X-rays are one of the main diagnostical tools in medicine X-rays are one of the main diagnostical tools in medicine since its discovery by Wilhelm Roentgen in 1895. since its discovery by Wilhelm Roentgen in 1895.

Current estimates show that there are approximately 650 Current estimates show that there are approximately 650 medical and dental X-ray examinations per 1000 patients per year. medical and dental X-ray examinations per 1000 patients per year.

X-rays are produced when high energetic electrons X-rays are produced when high energetic electrons interact with matter. interact with matter.

The kinetic energy of the electrons is converted into The kinetic energy of the electrons is converted into electromagnetic energy by atomic interactions (see chapter 7.1.)electromagnetic energy by atomic interactions (see chapter 7.1.)

The X-ray tube provides an environment for X-ray production The X-ray tube provides an environment for X-ray production via via bremsstrahlimgbremsstrahlimg and characteristic radiation mechanisms. and characteristic radiation mechanisms.

electron source electron source

electron acceleration potential electron acceleration potential

target for X-ray production target for X-ray production

The classical X-ray tube requires:The classical X-ray tube requires:

The intensity of the electron beam determines the intensity The intensity of the electron beam determines the intensity of the X-ray radiation. The electron energy determines the shape of of the X-ray radiation. The electron energy determines the shape of the bremsstrahlungs spectrum, in particular the endpoint of the the bremsstrahlungs spectrum, in particular the endpoint of the spectrum. Low energy X-rays are absorbed in the tube material.spectrum. Low energy X-rays are absorbed in the tube material.

The X-ray energy determines also the emission of The X-ray energy determines also the emission of characteristic lines from the target material. characteristic lines from the target material.

The major components of the modern X-ray tube are: The major components of the modern X-ray tube are:

cathode cathode (electron source) (electron source)

anode anode (acceleration potential) (acceleration potential)

rotor/stator rotor/stator (target device) (target device)

glass/metal envelope glass/metal envelope (vacuum tube) (vacuum tube)

The figure shows a modern X-ray tube and housing assembly. The figure shows a modern X-ray tube and housing assembly.

Typical operation conditions are: Typical operation conditions are:

Acceleration Voltage: 20 to 150 kV Acceleration Voltage: 20 to 150 kV

Electron Current: 1 to 5 mA (for continuous operation) Electron Current: 1 to 5 mA (for continuous operation)

Electron Current: 0.1 to 1.0 A (for short exposures) Electron Current: 0.1 to 1.0 A (for short exposures)

The The cathodecathode consists of: consists of:

a.a. a spiral of heated low resistance R tungsten wire (filament) for a spiral of heated low resistance R tungsten wire (filament) for electron emission. Wire is heated by filament current I = U / R. electron emission. Wire is heated by filament current I = U / R.

( U ( U 10 V, I 10 V, I 3-6 A ) 3-6 A )

Electrons are released by thermionic emission, the Electrons are released by thermionic emission, the electron current is determined by the temperature which depends electron current is determined by the temperature which depends on the wire current. The electron current is approximately 5 to 10 on the wire current. The electron current is approximately 5 to 10 times less than the wire current. times less than the wire current.

b.b. a focusing cup with a negative bias voltage applied to focus the a focusing cup with a negative bias voltage applied to focus the electron distribution. electron distribution.

The anode is the target electrode and is maintained at a positive The anode is the target electrode and is maintained at a positive potential difference potential difference VVaa with respect to the cathode. Electrons are therefore with respect to the cathode. Electrons are therefore

accelerated towards the anode: accelerated towards the anode: E = wE = wVVaa

Upon impact, energy loss of electrons takes place by scattering and Upon impact, energy loss of electrons takes place by scattering and excitation processes, producing heat, electromagnetic radiation and X-rays. excitation processes, producing heat, electromagnetic radiation and X-rays.

0.5% of the electron energy is converted into X-rays.0.5% of the electron energy is converted into X-rays.

