Dose Distribution and Scatter Analysis
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Phantoms
Depth Dose Distribution
Percentage Depth Dose
Tissue-Air Ratio
Scatter-Air Ratio
Phantoms
• Water phantom: closely approximates
the radiation absorption and scattering
properties of muscle and other soft
tissues; universally available with
reproducible
PHANTOMS
• Basic dose distribution data are usually
measured in a water phantom, which
closely approximates the radiation
absorption and scattering properties of
muscle and other soft tissue
• Another reason for the choice of water as
a phantom material is that it is
universally available with reproducible
radiation properties.
PHANTOMS
• Solid dry phantoms
– tissue or water equivalent, it must have the
same
• effective atomic number
• number of electrons per gram
• mass density
– For megavoltage photon beams in the clinical range,
the necessary condition for water equivalence
• same electron density (number of electrons per
cubic centimeter)
Compton effect is the
main interaction
Solid dry phantoms
Solid dry (Slab) phantoms
Alderson Rando Phantom
• anthropomorphic
phantom
– Frequently used for
clinical dosimetry
– Incorporates materials
to simulate various
body tissues, muscle,
bone, lung, and air
cavities
RANDO phantom
CT slice
through lung
Head with
TLD holes
Depth Dose Distribution
• The absorbed dose in the patient varies with depth
• The variation depends on depth, field size,
distance from source, beam energy and beam
collimation
• Percentage depth dose, tissue-air ratios, tissuephantom ratios and tissue-maximum ratios--measurements made in water phantoms using
small ionization chambers
Percentage Depth Dose
• Absorbed dose at any depth: d
• Absorbed dose at a fixed reference depth: d0
Dd
collimator
P
100
Dd 0
surface
d0
d
D d0
Dd
phantom
PERCENTAGE DEPTH DOSE
• For orthovoltage (up to
about 400 kVp) and
lower-energy x-rays, the
reference depth is usually
the surface (do = 0).
• For higher energies, the
reference depth is taken
at the position of the peak
absorbed dose (do = dm).
Percentage Depth Dose
• For higher energies, the reference depth is at the
peak absorbed dose ( d 0= d m)
• D max : maximum dose, the dose maximum, the
given dose
collimator
Dd
P
100
Dmax
surface
dm
D max
Dmax
Dd

100
P
d
Dd
phantom
Percentage Depth Dose
• (a)Dependence on beam quality and depth
• (b)Effect of field size and shape
• (c)Dependence on SSD
Percentage Depth Dose
(a)Dependence on beam quality and depth
• Kerma—
(1) kinetic energy released per mass in the medium;
(2) the energy transferred from photons to directly ionizing
electron;
(3) maximum at the surface and decreases with depth due to
decreased in the photon energy fluence;
(4) the production of electrons also decreases with depth
Percentage Depth Dose
(a)Dependence on beam quality and depth
• Absorbed dose:
• (1) depends on the electron fluence;
• (2) high-speed electrons are ejected from the surface and
subsequent layers;
• (3) theses electrons deposit their energy a significant
distance away from their site of origin
Dd
P
100
Dmax
Fig. 9.3 central axis depth dose distribution for
different quality photon beams
Percentage Depth Dose
(b)Effect of field size and shape
• Geometrical field size: the projection, on a plane
perpendicular to the beam axis, of the distal end of
the collimator as seen from the front center of the
source
• Dosimetric ( Physical ) field size: the distance
intercepted by a given isodose curve (usually 50%
isodose ) on a plane perpendicular to the beam
axis
PDD - Effect of Field Size and Shape
• Field size
– Geometrical
– Dosimetrical or
physical
SAD
FS
Percentage Depth Dose
(b)Effect of field size and shape
• As the field size is increased, the contribution of
the scattered radiation to the absorbed dose
increases
• This increase in scattered dose is greater at larger
depths than at the depth of D max , the percent
depth dose increases with increasing field size
Scatter dose
Dd
P
100
Dmax
Dmax
Dd
Percentage Depth Dose
(b)Effect of field size and shape
• Depends on beam quality
• The scattering probability or cross-section
decreases with energy increase and the higherenergy photons are scattered more predominantly
in the forward direction, the field size dependence
of PDD is less pronounced for the higher-energy
than for the lower-energy beams
Percentage Depth Dose
(b)Effect of field size and shape
• PDD data for radiotherapy beams are usually
tabulated for square fields
• In clinical practice require rectangular and
irregularly shaped fields
• A system of equating square fields to different
field shapes is required: equivalent square
• Quick calculation of the equivalent
c
B
c
rectangular field
A
square field
c=2x
AxB
A+B
Percentage Depth Dose
(b)Effect of field size and shape
• Quick calculation of the equivalent field
parameters: for rectangular fields
A
ab

P 2(a  b)
A a

• For square fields, since a = b,
P 4
• the side of an equivalent square of a rectangular
field is
A
4
P
A
4
a
P
b
4
A
P
Percentage Depth Dose(3)--(b)Effect of
field size and shape
• Equivalent circle has the same area as the
equivalent square
r 
4
A

