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Introduction to Biomedical Imaging
By Andrew G. Webb John Wiley & Sons
ISBN: 0-471-23766-3
Chapter One
X-Ray Imaging and Computed Tomography
1.1. GENERAL PRINCIPLES OF IMAGING WITH X-RAYS
X-ray imaging is a transmission-based technique in which X-rays from a source pass through the patient and are detected either by film or an ionization chamber on the opposite side of the body, as shown in Figure 1.1. Contrast in the image between different tissues arises from differential attenuation of X-rays in the body. For example, X-ray attenuation is particularly efficient in bone, but less so in soft tissues. In planar X-ray radiography, the image produced is a simple two-dimensional projection of the tissues lying between the X-ray source and the film. Planar X-ray radiography is used for a number of different purposes: intravenous pyelography (IVP) to detect diseases of the genitourinary tract including kidney stones; abdominal radiography to study the liver, bladder, abdomen, and pelvis; chest radiography for diseases of the lung and broken ribs; and X-ray fluoroscopy (in which images are acquired continuously over a period of several minutes) for a number of different genitourinary and gastrointestinal diseases.
Planar X-ray radiography of overlapping layers of soft tissue or complex bone structures can often be difficult to interpret, even for a skilled radiologist. In these cases, X-ray computed tomography (CT) is used. The basic principles of CT are shown inFigure 1.2. The X-ray source is tightly collimated to interrogate a thin "slice" through the patient. The source and detectors rotate together around the patient, producing a series of one-dimensional projections at a number of different angles. These data are reconstructed to give a two-dimensional image, as shown on the right of Figure 1.2. CT images have a very high spatial resolution (~1 mm) and provide reasonable contrast between soft tissues. In addition to anatomical imaging, CT is the imaging method that can produce the highest resolution angiographic images, that is, images that show blood flow in vessels. Recent developments in spiral and multislice CT have enabled the acquisition of full three-dimensional images in a single patient breath-hold.
The major disadvantage of both X-ray and CT imaging is the fact that the technique uses ionizing radiation. Because ionizing radiation can cause tissue damage, there is a limit on the total radiation dose per year to which a patient can be subjected. Radiation dose is of particular concern in pediatric and obstetric radiology.
1.2. X-RAY PRODUCTION
The X-ray source is the most important system component in determining the overall image quality. Although the basic design has changed little since the mid-1900s, there have been considerable advances in the past two decades in designing more efficient X-ray sources, which are capable of delivering the much higher output levels necessary for techniques such as CT and X-ray fluoroscopy.
1.2.1. The X-Ray Source
The basic components of the X-ray source, also referred to as the X-ray tube, used for clinical diagnoses are shown in Figure 1.3. The production of X-rays involves accelerating a beam of electrons to strike the surface of a metal target. The X-ray tube has two electrodes, a negatively charged cathode, which acts as the electron source, and a positively charged anode, which contains the metal target. A potential difference of between 15 and 150 kV is applied between the cathode and the anode; the exact value depends upon the particular application. This potential difference is in the form of a rectified alternating voltage, which is characterized by its maximum value, the kilovolts peak (k[V.sub.p]). The maximum value of the voltage is also referred to as the accelerating voltage. The cathode consists of a filament of tungsten wire (~200µm in diameter) coiled to form a spiral ~2 mm in diameter and less than 1 cm in height. An electric current from a power source passes through the cathode, causing it to heat up. When the cathode temperature reaches ~2200ºC the thermal energy absorbed by the tungsten atoms allows a small number of electrons to move away from the metallic surface, a process termed thermionic emission. A dynamic equilibrium is set up, with electrons having sufficient energy to escape from the surface of the cathode, but also being attracted back to the metal surface.
The large positive voltage applied to the anode causes these free electrons created at the cathode surface to accelerate toward the anode. The spatial distribution of these electrons striking the anode correlates directly with the geometry of the X-ray beam that enters the patient. Since the spatial resolution of the image is determined by the effective focal spot size, shown in Figure 1.4, the cathode is designed to produce a tight, uniform beam of electrons. In order to achieve this, a negatively charged focusing cup is placed around the cathode to reduce divergence of the electron beam. The larger the negative potential applied to the cup, the narrower is the electron beam. If an extremely large potential (~2 kV) is applied, then the flux of electrons can be switched off completely. This switching process forms the basis for pulsing the X-ray source on and off for applications such as CT, covered in Section 1.10.
