Photon Dosimetry concepts
and Calculations
Chapter 21
W/L
Dose Calculation
• The treatment planning team has to
quantify the overall prescribed dose of
radiation and determine how much dose
will be delivered over the time frame
outlined.
• There are many parameters of photon
beam calculation.
Monitor Units
• Monitor Units (MU): a measure of output
for linear accelerators.
• The dose rate varies slightly from one
moment to the next
• Normally the dose rate for the linear
accelerator is 1.0 cGy/MU for a 10 x 10
field size defined at the isocenter.
Radiation Therapy Prescription
• Radiation Therapy Prescription:
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Legal document defines the treatment volume
Intended tumor dose (TD)
Number of treatments
Dose per treatment
Frequency of treatment
States the type and energy of radiation
Beam-shaping devices such as wedges and
compensators
– Any other appropriate factors.
• Clear, precise and complete
Isodose Plan
• Isodose Plan: part of the prescription
– May show field sizes
– Machine angels
– Doses
– Beam weighting
– Wedges compensators or blocks
Treatment Time
• Treatment time: length of time a unit is
physically left on to deliver a measured
dose.
• Factors considered:
– Beam energy
– Distance from the source of radiation
– Field size
Dose
• Dose (absorbed dose): measured at a
specific point in a medium and refers to
the energy deposited at that point.
• Measured in gray (Gy), which is defined so
that 1 Gy equals 1J/kg.
Depth
• Depth: distance beneath the skin surface
where the prescribed dose is to be
delivered.
– Opposed fields: patient’s midplane is used
– Multiple field arrangements: isocenter used
• Depth affects measurements of dose
attenuation.
Separation
• Separation: a measurement of the
patients thickness from the point of beam
entry to the point of beam exit.
• Normally measured along the beams
central axis.
– Calipers
– ODI readings
Source Distance
• Source to Skin Distance (SSD): the
distance from the source or target of the
treatment machine to the surface of the
patient.
• Source-axis Distance: the distance from
the source of photons to the isocenter.
Setup
• SSD: Isocenter established at the patients
skin surface
– When the gantry rotates around the patient,
the SSD will continually change.
– Dose calculations often at DMAX. (Given dose)
• SAD: Isocenter established within the
patient
– The SAD and the isocenter are at a fixed
distance and therefore do not change.
Isocenter
• Isocenter: the intersection of the axis of
rotation of the gantry and the axis of
rotation of the collimator for the treatment
unit.
– Cobalt 60: SAD of 80 cm
– Linear Accelerators: SAD of 100 cm
Field Size
• Field Size: the physical size set on the
collimator of the therapy unit that
determines the size of the treatment field
at a reference distance (defined at the
machine’s isocenter)
– SAD: the field size set inside the patient (size
measured on patients skin will be smaller)
– SSD: field size set on the collimator will be the
same measured at the patients skin
Scatter
• Backscatter: radiation that is deflected
back toward the patient
• Most of the absorbed dose received by the
patient results from the collisions of the
scattered electrons produced when the
primary photon interacts with the
collimator.
DMAX
• DMAX: the depth at which electronic
equilibrium occurs for photon beams; the
point where dose reaches its maximum
value.
– Mainly depends on the energy of the beam
• The depth of maximum ionization increases as the
energy of the beam increases.
– Factors such as field size and distance may
also influence the depth
Photon Energy
Superficial
Orthovoltage
Cesium-137
Radium-226
Cobalt-60
4MV
6 MV
10 MV
15 MV
20 MV
25 MV
DMAX (cm)
0.0
0.0
0.1
0.1
0.5
1.0
1.5
2.5
3.0
3.5
5.0
DMAX
• DMAX dose occurs at the same depth for a
given energy regardless of field size or
distance from the source.
• The actual reading differs for different field
sizes.
Output
• Output: the dose rate of the machine, the
amount of radiation exposure produced by a
treatment machine or source as specified at a
reference field size and at a specified reference
distance.
– Changing the field size, distance, or attenuating
medium will change the dose rate.
