X-rays are one of the main diagnostical tools in medicine since its discovery by Wilhelm Roentgen in 1895. Current estimates show that there are approximately 650 medical and dental X-ray examinations per 1000 patients per year. X-rays are produced when high energetic electrons interact with matter. The kinetic energy of the electrons is converted into
electromagnetic energy by atomic interactions (see chapter 7.1.) The X-ray tube provides an environment for X-ray production via bremsstrahlimg and characteristic radiation mechanisms. The classical X-ray tube requires: electron source electron acceleration potential
target for X-ray production The intensity of the electron beam determines the intensity of the X-ray radiation. The electron energy determines the shape of the bremsstrahlungs spectrum, in particular the endpoint of the spectrum. Low energy X-rays are absorbed in the tube material.
The X-ray energy determines also the emission of characteristic lines from the target material. The major components of the modern X-ray tube are: cathode (electron source) anode (acceleration potential)
rotor/stator (target device) glass/metal envelope (vacuum tube) The figure shows a modern X-ray tube and housing assembly. Typical operation conditions are: Acceleration Voltage: 20 to 150 kV
Electron Current: 1 to 5 mA (for continuous operation) Electron Current: 0.1 to 1.0 A (for short exposures) The cathode consists of: a.
a spiral of heated low resistance R tungsten wire (filament) for electron emission. Wire is heated by filament current I = U / R. ( U 10 V, I 3-6 A ) Electrons are released by thermionic emission, the electron current is determined by the temperature which depends on the wire current. The electron current is approximately 5 to 10
times less than the wire current. b. a focusing cup with a negative bias voltage applied to focus the electron distribution. The anode is the target electrode and is maintained at a positive potential difference Va with respect to the cathode. Electrons are therefore
accelerated towards the anode: E = wVa Upon impact, energy loss of electrons takes place by scattering and excitation processes, producing heat, electromagnetic radiation and X-rays. 0.5% of the electron energy is converted into X-rays. Because of the relatively low X-ray production efficiency, most of the released energy comes in form of heat:
heat generation is a major limitation for X-ray machines high melting point material with high X-ray output tungsten (high melting point) good overall radiative emission molybdenum (high melting points) high emission of characteristic X-rays The two major anode configurations are:
The stationary anode is the classical configuration, tungsten target for X-ray production and copper block as heat sink The rotating anode is a tungsten disc, large rotating surface area warrants heat distribution, radiative heat loss (thermally decoupled from motor to avoid overheating of the shaft)
The anode angle is defined as the angle of the target surface to the central axis of the X-ray tube. The focal spot size is the anode area that is hit by the electrons. The anode angle determines the effective focal spot size:
effective focal length = focal length sin The angle also determines the X-ray field size coverage. For small angles the X-ray field extension is limited due to absorption and attenuation effects of X-ray photons parallel to the anode surface. Typical angles are: = T to 20.
A small angle in close distance is recommended for small spot coverage, a large angle is necessary for large area coverage. The X-rays pass through a tube window (with low X-ray absorption) perpendicular to the electron beam.
Usually the low energy component of the X-ray spectrum does not provide any information because it is completely absorbed in the body tissue of the patient. It does however contribute significantly to the absorbed dose of the patient which excess the acceptable dose limit.
These lower energies are therefore filtered out by aluminum or copper absorbers of various thickness. The minimum thickness d depends on the maximum operating potential of the X-ray tube but is typically d 2.5 mm for Va 100 kV
The intensity drops exponentially with the thickness d: with eff as material dependent absorption coefficient. The absorption coefficient is determined in terms of the Half-Value Layer HVL which is the thickness of a material necessary to reduce the intensity to 50% of its original value.
The solution yields: Graph showing how the intensity of an x-ray beam is reduced by an absorber whose linear absorption coefficient is = 0.10 cm1.
The spectral distribution of the X-rays can be defined by the appropriate choice of filters. The filter material depends on the energy range of the original X-ray distribution! The influence of different filter combinations for a 200 kV
X-ray spectrum is shown in the figure. The X-ray beam size is limited by a collimator system, the collimators are lead for complete absorption. Collimator design allows to optimize the point exposure!
