Review of fundamental photon dosimetry quantities Narayan Sahoo Main sources of the materials included in this lecture notes are: (1) Radiation Oncology Physics: A Handbook for Teachers and Students Edited by E. B. Podgorsak (2) The physics of Radiation Therapy by F. M. Khan (3) Previous lecture notes for this course by Karl Prado
Reading assignment Chapters 2 and 6 of the reference text for the course Reference Text: Radiation Oncology Physics: A Handbook for Teachers and Students, http://wwwpub.iaea.org/mtcd/publications/pdf/pub 1196_web.pdf
Distance, Depth, Scatter The dose to a point located on the central axis of a beam incident on a water phantom varies with: distance from the source of radiation depthin the phantom amount of radiation scattered to the point
Distance, Depth, Scatter
Field sectors are represented by equally-spaced radii from the calculation point to the edge of the field (either to the collimator jaw or to a block edge) Scatter Concepts
Effective Field Size Equivalent Square The equivalent square/effective field yields the same dosimetric characteristics as the rectangular or irregularly shaped fields. Equivalent square does not mean field with the same area.
Effective Field Size General Rules Attempt to maintain basic field shape for determination. Visualize the closest rectangular area that can be adapted to irregular field shape. Measure along perpendicular axis. If blocking is extensive or complex, best to use an irregular field calculation. Rectangular field is converted to equivalent square using BJR or 4A/P. Field size used to look up all phantom measured quantities.
Account for Flash
Asymmetric Field Sizes Must account for location of central axis or calculation point. There is an effective field even if there are no blocks. C. Ax... Calc. Pt.
The MLC as a block If MLC is a tertiary collimation system, then treat them as a block and calculate effective field accordingly. Will have a collimator field size and an effective field. If MLC replaces the jaw calculate the effective field defined by the MLC, this will be both the effective field and the collimator field size.
Inverse Square Law The intensity of the radiation is inversely proportional to the square of the distance from the source: x 1 d 12 = x 2 d 2 2 Example 1: If the dose at 80 cm from the source is 200 cgy. What is the Dose at 100 cm? x 1 = 200 cgy x 2 =? x 2 = x 1 (d 1 /d 2 ) x 2 = 200 cgy (80/100) 2 x 2 = 128 cgy d 1 = 80 cm d 2 = 100 cm
PERCENT DEPTH DOSE The Absorbed dose in the patient (phantom) will vary with depth. One way to characterize this variation is with the percent depth dose. Abbreviations: PDD or % dd Definition: PDD = (D d / D dmax ) x 100 = (dose at a depth d / dose at d max
PERCENT DEPTH DOSE The Percent Depth Dose is most commonly used for fixed SSD treatments. Where SSD = the source to surface (skin) Distance. The Percent Depth Dose is dependent upon a number of factors: 1. The Beam Quality or Energy 2. The Depth 3. The Field Size 4. The SSD
Percent Depth Dose Decreases with depth for all energies beyond build-up region. Increases with energy beyond build-up region. If ignore inverse square and scattering, follows exponential attenuation. Beam quality therefore affects PDD through average attenuation coefficient (µ). The attenuation coefficient decreases with energy, therefore the beam is more penetrating.
BUILDUP REGION: Gives rise to what is known as the skin sparing effect. The skin dose decreased with increasing beam energy. The buildup of dose is greater as the energy is increased. Orthovoltage-- no buildup; dose maximum at surface. Co-60 6X 18X D max at 0.5 cm D max is at 1.5 cm, D max is at 3.0 cm.
Buildup Region Interaction of incident photon with phantom yields an ejected secondary electron. Secondary electrons deposit energy downstream. The electron fluence and absorbed dose increase until reach a maximum ( approximate range of electrons) Same time -- photon fluence decreases with depth at constant rate. Therefore, fewer photons to eject electrons as increase depth. The combination of all these factors yields the dose buildup region
KERMA vs. Absorbed Dose
KERMA Kinetic Energy Released in Matter Energy transferred from Photons to Electrons. Is maximum at the surface and decrease with depth due to increase in photon energy fluence. Dose < KERMA at the surface Dose = KERMA at D max Dose > KERMA at depths beyond D max The areas beneath both curves must be the same.
Percent Depth Dose 10 cm. Depth 0 x 0 5 x 5 10 x 10 20 x 20 4x ------- 59.1 64.2 68.0 6x 55.2 64.5 68.2 71.4 10x 67.2 71.6 74.3 77.0 20x ------- 78.9 80.4 81.1
PERCENT DEPTH DOSE SSD DEPENDENCE
Percent Depth Dose SSD Dependence Percent depth dose increases with increasing SSD due to inverse square law. Dose rate at each point actually decreases Dose decrease at D max much greater than at depth. Therefore, ratio of dose at depth to dose at D max will increase. So %dd will increase.
Mayneord F-Factor It is not feasible to measure the %dd at every possible SSD that will be used clinically. How can you get the %dd at different SSD s?
