the atomic number of the target material (Z), the square of the kilovoltage [(kVp)2], and the milliampere of x- ray tube current (mA). 9 The quality (energy) of the x rays depends almost entirely on the kVp. TARGET MATERIAL: I- For continuous spectrum, the target material determines the quantity of x-ray produced at a given voltage. The ↑↑ the atomic number of target atoms → the ↑↑ the efficiency of x-ray production For example, Tungsten (Z = 74) would produce much more bremsstrahlung than Tin (Z = 50) if compared at identical tube potential (kVp) and current (mA). Tungsten is used as the target material because of its relatively high atomic number (74) and its high melting point (3370° C). Platinum, with a more favorable atomic number of 78, has a melting point of 1770°C, 23 and stable gold (Z = 79) melts at 1063° C. II- For characteristic radiation. ↑↑ Atomic number → ↑↑ photon energy (quality) of characteristic radiation For example, the K-shell characteristic x rays for Ð Tin (Z = 50) vary from 25 to 29 keV; Ð Tungsten (Z = 74) vary from 57 to 69 keV; Ð Lead (Z = 81) have energies between 72 and 88 keV. To summarize, The atomic number of the target material determines the quantity (number) of bremsstrahlung produced and determines the quality (energy) of the characteristic radiation. MOLYBDENUM TARGET With a high atomic number anode like tungsten, the x-ray beam consists almost entirely of bremsstrahlung radiation & the contribution from characteristic radiation varies with tube voltage, but it never makes up a large percentage of the total beam. With lower atomic number anodes, bremsstrahlung production is less efficient (& diminishes more as the tube voltage is decreased) ∴ The combination of a low atomic number anode & low tube voltage → ↓↓ efficiency of bremsstrahlung → characteristic radiation assumes greater importance Molybdenum anode tubes used to take advantage of this principle for Mammography. Maximum tube voltage for mammography is approximately 40 kVp. At this voltage the 17.5 keV K-alpha and 19.6 keV K-beta characteristic radiation of molybdenum makes up a significant portion of the total radiation output of a molybdenum target x-ray tube. VOLTAGE (kVp) APPLIED: The energy of the photons emitted from the x-ray tube depends on the energy of the electrons in the electron stream that bombards the target of the x-ray tube, which in turn, determined by the peak kilovoltage (kVp). ∴ The kVp determines the maximum energy (quality) of the x rays. In addition, higher kVp techniques will also increase the quantity of x rays. ∴ The amount of radiation produced increases as the square of the kilovoltage: Intensity is proportional to (kVp)2 The wavelength of the characteristic radiation produced by the target is not changed by the kVp. But, the applied kilovoltage must be high enough to excite the characteristic radiation. For example, using a tungsten target, at least 70 kVp must be used to cause the K- characteristic x rays to appear. X-RAY TUBE CURRENT ↑↑ mA → ↑↑ number of electrons that strike the target of the x-ray tube → ↑↑ number (quantity) of x ray photons 24 The effect of x-ray tube potential (kVp) and mA (x-ray tube current) on the wavelength (quality) and intensity of the x-ray beam is illustrated in Figure 2-17. To summarize, there are 5 factors affecting the X-ray spectrum. The following are the effects of altering each in turn, the other four remaining constant: ↑ kV Shifts the spectrum upward and to the right (Fig. 1.9) It increases the maximum and effective energies and the total number of X- ray photons Below a certain kV (70 kV for a tungsten target) the characteristic K- radiation is not produced ↑ mA Does not affect the shape of the spectrum ↑ both bremsstrahlung and characteristic radiation output in proportion ↑ Z number ↑ The output of bremsstrahlung but does not affect shape of spectrum. of Target The photon energy of the characteristic lines will also increase (Fig. 3.9) Change The maximum and minimum photon energies are unchanged. Kilovoltage However, a constant potential (3-phase) generator produces more X-rays waveform and at higher energies than those produced by a single-phase pulsating potential generator, at the same values of kVp and mA ∴Both the output & the effective energy of the beam is greater i.e. in Fig. l.5.c the tube voltage is at the same peak value throughout the exposure. In Fig. 1.5.b it is below peak value during the greater part of each half cycle. A single-phase generator produces useful X-rays in pulses, each lasting 30 ms during the middle of each 100 ms half cycle of the mains Filtration Section 1.9 25 1.4 THE INTERACTION OF X-AND GAMMA RAYS WITH MATTER Where the following refers to X-rays it applies equally well to gamma rays. When a beam of X- or gamma rays travels through matter → figure 1.10 illustrates the 3 possible fates of the photons. Transmitted: Pass through unaffected, as primary or direct radiation. Absorbed: Transferring to the matter all of their energy (complete absorption) or some of it (partial absorption) Scattered: Diverted in a new direction, with or