Attenuation of X-rays (AQA A Level Physics)

• When a collimated beam of X-rays passes through a patient’s body, the X-ray photons are absorbed and scattered

• Different materials absorb X-rays by different amounts
  • For example, bones absorb a large proportion of X-ray photons which is why they appear bright white on an X-ray image

• As the X-rays pass through a material, the intensity of the beam is found to decay exponentially
  • This decrease in intensity is known as attenuation

• The attenuation of X-rays can be calculated using the equation:

• Where:
  •  = the intensity of the incident beam (W m^-2)
  • = the intensity of the transmitted beam (W m^-2)
  •  = the linear absorption coefficient (m^-1)
  • = distance travelled through the material (m)

• The linear attenuation coefficient is defined as

The fraction of X-rays removed per unit thickness of the material for a specified energy of the X-rays

• The value of μ depends on the density of a substance and the energy of the X-ray photons 
  • The greater the density of a material, the greater the value of μ 
  • For example, bone absorbs a greater proportion of X-rays than soft tissue due to its higher density 

Absorption of X-rays by flesh and bone

Bone is denser than soft tissues, such as flesh, so X-rays are absorbed more over a shorter distance

Half-value thickness

• Similar to half-life in radioactivity, a material's ability to absorb X-rays is known as its half-value thickness

• The half-value thickness of a material can be defined as:

The thickness of the material which will reduce the intensity of X-rays to half its original level for a specified energy of the X-rays

• If the half-value thickness is , then intensity has a value of , so substituting this into the attenuation equation gives:

• Taking natural logarithms of both sides gives

• Hence, the half-value thickness of a substance is given by:

• The amount of attenuation of a beam of X-rays depends on
  • The density of the absorbing tissue
  • The energy of the X-ray photons

• The linear attenuation coefficient μ of an absorber is proportional to the density ρ of the absorbing substance
  • The higher the density of a material, the more X-ray energy that it absorbs
  • This is because the photons interact with more atoms, or a larger mass of atoms, in the same volume

• Therefore, dividing the value of μ of a material by its density gives a constant value for that particular substance
• This constant is known as the mass attenuation coefficient

• Where:
  • = mass attenuation coefficient (m² kg^–1)
  • = linear attenuation coefficient (m^–1)
  • = density of the absorbing material (kg m^–3)

• The mass attenuation coefficient of a substance describes how easily a beam of X-rays of a certain energy can penetrate it
  • The greater the mass attenuation coefficient, the stronger the absorption of X-rays by the material
  • The lower the mass attenuation coefficient, the greater the penetration of X-rays through the material

Mass attenuation coefficients for common elements

At very high and very low X-ray energies, differences in attenuation are very small. The optimum range for distinguishing different tissues is 30 keV to 100 keV

Photons of energies less than 30 keV...

• Are absorbed by soft tissue and bone
• Therefore, these photons are removed from the X-ray beam by placing a suitable metal filter (e.g. lead or tin) in the path of the X-ray beam

Photons of energies between 30 keV and 100 keV...

• Are absorbed more readily by bone than by soft tissue
• This is because the elements in bone have higher atomic numbers than the elements in soft tissues so bone can absorb photons in this energy range more readily
• Therefore, these photons are used to distinguish between soft tissue and bone

Photons of energies greater than 100 keV...

• Are absorbed more equally in all types of tissue, including bone
• This means they produce no distinction between any tissues
• Therefore, these photons are not used in diagnostic X-ray imaging

Attenuation in different elements

• The graph of mass attenuation coefficient and X-ray photon energy for elements with different values of atomic number Z shows that 
  • Elements with lower Z values tend to absorb a lower proportion of X-rays
  • Elements with higher Z values tend to absorb a greater proportion of X-rays

• The table below shows the composition of different substances and the effect of atomic number on attenuation

Substance	Elements	Effect on attenuation
soft tissue	hydrogen , carbon  and oxygen	lower Z values, less attenuation
bone	hydrogen , carbon , oxygen , calcium and phosphorus	higher Z values, more attenuation
contrast media	iodine  and barium	very high Z values, very large attenuation ideal for improving contrast
heavy metals	lead and tin	very high Z values, high attenuation at lower energies  ideal for use as metal filters