RTT 425 Radiation
Therapy Physics
Radiation Quality, Chapter 4
From
Stanton and Stinson: Applied physics
for Radiation Oncology
Intensity
• Amount of energy per unit time per unit
area.
• Depends on original energy of the beam,
divergence of the beam and attenuation.
Beam divergence (inverse square
law)
Beam divergence
• Intensity is inversely proportional to the
square of the distance from the source.
• This is due to the fact that the beam
spreads out.
• I1 /I2 = (D2)2 / (D1)2
Attenuation
• The removal of energy from the beam.
• This happens when a beam passes
through matter.
Attenuation
• If matter (a filter) is placed in the beam’s path,
some of the photons will be absorbed, some will
be scattered and some will pass through (be
transmitted) to the other side.
• The reduction in the number of photons is
proportional to the number of incident photons
and to the thickness of the absorber
• The ratio of the beam intensity on one side of
the matter to the other is called the transmission.
T = I/I0
Attenuation
• For a photon source with one energy, the
attenuation is given by:
I = I0 e-μx
e is the natural log or 2.718, x is the
thickness of the filter and μ is the linear
attenuation coefficient.
Linear attenuation coefficient represents the
probability per unit thickness that any one
photon will be attenuated.
Mathematics of attenuation
• μ is the constant of proportionality called
the attenuation coefficient.
• If the thickness is expressed in length,
then μ is called the linear attenuation
coefficient.
• The units of μ are 1/cm, or cm-1
Attenuation
• If the beam is heterogeneous, like an x-ray
beam made up of Bremstrahlung, this
exponential attenuation cannot occur, as
each photon energy will have its own
linear attenuation coefficient.
Attenuation
• Homogeneous beam
• Heterogeneous beam
Attenuation
• Why does this happen?
• As more layers of filter are added, the
lower energy photons are removed and so
the emerging beam is “harder”, or more
penetrating.
Half value layer
• The thickness of an absorber of specified
composition required to attenuate the intensity of
the beam to half its original value.
• All beams can be described in terms of its HVL,
but the quality is usually stated in terms of its
energy.
• Quality of gamma beam is stated as energy of
gamma ray OR its nuclide of origin.
HVL
• HVL is mostly used to describe the quality
of low energy x-ray beams, together with
kVp.
• An important fact about HVL is that for a
heterogeneous beam, each consecutive
layer has to be larger
• ie: 2nd HVL is larger than the first, 3rd is
larger than the 2nd.
Quality of an x-ray beam
• Penetrating ability of the beam.
• How much of the beam goes into the
patient?
Filters
• An x-ray beam has a distribution of
energies of bremsstrahlung photons on
which is superimposed lines of
characteristic radiation.
• Inherent filtration occurs because of the
glass envelope, oil, and exit window of the
tube.
Thoreaus filters
• Tube – tin – copper – aluminum – air –
patient.
• Highest atomic number nearest the x-ray
target.
HVL mathematics
• Attenuation equation:
I = I0e-μx
• When x = HVL, I0 is ½ therefore from the
above equation, we get
HVL = 0.693/μ
HVL
• If you increase the filtration, you reduce
the exposure rate, so a filter is carefully
chosen to give a suitable HVL and an
acceptable exposure rate.
Energies and HVL’s