The size of the collimator (object size) determines the geometric "unsharpness" (blurring) of the image. The blurring B in the image is given by: where a is the effective size of the collimator of the X-ray tube and m is the image magnification:
The resulting geometric unsharpeness Ug is defined: Additional unsharpeness can be caused by the image receptor (grain size, resolution of the film, etc) and by movement of the object (restless person). For general radiography purposes the geometric
unsharpeness dominates the other components Therefore the unsharpeness will increase with increasing magnification. To keep magnification small (close to m=1) requires the image receptor to be as close as possible to the patient and the focus patient distance to be large. Typical conditions are: a 1mm
d1 1 m 110cm m= =1.1 100cm
d2 10 cm 1 Ug =1mm 1- =0.091mm 1.1 For a close dental X-ray shot the conditions are:
a 1mm d1 5 cm d2 1 cm 6cm
m= =1.2 5cm 1 Ug =1mm 1=0.167mm
1.2 The radiographic image of the X-ray exposure is determined by the interaction of the X-rays which are transmitted through the patient with a photon detector (film, camera etc.) Primary X-ray photons have passed through the patient
without interaction, they carry useful information. They give a measure for the probability that a photon pass through the patient without interaction which is a function of the body tissue attenuation coefficients. Secondary photons result from interaction inside the patient, they
are usually deflected from their original direction and carry therefore only little information. They create background noise which degrades the contrast of the image. Scattered photons are often absorbed in grids between the patient and the image receptor.
The two dimensional image I(x, y) of the three dimensional distribution of the X-ray attenuating body tissue of the patient can be described as a function of the initial photon intensity N of energy E, the energy absorption efficiency of the image receptor (E) (film) and the attenuation coefficients which have to be considered along the photon path in z-direction.
with S(E) as distribution of the scattered secondary X-ray photons. The expression can be simplified to: with R as the ratio of secondary to primary radiation. As higher the attenuation coefficient, as larger absorption,
as lower the final intensity of the image. For bone tissue the attenuation coefficient is considerably larger than for soft body tissue, therefore increased absorption. The quality of the image can be assessed by a few physical parameters: radiographic contrast
noise and dose CONTRAST OF THE IMAGE Consider that you want to image clearly a target tissue of thickness x with an attenuation coefficient 2 inside the body of thickness t with a lower soft body tissue attenuation coefficient 1
The contrast C of the target tissue volume is defined in terms of the image distribution function I1 and I2: I1 gives the energy absorbed outside the target tissue I2 gives the energy absorbed inside the target volume. Approximating for an X-ray energy E:
The expression can be simplified to: The contrast depends mainly on the difference of attenuation coefficients 1 and 2 as well as on the ratio of scattered to primary X-ray photons. As higher the ratio R (the number of scattered photons), as lower the contrast. Therefore it is important to understand and to reduce secondary
scattered photon intensity to minimize R. The number of scattered photons depends on several parameters: X-ray field size; an increase in field size increases R 3.5 Thickness of radiated volume (increase is roughly proportional with thickness due to increase in scattering events)
X-ray energy dependence - decrease of scatter with increasing energy To reduce the number of secondary scattered photons a led grid is typically between object and image receptor. Because scattered photons will not meet the grid at normal incidence, they will be absorbed by the grid stripes.
NOISE AND DOSE Even if the imaging system may have high contrast the noise level may prevent identification of the object. Two major noise components are: statistical fluctuations in the number of X-ray photons
fluctuations in the receptor and display system The first component of the noise is called quantum noise can usually be reduced by increasing the number of photons used to form an image. This however will increase the dose absorbed by the patient which should be minimized.
What is the minimum surface dose required on a body of thickness t to see a contrast C for an object of size x over an area A against a background of pure quantum noise? The signal to be detect is: The image noise in an area A results from a statistical Poisson process and can be derived as:
This yields for the signal to noise ratio SNR: An object becomes detectable if the SNR exceeds a threshold value of: At these conditions the number of incident photons N for the patient can be calculated to:
The absorbed dose D for the patient is determined by the number of photons per area N, the mass energy absorption coefficient for tissue (), and the photon energy E: The minimum dose required to visualize a fixed object increases with the fourth power of the object size.
For a fixed dose and contrast there is a minimum object size which can be visualized.
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