Fundamental Dosimetry
Quantities and Concepts: Review
Introduction to Medical Physics III: Therapy
Steve Kirsner, MS
Department of Radiation Physics
Some Definitions
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SSD
SAD
Isocenter
Transverse (Cross-Plane)
Radial (In-plane)
Sagittal
Coronal
Axial
Supine
Prone
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Cranial
Caudal
Medial
Lateral
AP/PA
Rt. & Lt. Lateral
Superior
Inferior
RAO/RPO/LAO/LPO
Fundamentals
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Review of Concepts
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Distance, depth, scatter effects
Review of Quantities
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PDD, TMR, TAR, PSF
(definition/dependencies)
Scatter factors
Transmission factors
Off-axis factors
Distance, Depth, Scatter
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Distance
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Depth
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From source to point
of calculation
Within attenuating
media
Scatter
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From phantom and
treatment-unit head
Distance, Depth, Scatter
Scatter Concepts
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Contribution of scatter
to dose at a point
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Amount of scatter is
proportional to size and
shape of field (radius).
increase with increase in
length
Think of total scatter as
weighted average of
contributions from field
radii. SAR, SMR
Equivalent Square
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The “equivalent square”
of a given field is the
size of the square field
that produces the same
amount of scatter as
the given field, same
dosimetric properties.
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Normally represented by
the “side” of the
equivalent square
Note that each point
within the field may have
a different equivalent
square
Effective Field Size
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The “effective” field size
is that size field that best
represents the irregularfield’s scatter conditions
It is often assumed to be
the “best rectangular fit”
to an irregularly-shaped
field
These are only estimates
In small fields or in highly
irregular fields it is best to
perform a scatter
integration
Effective Field Size
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Must Account for
flash, such as in
whole brain fields.
Breast fields and
larynx fields.
Blocking and MLCs
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It is generally assumed that tertiary blocking
(blocking accomplished by field-shaping devices
beyond the primary collimator jaws) affects only
phantom scatter and not collimator or head scatter
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Examples of tertiary blocking are (Lipowitz metal alloy)
external blocks, and tertiary MLCs such as that of the
Varian accelerator
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When external (Lipowitz metal) blocks are supporte by trays,
attenuation of the beam by the tray must be taken into
account
It is also generally assumed that blocking
accomplished by an MLC that replaces a jaw, such
as the Elekta and Siemens MLCs, modifies both
phantom and collimator (head) scatter.
Effective Fields Asymmetric
Field Sizes
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Must Account for locaton of Central axis
or calculation point.
There is an effective field even if there
are no blocks.
cax
…
Calc.
Pt.
Inverse Square Law
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The intensity of the radiation is
inversely proportional to the square of
the distance.
X1D12 = X2D22
Percent Depth Dose (PDD)
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PDD Notes
Characterize variation of
dose with depth.
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Field size is defined at
the surface of the
phantom or patient
The differences in dose
at the two depths, d0 and
d, are due to:
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Differences in depth
Differences in distance
Differences in field size
at each depth
PDD  Dd / Dd 0
PDD: Distance, Depth, Scatter
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Note in mathematical description of PDD
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Inverse-square (distance) factor
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Dependence on SSD
Attenuation (depth) factor
Scatter (field-size) factor
PDD: Depth and Energy
Dependence
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PDD Curves
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Note change in depth of dmax
Can characterize PDD by PDD at 10-cm depth
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%dd10 of TG-51
PDD: Energy Dependence
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Beam Quality effects PDD primarily
through the average attenuation
coefficient. Attenuation coefficient
decreases with increasing energy
therefore beam is more penetrating.
PDD Build-up Region
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Kerma to dose
relationship
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Kerma and dose
represent two different
quantities
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Kerma is energy
released
Dose is energy
absorbed
Areas under both
curves are equal
Build-up region
produced by forwardscattered electrons that
stop at deeper depths
PDD: Field Size and Shape
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Small field sizes dose due to primary
Increase field size increase scatter
contribution.
Scattering probability decreases with
energy increase. High energies more
forward peaked scatter.
Therefore field size dependence less
pronounced at higher energies.
PDD: Effect of Distance
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Effect of inverse-square
term on PDD
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As distance increases,
relative change in dose
rate decreases (less
steep slope)
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This results in an
increase in PDD (since
there is less of a dose
decrease due to
distance), although the
actual dose rate
decreases
Mayneord F Factor
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The inverse-square term within the PDD
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PDD is a function of distance (SSD + depth)
PDDs at given depths and distances (SSD) can be corrected
to produce approximate PDDs at the same depth but at
other distances by applying the Mayneord F factor
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“Divide out” the previous inverse-square term (for SSD1),
“multiply in” the new inverse-square term (for SSD2)
Mayneord F Factor
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Works well small fields-minimal scatter
Begins to fail for large fields deep
depths due to increase scatter
component.
