1
Chapter 10 A System of Dosimetric Calculations
• Percent depth dose is suitable for SSD treatment technique.
• Tissue-air-ratios (TAR) suitable for SAD treatment technique, but limited to energies no higher than Co-60.
• Tissue-maximum-ratios (TMR) and Tissue-phantom-ratios (TPR) were designed to overcome the limitations of the TAR.
2
10.1 Dose Calculation Parameters
• Dose = Primary dose + Scattered dose
• Primary dose (includes those scattered in the head, so-called collimator scatter) = dose due to unscattered (in phantom) photons. Conceptually, primary dose can be achieved with a beam of zero field size, or a phantom column of zero radius. (In both cases, to eliminate scatter in the phantom.)
• (phantom) Scattered dose = dose due to photons scattered at least once in the phantom.
S S
P
3
10.1 Dose Calculation Parameters (collimator & phantom scatter factor)
air
Buildup cap
Reference field
SA
D
Field size
Reference field
Sc
Reference depth
phantom
Sc,p
Sp = Sc,p / Sc
4
Reference depth
phantomphantom
r r0
D0D
Phantom Scatter Factor (Sp)
keeping same collimator opening
block down to reference
field size
)()()( max rBSFrDdD fs )()()( 0max0 rBSFrDdD fs
)(
)(
)(
)()(
0max0
max
rBSF
rBSF
dD
dDrS p
Dfs unchanged, due to same collimator opening
5
10.1 Dose Calculation Parameters (tissue-phantom & tissue-maximum ratios)
d
rdDdrdDt0
0
),(t
dd D
DrdTPR where t0 is the reference depth
max
),(D
DrdTMR d
d if t0 = dmax
t0
TAR, TMR, and TPR depends on depth and field size, but is SSD independent.
6
10.1 Dose Calculation Parameters (properties of TMR)
Depth in water
TM
R
3030
101000
Like TAR, TMR is independent of SSD, increases with energy and field size.
)( max)0,( tdedTMR
7
Relationship between TMR and TAR
d
rdDdrdDmax
dmax
rdDfs
fs
dd D
DrdTAR ),(
max
),(D
DrdTMR d
d
fsd D
DrBSF max)(
)(
),(),(
d
dd rBSF
rdTARrdTMR
8
Relationship between TMR and PDD
d
rdDd
0100
),,(
D
DfrdPDD drdDmax
dmax
max
),(D
DrdTMR d
d
)(
)( 02
maxmax
0
dp
p
rS
rS
df
df
D
D
dmax
D0
f
r
r0
)(
)(
100
),,(
),(
02
max dp
p
d
rS
rS
df
dffrdPDD
rdTMR
9
Scatter-Maximum Ratio (SMR)
d
rdD1rdD2
dmax
)0,(
)0,(),(),(
max2
11
dD
dDrdDrdSMR dd
)0,()0(
)(),(),( dTMR
S
rSrdTMRrdSMR
p
dpdd
)0,(
)0,(
)0,(
),(
),(
),(
),(
),(),(
max2
1
max2
0max2
0max2
max2
max2
1
dD
dD
dD
rdD
rdD
rdD
rdD
rdDrdSMR d
d
dd
r0 = reference field size
10
SSD
rc
t0
r
SAD
r
SSD
r c
distance changed
10.2 Practical Applications (accelerator calculations)
SSD technique:
r0
K
t0
calibration conditions
SCD
2
0
tSSD
SCD
20)()(),,(
100)dosetarget (
tSSDSCDrSrSSSDrdPDDK
TDMU
pcc
×Sc(rc)×Sp(r)
xSA
D
r’t0
×Sc(rc)×Sp(r’)
xrc
SAD
r
tSCD
r c
0
'
field size changed
100
),,( SSDrdPDD
d
depth changed
11
10.2 Practical Applications (accelerator calculations, example 1)
Machine: 4 MV photons
Calibration conditions: SSD = 100 cm, dmax = 1 cm, field size = 10 10 cm.Calibration dose rate = 1 cGy / MU
Treatment conditions: SSD = 100 cm, d = 10 cm, field size = 15 15 cm, Sc(1515)=1.020, Sp(1515)=1.010, %DD=65.1, TD = 200 cGy.
Dose/MU at prescription point
= 1 1.02 1.01 65.1/100 = 0.6707
MU = 200 / 0.6707 = 298
SSD technique:
12
10.2 Practical Applications (accelerator calculations, example 2)
Machine: 4 MV photons
Calibration conditions: SSD = 100 cm, dmax = 1 cm, field size = 10 10 cm.Calibration dose rate = 1 cGy / MU
Treatment conditions: SSD = 120 cm, d = 10 cm, field size = 15 15 cm, Sc(12.512.5)=1.010, Sp(1515)=1.010, %DD=66.7, TD = 200 cGy.