Because of the relatively low X-ray production efficiency, Because of the relatively low X-ray production efficiency, most of the released energy comes in form of heat:most of the released energy comes in form of heat:

heat generation is a major limitation for X-ray machines heat generation is a major limitation for X-ray machines

high melting point material with high X-ray output high melting point material with high X-ray output

tungsten (high melting point) good overall radiative emission tungsten (high melting point) good overall radiative emission

molybdenum (high melting points) high emission of characteristic X-rays molybdenum (high melting points) high emission of characteristic X-rays

The two major The two major anodeanode configurations are: configurations are:

The stationary anode is the classical configuration, The stationary anode is the classical configuration, tungsten target for X-ray production and copper block as heat sink tungsten target for X-ray production and copper block as heat sink

The rotating anode is a tungsten disc, large rotating surface The rotating anode is a tungsten disc, large rotating surface area warrants heat distribution, radiative heat loss (thermally area warrants heat distribution, radiative heat loss (thermally decoupled from motor to avoid overheating of the shaft) decoupled from motor to avoid overheating of the shaft)

The The anode angleanode angle is defined as the angle of the target is defined as the angle of the target surface to the central axis of the X-ray tube. surface to the central axis of the X-ray tube.

The The focal spot sizefocal spot size is the anode area that is hit by the is the anode area that is hit by the electrons.electrons.

effective focal length = focal length • sineffective focal length = focal length • sin

The angle The angle also determines the X-ray field size coverage. For also determines the X-ray field size coverage. For small angles the X-ray field extension is limited due to absorption and small angles the X-ray field extension is limited due to absorption and attenuation effects of X-ray photons parallel to the anode surface. attenuation effects of X-ray photons parallel to the anode surface.

The anode angle The anode angle determines the effective focal spot size: determines the effective focal spot size:

Typical angles are: Typical angles are: = T= T to 20°. to 20°.

A small angle in close distance is recommended for A small angle in close distance is recommended for small spot coverage, a large angle is necessary for large small spot coverage, a large angle is necessary for large area coverage. area coverage.

The X-rays pass through a tube window (with low X-ray The X-rays pass through a tube window (with low X-ray absorption) perpendicular to the electron beam. absorption) perpendicular to the electron beam.

Usually the low energy component of the X-ray spectrum does Usually the low energy component of the X-ray spectrum does not provide any information because it is completely absorbed in the not provide any information because it is completely absorbed in the body tissue of the patient. It does however contribute significantly to body tissue of the patient. It does however contribute significantly to the absorbed dose of the patient which excess the acceptable dose the absorbed dose of the patient which excess the acceptable dose limit.limit.

These lower energies are therefore filtered out by aluminum These lower energies are therefore filtered out by aluminum or copper absorbers of various thickness.or copper absorbers of various thickness.

The minimum thickness d depends on the maximum The minimum thickness d depends on the maximum operating potential of the X-ray tube but is typically d operating potential of the X-ray tube but is typically d 2.5 mm for 2.5 mm for VVaa 100 kV 100 kV

The intensity drops exponentially with the thickness d: The intensity drops exponentially with the thickness d:

with with effeff as material dependent absorption coefficient. as material dependent absorption coefficient.

The absorption coefficient is determined in terms of The absorption coefficient is determined in terms of the the HHalf-alf-VValue alue LLayer ayer HVLHVL which is the thickness of a material which is the thickness of a material necessary to reduce the intensity to 50% of its original value. necessary to reduce the intensity to 50% of its original value.

The solution yields: The solution yields:

Graph showing how the intensity of an x-ray beam Graph showing how the intensity of an x-ray beam is reduced by an absorber whose linear absorption is reduced by an absorber whose linear absorption coefficient is coefficient is = 0.10 cm = 0.10 cm11..

The spectral distribution of the X-rays can be defined by The spectral distribution of the X-rays can be defined by the appropriate choice of filters. the appropriate choice of filters.

The filter material depends on the energy range of the The filter material depends on the energy range of the original X-ray distribution!original X-ray distribution!

The influence of different filter combinations for a 200 kV The influence of different filter combinations for a 200 kV X-ray spectrum is shown in the figure. X-ray spectrum is shown in the figure.

The X-ray beam size is limited by a collimator system, the The X-ray beam size is limited by a collimator system, the collimators are lead for complete absorption. collimators are lead for complete absorption.