In general overestimates the increase in
PDD with increasing SSD.
PDD Summary
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Energy- Increases with Energy
Field Size- Increases with field size
Depth- Decreases with Depth
SSD- Increases with SSD
Measured in water along central axis
Effective field size used for looking up
value
The TAR
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The TAR …
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The ratio of doses at two
points:
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Equidistant from the source
That have equal field sizes
at the points of calculation
Field size is defined at
point of calculation
Relates dose at depth to
dose “in air” (free space)
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Concept of “equilibrium
mass”
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Need for electronic
equilibrium – constant
Kerma-to-dose
relationship
TAR  Dd / Dfs
The PSF (BSF)
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The PSF (or BSF) is a special
case of the TAR when dose
in air is compared to dose at
the depth (dmax) of maximum
dose
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At this point the dose is
maximum (peak) since the
contribution of scatter is not
offset by attenuation
The term BSF applies strictly
to situations where the
depth of dmax occurs at the
surface of the phantom or
patient (i.e. kV x rays)
The PSF versus Energy as a
function of Field Size
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In general, scatter
contribution decreases
as energy increases
Note:
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Scatter can
contribute as much
as 50% to the dose
a dmax in kV beams
The effect at 60Co is
of the order of a few
percent (PSF 60Co
10x10 = 1.035
Increase in dose is
greatest in smaller
fields (note 5x5,
10x10, and 20x20)
TAR Dependencies
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Varies with energy like the pddincreases with energy.
Varies with field size like pdd- increases
with field size.
Varies with depth like pdd- decreases
with dept.
Assumed to be independent of SSD
The TPR and TMR
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Similar to the TAR, the
TPR is the ratio of doses
(Dd and Dt0) at two
points equidistant from
the source
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Field sizes are equal
Again field size is defined
at depth of calculation
Only attenuation by
depth differs
The TMR is a special
case of the TPR when t0
equals the depth of dmax
TPR  Dd / Dt 0
TPR/TMR Dependencies
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Independent of SSD
TMR increases with Energy
TMR increases with field size
TMR decreases with depth
Relationship between fundamental depthdependent quantities
From: ICRU 14
PDD / TAR / BSF Relation
Approximate Relationships:
PDD / TAR / BSF / TMR
BJR Supplement 17
Limitations of the application
of inverse-square corrections
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It is generally believed that
the TAR and TMR are
independent of SSD
This is true within limits
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Note the effect of purely
geometric distance corrections
on the contribution of scatter
Effect of scatter vs. distance:
TMR vs. field size
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The TMR (or TAR or PDD)
for a given depth can be
plotted as a function of field
size
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Shown here are TMRs at
1.5, 5.0, 10.0, 15.0, 20.0,
25.0, and 30.0 cm depths
as a function of field size
Note the lesser increase in
TMR as a function of field
size
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This implies that
differences in scatter are of
greater significance in
smaller fields than larger
fields, and at closer
distances to calculation
points than farther
distances
Varian 2107 6 MV X Rays (K&S Diamond)
Scatter Factors
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Scatter factors describe
field-size dependence of
dose at a point
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Need to define “field
size” clearly
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Often wise to separate
sources of scatter
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Many details …
Scatter from the head
of the treatment unit
Scatter from the
phantom or patient
Measurements
complicated by need
for electronic
equilibrium
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Kerma to dose, again
Wedge Transmission
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Beam intensity is also
affected by the
introduction of beam
attenuators that may be
used modify the beam’s
shape or intensity
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Such attenuators may be
plastic trays used to
support field-shaping
blocks, or physical
wedges used to modify
the beam’s intensity
The transmission of
radiation through
attenuators is often fieldsize and depth dependent
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The
Dynamic
Wedge
Enhanced Dynamic Wedge (EDW)
Wedged dose distributions can
be produced without physical
attenuators
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With “dynamic wedges”, a
