Interaction of x-ray photons

unkindnesskindUrban and Civil

Nov 15, 2013 (3 years and 11 months ago)

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Interaction of x
-
ray photons
(and gamma ray photons)

with matter

Interaction of x
-
ray photons with matter


When a beam of x
-
ray photons passes through
matter, its intensity (energy


or number of x
-
ray
photons
-

flowing per second) is reduced:

the beam has been
attenuated,
photon energy has
been
removed
from the beam


photon energy is attenuated by either being
absorbed by the matter
or
scattered out of the beam


Any photon energy not attenuated, is
transmitted
.


Electrical energy

x
-
ray photon energy

In the x
-
ray tube for
diagnostic imaging

or linear accelerator for
radiotherapy treatment

absorbed energy:
radiation dose

scattered x
-
ray energy

transmitted x
-
ray energy

Attenuation and transmission of
x
-
ray photon energy

in the patient

converted into

converted into

at the x
-
ray target

Absorption

some or all of the x
-
ray photon energy may be
absorbed

when energy is transferred to matter

The energy deposited per unit mass of matter is
called
absorbed dose


Units: joule per kg = 1 gray (Gy)

the energy deposited as absorbed dose causes
ionisation and subsequent chemical changes
that may result in biological effects


CT scan: differential absorption in tissues using
kilovoltage x
-
ray photons

RT treatment plan: absorbed dose distribution using
megavoltage x
-
ray photons

Scatter

Some x
-
ray photons are partially absorbed and their
remaining energy
scattered
: deflected from their
original path

at high photon energies in megavoltage
radiotherapy, scatter is in the forward direction and
contributes to absorbed dose

at low photon energies in diagnostic imaging,
scatter occurs in all directions and may contribute to
loss of image quality by increasing the overall
density of the image receptor

scattered x
-
ray photons contribute to the patient

s
dose (by internal scatter) and exposure of staff

scatter

Side scatter

Forward scatter

Back scatter

x
-
ray source

patient

image receptor

lead
-
glass screen

air

Scattered radiation reaching image receptor

blackening due to
collimated x
-
ray photons in
primary beam

low density blackening
around collimated beam
due to scattered x
-
ray
photons from collimators
and object

object

attenuation is exponential…

Attenuation in matter is due to some x
-
ray photons
being totally absorbed



and some x
-
ray photons being partially absorbed
and their remaining energy scattered

X
-
ray photons that are not attenuated, are transmitted

X
-
ray photons are attenuated differently in different
materials depending on various factors: the individual
x
-
ray photon

s energy, the material

s physical density,
electron density, proton number and its thickness

For a specific photon energy, an equal percentage (or
fraction) of the energy in the beam is attenuated in
equal thicknesses of material



This is an exponential relationship: equal changes in
one quantity give equal fractional changes in another


Exponential attenuation

The linear attenuation coefficient (
m
) gives the
fractional reduction in intensity of a homogenous
beam of x
-
ray photons per cm thickness of matter

For example, the linear attenuation coefficient of soft
tissue for 100 keV x
-
ray photons is approximately 0.2
(20%)
(Bushong: table 29.1 in 6
th

ed)

20% of photon energy is attenuated in each cm
thickness of soft tissue; 80% is transmitted

1 cm

1 cm

1 cm

1 cm

1 cm

100%

80%

64%

51%

41%

33%

Exponential attenuation


The exponential relationship between the intensity
of transmitted x
-
ray photons and the thickness of a
specific material can be given as:





Where

I
t

= transmitted intensity




I
o

= original intensity




e = exponential constant (2.718)




m

= linear attenuation coefficient of material




x = thickness of material


Provided the x
-
ray beam is


i) homogenous







ii) parallel

I
t

=
I
o

e
-
m
x

Exponential attenuation of a beam of x
-
ray photons
in equal thicknesses of aluminium is used to
measure
half value thickness (HVT)

in an x
-
ray
beam as part of routine quality assurance

The linear attenuation coefficient is calculated for
each individual voxel of tissue during a
CT
(computerised tomography) scan

and mapped to a
grey scale. Different tissues have slightly different
coefficients and therefore map to a different grey to
give the image

Exponential attenuation in practice


Interaction Processes



There are various interaction processes
of x
-
ray (and gamma ray) photons, that
may occur alongside each other:

coherent (elastic) scatter (negligible)