Collimator design allows to optimize the point exposure! Collimator design allows to optimize the point exposure!

The size of the collimator (object size) determines the The size of the collimator (object size) determines the geometric "unsharpness" (blurring) of the image. geometric "unsharpness" (blurring) of the image.

The blurring The blurring B B in the image is given by: in the image is given by:

where where aa is the effective size of the collimator of the is the effective size of the collimator of the X-ray tube and X-ray tube and mm is the image magnification: is the image magnification:

The resulting geometric unsharpeness The resulting geometric unsharpeness UUgg is defined: is defined:

Additional unsharpeness can be caused by the image Additional unsharpeness can be caused by the image receptor (grain size, resolution of the film, etc) and by movement of receptor (grain size, resolution of the film, etc) and by movement of the object (restless person). the object (restless person).

For general radiography purposes the geometric For general radiography purposes the geometric unsharpeness dominates the other components unsharpeness dominates the other components

Therefore the unsharpeness will increase with increasing Therefore the unsharpeness will increase with increasing magnification. To keep magnification small (close to m=1) requires magnification. To keep magnification small (close to m=1) requires the image receptor to be as close as possible to the patient and the the image receptor to be as close as possible to the patient and the focus patient distance to be large. focus patient distance to be large.

Typical conditions are: Typical conditions are:

a a 1mm 1mm

dd11 1 m 1 m

dd22 10 cm 10 cm

110cm = =1.1 100cm

m

1 =1mm 1- =0.091mm

1.1gU

For a close dental X-ray shot the conditions are: For a close dental X-ray shot the conditions are:

a a 1mm 1mm

dd11 5 5

cmcm

dd22 1 cm 1 cm

6cm = =1.2 5cm

m

1 =1mm 1- =0.167mm

1.2gU

The radiographic image of the X-ray exposure is The radiographic image of the X-ray exposure is determined by the interaction of the X-rays which are transmitted determined by the interaction of the X-rays which are transmitted through the patient with a photon detector (film, camera etc.) through the patient with a photon detector (film, camera etc.)

Primary X-ray photons have passed through the patient Primary X-ray photons have passed through the patient without interaction, they carry useful information. without interaction, they carry useful information.

They give a measure for the probability that a photon pass through They give a measure for the probability that a photon pass through the patient without interaction which is a function of the body tissue the patient without interaction which is a function of the body tissue attenuation coefficients. attenuation coefficients.

Secondary photons result from interaction inside the patient, they Secondary photons result from interaction inside the patient, they are usually deflected from their original direction and carry therefore only are usually deflected from their original direction and carry therefore only little information. They create background noise which degrades the little information. They create background noise which degrades the contrast of the image. contrast of the image.

Scattered photons are often absorbed in grids between the patient Scattered photons are often absorbed in grids between the patient and the image receptor. and the image receptor.

The two dimensional image The two dimensional image II((x, yx, y)) of the three dimensionalof the three dimensionaldistribution of the X-ray attenuating body tissue of the patient can be distribution of the X-ray attenuating body tissue of the patient can be described as a function of the initial photon intensity described as a function of the initial photon intensity NN of energy of energy EE, , the energy absorption efficiency of the image receptor the energy absorption efficiency of the image receptor ((EE)) (film) and (film) and the attenuation coefficients the attenuation coefficients which have to be considered along the which have to be considered along the photon path in z-direction. photon path in z-direction.

with with SS((EE)) as distribution of the scattered secondary X-ray photons. as distribution of the scattered secondary X-ray photons.

The expression can be simplified to: The expression can be simplified to:

with with RR as the ratio of secondary to primary radiation. as the ratio of secondary to primary radiation.

As higher the attenuation coefficient, as larger absorption, As higher the attenuation coefficient, as larger absorption, as lower the final intensity of the image. as lower the final intensity of the image.

For bone tissue the attenuation coefficient is considerably larger For bone tissue the attenuation coefficient is considerably larger than for soft body tissue, therefore increased absorption. than for soft body tissue, therefore increased absorption.

