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Fundamental Dosimetry Quantities and Concepts: Review

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

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Fundamental Dosimetry Quantities and Concepts: Review

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  1. Fundamental Dosimetry Quantities and Concepts: Review Introduction to Medical Physics III: Therapy Steve Kirsner, MS Department of Radiation Physics

  2. 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 Some Definitions

  3. Fundamentals • Review of Concepts • Distance, depth, scatter effects • Review of Quantities • PDD, TMR, TAR, PSF (definition/dependencies) • Scatter factors • Transmission factors • Off-axis factors

  4. Distance, Depth, Scatter • Distance • From source to point of calculation • Depth • Within attenuating media • Scatter • From phantom and treatment-unit head

  5. Distance, Depth, Scatter

  6. Scatter Concepts • 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

  7. Equivalent Square • 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

  8. Effective Field Size • 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

  9. Effective Field Size • Must Account for flash, such as in whole brain fields. Breast fields and larynx fields.

  10. Blocking and MLCs • 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 • 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.

  11. Effective Fields Asymmetric Field Sizes • Must Account for locaton of Central axis or calculation point. • There is an effective field even if there are no blocks. … Calc. Pt. cax

  12. Inverse Square Law • The intensity of the radiation is inversely proportional to the square of the distance. • X1D12 = X2D22

  13. Percent Depth Dose (PDD) • 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

  14. PDD: Distance, Depth, Scatter • Note in mathematical description of PDD • Inverse-square (distance) factor • Dependence on SSD • Attenuation (depth) factor • Scatter (field-size) factor

  15. PDD: Depth and Energy Dependence • PDD Curves • Note change in depth of dmax • Can characterize PDD by PDD at 10-cm depth • %dd10 of TG-51

  16. PDD: Energy Dependence • Beam Quality effects PDD primarily through the average attenuation coefficient. Attenuation coefficient decreases with increasing energy therefore beam is more penetrating.

  17. PDD Build-up Region • 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

  18. PDD: Field Size and Shape • 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.

  19. PDD: Effect of Distance • 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

  20. Mayneord F Factor • 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)

  21. Mayneord F Factor • 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.

  22. PDD Summary • 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

  23. The TAR • 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

  24. The PSF (BSF) • 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)

  25. The PSF versus Energy as a function of Field Size • 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)

  26. TAR Dependencies • 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

  27. The TPR and TMR • 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

  28. TPR/TMR Dependencies • Independent of SSD • TMR increases with Energy • TMR increases with field size • TMR decreases with depth

  29. Relationship between fundamental depth-dependent quantities From: ICRU 14

  30. PDD / TAR / BSF Relation

  31. Approximate Relationships:PDD / TAR / BSF / TMR BJR Supplement 17

  32. Limitations of the application of inverse-square corrections • 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

  33. Effect of scatter vs. distance:TMR vs. field size • 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)

  34. Scatter Factors • 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

  35. Wedge Transmission • 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

  36. The Dynamic Wedge • 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 determination of dynamic wedge factors is relatively complex Gibbons

  37. Off-Axis Quantities • 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 where x = distance off-axis

  38. Off-Axis Factors:Measured Profiles • Off-axis factors are extracted from measured profiles • Profiles are smoothed, may be “symmetrized”, and are normalized to the central axis intensity

  39. Off-Axis Factors: Typical Representations • 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

  40. Off-Axis Wedge Corrections • 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

  41. Examples • 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

  42. Example Problems • 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

  43. Examples • 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

  44. Examples • 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

  45. Examples • 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

  46. Examples • 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

  47. Examples • 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

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