Electron Beams: - PowerPoint Presentation

Slide1

Electron Beams:Physical Principles and Dosimetry

Kent A. Gifford, Ph.D.Department of Radiation PhysicsUT M.D. Anderson Cancer Centerkagifford@mdanderson.org

Medical Physics III: Spring 2015Slide2

Physical aspectsSlide3

Electron Interactions w/matter (b >> a)Slide4

Electron Interactions w/matter (b >> a)

Coulomb force on atom resulting in:

Ionization (ejection of valence e-) ExcitationTermed “soft” interactionsSlide5

Electron Interactions w/matter (b ~ a)Slide6

Electron Interactions w/matter

Head on collision resulting in:

Ionization (ejection of e- w/ high K.E.) Ejected e- (δ ray) dissipates energy along its path Characteristic X-ray or Auger e- producedSlide7

Electron Interactions w/matter (b << a)Slide8

Electron Interactions w/matter (b << a)

Coulomb interaction resulting in:

Deflection of primary e-, large deflection BremmstrahlungSlide9

Electron Interactions w/ matterStopping powerSlide10

Electron Interactions w/ matterStopping power

For what do the four terms in the brackets account?Slide11

Electron Interactions w/ matterStopping power

For what do the four terms in the brackets account?First term- soft collisionsSlide12

Electron Interactions w/ matterStopping power

For what do the four terms in the brackets account?First term- soft collisions

Second term- Möller (e-) or Bhabha (e+) scattering (hard coll.)Slide13

Electron Interactions w/ matterStopping power

For what do the four terms in the brackets account?

First term- soft collisionsSecond term- Möller (e-) or Bhabha (e+) scattering (hard coll.)Third term- density effect

Condensed medium stopping power reduced due to atoms closer to particle polarized and screen distant atoms from particle’s electric fieldSlide14

Electron Interactions w/ matterStopping power

For what do the four terms in the brackets account?

First term- soft collisionsSecond term- Möller (e-) or Bhabha (e+) scattering (hard coll.)Third term- density effect

Fourth term- shell correction

Born approximation did not account for binding energy of electronsSlide15

Electron Interactions w/ matterStopping powerSlide16

Electron Interactions w/ matterStopping powerSlide17

Electron Interactions w/ matterStopping powerSlide18

Electron Interactions w/ matterStopping power

How does Scoll/ρ depend on the interacting medium?Slide19

Electron Interactions w/ matterStopping power

How does Scoll/ρ depend on the interacting medium?

Z/ASlide20

Electron Interactions w/ matterStopping power

How does Scoll/ρ depend on the interacting medium?

Z/A -ln ISlide21

Electron Interactions w/ matterStopping power

How does Scoll/ρ depend on the interacting medium?

Z/A ln IWhich is greater S

coll

/ρ

(

Pb

or Be) at 20

MeV

?Slide22

Electron Interactions w/ matterStopping power

How does Scoll/ρ depend on the interacting medium?

Z/A ln IWhich is greater S

coll

/ρ

(

Pb

or Be) at 20

MeV

?

Be 1.623

MeV

cm

2

g

-1

vs.

Pb

1.277

MeV

cm

2

g

-1

Slide23

Electron Interactions w/ matterStopping power

How does Scoll/ρ depend on particle velocity?Slide24

Electron Interactions w/ matterStopping power

How does Scoll/ρ depend on particle velocity?1/β

2Slide25

Electron Interactions w/ matterStopping power

How does Scoll/ρ depend on particle velocity?1/β

2This is the reason for the steep rise in Scoll/ρ and Bragg peak (Heavy ions)Slide26

