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Fundamental Dosimetry Quantities and Concepts: Review

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Fundamental Dosimetry Quantities and Concepts: Review

Introduction to Medical Physics III: Therapy

Steve Kirsner, MS

Department of Radiation Physics

SSD

SAD

Isocenter

Transverse (Cross-Plane)

Radial (In-plane)

Sagittal

Coronal

Axial

Supine

Prone

Cranial

Caudal

Medial

Lateral

AP/PA

Rt. & Lt. Lateral

Superior

Inferior

RAO/RPO/LAO/LPO

- Review of Concepts
- Distance, depth, scatter effects

- Review of Quantities
- PDD, TMR, TAR, PSF (definition/dependencies)
- Scatter factors
- Transmission factors
- Off-axis factors

- Distance
- From source to point of calculation

- Depth
- Within attenuating media

- Scatter
- From phantom and treatment-unit head

- Contribution of scatter to dose at a point
- 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

- 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.
- Normally represented by the “side” of the equivalent square
- Note that each point within the field may have a different equivalent square

- The “effective” field size is that size field that best represents the irregular-field’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

- Must Account for flash, such as in whole brain fields. Breast fields and larynx fields.

- 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
- Examples of tertiary blocking are (Lipowitz metal alloy) external blocks, and tertiary MLCs such as that of the Varian accelerator
- When external (Lipowitz metal) blocks are supporte by trays, attenuation of the beam by the tray must be taken into account

- Examples of tertiary blocking are (Lipowitz metal alloy) external blocks, and tertiary MLCs such as that of the Varian accelerator
- 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.

- Must Account for locaton of Central axis or calculation point.
- There is an effective field even if there are no blocks.

…

Calc.

Pt.

cax

- The intensity of the radiation is inversely proportional to the square of the distance.
- X1D12 = X2D22

- PDD Notes
- Characterize variation of dose with depth.
- 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:
- Differences in depth
- Differences in distance
- Differences in field size at each depth

- Note in mathematical description of PDD
- Inverse-square (distance) factor
- Dependence on SSD

- Attenuation (depth) factor
- Scatter (field-size) factor

- Inverse-square (distance) factor

- PDD Curves
- Note change in depth of dmax
- Can characterize PDD by PDD at 10-cm depth
- %dd10 of TG-51

- Beam Quality effects PDD primarily through the average attenuation coefficient. Attenuation coefficient decreases with increasing energy therefore beam is more penetrating.

- Kerma to dose relationship
- Kerma and dose represent two different quantities
- Kerma is energy released
- Dose is energy absorbed

- Areas under both curves are equal
- Build-up region produced by forward-scattered electrons that stop at deeper depths

- Kerma and dose represent two different quantities

- 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.

- Effect of inverse-square term on PDD
- As distance increases, relative change in dose rate decreases (less steep slope)
- This results in an increase in PDD (since there is less of a dose decrease due to distance), although the actual dose rate decreases

- As distance increases, relative change in dose rate decreases (less steep slope)

- The inverse-square term within the PDD
- 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
- “Divide out” the previous inverse-square term (for SSD1), “multiply in” the new inverse-square term (for SSD2)

- 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.

- 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 …
- The ratio of doses at two points:
- 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)
- Concept of “equilibrium mass”
- Need for electronic equilibrium – constant Kerma-to-dose relationship

- Concept of “equilibrium mass”

- The ratio of doses at two points:

- 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
- 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)

- In general, scatter contribution decreases as energy increases
- Note:
- 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)

- Varies with energy like the pdd-increases 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

- Similar to the TAR, the TPR is the ratio of doses (Dd and Dt0) at two points equidistant from the source
- 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

- Independent of SSD
- TMR increases with Energy
- TMR increases with field size
- TMR decreases with depth

From: ICRU 14

BJR Supplement 17

- It is generally believed that the TAR and TMR are independent of SSD
- This is true within limits
- Note the effect of purely geometric distance corrections on the contribution of scatter

- The TMR (or TAR or PDD) for a given depth can be plotted as a function of field size
- 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
- 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 describe field-size dependence of dose at a point
- Need to define “field size” clearly
- Many details …

- Often wise to separate sources of scatter
- Scatter from the head of the treatment unit
- Scatter from the phantom or patient

- Measurements complicated by need for electronic equilibrium
- Kerma to dose, again

- Need to define “field size” clearly

- Beam intensity is also affected by the introduction of beam attenuators that may be used modify the beam’s shape or intensity
- 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 field-size and depth dependent

- Enhanced Dynamic Wedge (EDW)

- Wedged dose distributions can be produced without physical attenuators
- With “dynamic wedges”, a wedged dose distribution is produced by sweeping a collimator jaw across the field duration irradiation
- The position of the jaw as a function of beam irradiation (monitor-unit setting) is given the wedge’s “segmented treatment table (STT)
- The STT relates jaw position to fraction of total monitor-unit setting

- The position of the jaw as a function of beam irradiation (monitor-unit setting) is given the wedge’s “segmented treatment table (STT)
- The determination of dynamic wedge factors is relatively complex

- With “dynamic wedges”, a wedged dose distribution is produced by sweeping a collimator jaw across the field duration irradiation

Gibbons

- 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”
- Two equivalent quantities are used
- Off-Axis Factors (OAF)
- Off-Center Ratios (OCR)

- These two quantities are equivalent

- Two equivalent quantities are used

where x = distance off-axis

- Off-axis factors are extracted from measured profiles
- Profiles are smoothed, may be “symmetrized”, and are normalized to the central axis intensity

- OAFs (OCRs) are often tabulated and plotted versus depth as a function of distance off axis
- 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

- Descriptions vary of off-axis intensity in wedged fields
- 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
- Open-field off-axis intensity is divided out of the profile
- The corrected profile is normalized to the central axis value

- 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

- 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

- 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

- 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

- 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

- 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

- 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