without loss of energy, and so may leave the beam (as scattered or secondary radiation). X-ray absorption and scattering processes are stochastic ‫ احتمالي ه‬processes, governed by the statistical laws of chance. It is impossible to predict which of the individual photons in a beam will be transmitted by 1 mm of a material, but it is possible to be quite precise about the fraction of them that will be, on account of the large numbers of photons in the beam. ATTENUATION 8 Definitions: X-ray beam Quantity: the number of photons in the beam. X-ray beam Quality: refers to the energies of the photon in the beam. Intensity: the product of number & energy of photons (depends on both the quantity & quality). Attenuation = the reduction in the X-ray beam intensity as it traverses a matter by either absorption or scattering of photons. ATTENUATION = ABSORPTION + SCATTER ∴ It depends on both the quantity & quality of the X-ray beam. ATTENUATION OF NARROW MONOENERGETIC BEAM OF X-RAY: In the module of monochromatic radiation → attenuation = reduction of quantity only The fundamental law of X-ray attenuation Equal thicknesses of an absorber transmit equal percentages of the radiation entering them. In Fig. 1.11a, where each cm of the matter remove 20% of beam photons (↓ quantity) with no change in energy of transmitted photons (quality) 26 Fig. 1.11 Examples of exponential attenuation for narrow mono-energetic beams. Linear Attenuation Coefficient (μ): 8 Def: The linear attenuation coefficient measures the probability that a photon interacts (i.e. is absorbed or scattered) per unit length of the path it travels in a specified material. Quantitative parameter → measures the attenuating properties of the material. 8 The unit of μ is cm-1. 8 The linear attenuation coefficient only applies to narrow monoenergetic beams. 8 μ is specific for both the energy of X-ray beam & the type of absorber. When the radiation energy ↑ → ↓ no. of attenuated X-ray photons → ↓ μ. 8 The exponential equation for X-ray attenuation: N = N e − μX 0 where: N0 = no. of incident photons. N = no. of transmitted photons. E = base of natural logarithm μ = Linear attenuation coefficient. X = thickness of absorber in cm. Half-Value Layer (HVL) HVL is the thickness of stated material required to reduce the intensity of a narrow beam of X-radiation to 1/2 of its original value. Two successive half-value layers reduce the intensity of the beam by a factor 2x2 = 4. Ten HVLs reduce the intensity of the beam by a factor 210 = 1000. The HVL is a measure of the penetrating power (quality) of the X-ray beam "i.e. a beam with high HVL is more penetrating than one with low HVL". The linear attenuation coefficient (μ) is inversely proportional to the HVL: μ = 0.69 / HVL → HVL = 0.69 / μ The HVL applies only to narrow beams, but they need not be monoenergetic. The HVL decreases and the linear attenuation coefficient therefore increases as: 1. The density of the material increases. 2. The atomic number of the material increases; 3. The photon energy of the radiation decreases. For example, lead is more effective than either aluminum or tissue at absorbing X-rays because of its higher density and atomic number. 27 The mass attenuation coefficient (μ / ρ) S The unit of the mass attenuation coefficient is per gm \ cm2 (or cm2 \ gm) S Is obtained by dividing the linear coefficient by the density of the material → depends only on the atomic number and photon energy. EXPONENTIAL GRAPH When no. of transmitted photons are plotted on linear scale against absorber thickness → Curved line (Fig. 1.12a) S However thick the absorber, it is never possible to absorb an X-ray beam completely. This is shown, in Fig. 1.12a, by the shape - an exponential curve. If, as in Fig. 1.12b the percentage transmission is plotted on a logarithmic scale → Linear graph = exponential curve "i.e. decrease with constant percentage with each increment of absorber, making it easier to read off the HVL and calculate μ. The experimental arrangement for measuring HVL and the attenuation coefficient is illustrated in Fig. 1.13a Fig. 1.13 (a) A narrow beam is used for the measurement of the HVL (b) Transmission of a wide beam. This arrangement, referred to as 'good geometry' → minimizes the amount of scattered radiation SS entering the detector The beam is restricted by means of a lead diaphragm to just cover a small detector. The diaphragm b and sheets of the absorbing material c are positioned halfway between the source a and detector d. A second collimator may be placed in front of the detector. 28 FACTORS AFFECTING ATTENUATION: I- Energy: ↑ beam energy → ↓ attenuation (µ ) → ↑ percentage of transmitted photons. ↑ beam energy → ↑ HVL. Beam energy determines the dominant interaction type: 1. With low radiation energy → photoelectric effect is dominant → ↓ transmitted photons. 2. With increasing the energy → ↑ Compton scattering & ↓ PEE → ↑ transmitted photons. 