Monitor Unit Calculations for
Photons and Electrons:
Report of TGTG-71
John P. Gibbons1 and Donald M. Roback2
1Mary
Bird Perkins Cancer Center
Baton Rouge, Louisiana
2Maplewood Cancer Center
Minneapolis, Minnesota
AAPM Task Group 71
There is a need for AAPM to endorse a
national protocol for MU calculations
Recognizing this need, TGTG-71 was
established
TGTG-71 Membership:
– John Gibbons (chair), Eric Klein, Kwok Lam,
Don Roback,
Roback, Jatinder Palta,
Palta, Saiful Huq,
Huq, John
Antolak,
Antolak, David Followill,
Followill, Mark Reid (AAMD
liason),
liason), Faiz Khan (consultant)
Outline
TG71 Formation and Charge
II. Photon Calculations
III. Electron Calculations
IV. Conclusions
I.
TGTG-71
Task Group Charge
• Emphasize the importance of a unified methodology
• Recommend of consistent terminology for MU calcs
• Recommend measurement and/or calculation methods
• Recommend QA tests
• Provide example calculations for common clinical setups
1
TG71 Report Status
Formulated in 2001
– First meeting 2001 AAPM Meeting
– TwoTwo-year sunset date; Extended last year
Draft report submitted to RTC 2004
Final report due end of 2004
TG71 Report Outline
1. Introduction
2. Nomenclature
3. Calculation Formalism
1. MU Equations
2. Input Parameters (Depth, Field Size)
4. Measurements
5. Interface to TPS
6. Quality Assurance
7. Examples
Monitor Unit Calculations
Overview
• Accuracy within ±5%
• Absolute versus Relative Dosimetry
• Consistency with Treatment Plan
• QA program
Reference and Normalization
Depths
Reference depth (dref ): Defined within
calibration protocols as the depth for
measurement of absolute beam output.
– TG51: dref = 10cm
Normalization depth (d0): The depth at
which all relative dosimetry functions (e.g.,
Scp, TPR) are set to unity.
– Most clinics d0=dm
2
Outline
Normalization vs. Reference Conditions
I. Introduction
II. Photon Calculations
III. Electron Calculations
IV. Future Efforts
d0
dref
dmax
Nomenclature
Photon Calculations
Nomenclature Principals
(3 Laws of Nomenclature)
Law 1: Use commonly understood
symbols
Law 2: Maintain consistency with other
TG reports, unless it conflicts with Law 1
Law 3: Avoid multiplemultiple-letter subscripts
and/or variables, unless it conflicts with
Laws 1 or 2
Constants
D0’
d0
r0
SAD
SSD0
Dose rate at normalization point
Reference depth
Normalization field size
Source to Isocenter (Axis) Distance
Source to Surface Distance under
normalization conditions
3
d
deff
dm
r
rd
rc
Nomenclature
Photon Calculations
Nomenclature
Photon Calculations
Independent Variables
Independent Variables
Depth to point of calculation
Effective or radiological depth
Depth of maximum dose
Field size at the surface
Field size at the depth of the calc pt.
Field size defined by the collimator
jaws
SPD
SSD
x
Nomenclature
Photon Calculations
Nomenclature
Photon Calculations
Dependent Variables
D
OAR
PDD
PDDN
Sc,p
Sc
Sp
Dose to the calculation point
OffOff-Axis Ratio
Percentage Depth Dose
Normalized Percentage Depth Dose
Output Factor
In Air Output Ratio
Phantom Scatter Factor
Source to (calculation) Point Distance
Source to Surface Distance
Off Axis Distance
Dependent Variables
TPR
TF
WF
Tissue Phantom Ratio
Tray Factor
Wedge Factor
4
Depth of Normalization
All quantities should be determined at this
depth
Recommended beyond the range of electron
contamination
Extrapolated dm for largest SSD, smallest r
ESTRO Report recommends depth of 10cm.
