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Electron Beams: Physical Principles and Dosimetry Kent A. Gifford, Ph.D. Department of Radiation Physics UT M.D. Anderson Cancer Center [email protected] Medical Physics III: Spring 2010

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Page 1: Electrons kag

Electron Beams:Physical Principles and Dosimetry

Kent A. Gifford, Ph.D.

Department of Radiation Physics

UT M.D. Anderson Cancer [email protected]

Medical Physics III: Spring 2010

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Physical aspects

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Electron Interactions

Inelastic collisions

1. atomic electrons (ionization & excitation)

2. nuclei (bremsstrahlung)

Elastic collisions

1. w/ atomic electrons

2. w/ nuclei

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Electron Interactions

• Collisional (ionization and excitation)– Energy loss electron density (Z/A)

Radiation losses (bremsstrahlung)

– Energy loss Energy & Z2

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Electron Interactions– Mass Stopping Power (S/):

• Rate of energy loss (units: Mev-cm2/g)

• Collision losses (ionization and excitation) & radiation losses (bremsstrahlung):

ρdl

dΕ ρ

S

rct )ρS( )ρ

S( ) ρS(

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Electron Interactions

– Restricted Mass Stopping Power (L/:

• AKA LET (linear energy transfer) or energy loss per

unit path length (for local absorption not radiated

away)

ρdldE

ρL

Δ

E

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Electron interactionsAbsorbed dose

• Fluence

• Dose

dE (E) ρ

L (E)

E D

0

Δ

dE

EdE

)(

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Electron beam characteristics• Rapid rise to 100%

• Region of uniform dose (proximal 90% to distal 90%)

• Rapid dose fall-off

• High surface dose

• Clinically useful range 5-6 cm depth

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Electron Energy Specification• (the average energy of the spectrum)

• (most probable energy @ surface)

• (average energy at depth z)

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From: Khan

Electron Energy Specification

• Energy specification:– R50 - depth of the 50%

dose

– Rp - maximum range of electrons

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Electron Energy Specification

– Average Energy (E0):

– Most Probable Energy (Ep0):

– Energy (Ez) at depth z

500 332 ) R. (Ε

2002509812200, pp R.R.. E p

MDACC 21EX

AAPM TG-25 Med Phys 18(1), 73-109 (1991))Rz- (E E

pz 10

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Determination of Absorbed Dose• Calibration in water with ion chambers

– ADCL-calibrated system• Cylindrical-chamber reference point located

upstream of the chamber center by 0.5 rcav

– Reference conditions 100 cm SSD for a 1010 cm2 field

– Formalism:

N CowD

60

,kM D QQw

1.06.0 50 Rd ref

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Depth-Dose DistributionDose is calculated from ionization

measurements:

• M is ionization

• is the ratio of water-to-air mean restricted stopping powers

• is the ratio of water-to-air fluence

• Prepl is a chamber replacement correction

100

}{

}{

%max

numerator

LM

D

repl

W

air

W

airW

W

airρ

L

W

air

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Clinical aspects and dosimetry

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Characteristics of clinical electron beams

X-Ray Contamination

Surface

DoseDepth of

80% Dose

Depth of 50 % dose

Depth of 90% Dose

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Characteristics of Clinical Electron Beams

• Surface Dose:– Surface dose increases with increasing electron energy

From: Khan

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Characteristics of Clinical Electron Beams

• Depth of the 80% Dose:– Equal to approximately Enom/2.8 :

– Depth of 90% is approximately Enom/3.2

MDACC 21EX

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Characteristics of clinical electron beams

• Practical Range:– Equal to approximately 1/2 nominal energy:

– Energy loss is about 2 MeV / cm

MDACC 21EX

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Characteristics of clinical electron beams

• X-Ray Contamination:– Increases with energy:

– Varies with accelerator design

– Defined as RP+2 cm

MDACC 21EX

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Characteristics of clinical electron beams

• Accelerator design variations– Penumbra– X-ray Contamination

From: Tapley

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Characteristics of clinical electron beams

• Penumbral Effects:

– Low energies show expansion of isodose values

– High energies show constriction of high isodose values with bowing of low values.