3. With high energy → most interactions are Compton interaction. & with increasing the energy within high ranges → ↑ % transmitted photons but with small differences (both within Compton interaction) II- Atomic number (A): Generally, ↑ atomic no. → ↑ attenuation. The only exception is with high atomic no. absorber, if the beam energy exceeded the binding energy of an inner shell electron (see absorption edge). III- Density: Density determines the no. of electrons in a given thickness. So, ↑ density → ↑ attenuation in a linear relationship ∴ Doubling the density for the same thickness → doubles attenuation of that thickness The difference in tissue densities is responsible for the X-ray film contrast. IV- Electrons per gram: Mass unit → depends on the no. of neutrons in the absorber atoms. Actually, the no. of electrons \ cm3 "which is a volume unit" is more important. We obtain the e \ cm3 by multiplying e \ gm in density. e gm e x 3 = gm cm cm3 When Compton interactions predominate, the no. of e \ cm3 becomes the most important factor in attenuation. Example: bone has fewer e \ gm than water, but attenuates radiation more because it has more e \ cm3. ATTENUATION OF A WIDE BEAM The percentage transmission by the same object of a wide beam of X- or gamma rays is greater than that of a narrow beam of photons of the same energy because a wide beam produces more scatter SS and much of it stays within the beam. Fig. 1.13b Attenuation of a heterogeneous beam The beams produced by X-ray tubes are Heterogeneous (Polyenergetic), i.e. they comprise photons of a wide range of energies (spectrum of energies). The max. energy of the beam = peak kVp. The mean energy is between 1/2 – 1/3 of peak energy. As the beam travels through an attenuating material, S ↓ Beam quantity → same as monochromatic radiation. S ↑ Beam quality as, the lower-energy photons are attenuated proportionally more 29 than the higher-energy photons & as the lower energy photons are removed from the beam → ↑ mean energy of the remaining photons. The exponential law does not apply for a heterogenous beam. However, it is still correct to refer to the HVL of the beam. As the beam penetrates the material: a process of FILTRATION occurs The beam becomes progressively more homogeneous. ↑↑ Proportion of higher-energy photons in beam → ↑↑ average energy → the beam becomes 'harder' or more penetrating. The 'second HVL' which would reduce the beam intensity from 50 to 25% > the 'first HVL', which reduces it from 100 to 50%. When the transmission % of polyenergetic radiation plotted on logarithmic scale → Curved line. The HVL of a typical diagnostic beam is 30 mm in tissue 12 mm in bone 0.15 mm in lead INTERACTION PROCESSES 5 processes of interaction between X-rays and matter contribute to attenuation 1. Interaction with a loosely bound or 'free' electron → Compton process "modified scatter" 2. Interaction with inner shell or 'bound' electron → Photoelectric absorption. 3. Interaction with a bound electron → Unmodified scatter. 4. Pair production. 5. Photodisintegration. Unmodified scatter It is also known variously as coherent, classical, elastic, or Thomson scattering The photon bounces off an electron which is firmly bound to its parent atom → the photon is scattered with no loss of energy. ∴ No secondary electron - No ionization. This process occurs with low-energy photons and at very small angles of scattering ∴ The scattered radiation does not leave the beam → little significance in radiology. PAIR PRODUCTION & PHOTODISINTEGRATION: Both interactions don't occur within the diagnostic energy range (which rarely use energies > 150 keV). 30 1.5 COMPTON PROCESS (MODIFIED SCATTER) Responsible for almost all the scatter radiation in diagnostic radiology The photon bounces off a free electron which recoils, taking away some of the energy of the photon as kinetic energy → the photon is scattered with reduced energy. ∴ The energy of the incident photon is distributed between: 1. Kinetic energy of the recoil electron. 2. Energy retained by deflected photon Compton photon never gives up all its energy unlike in photoelectric interaction The reaction produces: S Ion pair "+ve ion & -ve electron – called recoil electron" S Scattered photon. The energy carried off by the recoil electron is said to be absorbed by the material, and the remainder, carried by the photon, to have been scattered. In the diagnostic range of energies no more than 20% of the energy is absorbed, the rest being scattered. ∴ The Compton process is partial absorption. The angle of scatter θ is the angle between the scattered ray and the incident ray. Photons may be scattered in all directions. The electrons are projected only in sideways and forward directions. Unlike PEE in which most of photon's energy is expended to free electron bond → Recoil electron is already free (so no energy needed for this). 2 factors determine the amount of energy retained by scattered photon: 1. Initial photon energy. 2. Angle of scatter θ. EFFECT OF THE ANGLE OF SCATTERING It will be seen that The greater the angle of scatter 1. The greater the energy and range of the recoil electron 2. The lower the energy of the scattered photon (i.e. the greater the loss of energy). 