Dose Distribution and Scatter Analysis

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15 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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Dose Distribution and Scatter Analysis


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



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


n
umber 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)


PHANTOMS

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, tissue
-
phantom 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
: d
0

100
0


d
d
D
D
P
collimator

surface

phantom

D
d0

D
d

d

d
0

PERCENTAGE DEPTH DOSE


For orthovoltage (up to
about 400 kVp) and
lower
-
energy x
-
rays, the
reference depth is usually
the surface (d
o

= 0).


For higher energies, the
reference depth is taken
at the position of the peak
absorbed dose (d
o

= 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

100
max


P
D
D
d
100
max


D
D
P
d
collimator

surface

phantom

D
max

D
d

d

d
m

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

Fig. 9.3 central axis depth dose distribution for
different quality photon beams

100
max


D
D
P
d
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


G
eometrical


Dosimetrical

or
physical

SAD

FS


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

Percentage Depth Dose

(b)
Effect of field size and shape

100
max


D
D
P
d
D
d

D
max

Scatter dose

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 higher
-
energy 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


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

Percentage Depth Dose

(b)
Effect of field size and shape


square field

B

A

c = 2 x

A x B

A + B

rectangular field

c

c

Percentage Depth Dose

(b)
Effect of field size and shape



Quick calculation of the equivalent field
parameters: for rectangular fields




For square fields, since a = b,


the side of an
equivalent square

of a rectangular
field is

)
(
2
b
a
b
a
P
A



a

b

4
a
P
A

P
A

4
P
A

4
P
A

4
Percentage Depth Dose(3)
--
(b)
Effect of
field size and shape



Equivalent circle

has the same area as the
equivalent square

P
A
r



4
a

b

P
A

4
P
A

4
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 Source
-
Surface 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

dm

d

d

dm

SSD

SSD’

Fig. 9.5 Plot of relative dose rate as inverse square law function
of distance from a point source. Reference distance = 80 cm

Percentage Depth Dose

(c) dependence on SSD

F1+dm

F2+dm

F1+d

F2+d

100
max


D
D
P
d
s
d
d
m
K
e
d
f
d
f
f
r
d
P
m
.
.
100
)
,
,
(
)
(
2
1
1
1















s
d
d
m
K
e
d
f
d
f
f
r
d
P
m
.
.
100
)
,
,
(
)
(
2
2
2
2















2
2
1
2
1
2
1
2
)
,
,
(
)
,
,
(






















d
f
d
f
d
f
d
f
f
r
d
P
f
r
d
P
m
m
d

d
m

f1

r

d

d
m

r

f2

f2

d

d
m

d

d
m

f1

r

r

PDD increases with SSD

the
Mayneord
F
Factor
(
without considering changes in
scattering )

2
2
1
2
1
2






















d
f
d
f
d
f
d
f
F
m
m
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 (C
0
-
60
Beam).

Find the PDD for the same field size and
depth for a
100
-
cm SSD

Assuming d
m
=
0.5
-
cm for (C
0
-
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
r
d

at the depth:

fs
d
d
D
D
r
d
TAR

)
,
(
d

D
d

r
d

D
f s

r
d

phantom

Equilibrium mass

(BSF)

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




Above 8 MV, the scatter at the depth of D
max

becomes negligibly small and the BSF approaches its
minimum value of unity





fs
dm
m
D
D
r
d
TAR
BSF
max
,


Fig. 9.8 Variation of backscatter factors with beam quality

The meaning of Backscatter factor


For example, BSF for a 10x10 cm field for
60
Co is
1.036 means that D
max

will be 3.6% higher than the
dose in free space



This increase in dose is the result of
radiation scatter

reaching the point of D
max

from the overlying and
underlying tissues

036
.
1
max

fs
D
D
Tissue
-
Air ratio

( c ) relationship between TAR and PDD

100
)
(
1
)
,
(
)
,
,
(
2














d
f
d
f
r
BSF
r
d
TAR
f
r
d
P
m
d
Tissue
-
Air ratio

( c ) relationship between TAR and PDD
--

Conversion
of PDD from one SSD to another :
The TAR method

Burns’s equation:



F
r
BSF
F
r
BSF
f
F
r
d
P
f
r
d
P









)
(
/
,
,
)
,
,
(
1
2
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


)
0
,
(
)
,
(
)
,
(
d
TAR
r
d
TAR
r
d
SAR
d
d


d

D
d

r
d

D
f s

r
d

phantom

Equilibrium mass

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

SAR
TAR
TAR


)
0
(

TAR

SAR
Average tissue
-
air ratio

Average scatter
-
air ratio

TAR

( 0 ) = tissue
-
air ratio for
0 x 0

field