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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

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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

Some definitions




Transverse (Cross-Plane)

Radial (In-plane)











Rt. & Lt. Lateral




Some Definitions


  • Review of Concepts

    • Distance, depth, scatter effects

  • Review of Quantities

    • PDD, TMR, TAR, PSF (definition/dependencies)

    • Scatter factors

    • Transmission factors

    • Off-axis factors

Distance depth scatter
Distance, Depth, Scatter

  • Distance

    • From source to point of calculation

  • Depth

    • Within attenuating media

  • Scatter

    • From phantom and treatment-unit head

Scatter concepts
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

Equivalent square
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

Effective field size
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

Effective field size1
Effective Field Size

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

Blocking and mlcs
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.

Effective fields asymmetric field sizes
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.




Inverse square law
Inverse Square Law

  • The intensity of the radiation is inversely proportional to the square of the distance.

  • X1D12 = X2D22

Percent depth dose pdd
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

Pdd distance depth scatter
PDD: Distance, Depth, Scatter

  • Note in mathematical description of PDD

    • Inverse-square (distance) factor

      • Dependence on SSD

    • Attenuation (depth) factor

    • Scatter (field-size) factor

Pdd depth and energy dependence
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

Pdd energy dependence
PDD: Energy Dependence

  • 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
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

Pdd field size and shape
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.

Pdd effect of distance
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

Mayneord f factor
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)

Mayneord f factor1
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.

Pdd summary
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

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

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)

The psf versus energy as a function of field size
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)

Tar dependencies
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

The tpr and tmr
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

Tpr tmr dependencies
TPR/TMR Dependencies

  • Independent of SSD

  • TMR increases with Energy

  • TMR increases with field size

  • TMR decreases with depth

Approximate relationships pdd tar bsf tmr
Approximate Relationships:PDD / TAR / BSF / TMR

BJR Supplement 17

Limitations of the application of inverse square corrections
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

Effect of scatter vs distance tmr vs field size
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)

Scatter factors
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

Wedge transmission
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

The dynamic wedge
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


Off axis quantities
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

Off axis factors measured profiles
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

Off axis factors typical representations
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

Off axis wedge corrections
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


  • 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
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


  • 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