31 ∴ Scattered photons at small angles retain most of original energy: 1. As they scatter at small angle → they remain within the 1ry beam → film fogging. 2. They are too energetic → can't be removed by filters. 3. Scattered radiation - even those scattered at large angles – still have much energy → safety hazards to medical staff especially in fluoroscopy. ∴ A back-scattered photon (θ = 180°) is less energetic 'softer' than a side-scattered photon (θ = 90°), which in turn is softer than a forward-scattered photon (θ = 0°). EFFECT OF INITIAL PHOTON ENERGY Higher energy photons are more difficult to deflect (more momentum). ↑↑ initial photon energy 1. ↑↑ the remaining photon energy of the scattered radiation → more penetrating. However, ↑ photon energy → ↓ no. of reactions → ↑ probability to pass through body than low energy photons 2. ↑↑ the kinetic energy of the recoil electron and ↑↑ its range. This is seen in the following examples: Incident photon Back-scattered photon Recoil electron 25 keV 22 keV 3 keV 150 keV 100 keV 50 keV ∴ The softening effect of Compton scatter is greatest with large scattering angles & high energy X-rays. The Compton process contributes to the total linear attenuation coefficient μ, an amount σ which is called the Compton linear attenuation coefficient. In diagnostic energy range (up to 150 keV): Photon retains most of its original energy (i.e. very little transferred to recoil electron) The probability σ that the Compton process will occur 1. Proportional to the physical density, as with all attenuation processes. 2. Proportional to electron density. 3. Independent of the atomic number, as it concerns only 'free' electrons. 4. Approximately proportional to l / E. To summarize σ is proportional to ρ / E and is independent of Z. The mass Compton attenuation coefficient σ / ρ is the same within 10% for such materials as air, tissue, bone, contrast media, and lead → represented by a single curve in Fig. 1.16, which shows how σ/ρ varies with photon energy. Free electron: An electron which binding energy is much less than energy of incident photon. In diagnostic radiology range (10 – 150 keV): S In high atomic no. elements → outer shell electrons are free. S In low atomic no. elements (as in soft tissue) → all electrons are free. 32 1.6 PHOTOELECTRIC ABSORPTION When a photon (a) 'collides' with an electron (b) in the K-shell of an atom & if its energy > the binding energy of the shell → it can eject the electron b from the atom. The photon disappears: 1. Part of its energy, equal to the binding energy of the K-shell, is expended in removing the electron from the atom. 2. The remainder becomes the kinetic energy (KE) of that electron. KE of the electron = photon energy - EK Less often, the X- or gamma ray photon may interact with an electron in the L-shell of an atom → ejected from the atom with KE = photon energy - KL. The electrons so ejected are called photoelectrons. The 'holes' created in the atomic shell are filled by electrons falling in from a shell farther out, with the emission of a series of photons of characteristic radiation. The photoelectric interaction yields 3 end products: 1. –ve Ion (photoelectron). 2. +ve ion (atom deficient by one electron). 3. Characteristic radiation In the case of air, tissue & bone (light-atom materials): Calcium which has highest atomic no. of all body elements, emits only 4 keV max. energy of characteristic radiation ∴ The characteristic radiation is so soft → absorbed immediately with the ejection of a further, low-energy, photoelectron or 'AUGER' ELECTRON. ∴ All the original photon energy is converted into the energy of electronic motion. ∴ Photoelectric absorption in such materials is complete absorption. In the case of barium and iodine in CM (high atomic number materials): Characteristic radiation is sufficiently energetic to leave the patient & fog x-ray film → only partial absorption "like Compton effect". Photoelectric absorption contributes to the total linear attenuation coefficient μ an amount τ which is called the photoelectric linear-attenuation coefficient. 33 ∴μ=σ+τ 34 The more tightly the electron is bound to the atom and the nearer the photon energy is to its binding energy, the more likely photoelectric absorption is to happen. The probability τ that photoelectric absorption: 1. τ is inversely proportional to the cube of the photon energy E3 → decreases markedly as the photon energy of the radiation increases. (Provided that photon energy > binding energy) 2. τ is proportional to the cube of the atomic number Z3 → increases markedly as the atomic number of the material increases. 3. τ is proportional to the density of the material, as with all attenuation processes. Photoelectric effect can't take place with free electron → called forbidden interaction. To summarize: τ ∝ ρ Z3 / E3 Fig. 1.16 shows how the mass photoelectric attenuation coefficient τ / ρ varies with photon energy in the case of soft tissue with Z = 7.4, bone with Z = 13, and iodine with Z = 53. The graphs are straight lines because logarithmic scales are used on both axes. Applications of photoelectric effect in diagnostic radiology: Good role Photoelectric effect produces radiographic images of excellent quality due to: 1. No scattered radiation. 