Compton (inelastic) scatter

photoelectric absorption

pair production


Relative importance of each
interaction process in water

x
-
ray photon
energy

photoelectric
absorption

Compton
scatter

Pair
production

10 keV

95%

5%

0

25 keV

50%

50%

0

60 keV

7%

93%

0

150 keV

0

100%

0

4 MeV

0

94%

6%

10 MeV

0

77%

23%

24 MeV

0

50%

50%



Mass attenuation coefficients in air

Graham & Cloke (2003) p 299

Occurs when an x
-
ray photon interacts with a
bound electron, in the inner shells of an atom

Only occurs if the energy of the x
-
ray photon
exceeds the binding energy of the shell

The x
-
ray photon disappears by transferring all its
energy to the bound electron

This energy is used to overcome the binding
energy of the electron, which then escapes the
atom as a photoelectron carrying kinetic energy

The photoelectron loses its KE via ionisation of
surrounding atoms


Photoelectric absorption

Photoelectric absorption

incident x
-
ray
photon


photoelectron
c
arrying KE


photons of
electromagnetic radiation

z
3

E
3




The probability of
photoelectric absorption




and is more likely to occur:


in beams of low energy when the average x
-
ray photon
energy is < 25 keV


in dense matter with atoms of higher proton number eg
bone, metal (shielding, filters), positive contrast media
(barium sulphate, iodine)


With a bound electron in an atom where the x
-
ray photon
energy is just above the binding energy:




this results in absorption edges: a large increase in
photoelectric absorption of x
-
ray photons with an energy just
above the binding energy of a specific shell


and an
increase in x
-
ray photons being transmitted just below the
binding energy


z
3

E
3

Photoelectric absorption:

absorption edges

Photoelectric absorption
only occurs when the x
-
ray
photon energy is equal to,
or slightly greater than, the
electron binding energy

This results in bursts of
absorption at the binding
energy of each shell

Compton scatter

Occurs alongside photoelectric absorption

An x
-
ray photon interacts with a bound electron,
whose binding energy is negligible in comparison
with the x
-
ray photon energy

Some of the x
-
ray photon energy is transferred to
the electron, to overcome its binding energy. It
escapes the atom as a Compton electron carrying
kinetic energy

The Compton electron loses its KE via ionisation of
surrounding atoms

The x
-
ray photon with reduced energy is deviated,
or scattered, from its original path and will interact
again until all its energy is lost and it disappears.



Compton scatter

Compton
electron
carrying KE

scattered x
-
ray photon
with reduced energy

incident x
-
ray
photon

angle of scatter



electron density



E

The probability of

Compton scatter


and is more likely to occur


In higher energy x
-
ray beams (average energy >25 keV)


when electron binding energies in the attenuating material are
negligible in comparison;


as photon energy increases, the proportion of forward scatter
increases.


In diagnostic imaging, Compton scatter results in a loss of
image quality. In megavoltage radiotherapy, it results in poor
quality portal images but gives the main contribution to
absorbed dose


In materials containing atoms with a high electron density eg
hydrogen.


In diagnostic imaging, this results in more scatter in soft
tissues…increasing the importance of collimation and shielding.
In megavoltage radiotherapy, inhomogeneity correction is
important in treatment planning



electron density



E

Megavoltage imaging: example of DRR
and portal image

Pair production

A high energy x
-
ray photon (>1.02 MeV) interacts
with a nucleus

Its energy is converted into an electron and a
positron, carrying any excess energy as kinetic
energy

The positron annihilates with an electron: the two
particles are converted back into energy


two
gamma ray photons of 511 keV


Pair production only becomes important in very high
energy beams of photons above 10 MeV

Pair

production

incident x
-
ray
photon


electron

+ KE


positron

+ KE


g
-
ray photon

0.511 MeV

g
-
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E.z

Summary: Interaction of x
-
ray
photons with matter


When a beam of x
-
rays passes through
matter, its intensity is reduced:
attenuated

attenuation is due to the interaction
processes of photoelectric absorption,
Compton scatter or pair production

Attenuation increases with thickness and
density of matter

interaction process depends on x
-
ray photon
energy, proton number and electron density
of the matter

Energy transfer to matter

Electrical energy


KE of electrons


x
-
ray production: characteristic/bremss


x
-
ray photon energy and heat energy



Interaction of x
-
ray photons

Photoelectric absorption

Compton scatter

Pair production


Secondary electrons carrying KE



x
-
ray photon energy deposited


Excitation and ionisation


Chemical/biological effects




at x
-
ray target

in matter