PDD from SSD 1 to SSD 2 F = SSD SSD 2 1 + + d d max max SSD SSD 2 1 + + d d 2
Examples 1. What is the given dose if the dose prescribed is 200 cgy to a depth of 10cm. The energy of the beam is 6 MV. The %dd at 10 cm is 67%. 100cm SSD. Given dose is TD/%dd: 200 /.67 = 299 cgy
2. If a single anterior field of 6 MV photons delivers 200 cgy to a depth of 5cm. What is the dose at a depth of the cord, if it lies at a point 12 cm from the anterior surface? Patient is treated 100 cm SSD with a 10 x 15 field. Equivalent square for 10 x 15 field is 12cm 2 %dd for a 12 cm field at 5cm is.877 %dd for a 12 cm field at 12cm is.620 dose to cord = 200 x (.620 /.877) = 141 cgy
A patient is treated with parallel opposed Co-60 fields to midplane. The patient has a lateral neck thickness of 12cm. The field size is 6x6 and the dose to midplane is 200 cgy. What is the dose per fraction to a node that may be located at 3 cm from the right? %dd at 6 cm = 0.707 %dd at 3cm = 0.865 %dd at 9cm = 0.562 Dose to node from right: (100/0.707) x 0.865 = 122.4 Dose to node from left: (100/.707) x.562 = 79.5 Total dose to the node: 122.4 + 79.5 = 201.9 cgy
Tissue Air Ratio (TAR) TAR= (Dose at depth d / Dose at same point in air) TAR = D d / D air The points are for the same field size and constant SAD. Dose in air is commonly referred to as dose in free space (sufficient mass around point to provide electronic equilibrium, but not introduce scatter). The TAR depends on the following: 1. Energy 2. Depth 3. Field Size 4. It is relatively independent of SSD
SSD EFFECT 1. The TAR is a ratio of doses at the same distance, therefore, the distance dependence of photon fluence is removed. 2. The attenuation and scattering components are left as the ones modified in the TAR. 3. Primary beam is attenuated exponentially with depth.
Tissue Air Ratio Varies with depth like %dd. Decreases with depth beyond buildup. Varies with energy like %dd. Increase energy increase the TAR. Varies with field size like the %dd. Increase field size increase the TAR.
The BSF (or PSF): A Special Tissue Air Ratio
Backscatter / Peakscatter Factor Energy dependent Field size dependent; increases with field size Not depth dependent; specified at d max Independent of SSD; is a specific TAR BSF/PSF are used interchangeably. BSF specifically applies when maximum is at the surface.
Back Scatter Factor / Peak Scatter Factor
Example 1. Cobalt-60 : output = 100 cgy/min at 80.5 cm. in a mini-phantom of muscle (in air). Field Size is 10 x 10. A. What is the dose rate in tissue at 0.5 cm? B. What is the dose rate at 10 cm depth 80 cm SSD? C. What is the dose rate at D max if set up 80 SAD? D. What is the dose rate at 10 cm depth, 80 SAD?
A. Dose rate (DR) in tissue = dose rate in air x BSF = 100 cgy/min x 1.035 = 103.5 cgy/min B. DR at 10 cm = Dose rate at D max x %dd at 10 cm = 103.5 cgy/min x.556 = 57.5 cgy/min C. DR at D max (80 cm SAD) = Dose rate in air (80.5) x IS x BSF ; IS = (80.5/80) 2 = 1.0125; DR at d max (80 cm SAD) = 100 x 1.0125 x 1.035 = 104.8 cgy/min D. DR at 10 cm = DR in air (80.5) x IS x TAR at 10 cm = 100 x 1.0125 x.718 = 72.7 cgy/min
TMR / TPR Ratio of dose at a given point in phantom to the dose at a fixed reference point at the same distance. TPR = dose at depth / dose at reference depth = D d / D ref If reference depth is at D max then the TPR becomes a TMR TMR = dose at depth / dose at d max = D d / D dmax For both cases points are measured with constant SAD Reference depth should not be in the build up region. Common depths are 5cm and 10 cm
Tissue Phantom Ratio (TPR) Tissue Maximum Ratio (TMR)
TMR (TPR) are dependent upon the following: 1. They are independent of SSD for the same reasons as the TAR 2. The TMR increases with Energy 3. The TMR increases with Field Size 4. The TMR decreases with Depth. Measuring the TMR and TAR values is very time consuming and difficult process. Therefore, the TMR and TAR an be calculated from measured %dd values. The TMR data can also be calculated from TAR data.
Output Factor Ratio of the dose in phantom at a given reference depth for a given field size to the dose at the same point and depth for the reference field size. Most common reference field size is 10 x 10 Commonly known as total scatter factor S T or S c,p Total scatter factor can be broken up into two components. Collimator and flattening filter scatter, and scatter arising from interactions in the phantom.