The quality of the image can be assessed by a few physical parameters: The quality of the image can be assessed by a few physical parameters:

radiographic contrast radiographic contrast

noise and dose noise and dose

CONTRAST OF THE IMAGECONTRAST OF THE IMAGE

Consider that you want to image clearly a target tissue of thickness Consider that you want to image clearly a target tissue of thickness xx with an attenuation coefficient with an attenuation coefficient 22 inside the body of thickness inside the body of thickness tt with a lower soft with a lower soft

body tissue attenuation coefficient body tissue attenuation coefficient 11

The The contrast contrast CC of the target tissue volume is defined in of the target tissue volume is defined in terms of the image distribution function terms of the image distribution function II11 and and II22::

II11 gives the energy absorbed outside the target tissue gives the energy absorbed outside the target tissue

II22 gives the energy absorbed inside the target volume. gives the energy absorbed inside the target volume.

Approximating for an X-ray energy Approximating for an X-ray energy EE: :

The expression can be simplified to:The expression can be simplified to:

The contrast depends mainly on the difference of attenuation coefficients The contrast depends mainly on the difference of attenuation coefficients 11 and and 22 as well as on the ratio of scattered to primary X-ray photons. as well as on the ratio of scattered to primary X-ray photons.

As higher the ratio As higher the ratio RR (the number of scattered photons), as lower the contrast. (the number of scattered photons), as lower the contrast.

Therefore it is important to understand and to reduce secondary Therefore it is important to understand and to reduce secondary scattered photon intensity to minimize scattered photon intensity to minimize RR..

The number of scattered photons depends on several parameters: The number of scattered photons depends on several parameters:

X-ray field size; an increase in field size increases X-ray field size; an increase in field size increases R R 3.5 3.5

Thickness of radiated volume (increase is roughly proportional Thickness of radiated volume (increase is roughly proportional with thickness due to increase in scattering events) with thickness due to increase in scattering events)

X-ray energy dependence - decrease of scatter with increasing energyX-ray energy dependence - decrease of scatter with increasing energy

To reduce the number of secondary scattered photons a To reduce the number of secondary scattered photons a led grid is typically between object and image receptor. Because led grid is typically between object and image receptor. Because scattered photons will not meet the grid at normal incidence, they scattered photons will not meet the grid at normal incidence, they will be absorbed by the grid stripes. will be absorbed by the grid stripes.

NOISE AND DOSENOISE AND DOSE

Even if the imaging system may have high contrast the noise Even if the imaging system may have high contrast the noise level may prevent identification of the object. level may prevent identification of the object.

Two major noise components are: Two major noise components are:

statistical fluctuations in the number of X-ray photons statistical fluctuations in the number of X-ray photons

fluctuations in the receptor and display system fluctuations in the receptor and display system

The first component of the noise is called quantum noise can usually 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. be reduced by increasing the number of photons used to form an image.

What is the minimum surface dose required on a body of What is the minimum surface dose required on a body of thickness thickness t t to see a contrast to see a contrast C C for an object of size for an object of size x x over an area over an area A A against a background of pure quantum noise? against a background of pure quantum noise?

The signal to be detect is: The signal to be detect is:

The image noise in an area The image noise in an area A A results from a statistical Poisson process results from a statistical Poisson process and can be derived as: and can be derived as:

This however will increase the dose absorbed by the patient which This however will increase the dose absorbed by the patient which should be minimized.should be minimized.

This yields for the signal to noise ratio This yields for the signal to noise ratio SNRSNR: :

An object becomes detectable if the An object becomes detectable if the SNR SNR exceeds a threshold value of: exceeds a threshold value of:

At these conditions the number of incident photons At these conditions the number of incident photons N N for the patient can for the patient can be calculated to: be calculated to:

The absorbed dose The absorbed dose DD for the patient is determined by the for the patient is determined by the number of photons per area number of photons per area NN, the mass energy absorption coefficient , the mass energy absorption coefficient for tissue (for tissue (), and the photon energy ), and the photon energy EE::

The minimum dose required to visualize a fixed object increases withThe minimum dose required to visualize a fixed object increases withthe fourth power of the object size. the fourth power of the object size.

For a fixed dose and contrast there is a minimum object size which For a fixed dose and contrast there is a minimum object size which can be visualized. can be visualized.