Reference Depth
• TG71 Recommends d0=10cm
• Why d0=10cm?
1. Consistency with TG-51
2. PDD(dmax) is inaccurate.
3. Electron Contamination at dm creates problems
• TG71 Formalism Valid for d0= maximum dm
Photon Calculation Formalism
Photon Calculation Formalism
Isocentric Calculation Technique
Isocentric Calculation Technique
c)
b)
a)
d)
r
rc
d
SPD
SPD
d
rd
rd
do
SPD0
0
SPD
r
d
rd
g)
SPD0
SPD
x
f)
e)
d)
SPD
0
do
SPD
rc
ro
rd
rd
rd
5
Isocentric Calculations
Isocentric Calculations
Calculations to Arbitrary Points
Calculation to the Isocenter
D
MU =
D S ( r ) S ( r ) TPR(d , r ) WF ( d , r ) TF
'
c
0
c
p
d
d
d
SSD + d
SAD
0
2
D S ( r ) S ( r ) TPR( d , r ) WF ( d , r ) TF OAR( d , x )
'
0
NonNon-Isocentric (SSD)
Calculations
D S ( r ) S ( r ) PDD ( d , r , SSD ) WF ( d , r ) TF OAR (d , x )
'
0
c
c
p
d0
N
c
c
p
d
d
d
SSD + d
SPD
0
2
0
Determination of Field Size
Method of Equivalent Square
Rectangular fields may be calculated using
the dosimetric quantities for an equivalent
square:
D 100%
MU =
D
MU =
0
SSD + d
SSD + d
0
2
0
0
– Equivalent Square Approximation: 4*A/P
– Equivalent Square Tables (e.g
(e.g,, Day and Aird,
Aird,
‘83)
Highly irregular fields may be calculated using
a Clarkson integration
These relationships should be verified for Sc
6
Determination of Field Size for Sc
Determination of Field Size for Sc
Sources of Head Scatter
Open or Blocked (Cerrobend) Fields
– Protocol uses Equivalent Square of Collimator
Field Size
– More accurate methods (e.g., PEV model)
may be required if:
Rectangular Fields of large aspect ratio
Highly Irregular Fields
• Backscatter
to monitor chamber
• Head Scatter
• Adjustable Collimators
• Flattening Filter
Determination of Field Size for Sc
Points Eye View Model
Determination of Field Size for Sc
Collimator Exchange Effect
Defined: Sc(a,b)
(a,b) ? Sc(b,a)
(b,a)
Demonstrated for Open and Wedged
Fields
Magnitude is typically < 2%
7
Determination of Field Size for Sc
Determination of Field Size for Sc
Determination of Field Size for Sc
MLC Types
Collimator Exchange Effect
Points Eye View Model
MLC Fields
– Under PEV model, only apertures close to FF
will effect Sc
– Thus Field Size depends on MLC model
Upper Collimator Replacement
Lower Collimator Replacement
Tertiary MLC
Upper Jaw Replaced
(Elekta)
Lower Jaw Replaced
(Seimens)
Tertiary Collimation
(Varian)
8
Determination of Field Size for Sc
Collimator Scatter with MLCs
Upper Jaw Replacement:
– Palta found Sc best described by MLC field
Lower Jaw Replacement:
– Das found Sc best described by MLC field
Tertiary Collimator:
– Klein found Sc best described by collimator
jaws
Determination of Field Size
Sp
– Use effective field size at depth (isocentric) or
at the normalization depth (SSD)
TPR, WF
– Use effective field size at depth
PDDN
– Use effective field size on the surface
Determination of Field Size
Other parameters are affected by the
amount of scatter within the phantom
material.