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Electron Beam DosimetryIsodoses (6 MeV)

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Electron Beam DosimetryIsodoses (20 MeV)

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Electron Beam DosimetryPDD- effect of field size (6 MeV)

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Electron Beam DosimetryPDD- effect of field size (20 MeV)

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Electron Beam DosimetryBeam abutment

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Electron Beam DosimetryBeam abutment- electrons (6 & 20 MeV)

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Electron Beam DosimetryBeam abutment- electrons (6 & 12 MeV)

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Electron Beam DosimetryBeam abutment- electrons

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Electron Beam DosimetryBeam abutment- photon & electron (6 MeV & 6 MV)

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Electron Beam DosimetryBeam abutment- photon & electron (6 MeV & 18 MV)

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Electron Beam DosimetryBeam abutment- photon & electron (IMC & tangents)

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Electron Beam Dosimetry• Obliquity Effects

– Oblique incidence results in pdd shifts

From: Khan

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Electron Beam DosimetryObliquity effects

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Electron Beam Dosimetry• Field Shaping:

– Lead and/or Cerrobend is normally used– Thickness should be sufficient to stop electrons:

12E 0 t

t = mm PbE0 = Nom E (MeV)

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Electron Beam Dosimetry• Contour Irregularities:

– Sharp contour irregularities result in hot and cold spots

• Bolus:– Place as close to skin as

possible

– Use tissue-equivalent material

– Bevel bolus to smooth sharp edges

From: Khan

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Electron Beam Dosimetry

• Effects of inhomogeneities:– CET - coefficient of equivalent

thickness– The CET of a material is

approximately equal to its electron density relative to water

From: Khan

CET)- (1 z- d deff

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Electron Beam Dosimetry

• CET:– Sample calculation CET)- (1 z- d deff

1 cm

cm 2.25 0.25)- (1 1- 3 deff

cm 3.65 1.65)- (1 1- 3 deff

For Lung:

For Bone:

3 cm

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Electron Beam Dosimetry• Internal

Shielding:– Used to protect

tissues beyond treatment volume

– Backscattered electrons produce “dose enhancement”

From: Khan (Note E in MeV)

A dose enhancement of about 50% could be expected in a 6-MeV electron beam

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Electron Beam Dosimetry• Internal Shielding:

– Reduce the intensity of backscatter by introducing a tissue-equivalent absorber upstream from the shield

Electron energy at the scatterer

From: Khan

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Electron BeamMonitor-Unit Calculations

• Electron-beam monitor units (MU) are normally calculated to a point at dmax along the central axis

• A dose DRx that is prescribed to a point other than dmax, can be related to the dmax dose Ddmax through the precription isodose level %D:

%D

DD Rxdmax

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Electron BeamMonitor-Unit Calculations

• The MU setting (MU) that is necessary to deliver a dose Ddmax is a function of the electron beam’s “output” (in cGy per MU) at the calculation point:

• Here OFS,SSD is the dose output as a function of field size (FS) and distance (SSD)

SSDFS,

dmaxO

DMU

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Electron BeamMonitor-Unit Calculations

• For an electron beam calibrated such that 1 MU = 1 cGy at 100 cm SSD for a 1010 field at dmax:

Calibrated output for a 10X10 cm field at 100

cm SSD

Output factor for field size FS relative to field

size 10X10

Distance-correction factor for distance SSD relative

to 100 cm SSD

Electron-beam output for a field size FS at a distance SSD

)(F)(OF)(OO SSDFS10,100SSDFS,

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Monitor-Unit Calculations

• Field-Size Corrections OFFS:– Field-size corrections generally account for the aperture produced by two

devices:• Cones or Applicators, and Customized Inserts

– The field-size dependent output factor OFFS can then be thought to consist of

cone and insert output factors, OFCS and OFIS:

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Monitor-Unit Calculations• Field-Size Corrections - OFCS, IS :

– When used separately, cone factors, OFCS, are normalized to the 1010 (or 1515) cone, and insert factors, OFIS, are normalized to the open cone into which inserts are placed

– Alternatively, they can be combined into a single factor, OFCS, IS , that is

normalized to the open 1010 (or to the 1515) cone :

ISCSISCSFS OFOFOFOF ,

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Monitor-Unit Calculations• Field-Size Corrections - OFLW :