At the anode, X-rays are produced as the accelerated electrons penetrate a few tens of micrometers into the metal target and lose their kinetic energy. This energy is converted into X-rays by mechanisms covered in detail in Section 1.2.3. The anode must be made of a metal with a high melting point, good thermal conductivity, and low vapor pressure (to enable a vacuum of less than [10.sup.-7] bar to be established within the vessel). The higher the atomic number of the metal in the target, the higher is the efficiency of X-ray production, or radiation yield. The most commonly used anode metal is tungsten, which has a high atomic number of 74, a high melting point of 3370ºC, and the lowest vapor pressure, [10.sup.-7] bar at 2250ºC, of all metals. Elements with higher atomic number, such as platinum (78) and gold (79), have much lower melting points and so are not practical as anode materials. For mammography, in which the X-rays required are of much lower energy, the anode usually consists of molybdenum rather than tungsten. Even with the high radiation yield of tungsten, most of the energy absorbed by the anode is converted into heat, with only ~1% of the energy being converted into X-rays. If pure tungsten is used, then cracks form in the metal, and so a tungsten-rhenium alloy with between 2% and 10% rhenium has been developed to overcome this problem. The target is about 700 µm thick and is mounted on the same thickness of pure tungsten. The main body of the anode is made from an alloy of molybdenum, titanium, and zirconium and is shaped into a disk.
As shown in Figure 1.4, the anode is beveled, typically at an angle of 5-20º, in order to produce a small effective focal spot size, which in turn reduces the geometric "unsharpness" of the X-ray image (Section 1.6.2). The relationship between the actual focal spot size F and the effective focal spot size is given by
(1.1) = F sin [theta]
where [theta] is the bevel angle. Values of the effective focal spot size range from 0.3 mm for mammography to between 0.6 and 1.2 mm for planar radiography. In practice, most X-ray tubes contain two cathode filaments of different sizes to give the option of using a smaller or larger effective focal spot size. The effective focal spot size can also be controlled by increasing or decreasing the value of the negative charge applied to the focusing cup of the cathode.
The bevel angle [theta] also affects the coverage of the X-ray beam, as shown in Figure 1.4. The approximate value of the coverage is given by
(1.2) coverage = 2(source-to-patient distance) tan [theta]
All of the components of the X-ray system are contained within an evacuated vessel. In the past, this was constructed from glass, but more recently glass has been replaced by a combination of metal and ceramic. The major disadvantage with glass is that vapor deposits, from both the cathode filament and the anode target, form on the inner surface of the vessel, causing electrical arcing and reducing the life span of the tube. The evacuated vessel is surrounded by oil for both cooling and electrical isolation. The whole assembly is surrounded by a lead shield with a glass window, through which the X-ray beam is emitted.
1.2.2. X-Ray Tube Current, Tube Output, and Beam Intensity
The tube current (mA) of an X-ray source is defined in terms of the number of electrons per second that travel from the tungsten cathode filament to the anode. Typical values of the tube current are between 50 and 400 milliamps for planar radiography and up to 1000mA for CT. Much lower tube currents are used in continuous imaging techniques such as fluoroscopy. If the value of k[V.sub.p] is increased, the tube current also increases, until a saturation level is reached. This level is determined by the maximum temperature in, or current through, the cathode filament. X-ray tubes are generally characterized in terms of either the tube output or tube power rating. The tube output, measured in watts, is defined as the product of the tube current and the applied potential difference between the anode and cathode. In addition to the k[V.sub.p] value, the tube output also depends upon the strength of the vacuum inside the tube. A stronger vacuum enables a higher electron velocity to be established, and also a greater number of electrons to reach the anode, due to reduced interactions with gas molecules. A high tube output is desirable in diagnostic X-ray imaging because it means that a shorter exposure time can be used, which in turn decreases the possibility of motion-induced image artifacts in moving structures such as the heart.