Define the “Effective Field Size”
Size” as the
equivalent square of the field size incident
on the phantom. This field size is reduced
by
– Custom Blocking/MLCs
Blocking/MLCs
– Missing Tissue (“
(“Fall Off”
Off”)
Determination of Depth
Use of Heterogeneity Corrections
Not universally used
Importance of physician awareness
Two possible methods for manual
calculations
– Ratio of TAR (RTAR) method
– Power law TAR (“
(“Batho Method”
Method”)
9
Measuring Dosimetric Parameters
Photon Output Factors
Photon Output Factors
• Sc,p measured in phantom at reference depth
• Important to separate collimator and phantom
scatter
• Sp usually determined indirectly:
Sp =
Scp
Sp
6 MV, d=1.5
20
25
Field Size [cm]
30
35
40
Measuring Dosimetric Parameters
6MV Output Comparisons
6 MV, d=10
15
• Larger do will require mini-phantoms
Sc
1.24
1.22
1.20
1.18
1.16
1.14
1.12
1.10
1.08
1.06
1.04
1.02
1.00
0.98
0.96
0.94
0.92
0.90
0.88
0.86
0.84
0.82
0.80
10
• Traditionally, measured with buildup cap
Sc , p
6MV Output Comparisons
5
• Sc measured in air at reference depth.
• Should avoid scatter from surrounding
structures (support stands, floor, wall)
Measuring Dosimetric Parameters
0
Measuring Dosimetric Parameters
45
1.24
1.22
1.20
1.18
1.16
1.14
1.12
1.10
1.08
1.06
1.04
1.02
1.00
0.98
0.96
0.94
0.92
0.90
0.88
0.86
0.84
0.82
0.80
6 MV, d=10
6 MV, d=1.5
0
5
10
15
20
25
Field Size [cm]
30
35
40
45
10
Measuring Dosimetric Parameters
Sc
6MV Output Comparisons
1.24
1.22
1.20
1.18
1.16
1.14
1.12
1.10
1.08
1.06
1.04
1.02
1.00
0.98
0.96
0.94
0.92
0.90
0.88
0.86
0.84
0.82
0.80
Measuring Dosimetric Parameters
24 MV Photon Beams
6 MV, d=10
6 MV, d=1.5
0
5
10
15
20
25
Field Size [cm]
30
35
40
45
Measuring Dosimetric Parameters
Which Sc to use?
Frye et al., Med Phys 22 (1995)
Measuring Dosimetric Parameters
Which Sc?
The Ratio of Dose Rates from these two
scenarios is:
D(d,rc,rd) / D(d,rc’,rd) = Sc(rc) / Sc(rc’)
But…
But…this is irrespective of normalization depth
rd
rd
Explanation is found in Collimator Field Size
dependence of other parameters (Sp, TMR) for
d0=dm.
11
Measuring Dosimetric Parameters
High Energy TMRs (18X)
Measuring Dosimetric Parameters
Wedge Factors
1.2
1.1
• Internal (Motorized) Wedges
TPR(d,20x20,6x6)
1
• Single, large (e.g., 60o) wedge placed above jaws
• Universal wedge concept
TMR
TPR(d,6x6,6x6)
0.9
• External Wedges
0.8
• Wedge placed below jaws by user
• Selection of wedge angles available
0.7
0.6
0
5
10
15
Depth [cm]
20
25
Measuring Dosimetric Parameters
WF Field Size Dependence
• Extensively studied (>20 papers)
• Review by Arrans et al.,
• SWD => Field Size Dependence
• Not hold for Internal Wedges
• RPC Review:
WF=WF(R) if WF<0.65
12
Measuring Dosimetric Parameters
WF Depth Dependence
• McCullough et al.,
• Introduced RWF(d)
• No significant effect >2% for d<10cm
• RPC Review:
WF=WF(d) if E<10MV or
if WF<0.65
Determining Dosimetric Parameters
Determining Dosimetric Parameters
Filterless Wedge Factors
EDW Factors
EDW Factors
– Direct Inspection of Final STT
– Use of Normalized Golden STT
– Analytic Equations
VW Factors
– Very close to unity for all Wedge Angles, Field
Sizes
– Exponential OffOff-Axis Relationship
13
Measuring Dosimetric Parameters
Asymmetric Fields Filterless Wedges
Off Axis Ratios