2. Enhancement of natural tissue contrast (i.e. PEE interaction depends on 3rd power of atomic no. → magnify contrast between tissues) ∴ PEE is desirable from point of view of film quality. Bad role: PEE increase patient exposure, as all the incident photon is absorbed by the pt. while in Compton reaction, only part of the incident photon's energy is absorbed. ∴ PEE is undesirable from point of view of patient exposure. ∴We should use highest energy (kVp) techniques which not distort the diagnostic quality of X-ray ray films. MCQ: Radiographic image contrast is less with Compton reaction than with PEE. 35 Characteristic radiation in photoelectric interactions: Ì Same principle as characteristic radiation production either in the X-ray target or in photoelectric effect, the only difference is the method used to eject the inner shell electron (high speed electron in the x-ray tube & x-ray photon in PEE) Ì Characteristic radiation is usually referred to as 2ry radiation, to differentiate from Scatter radiation. EFFECTIVE ATOMIC NUMBER Effective atomic number = a (weighted) average of the atomic numbers of the constituent elements. = the cube root of the average of the cube roots of the atomic numbers of the constituents ‫الجذر التربيعى لمتوسط الجذور الجذور التربيعيه‬. Fat Air Water, muscle Bone 6 7.6 7.4 13 ABSORPTION EDGES The K-absorption edge: i.e. as the photon energy is increased, photoelectric attenuation decreases until the binding energy E K of the material is reached → the photoelectric absorption jumps to a higher value and start to decrease again as the photon energy further increases. The reason is that photons with less energy than EK can only eject L-electrons and can only be absorbed in that shell. Photons with greater energy than EK can eject K-electrons as well, and can therefore be absorbed in both shells. This is an exception to the general rule that attenuation decreases with increasing energy K-absorption edge occurs at different photon energies with different materials. Fig. 1.16 illustrated K-absorption edge for iodine. For example, In the case of iodine, EK = 33 keV and photons of energy 31 keV are attenuated much less than photons of energy 35 keV. The K-edges of low atomic number materials such as air, water, tissue, and aluminum have no significance as they occur at EK = 1 keV or less. The higher the atomic number of the material, the greater is EK and the greater is the photon energy at which the edge occurs. When max. X-ray absorption is desired, the K-edge of an absorber should be close to the energy of the X-ray beam e.g. In Xeroradiography, Selenium is used for low energy radiation (30-35 kVp) like mammography. While, Tungsten is used for high energy radiation (350 kVp) like CXR. The absorption edge is important in: 1. Choosing materials for 'K-edge filters'. 2. Contrast media. 3. Imaging phosphors. 36 Relative Importance of Compton and photoelectric attenuation The photoelectric coefficient is proportional to Z3 / E3, and is particularly high when the photon energy is just greater than EK. The Compton coefficient is independent of Z and little affected by E. Accordingly, 1. Photoelectric absorption is more important with high-Z materials & low-energy photons. 2. Compton process is more important with low-Z materials & high-energy photons. The photon energy at which the two processes happen to be equally important depends on the atomic number of the material: 30 keV for air, water, and tissue 50 keV for aluminum and bone 300 keV for iodine and barium 500 keV for lead As regards diagnostic imaging with X-rays (20-140 keV), therefore: 1. The Compton process is the predominant process for air, water, and soft tissues (except at very low photon energy "20 – 30 keV" →PEE reaction predominate) 2. Photoelectric absorption predominates for contrast media, lead, and the materials used in films, screens, and other imaging devices; 3. While both are important for bone (intermediate atomic no.). S PEE is more common at low energies. S Compton scattering in dominant at high energies. 4. Coherent scattering play only a minor role throughout diagnostic energy range. 5. Attenuation is greater when the PEE predominates (complete absorption). SECONDARY ELECTRONS 'Secondary radiation' refers to Compton scattered radiation; 'Secondary electrons' to the recoil electrons and photoelectrons As they travel through the material, the secondary electrons interact with the outer shells of the atoms they pass nearby, and excite or ionize them → the track of the electron is tortuous & dotted with ion pairs. When traveling through air the electron loses an average of 34 eV per ion pair. 3 eV needed to excite an atom & 10 eV to ionize it, and there & there about 8 times as many excitations as ionizations. When it loses the whole of its initial energy → the electron comes to the end of its range. The greater the initial energy of the electron, the greater its range The range is inversely proportional