• Increases with field size: primary component the same,
increased scatter adds to the output
• If the distance increases, dose rate decreases due to ISL
Cobalt-60 Output
• Dose rate for Co-60 machine in cGy/min
• Dose rate due to the radioactive decay of
the isotope Co-60
– Can be assumed constant over short periods
of time
– The Time that a machine is left On is adjusted
by 1% increase every month
TO2 = TO1 x 1.01
Linac Output
• Dose rate for Linac in cGy/MU
• Dose rate varies from one moment to the
next
– Ionization chamber shuts down machine after
predetermined dose has been given
Output Factor
• Output Factor: the ratio of the dose rate
of a given field size to the dose rate of the
reference field size
– Allows for the change in scatter as the
collimator setting changes
– Relates the dose rate of a given collimator
setting to the dose rate of the reference field
size
Dose Rate
• Commonly measured at the isocenter of the
treatment machine.
• The dose rate of the beam is inversely
proportional to the square of the distance
• Dose rate(Given f.s.) = Dose rate(Reference f.s.) x Output factor(Given f.s.)
• Dose Rate:
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Output (of machine)
Output factor (C.S. field size)
Scatter Ratio BSF or PSF (EFS/CS)
PDD(EFS)/100
Tray factor
Inverse square correction
Equivalent Squares
• Equivalent Squares: rectangular field
size that demonstrate the same
measurable scattering and attenuation
characteristics of a square field size.
• Used to find the output, output factor, and
tissue absorption factors.
• 4 (A/P)
Effective Field Size
• Effective Field Size (EFS): the equivalent
rectangular field dimension of the open or
treated area within the collimator field
dimensions when blocks are used to
customize the shape of the treatment
area.
• The EFS equivalent square is normally
used to determine the tissue absorption
factors.
Tissue Absorption Factors
• Tissue absorption factors: different
methods for measuring the attenuation of
the beam as it travels through matter.
– Percent Depth Dose (PDD):
• works best with SSD setups
– Tissue Air Ratio (TAR)
– Tissue Phantom Ratio (TPR)
– Tissue Maximum Ratio (TMR)
Percent Depth Dose (PDD)
• Percent Depth Dose (PDD): the ratio expressed as a
percentage, of the absorbed dose at a given depth to
the absorbed dose at a fixed reference depth usually
DMAX.
• Calculated from two measurements at two different
points in space.
• Requires SSD be constant.
• Written as PDD(d,s,SSD)=
• Dependant on:
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↑ Energy- more penetrating- ↑ PDD
↑ Depth- ↓ PDD due to attenuation through matter
↑ Field size- more scatter- ↑ PDD
↑ SSD- ↑ PDD- ISL
Percent Depth Dose (PDD)
PDD = Dose @ d
.
Dose @ Dmax
Tissue Air Ratio (TAR)
• Tissue Air Ratio (TAR): the ratio of the
absorbed dose at a given depth in tissue
to the absorbed dose at the same point in
air.
• Dependant of:
– ↑Energy- ↑TAR
– ↑Field size- ↑ TAR
– ↑Depth- ↓ TAR
• Independent of SSD
Tissue Air Ratio (TAR)
• Calculated using two measurements at the
same point in space
• When the depth in tissue corresponds to
the level of DMAX, the TAR is known as the
backscatter factor.
• Build-up cap: device made of acrylic or
other phantom material that is placed over
an ionization chamber to produce
conditions of electronic equilibrium.
Tissue Air Ratio (TAR)
TAR = Dose in tissue
Dose in Air
*Normally used to
perform calcs for
SAD treatments
of low energy
machines.
*There is no patient
backscatter in the “in
Air” measurements.
Backscatter Factor (BSF)
• When blocks are used.
• Backscatter Factor (BSF): the ratio of the
dose rate with a scattering medium to the
dose rate at the same point without a
scattering medium at the level of
maximum equilibrium. (TAR at the level of
DMAX)
• PSF for megavoltage units.
Backscatter Factor (BSF)
The % change in dose
due to a change in
field size.
Readings are made at
Dmax and compared to
the dose in air.