The tube power rating is defined as the maximum power dissipated in an exposure time of 0.1 s. For example, a tube with a power rating of 10 kW can operate at a k[V.sub.p] of 80 kV with a tube current of 1.25 A for 0.1 s. The ability of the X-ray source to achieve a high tube output is ultimately limited by anode heating. The anode rotates at roughly 3000 rpm, thus increasing the effective surface area of the anode and reducing the amount of power deposited per unit area per unit time. The maximum tube output is, to a first approximation, proportional to the square root of the rotation speed. Anode rotation is accomplished using two stator coils placed close to the neck of the X-ray tube, as shown in Figure 1.3. The magnetic field produced by these stator coils induces a current in the copper rotor of the induction motor which rotates the anode. A molybdenum stem joins the main body of the anode to the rotor assembly. Because molybdenum has a high melting point and low thermal conductivity, heat loss from the anode is primarily via radiation through the vacuum to the vessel walls.
The intensity I of the X-ray beam is defined to be the power incident per unit area and has units of joules/square meter. The power of the beam depends upon two factors, the total number of X-rays and the energy of these X-rays. The number of X-rays produced by the source is proportional to the tube current, and the energy of the X-ray beam is proportional to the square of the accelerating voltage. Therefore, the intensity of the X-ray beam can be expressed as
(1.3) I [varies] [(k[V.sub.p]).sup.2](mA)
In practice, the intensity is not uniform across the X-ray beam, a phenomenon known as the heel effect. This phenomenon is due to differences in the distances that X-rays created in the anode target have to travel through the target in order to be emitted. This distance is longer for X-rays produced at the "anode end" of the target than at the "cathode end." The greater distance at the anode end results in greater absorption of the X-rays within the target and a lower intensity emitted from the source. An increase in the bevel angle can be used to reduce the magnitude of the heel effect, but this also increases the effective focal spot size.
1.2.3. The X-Ray Energy Spectrum
The output of the source consists of X-rays with a broad range of energies, as shown in Figure 1.5. High-energy electrons striking the anode generate X-rays via two mechanisms: bremsstrahlung, also called general, radiation and characteristic radiation. Bremsstrahlung radiation occurs when an electron passes close to a tungsten nucleus and is deflected by the attractive force of the positively charged nucleus. The kinetic energy lost by the deflected electron is emitted as an X-ray. Many such encounters occur for each electron, with each encounter producing a partial loss of the total kinetic energy of the electron. These interactions result in X-rays with a wide range of energies being emitted from the anode. The maximum energy [E.sub.max] of an X-ray created by this process corresponds to a situation in which the entire kinetic energy of the electron is transformed into a single X-ray. The value of [E.sub.max] (in units of keV) therefore corresponds to the value of the accelerating voltage k[V.sub.p]. The efficiency [eta] of bremsstrahlung radiation production is given by
(1.4) [eta] = k(k[V.sub.p])Z
where k is a constant (with a value of 1.1 × [10.sup.-9] for tungsten) and Z is the atomic number of the target metal. Bremsstrahlung radiation is characterized by a linear decrease in X-ray intensity with increasing X-ray energy. However, many X-rays with low energies are absorbed within the X-ray tube and its housing, resulting in the "internally filtered" spectrum shown in Figure 1.5. Additional filters external to the tube are used in order to reduce further the number of X-rays with low energies that are emitted from the tube because such X-rays do not have sufficient energy to pass through the patient and reach the detector, and therefore add to the patient dose, but are not useful for imaging. For values of k[V.sub.p] up to 50 kV, 0.5-mm-thick aluminum is used; between 50 and 70 kV, 1.5-mm-thick aluminum is used; and above 70 kV, 2.5-mm-thick aluminum is used. These filters can reduce skin dose by up to a factor of 80. For mammography studies, where the k[V.sub.p] value is less than 30 kV, a 30-µm-thick molybdenum filter is typically used.
Sharp peaks are also present in the X-ray energy spectrum, and these arise from the second mechanism, characteristic radiation. Surrounding the nucleus of any atom are a number of electron "shells" as shown in Figure 1.6.
Continues...
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