to the density of the material. The ranges in air are some 800 times greater than in tissue For example, when 140 keV photons are absorbed in soft tissue, Some of the secondary electrons are photoelectrons having energy of 140 keV, able to produce some 4000 ion pairs and having a range of about 0.2 mm. Most of the secondary electrons are recoil electrons with a spectrum of energies averaging 25 keV and an average range of about 0.02 mm. 37 1.9 FILTRATION The lower-energy photons in the X-ray beam are mainly absorbed by and deposit dose in the patient → so, don't reach the film or contribute to the image. Filtration remove a large proportion of the lower-energy photons before they reach the skin "so, reduces the patient dose" while hardly affecting the radiation producing image. Filtration is the process of shaping the X-ray beam to increase the ratio of useful photons to the photons that increase the patient dose or decrease image contrast. INHERENT Filtration: The X-ray photons produced in the target are first filtered by: Principally, the target material itself. The window of the tube housing. The glass envelope. The light beam diaphragm mirror The insulating oil. Inherent filtration is measured in Aluminum Equivalents = the thickness of Al that would produce the same degree of attenuation as the inherent filtration. Typically, inherent filtration = 0.5-1 mm Al equivalent. In few cases, unfiltered radiation is desirable As filtration ↑↑ the mean energy of an X-ray beam → it ↓↓ tissue contrast Ì With lower energy radiation (< 30 kVp) this loss of contrast affects image quality Ì When inherent filtration must be minimized, a tube with a window of beryllium (Z = 4) instead of glass is used e.g. Mammography. ADDED "or Additional" Filtration: Uniform flat sheet of metal, usually Aluminum placed between the X-ray tube & patient Ideal filter material → the one which absorbs all low energy photons & transmit all high energy photons (such material doesn't exist). The predominant attenuation process should be photoelectric absorption, which varies inversely as the cube of the photon energy. The filter will therefore attenuate the lower- energy photons much more than it does the higher-energy photons. The total filtration is the sum of the added filtration and the inherent filtration. For general diagnostic radiology it should be at least 2.5 mm Al equivalent. (This will produce a beam with effective energy of HVL = 2.5 mm Al at 70 kV, and 4.0 mm at 120 kV.) CHOICE OF FILTER MATERIAL The Atomic Number should be sufficiently high to make the energy-dependent attenuating process, photoelectric absorption, predominate. It should not be too high, since the whole of the useful X-ray spectrum should lie on the high-energy side of the absorption edge. If not, the filter might soften the beam. Aluminum (Z= 13) is generally used: has sufficiently high atomic number to be suitable for low energy radiation & most diagnostic X-ray beams (general purpose filter). With the higher kV values, Copper (Z = 29) is used, being a more efficient filter. 38 Disadv.: Copper filters can't be used alone because photoelectric interaction with the copper emits 9 keV characteristic X-rays → if reaches patient skin, will increase the skin dose → must be absorbed by a 'backing filter' of aluminum on the patient side of the 'compound filter'. Molybdenum or Palladium filters have absorption edges (20 or 24 keV, respectively) favorable for mammography. Erbium (58 keV) has been used at moderate kV values, called 'K-edge filter'. FILTER THICKNESS: The total filtration for diagnostic radiology as recommended by The national council of radiation protection and measurements: kVp Total filtration Below 50 kVp 0.5 mm Al 50 – 70 kVp 1.5 mm Al Above 70 kVp 2.5 mm Al Increased filtration has definite disadvantage; Excessive filtration → absorption of high energy photons → the quality of the beam is not altered significantly but the intensity is greatly diminished → needs ↑ exposure time which may ↑ movement blurring. EFFECTS OF FILTRATION Figure 1.18 shows the spectrum of X-rays generated at 60 kV after passing through 1, 2, and 3 mm aluminum. Filters attenuates lower-energy X-rays more in proportion than higher-energy X-rays → ↑↑ the penetrating power (HVL) of the beam but ↓↓ intensity It is responsible for the low-energy cut-off of the X-ray spectrum. Increasing the filtration has the following effects: It causes the continuous X-ray spectrum to shrink and move to the right, Fig. 1.18. 1. It selectively reduces the total number of photons "the area of the spectrum" and the total output of X-rays → removes much more low energy photons than high energy. 2. ↑↑ Minimum & Effective photon energies but not affect maximum photon energy 3. ↑↑ the exit dose/entry dose ratio, or film dose/skin dose ratio. COMPENSATING OR WEDGE FILLER A wedge-shaped filter may be attached to the tube to make the exposure across the film more uniform and compensate for the large difference in transmission, for example, between the upper and lower thorax, neck and shoulder, or foot and ankle. Similarly, a compensating filter may sometimes be used in mammography. 