Dose/MU at prescription point
= 1 1.01 1.01 [(100+1)/(120+1)]2 0.667 = 0.474
MU = 200 / 0.474 = 422
SSD technique:
13
10.2 Practical Applications (accelerator calculations)
SAD technique:
r0
K
t0
calibration conditions
SCD
2)()(),(
)doseisocenter (
SADSCDrSrSrdTMRK
IDMU
dpccd
x
SAD
SAD
r
SCD
r c'
r’t0
×Sc(rc)×Sp(r’)
rcx
field size changed
xt0
rd
2
SAD
SCD
×Sc(rc)×Sp(rd)
distance changed
t0
d
),( drdTMR
rd
depth changed
14
Machine: 4 MV photons
Calibration conditions: SCD = 100 cm, dmax = 1 cm, field size = 10 10 cm.Calibration dose rate = 1 cGy / MU
Treatment conditions: SAD = 100 cm, d = 8 cm, field size = 6 6 cm, Sc(66)=0.970, Sp(66)=0.990, TMR(8, 66)=0.787, TD = 200 cGy.
Dose/MU at prescription point
= 1 0.970 0.990 0.787 = 0.756
MU = 200 / 0.756 = 265
SAD technique:
10.2 Practical Applications (accelerator calculations, example 3)
15
10.2 Practical Applications (accelerator calculations, example 4)
Machine: 4 MV photons
Calibration conditions: SCD = 101 cm, dmax = 1 cm, field size = 10 10 cm.Calibration dose rate = 1 cGy / MU
Treatment conditions: SAD = 100 cm, d = 8 cm, field size = 6 6 cm, Sc(66)=0.970, Sp(66)=0.990, TMR(8, 66)=0.787, TD = 200 cGy.
Dose/MU at prescription point
= 1 0.970 0.990 [(100+1)/(100)]2 0.787 = 0.771
MU = 200 / 0.771 = 259
SAD technique:
16
10.2 Practical Applications (Co-60 unit, example 5)
Machine: Co-60 photons
Calibration conditions: SSD = 80 cm, dmax = 0.5 cm, field size = 10 10 cm.Calibration dose rate = 130 cGy / min
Treatment conditions: SSD = 100 cm, d = 8 cm, field size = 15 15 cm, Sc(1212)=1.012, Sp(1515)=1.014, %DD(8,15 15,100)=68.7, TD = 200 cGy.
Dose/MU at prescription point
= 130 1.012 1.014 [(80+0.5)/(100+0.5)]2 68.7/100 = 58.80
MU = 200 / 58.80 = 3.40 min
SSD technique:
17
)0,()0(
)(),(),( dTMR
S
rSrdTMRrdSMR
p
dpdd
10.2 Practical Applications (irregular fields)
)(
)0(),()0,(),(
dp
pdd rS
SrdSMRdTMRrdTMR
(from slide #9)
For off-axis point:
)(
)0()()0,()(
dp
pp
rS
SdSMRdTMRKdTMR
off-axis ratio
ri
n
iirdSMR
ndSMR
1
),(1
)(
n
iipdp rS
nrS
1
)(1
)(
BEV )(
)0()()0,()(
dp
p
rS
SdSMRdTMRdTMR
18
2
0
)(
)(
)(
)0()()0,(
100
),,(
0
df
tf
rS
rS
rS
SdSMRdTMRK
frdP
tp
dp
dp
pp
d
rd
f
rt0
)(
)(
100
),,(),( 0
2
0 dp
tpd rS
rS
tf
dffrdPDDrdTMR
From slide #8:
2
0
0 ),(1
1)()0,(
100
),,(
0
df
tf
rtSMRdSMRdTMRK
frdP
tp
)0,()0(
)(),(),( dTMR
S
rSrdTMRrdSMR
p
dpdd
(from slide #9)
1)0(
)(1),( 0
p
dpd S
rSrtSMR
(when d = t0)
19
10.2 Practical Applications (asymmetric fields)
SSD technique:
Dose / MU = K
Sc (rc) Sp(r)
(SSD factor)
PDD(d,r)/100 OARd(x)
SAD technique:
Dose / MU = K
Sc (rc) Sp(rd) (SAD factor)
TMR(d,rd)
OARd(x)
MU = TD / (Dose / MU) MU = ID / (Dose / MU)
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10.3 Other Practical Methods of Calculating Depth Dose Distribution (Irregular fields)
Collimator field vs. effective fields
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10.3 Other Practical Methods of Calculating Depth Dose Distribution (off-axis points)
baD 224
12 dbD 22
4
11
caD 224
13
d
c
a
b Q
ca
Q
Qa
b
2a
2a
2c
2b
Qd
c2c
2d
Qd b
2d
2b
Px
caD 224
13 cdD 22
4
14
22
10.3 Other Practical Methods of Calculating Depth Dose Distribution (off-axis points)
]100/22%22100/22%22
100/22%22100/22%22[4
)(
cdDDcdBSFcaDDcaBSF
baDDbaBSFdbDDdbBSF
KPDcbdaD Qfs
Q
d
c
a
b Q
Px
Let the dose in free space at P = Dfs(P), then the dose at P(dmax) =Dfs(P)×BSF[(a+d)×(b+c)].