↑FS  ↑Backscatter  ↑BSF
Dose to a Point
• The dose to any point in a medium is
made up of two parts:
– Primary radiation: the photons that originate
in, and fan out from the source.
– Scatter radiation: other parts in the medium
interact with the primary photons.
Scatter Air Ratio (SAR)
• Scatter Air Ratio (SAR): the difference
between the TAR for a field of definite area
and that for a zero area.
• The primary part of the total absorbed
dose is represented by the zero area TAR.
• A measure of the contribution from
scattered radiation.
Tissue Phantom Ratio (TPR)
• Tissue Phantom Ratio (TPR): the
absorbed dose at a given depth in
phantom to the absorbed dose at the
same point at a reference depth in
phantom.
• The deeper the reference depth the
greater the TPR.
Tissue Maximum Ratio (TMR)
*Tissue Maximum
Ratio (TMR): TPR
at DMAX
*TAR = TMR x BSF
Transmission Factors
• Transmission Factors: the ratio of the
radiation dose with the device to the
radiation dose without the device and
accounts for the material in the beams
path.
– Tray transmission factor
– Wedge factor
– Compensator factor
Other Factors
• Tray transmission factor: defines how
much of the radiation is transmitted
through a block tray.
– Tray factors vary with beam energy- as
energy increases, the effect of the material in
the beams path is lessened because of the
greater penetrating power of the higher
energy.
• Wedge: attenuates the radiation beam
progressively across a field
Given Dose
• Given dose: the dose at DMAX
• AKA: applied dose, entrance dose, peak
absorbed dose, or DMAX dose
• Point where PDD is 100%
Given dose = TD/ PDD x 100
TD: tumor dose, dose at depth
• Direct relationship:
DoseA/PDDA = DoseB/PDDB
Exit Dose
• Exit dose: the dose absorbed by a point
that is located at the depth of DMAX at the
exit of the beam.
Calculations
• Field size variations, energy changes, and
modifiers in the beam’s path can alter the
amount of radiation received by the patient.
Time setting = Dose at a point/Dose rate at that point
• Dose at a point: the prescribed dose as
determined by the doctor
• Dose rate at that point: represents the dose
rate of the treatment unit at the point of
calculation
Calculations
• When calculating dose to a given depth,
all other points in the radiation field will be
exposed to radiation for the same amount
of time.
• The dose to these points is dependant on
their depth.
SSD Calculations
• Output or dose rate of the machine should be
expressed at the depth of DMAX
• Field size: defined at the skin surface
• Dose rate: measured in tissue at the depth of
DMAX
1. Find equivalent square of the collimator setting (used for output
factor)
2. Find equivalent square of the EFS (used for PDD)
3. Determine the PDD
4. Determine prescribed dose
5. Determine the treatment unit setting
Extended Distance
• Extended Distance: patient is set up at a
distance beyond the isocenter or reference
distance.
• PDD is used because its nonisocentric
• When MUs are calculated for setup at
distances greater than the standard, ISL is
used to account for the decrease in dose
rates beyond the isocenter.
Inverse Square Law
• Inverse Square Law: describes the
change in beam intensity caused by the
divergence of the beam.
I1 / I2 = D22 / D12
I1 = original dose rate
I2 = new dose rate
D22 = original distance
D12 = new distance
Mayneord’s Factor
• Mayneord’s Factor: a special application of the
inverse square law.
• Does not account for changes in scatter
because of a change in beam divergence.
New PDD = PDD x (SSD1 + d / SSD1 + DMAX)2 x (SSD2 + DMAX / SSD1 + d)2
• Inverse Square Factor:
= (Reference source calibration distance
Treatment SSD + DMAX)2
• SSD: reference point typically at DMAX
• SAD: reference point at isocenter
TMR/TPR SAD
• COF(C.S.) (collimator output factor): used
to determine scatter, measured in air, from
the collimators
– The increase in the collimator opening, the
more collimator surface area the photons will
have to interact with.
• PSF(EFS) (phantom scatter factor): used
to determine scatter from the patient.