Fundamental Dosimetry Quantities and Concepts: Review

Introduction to Medical Physics III: Therapy

Steve Kirsner, MSDepartment of Radiation Physics

Some Definitions 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

Fundamentals

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

From source to point of calculation

Depth Within attenuating

media Scatter

From phantom and treatment-unit head

Distance, Depth, Scatter

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 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 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 Size Must Account for

flash, such as in whole brain fields. Breast fields and larynx fields.

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

Must Account for locaton of Central axis or calculation point.

There is an effective field even if there are no blocks.

…cax

Calc.Pt.

Inverse Square Law

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

X1D12 = X2D2

2

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

0/ dd DDPDD

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 Curves

Note change in depth of dmax

Can characterize PDD by PDD at 10-cm depth

%dd10 of TG-51

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 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 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 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 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 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

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

fsd DDTAR /

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 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

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 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

0/ td DDTPR

TPR/TMR Dependencies

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

From: ICRU 14

Relationship between fundamental depth-dependent quantities

PDD / TAR / BSF Relation

Approximate Relationships:PDD / TAR / BSF / TMR

BJR Supplement 17

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 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 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 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)

Gibbons

The Dynamic Wedge 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 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

0, ,/),( dxd DDdxOAF where x = distance off-axis

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 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

Varian 2100C SN 241 6 MV Open-Field Off-Axis Factors

0.95

0.96

0.97

0.98

0.99

1.00

1.01

1.02

1.03

1.04

1.05

0.00 0.02 0.04 0.06 0.08 0.10

Off-Axis "Tangent"

Off

-Axi

s F

acto

r

Depth 1.7

Depth 5.0

Depth 10

Depth 15

Depth 20

Depth 25

Depth 30

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

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

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

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

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

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

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

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