Collimator Scatter Factor (S c ) Ratio of output in air for a given field size to that of the reference field size. Field sizes are defined by collimator setting Measured with ion chamber in air. Buildup cap must provide dose scatter equilibrium. Field must cover entire buildup cap. To cover buildup cap may have to extend SAD
Phantom Scatter Factor (S p ) Accounts for changes in scatter originating in phantom/patient as the field size changes. Ratio of dose for a given field size to that for the reference field size. Measured at same depth. Field size is actual field irradiating the phantom. Collimator opening must remain the same. Actually relates to the change in volume of phantom/patient irradiated given the same collimator defined field size.
Phantom Scatter Factor (S p ) More practical to measure total scatter factor and obtain S p from this measurement. S p = S cp /S c Total scatter factor and phantom scatter factor usually defined at reference depth of D max. Measuring at this point can create problems due to dose buildup region, and possible electron contamination. Can avoid by measuring at deeper depths and converting to the D max depth using %dd or TMR. At low energies S p = BSF (fs) / BSF (10 x 10) = NPSF
Wedge Factors Ratio of dose at a reference depth with the wedge present to that without the wedge. Measurements are at same reference depth and with the same field size. Reference depths are commonly d max 5 cm, or 10 cm. Wedge factor accounts for reduction of dose due to the presence of the wedge. Energy, depth and field size dependent. Depth dependence can be eliminated by using measured wedged %dd and TPR values.
Varian Enhanced Dynamic Wedge Wedge created by moving upper jaw with variable dose rate and speed. Deliver fraction of MUs with open field and then jaw closes to final position. Variations are driven by STT table, which are unique for each energy and wedge angle. All STT derived from single 60 degee golden table. Wedge factor depends on final position of jaw and can be extracted from STT table.
Enhanced Dynamic Wedge (EDW) Gibbons
Universal Wedge (Elekta, GE) Single 60 degree physical wedge moved in and out of beam to achieve desired wedge. Mix open beam with 60 degree wedge based on ratio of tangents to achieve other angles. Wedge is internal in the machine and usually made of tungsten. Desired wedge is chosen, machine moves 60 degree wedge in for set amount of monitor units, then it is moved out and remaining fraction of monitor units delivered open. Same dependencies as conventional wedges since it is a hard wedge.
Tray Factor Tray factor accounts for the reduction in dose rate due to the blocking tray being placed in the beam. Ratio of dose with tray present to that without the tray. Measured at a fixed reference depth. Energy and field size dependent.
Tray Factors
Off-Axis Factors / Off-Center Ratios The terms Off-Axis Factor (OAF) and Off- Center Ratio (OCR) are often used interchangeably. We will define the OAF as the ratio of the dose at a distance x from the central axis to the dose existing at the central axis at the same depth OAFs are obtained from measured profiles:
Off-Axis Quantities Beam Profile - Intensity across a beam at a given depth (Khan)
Open-Field Off-Axis Factors: Sample Table: 2100C 6 MV Depth Off-Axis "Tangent" 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.08 0.10 Off Axis Distance (at 100 cm field-size definition distance) 0 0 1 2 3 4 5 6 8 10 1.7 1.000 1.007 1.012 1.020 1.028 1.035 1.040 1.046 1.051 5 1.000 1.009 1.016 1.023 1.030 1.035 1.037 1.041 1.045 10 1.000 1.007 1.013 1.020 1.024 1.024 1.025 1.025 1.024 15 1.000 1.001 1.007 1.011 1.015 1.016 1.015 1.011 1.003 20 1.000 1.003 1.007 1.011 1.012 1.014 1.009 1.001 0.988 25 1.000 1.003 1.005 1.005 1.006 1.007 1.001 0.986 0.971 30 1.000 1.004 1.006 1.008 1.008 1.006 0.998 0.981 0.963
Off-Axis Quantities Of-Axis Factor: OAF (x,d) Varian 2100C SN 241 6 MV Open-Field Off-Axis Factors Off-Axis Factor 1.05 1.04 1.03 1.02 1.01 1.00 0.99 0.98 0.97 0.96 0.95 0.00 0.02 0.04 0.06 0.08 0.10 Off-Axis "Tangent" Depth 1.7 Depth 5.0 Depth 10 Depth 15 Depth 20 Depth 25 Depth 30 Off-axis distance must be clearly defined!!
Off Axis Wedge Corrections
Wedged-Field Off-Axis Correction 45 Wedge Off-Axis Factors Off-Axis Factor 1.500 1.400 1.300 1.200 1.100 1.000 0.900 0.800 0.700-0.10-0.05 0.00 0.05 0.10 Off-Axis "Tangent" Toe Slope Heel Slope d5 d10 d20
Summary: Fundamental Concepts, Quantities and Parameters Depth / Distance / Scatter Inverse-Square PDD TAR / PSF (BSF) TMR/TPR Relationships between: PDD / TAR / Inv Sq Output Factor (S c,p and S p ) Wedge Factors / Tray Factors Off-Axis Factors