39 1.7 PROPERTIES OF X-AND GAMMA RAYS The excitations and ionizations produced by the secondary electrons which account for the various properties of X- and gamma rays: 1. The ionization of air and other gases → makes them electrically conducting: used in the measurement of X- and gamma rays. 2. The ionization of atoms in the constituents of living cells cause biological damage & the hazards of radiation exposure. 3. The excitation of atoms of certain materials (phosphors) → makes them emit light (luminescence, scintillation, or fluorescence): used in the measurement of X- and gamma rays and as a basis of radiological imaging. 4. The effect on the atoms of silver and bromine in a photographic film → leads to blackening (photographic effect): used in the measurement of X- and gamma rays and as a basis of radiography. LUMINESCENCE 1. When a phosphor absorbs X-rays, the secondary electrons set in motion raise valence electrons to a higher energy level. 2. The electrons stay in energy 'traps' and the absorbed energy is stored in the phosphor until the electrons return to the valence shells, with the emission of photons of light. 1. This may happen spontaneously, either: 9 Instantaneously → fluorescence 9 After a noticeable interval of time → phosphorescence. The latter is called afterglow or lag, and is generally to be avoided in imaging. OR 2. The emission of the light may require stimulation: 9 By heat → thermoluminescence. 9 By intense light from a laser → photostimulation. Other ionizing radiations Some ultraviolet radiation has a sufficiently high photon energy to ionize air. Beta particles, emitted by many radioactive substances and other moving electrons (in a television monitor, for example) also possess the above properties. Alpha rays (helium nuclei 4He), (which are particularly stable combinations of two neutrons and two protons) are also emitted by some radioactive substances. Both alpha and beta rays are charged particles and are directly ionizing. X- and gamma rays are indirectly ionizing, through their secondary electrons; the 'secondary' ions produced along the track of a secondary electron being many times more than the single 'primary' ionization caused by the initial Compton or photoelectric interaction. Neutrons also ionize tissue indirectly through the hydrogen nuclei they collide with. 40 1.8 ABSORBED DOSE The SI unit of absorbed dose is GRAY (Gy); 1 Gy = 1 J \ kg. The absorbed dose is the energy absorbed as ionization or excitation per unit mass of the material irradiated (in joules per kilogram). Dose rate is measured in Grays per Second. The concept of absorbed dose applies to all kinds of direct and indirect ionizing radiations and to any material. Before 1980 the international unit of absorbed dose was the RAD, 1 Gy = 100 rad & 1 rad = 1 cGy = 10 mGy. KERMA Kerma is the kinetic energy (of the secondary electrons) released per unit mass of irradiated material. Absorbed Dose is energy deposited (as ionization & excitation) by those 2ry electrons Kerma is measured in GRAY & is synonymous with absorbed dose. In most radiodiagnostic situations they are equal and can be used interchangeably. MEASUREMENT OF X- AND GAMMA RAY DOSE It is extremely difficult to measure dose in solids or liquids directly. First we measure the dose delivered to air ('air kerma') under same conditions & then multiply it by a conversion factor to obtain the dose in the material. The conversion factor: Dose in stated material Dose in air ∴Depends on the relative amounts of energy absorbed in air and the material. Like the mass absorption coefficients, the factor depends on: 1. The effective atomic number of the material. 2. The effective energy of the X- or gamma rays. For X-rays used in radiology, approximate values of the conversion factors are: 1. For muscle, Muscle atomic number nearly equal that of air & Compton process predominates ∴ The ratio is close to unity and only varies between 1.0 - 1.1 over the kilovoltage range 2. For compact bone, With higher atomic number and Photoelectric absorption is important. The ratio varies from about 4.5 at low keV energies to 1.2 at high keV. 3. For fat, With lower atomic number → ∴ the ratio varies in the opposite direction, from about 0.6 at low keV energies to 1.1 at high keV energies. 4. For the soft tissue elements in cavities within bone The ratio lies between bone and muscle → depends on the size of cavity & photon energy. 