wedged dose distribution is
produced by sweeping a
collimator jaw across the field
duration irradiation
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The position of the jaw as a
function of beam irradiation
(monitor-unit setting) is given
the wedge’s “segmented
treatment table (STT)
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The STT relates jaw position
to fraction of total monitorunit setting
The determination of dynamic
wedge factors is relatively
complex
Gibbons
Off-Axis Quantities
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To a large degree, quantities
and concepts discussed up to
this point have addressed dose
along the “central axis” of the
beam
It is necessary to characterize
beam intensity “off-axis”
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Two equivalent quantities are
used
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Off-Axis Factors (OAF)
Off-Center Ratios (OCR)
These two quantities are
equivalent
OAF( x, d )  Dd , x / Dd ,0
where x = distance off-axis
Off-Axis Factors:
Measured Profiles
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Off-axis factors are extracted from measured profiles
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Profiles are smoothed, may be “symmetrized”, and are
normalized to the central axis intensity
Off-Axis Factors:
Typical Representations
OAFs (OCRs) are
often tabulated and
plotted versus
depth as a function
of distance off axis
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Where “distance off
axis” means radial
distance away from
the central axis
Note that, due to
beam divergence,
this distance varies
with distance from
the source
Varian 2100C SN 241 6 MV Open-Field Off-Axis
Factors
1.05
1.04
Off-Axis Factor
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1.03
Depth 1.7
1.02
Depth 5.0
1.01
Depth 10
1.00
Depth 15
0.99
Depth 20
0.98
0.97
Depth 25
0.96
Depth 30
0.95
0.00
0.02
0.04
0.06
Off-Axis "Tangent"
0.08
0.10
Off-Axis Wedge Corrections
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Descriptions vary of off-axis
intensity in wedged fields
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Measured profiles contain
both open-field off-axis
intensity as well as differential
wedge transmission
We have defined off-axis
wedge corrections as
corrections to the central axis
wedge factor
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Open-field off-axis intensity is
divided out of the profile
The corrected profile is
normalized to the central axis
value
Examples
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The depth dose for a 6 MV beam at 10 cm depth for
a 10 x 10 field; 100 cm ssd is 0.668. What is the
percent depth dose if the ssd is 120 cm.
F=((120 +1.5)/(100+1.5))2 x((100 +10)/(120 +10))2
F= 1.026
dd at 120 ssd = 1.026 x 0.668 = 0.685
Example Problems
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What is the given dose if the dose
prescribed is 200 cGy to a depth of 10
cm. 6X, 10 x 10 field, 100 cm SSD.
DD at 10 cm for 10 x 10 is 0.668.
Given Dose is 200/0.668 = 299.4 cGy
Examples
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A single anterior 6MV beam is used to deliver 200
cGy to a depth of 5cm. What is the dose to the cord
if it lies 12 cm from the anterior surface. Patient is
set-up 100 ssd with a 10 x 15 field.
Equivalent square for 10 x 15 = 12cm2
dd for 12 x 12 field at 5cm =.866
dd for 12 x 12 field at 12 cm = .608
Dose to cord = 200/.866 x .608 = 140.4 cGy
Examples
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A patient is treated with parallel opposed fields to midplane.
The patient is treated with 6 MV and has a lateral neck
thickness of 12cm. The field size used is 6 x 6. The prescription
is 200 cGy to midplane. What is the dose per fraction to a node
located 3 cm from the right side. The patient is set-up 100 cm
SSD.
dd at 6cm=0.810; dd at 9cm=.686 ; dd at 3 cm= 0.945
Dose to node from right= (100/.810) x 0.945 =116.7 cGy
Dose to node from left = (100/.810) x .686 = 84.7 cGy
Total dose = 116.7 + 84.7 = 201.4 cGy
Examples
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A patient is treated with a single anterior field. Field Size is 8 x
14. Patient is set-up 100 cm SAD. Prescription is 200 cGy to a
depth of 6cm. A 6 MV beam is used for treatment. What is the
dose to a node that is 3 cm deep? Assume field size is at
isocenter.
Equivalent square of field is 10.2 cm2
TMR at 6cm = .8955
TMR at 3 cm = .9761
Dose to node = (200/.8955) x .9761 x (100/97)2 = 231.7 cGy
Examples
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A patient is treated with parallel opposed 6 MV fields. The
patient’s separation is 20 cm. Prescription is to deliver 300 cGy
to Midplane. Field size is 15 x 20.(100cm SAD) What is the dose
to the cord on central axis if the cord lies 6cm from the
posterior surface?
Equivalent square is 17.1
TMR at 10 cm = .8063
TMR at 6 cm = .9088
TMR at 14 cm = .7041
Examples
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Dose to the Cord from the Anterior
(150/.8063) x (100/104)2 x .7041 = 121 cGy
Dose to the Cord from the Posterior
(150/.8063) x (100/96)2 x .9088 = 183 cGy
Total dose to the cord
183 +121 = 304 cGy