P

4
a
b
4
A
P
A
P
r
Percentage Depth Dose
(c) dependence on SSD
• Photon fluence emitted by a point source of
radiation varies inversely as a square of the
distance from the source
• The actual dose rate at a point decreases with
increase in distance from the source, the percent
depth dose, which is a relative dose, increases with
SSD
• Mayneord F factor
PDD - Dependence on SourceSurface Distance
• Dose rate in free space from a point source varies
inversely as the square of the distance. (IVSL)
– scattering material in the beam may cause deviation
from the inverse square law.
• PDD increases with SSD
– IVSL
SSD’
SSD
dm
dm
d
d
Percentage Depth Dose
(c) dependence on SSD
Dd
P
100
Dmax
F1+dm
F2+dm
F1+d
F2+d
Fig. 9.5 Plot of relative dose rate as inverse square law function
of distance from a point source. Reference distance = 80 cm
f1
f2
r
dm
r
d
dm
d
2
 f1  d m    ( d  d m )
 .e
P(d , r , f1 )  100 
.K s
 f 1 d  2
 f 2  d m   ( d d m )
 .e
P(d , r , f 2 )  100 
.K s
 f2  d 
P(d , r , f 2 )  f 2  d m
 
P (d , r , f1 )  f1  d m
2

 f1  d
  
 f2  d




2
f1
f2
r
dm
r
d
dm
d
PDD increases with SSD
the Mayneord F Factor ( without considering changes in
scattering )
2
2
 f2  dm
F  
 f1  d m

 f1  d
  
 f2  d




PDD - Dependence on Source-Surface Distance
• PDD increases with SSD
Example
The PDD for a 15×15 field size, 10-cm depth,
and 80-cm SSD is 58.4-Gy (C0-60 Beam).
Find the PDD for the same field size and
depth for a 100-cm SSD
Assuming dm=0.5-cm for (C0-60 Gamma
Rays).
F=1.043
P= 58.4*1.043=60.9
Percentage Depth Dose
(c) dependence on SSD
• Under extreme conditions such as lower energy,
large field (the proportion of scattered radiation is
relatively greater), large depth, and large SSD, the
Mayneord F factor is significant errors
• In general, the Mayneord F factor overestimates
the increase in PDD with increase in SSD
PDD - Dependence on Source-Surface Distance
• PDD increases with SSD
– the Mayneord F Factor
• works reasonably well for small fields since the
scattering is minimal under these conditions.
• However, the method can give rise to significant
errors under extreme conditions such as lower energy,
large field, large depth, and large SSD change.
Tissue-Air ratio
• The ratio of the dose ( D d ) at a given point in the
phantom to the dose in free space ( D f s )
• TAR depends on depth d and field size rd at the depth:
Dd
TAR(d , rd ) 
D fs
(BSF)
Equilibrium mass
phantom
d
rd
rd
Dd
D fs
Tissue-Air ratio
( a ) Effect of Distance
• Independent of the distance from the source
• The TAR represents modification of the dose at a
point owing only to attenuation and scattering of
the beam in the phantom compared with the dose
at the same point in the miniphantom ( or
equilibrium phantom ) placed in free air
Tissue-Air ratio
( b ) Variation with energy, depth, and field size
• For the megavoltage beams, the TAR builds up to
a maximum at the d m and then decreases with
depth
• As the field size is increased, the scattered
component of the dose increases and the variation
of TAR with depth becomes more complex
Tissue-Air ratio
( b ) Variation with energy, depth, and field size: BSF
• Backscatter factor (BSF) depends only on the beam
quality and field size
Dmax
BSF  TARd m , rdm  
D fs
• Above 8 MV, the scatter at the depth of Dmax
becomes negligibly small and the BSF approaches its
minimum value of unity
Fig. 9.8 Variation of backscatter factors with beam quality
The meaning of Backscatter factor
• For example, BSF for a 10x10 cm field for 60Co is
1.036 means that D max will be 3.6% higher than the
dose in free space Dmax
D fs
 1.036
• This increase in dose is the result of radiation scatter
reaching the point of D max from the overlying and
underlying tissues
Tissue-Air ratio
( c ) relationship between TAR and PDD
 f  dm
1
P ( d , r , f )  TAR ( d , rd ) 

BSF ( r ) 
 f d
2


  100

Tissue-Air ratio
( c ) relationship between TAR and PDD-- Conversion
of PDD from one SSD to another : The TAR method
Burns’s equation:


r

 BSF r / F
P(d , r , f 2 )  P d ,
, f1  
F
BSF(r )
F


Tissue-Air ratio
( d ) calculation of dose in rotation therapy
d=16.6
Scatter-Air Ratio(SAR)
• Calculating scattered dose in the medium
• The ratio of the scattered dose at a given point in
the phantom to the dose in free space at the same
point
• TAR(d,0): the primary component of the beam
Equilibrium mass
phantom
d
rd
rd
Dd
D fs
SAR(d , rd )  TAR(d , rd )  TAR(d ,0)
Scatter-Air Ratio--Dose calculation in irregular
fields: Clarkson’s Method
Based on the principle that the scattered component
of the depth dose can be calculated separately from
the primary component
TAR  TAR(0)  SAR
TAR  Average tissue-air ratio
SAR  Average scatter-air ratio
TAR ( 0 ) = tissue-air ratio for 0 x 0 field