Dose Distribution and Scatter Analysis

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

• 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)

PHANTOMS

Compton effect is the main interaction

Solid dry phantoms

Solid dry (Slab) phantoms

Alderson Rando Phantom

• anthropomorphic phantom– Frequently used for cli

nical dosimetry– Incorporates materials

to simulate various body tissues, muscle, bone, lung, and air cavities

RANDO phantomRANDO phantom

CT slice through lung

Head withTLD 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: d0

1000

d

d

D

DP collimator

surface

phantom

D d0

D d

d

d0

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

100max P

DD d

100max

D

DP d

collimator

surface

phantom

D max

D d

d

dm

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 el

ectron; (3) maximum at the surface and decreases with depth due to d

ecreased 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 s

ubsequent layers;• (3) theses electrons deposit their energy a significant distan

ce away from their site of origin

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

100max

D

DP 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– Geometrical

– 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

100max

D

DP d

Dd

Dmax

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 fieldB

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 ba

ba

P

A

a

b

4

a

P

A

P

A4

P

A4

P

A4

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

• Equivalent circle has the same area as the equivalent square

P

Ar

4

a

b

P

A4

P

A4

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

dmd 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

100max

D

DP d

sddm Ke

df

dffrdP m ..100),,( )(

2

1

11

sddm Ke

df

dffrdP m ..100),,( )(

2

2

22

2

2

1

2

1

2

1

2

),,(

),,(

df

df

df

df

frdP

frdP

m

m

d

dm

f1

r

d

dm

r

f2

f2

d

dm

d

dm

f1

r

r

PDD increases with SSD the Mayneord F Factor ( without considering changes in scattering ) 2

2

1

2

1

2

df

df

df

dfF

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 (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=1.043P= 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:

fs

dd D

DrdTAR ),(

d

Dd

rd

D f s

rd

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

fs

dmm D

DrdTARBSF 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 60Co 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

036.1max fsD

D

Tissue-Air ratio

( c ) relationship between TAR and PDD

100)(

1),(),,(

2

df

df

rBSFrdTARfrdP 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

rBSF

FrBSFf

F

rdPfrdP

)(

/,,),,( 12

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,(),(),( dTARrdTARrdSAR dd

d

Dd

rd

D f s

rd

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

SARTARTAR )0(

TAR

SAR

Average tissue-air ratio

Average scatter-air ratio

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