Calculations to offoff-axis points may be
performed in two methods:
1. Use of offoff-axis dosimetry functions
2. Use of CA dosimetry functions with a offoffaxis ratio: OAR(x,d,r)
1.4
1.2
1
0.8
VWF
Measuring Dosimetric Parameters
0.6
0.4
0.2
0
-20
-15
-10
-5
0
5
10
OFFAXISDISTANCE
Measuring Dosimetric Parameters
Measuring Dosimetric Parameters
OffOff-Axis Ratios
OffOff-Axis Ratios
OffOff-Axis Ratios have been determined in
several ways
1. Large field profile data
2. Primary OffOff-Axis Ratios (POAR(x,d))
3. Analytic Equations
OAR Comparisons (Gibbons & Khan, ’95):
[6, 24MV photons at 5,10,15cm OADs/depths
OADs/depths]
Large Field Profiles:
POARs:
POARs:
Analytic Equation:
Average (Max) Error
2.5% (6.7%)
0.8% (1.8%)
0.5% (1.7%)
14
Nomenclature
Electron Calculations
Outline
Independent Variables
I. Introduction
II. Photon Calculations
III. Electron Calculations
IV. Future Efforts
Nomenclature
Electron Calculations
Dependent Variables
fair
Se
Air gap correction factor
Electron Output Factor
ra
r
g
SSDeff
Applicator size for electron beams
Effective field size on the surface
Difference between treatment SSD
and normalization SSD (SSD0=100)
Effective Source to Surface Distance
Electron Calculations
(SSD0=100cm)
MU =
D
D S (r , r)
'
0
e
a
15
Electron Calculations
Electron Calculations
(SSD>SSD0)
(SSD>SSD0)
Method 2: Air Gap Technique
Method 1: SSDeff Technique
MU =
D
D S ( r , r ) ( ( SSD + d ) ( SSD + d + g ) )
'
0
e
a
eff
0
eff
0
Electron Output Factors
2
MU =
D
D S ( r , r ) ( ( SSD + d ) ( SSD + d + g ) )
'
0
e
a
0
0
2
f ( r , SSD )
air
Electron Cone Inserts
For square fields, Se measured at
commissioning
For rectangular fields, use Square Root
Method:
Se(ra,LxW) = [Se(ra,LxL) · Se(ra,WxW)]1/2
Many irregular fields can be approximated
by rectangular fields.
From Hogstrom et al., “MU Calculations for
Electron Beams”, 2000
16
Electron Irregular Fields
Electron Irregular Fields
Special considerations required if FS very
small (r < E/2.5)
For these conditions, Se may be
determined by
– Special Dosimetry
– Method of Lateral Buildup Ratio (LBR)
Electron Irregular Fields
S =D
e
'
0
PDD
f
100%
a
f LBR
i
Electron
Extended SSD Calculations
Many treatment geometries require
extended SSDs
Where
PDD is the percentage depth dose for a broad field
fa is the ratio of applicator to reference fluence
fi is the ratio of insert to reference fluence
LBR is the average lateral buildup ratio
LBR is the ratio of the central axis depth dose in a given circular
field to the central axis depth dose in a broad field for the same
incident fluence - measured data
The Air Gap Factor may be determined
– Using inverse square correction with virtual
SSD
requires air gap scatter correction term
– Using inverse square correction with effective
SSD
17
Electron Extended SSDs
Electron Extended SSDs
From Roback et al., “Effective SSD for Electron Beams
…”, Med Phys 1995
Conclusions
Task Group 71 of the RTC was formed to
create a consistent nomenclature and
formalism for MU Calculations
For photon beams, TG71 recommends a
normalization depth of 10cm, although the
formalism is valid for (maximum) dm.
For electron beams, TG71 allows for both
effective SSD or Air Gap correction
methods for extended SSD calculations
18