– For rectangular fields, the field-size dependent output factor, OFFS, is determined from square-field output factors using the “square root method”. Thus, for a rectangular field LW:

– For example, the 412 output factor OF412 is the square-root of the product of the 44 output

factor, OF44, and the 1212 output factor, OF1212

WxWLxLLxW OFOFOF

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Monitor-Unit Calculations

• Distance (SSD) Corrections FSSD:– The variation of electron-beam output with distance does

not follow a simple conventional inverse-square relationship

• Due to attenuation and scattering in air and in beam collimation and shaping devices

– Distance corrections take two forms:• Use of an “effective SSD” that can be used in an inverse-square

fashion

• Use of an “air-gap factor” that can be used in addition to a conventional inverse-square factor

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Monitor-Unit Calculations• Distance Corrections - SSDeff:

– Assuming that an inverse-square relationship exists in which a reduced distance to a “virtual” source of electrons

exists, then the distance correction, FSSD is:

• where SSDeff is the effective (or virtual) SSD and g is the distance (gap) between the “nominal” SSD (100 cm) and the actual SSD; dm is

the dmax depth

2

gdSSD

dSSDISFF

m

meffSSDSSD

eff

EFF

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Monitor-Unit Calculations• Distance Corrections - SSDeff :

– The “effective SSD” is a virtual distance that is utilized so that an inverse-square approximation can be used

• Effective SSDs vary with energy and field size as well as with electron collimation design

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Monitor-Unit Calculations• Distance Corrections - fair :

– An alternative method of applying distance corrections utilizes a conventional inverse-square correction and an air gap factor, fair , that accounts for the further reduction in output that is unaccounted-for by the inverse-square correction alone:

• SSDnom is the nominal (100 cm) SSD

airmnom

mnomgSSDSSD f

gdSSD

dSSDISFF nom

2

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Monitor-Unit Calculations

• Distance Corrections - fair:

– fair also varies with energy and field size (it is derived from the same data set that can be used to also determine SSDeff)

– For rectangular fields, as with any electron field-size correction, the square-root method is used:

WxWLxLLxW airairair fff

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Monitor-Unit Calculations• Use of Bolus:

– When bolus is used, the depth-dose curve shifts “upstream” by a distance equal to the bolus thickness (e.g. if 1 cm bolus is used, the depth of dmax shifts by a distance of 1 cm toward the skin surface)

– The output at this shorter distance is:

• where b is the bolus thickness in cm, and SSD is the nominal SSD

2, bdSSDdSSDOO

mSSDbSSD m

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Electron Monitor-Unit Calculations - Sample Problems

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Electron Monitor-Unit Calculations - Sample Problems

3 . R o u g h l y , w h a t i s t h e e n e r g y o f a 1 2 M e V e l e c t r o nb e a m a t a d e p t h o f 5 c m ?

MeVEEE lostinitialleft 21012

MeVdcmMevE cmlost 1052/2

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Electron Monitor-Unit Calculations - Sample Problems

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Electron Monitor-Unit Calculations - Sample Problems

5 . W h a t i s t h e m o n i t o r - u n i t s e t t i n g n e c e s s a r y t o d e l i v e ra d o s e o f 2 0 0 c G y p e r f r a c t i o n t o d m a x u s i n g 9 M e Ve l e c t r o n s , 6 x 1 0 f i e l d i n a 1 0 x 1 0 c o n e , a t 1 0 0 c m S S D ?

WxWLxLLxW OFOFOF 002.10.1003.1101066106 xxx OFOFOF

2006.199200

1.0(1.002)(1.0)UM

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Electron MU Sample Problems6 . W h a t i s t h e m o n i t o r - u n i t s e t t i n g n e c e s s a r y t o d e l i v e r ad o s e o f 2 0 0 c G y p e r f r a c t i o n t o t h e 9 0 % i s o d o s e u s i n g 9M e V e l e c t r o n s , 6 x 1 0 f i e l d i n a 1 5 x 1 5 c o n e , a t 1 0 5 c m S S D ?

airmnom

mnomgSSDSSD f

gdSSD

dSSDISFF nom

2

892.0981.0909.0984.0978.053.2100

3.21002

SSDF

0.1003.1997.010106615

106 xxCone

x OFOFOF

2491.249

892.0

2.222

892.00.10.1

10090200

MU