41 THIMBLE OR CAVITY CHAMBER The air dose or kerma can be measured by placing at the point in question a plastic 'thimble' (a) containing a small mass of air (b), which is indirectly ionized by the X- radiation. Each X-ray photon (X) absorbed in the wall liberates a secondary electron (e), which produces ion pairs along its tortuous track. For each ion pair, 34 eV of energy will have been deposited. Therefore, For each coulomb of charge (either positive or negative) carried by the ions, 34 J of energy will have been deposited. To measure the charge, the ions are separated before they can recombine by applying a polarizing voltage between the outer thimble wall and a thin central electrode (c) → Ionization current (I) flows, proportional to the dose rate of the radiation & the mass of air in the chamber. Charge can be collected → Air Kerma indicated on a meter or digital read-out; or Current can be measured → Air Kerma Rate. A polarizing voltage of 100 V is usually sufficient to collect all the ions and produce 'SATURATION CURRENT'. If the voltage is too low, some of the positive and negative ions recombine, and the ionization current measured is too low. Above a certain 'saturation' voltage, all the ions are separated, and ionization current is constant. Air has been chosen as the standard material for dosimetry because: 1. Effective atomic number of air (7.6) is close to that of tissue (7.4) → ∴the conversion factor is close to unity 2. Applicable to the measurement of a wide range of X- and γ ray photon energies. 3. Large & small doses and large & small dose rates are easily and accurately measured. 4. Air is available, cheap, universal with invariable composition. WALL MATERIAL The chamber wall must be made of a suitable material. The material of wall and electrode must be indistinguishable from air, except in density. They must be made of air-equivalent material (specially compounded plastic is used). An air-equivalent material matches air as regards Effective atomic number → absorbs energy from an X-ray beam to the same extent as the same mass of air. Density is not important; it can conveniently be a solid. The thimble wall is made of plastic (Z = 6), made conducting by an internal coat of graphite, and the inner electrode made of thin aluminum wire (Z = 13). By adjusting the length of the wire, the average or effective atomic number of 42 the combination can be made equal to that of air. The chamber is said to be 'air wall' Air thimble measures the air dose whatever the photon energy of the radiation → 'energy-independent' "However, corrections are needed, as discussed below". WALL THICKNESS The chamber wall must be sufficiently thick The dosemeter is designed to measure the air dose at the center of the thimble → the overall dimensions should be small. Typical values are length 17 mm, diameter 7 mm, and wall thickness 0.7 mm. If the wall is too thin, electrons which have been set moving by the X-rays at points in the surroundings can penetrate into the air cavity and contribute to the ionization, giving a false reading. ∴ The wall thickness should be greater than the maximum range of the secondary electrons set in motion by the hardest X-rays to be measured (For example, 0.2 mm for the photoelectrons from 140 keV X-rays) So, the ionization is unaffected by the X- and gamma dose rate at points outside thimble However, if the wall is too thick it attenuates unduly the radiation being measured. AIR VOLUME: The larger the air volume, the more sensitive the dosemeter. A 30 ml chamber is often used to check the output of an X-ray set A larger one to measure the low-intensity stray radiation near an X-ray set or in a radionuclide calibrator to assess radioactivity (see Section 5.6). ENERGY DEPENDENCE: CORRECTION FACTORS 8 In practice, the dosemeter is likely to give an incorrect measure of the air dose for two reasons: 1. It is not possible to make the wall and electrode exactly air-equivalent. 2. The X- or gamma rays being measured are attenuated by the walls of the chamber, thus reducing the reading, particularly when measuring low-energy X-rays. 9 Accordingly, the dosemeter reading has to be multiplied by a correction factor, N, which varies with the photon energy, i.e. the dosemeter is 'energy-dependent'. 8 Another correction has to be applied if the ambient temperature or pressure differ from standard values. If the pressure is too high or if the temperature is too low, air will leak out of the chamber, and the reading will be too low; and vice versa. Such a correction is not needed with sealed chambers. STANDARD, FREE AIR CHAMBER The correction factor N is measured at a national standards laboratory (such as the National Physical Laboratory in the UK), where the thimble dosemeter is compared with a standard instrument, The Free Air Chamber. This is designed to measure air dose exactly, whatever the energy of the radiation. The 'wall' of the chamber is ordinary air, and so its 'thickness' has to be some 800 times that appropriate for a thimble chamber. This makes it a very large chamber which is inconvenient for departmental use. 43 SEALED PARALLEL PLATE CHAMBERS These are mounted on the light beam diaphragm for measuring the product (air kerma x area of beam). It effectively measures the total energy entering the patient, most of which is deposited in the tissues, although some re-emerges as scatter. It is referred to as a kerma-area or Jose-area product monitor. This is easier to measure than the skin dose and is also a better index of the risk to the patient. This chamber must be: 1.

Farr's Physics for Medical Imaging (PDF) - Radiation Physics

Document Details

Tags

Related

Summary

Full Transcript

Upgrade to continue