Moreover, let KQ be the off-axis ratio at Q, then the dose at Q is:
]22%2222%22
22%2222%22[
)]()[(4)(
%
max
cdDDcdBSFcaDDcaBSF
baDDbaBSFdbDDdbBSF
cbdaBSF
K
dD
D Q
P
Q
23
d=5
c=10
a=10
b=5
Q
Px
Example 6:
For a = 10cm, b = 5cm, c = 10cm, d = 5cm and a Co-60 beam with KQ = 0.98 and SSD = 80cm, what is %DQ(d=10cm) relative to DP(dmax)?
Given:
Field size 10x10 20x10 20x20 15x15
BSF 1.036 1.043 1.061 1.052
%DD(SSD=80cm,d=10cm) 55.6 56.3 60.2 58.4
8.55
]3.56043.12.60061.13.56043.16.55036.1[052.14
98.0
)(
%
max
dD
D
P
Q
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10.3 Other Practical Methods of Calculating Depth Dose Distribution (points outside the field)
2
1
bcDbcaDcbaD 2222
1;
a
b ca
b ca
bc
a
b2c a
b2c
25
Example 7:
For a = 15cm, b = 10cm, c = 5cm, and a Co-60 beam with SSD = 80cm, what is %DQ(d=10cm) relative to DP(dmax)?
Given:
Field size 10x10 40x10 15x10
BSF 1.036 1.054 1.043
%DD(SSD=80cm,d=10cm) 55.6 58.8 56.9
1.22
]6.55036.18.58054.1[
043.1
1
2
)]1010(%)1010()1040(%)1040([
)1510(
1
)(
%
max
DDBSFDDBSF
BSFdD
D
P
Q
a=15
b=10 c=5
QPx
26
10.3 Other Practical Methods of Calculating Depth Dose Distribution (points under a block)
a
b
c
tcaDbaDblockaunderD 1
t = block transmission
27
a=15
b=15
c=4
Example 8:
For a = 15cm, b = 15cm, c = 4cm, and Co-60 beam with SSD = 80cm.
Given:
Dfs(15x15,f=80.5) = 120 cGy/min
Block transmission = 5%
Tray transmission = 97%.
QPx
(a) What is the treatment time to deliver 200 cGy to P(d=10cm)? (i.e. DP(d=10) = 200 cGy)
(b) What is the %[DQ(d=10)/DP(d=10)]?
029.1)88(
0.54)80,88,10(%
885.515/
BSF
DD
PA
min09.397.054.0029.1120/200
100/%
time
transDDBSFDtimeDP(a)
28
Method 1: Negative weight PDD
6.3×6.3
a=15
b=15
c=4
QPx
%202003.39
3.39
154%15412009.3154
1515%151512009.31515
05.011541515
PQ
Q
Q
Q
QQQ
DD
cGyD
DDBSFD
DDBSFD
DDD
29
%20694.0
05.01667.0771.0
99,10
177,101717,10
99172.6125.1155.5
77175.4125.1154
1717125.11515
/
/
TAR
transTARTAR
D
D
cmcmcm
cmcmcm
cmcm
P
Q
PA
PA
a=15
b=15
c=4
QPx
Field size magnification at d=10cm: (80+10)/10=1.125
Method 2: Negative weight TAR
30
%20
997.0672.0
05.01989.0651.002.1733.0
9999,10
17777,1017171717,10
p
pp
P
Q
STAR
transSTMRSTMR
D
D
a=15
b=15
c=4
QPx
From slide #7: TAR(d,rd) = TMR(d,rd) × Sp(rd)
Method 3: Negative weight TMR