Electron Interactions w/ matterStopping power

How does Scoll/ρ depend on particle mass and charge?Slide27

Electron Interactions w/ matterStopping power

How does Scoll/ρ depend on particle mass and charge?NoneSlide28

Electron Interactions w/ matterStopping power

How does Scoll/ρ depend on particle mass and charge?None

z2Slide29

Electron Interactions w/ matterStopping power

How does Scoll/ρ depend on particle mass and charge?None

z2Slide30

Electron Interactions w/ matterRange

What is the Range, R, of a charged particle?Slide31

Electron Interactions w/ matterRange

What is the Range, R, of a charged particle? Expectation value of pathlength, <p>, until it comes to restSlide32

Electron Interactions w/ matterRange

What is the projected range, <t>, of a charged particle?Slide33

Electron Interactions w/ matterRange

What is the projected range, <t>, of a charged particle? Expectation value of farthest depth, t

f, of the particle in its initial direction Slide34

Electron Interactions w/ matterRangeSlide35

Electron Interactions w/ matterRange

What is the CSDA range, of a charged particle?Slide36

Electron Interactions w/ matterEnergy deposition

Assume parallel beam of e-, perpendicular to “thin” foil, BeElectron energy, 10 MeVCalculate average energy deposition in foilSlide37

Electron Interactions w/ matterEnergy deposition

Scoll/ρ for Be at 10 MeV

= (1.527 MeV∙cm2/g)(1.848 g/cm3) =2.905 MeV

/cm

∆E=(2.905

MeV

/cm)(0.1 cm)= 0.2905

MeVSlide38

Electron Interactions w/ matterEnergy deposition

Scoll/ρ for Be at 10 MeV

= (1.527 MeV∙cm2/g)(1.848 g/cm3) =2.905 MeV

/cm

∆E=(2.905

MeV

/cm)(0.1 cm)= 0.2905

MeV

Actual answer = 0.262

MeV

or an 11% overestimate

Why?Slide39

Electron Interactions w/ matterEnergy deposition

Actual answer = 0.262 MeV or an 11% overestimateWhy?

Delta rays escape the foil and for higher Z foils, bremsstrahlungHow to rectify?Slide40

Electron Interactions w/ matterEnergy deposition

Actual answer = 0.262 MeV or an 11% overestimateWhy?

Delta rays escape the foil and for higher Z foils, bremsstrahlungHow to rectify? Add buildup to establish CPE0.2905 MeV

vs. 0.28

MeV

, ~3% error or lessSlide41

Electron Interactions w/ matterEnergy deposition

Do all electrons lose an identical amount of energy when traversing foil?Slide42

Electron Interactions w/ matterEnergy deposition

Do all electrons lose an identical amount of energy when traversing foil?No, why?And what would the energy loss distribution look like?Slide43

Electron Interactions w/ matterEnergy deposition

And what would the energy loss distribution look like?Slide44

Restricted Mass Stopping Power (L/r)

D:AKA LET (linear energy transfer) or energy loss per unit path length (for local absorption not radiated away)

E

< D

Electron

Interactions w/ matter

Restricted Stopping powerSlide45

Electron beam characteristicsRapid rise to 100%

Region of uniform dose (proximal 90% to distal 90%)Rapid dose fall-off

High surface doseClinically useful range 5-6 cm depthSlide46

Electron beam characteristics- surface dose6 × 6 cm2

4 & 20 MeV e- beams on large H2O tank

Net E entering

4

MeV

: 3.99334

MeV

20

MeV

: 19.99691

MeV

Net E leaving

4

MeV

: 3.97598

MeV

20

MeV

: 19.97595

MeV

∆

E

4

MeV

:

0.01736

MeV

20

MeV

: 0.02096

MeVSlide47

Electron Energy Specification (the average energy of the spectrum)

(most probable energy @ surface) (average energy at depth z)Slide48

From: Khan

Electron Energy Specification

Energy specification:R50 - depth of the 50% doseRp

- maximum range of electronsSlide49

Electron Energy Specification

Average Energy (E0):Most Probable Energy (Ep0):

Energy (Ez) at depth z

MDACC 21EX

AAPM TG-25 Med Phys 18(1), 73-109 (1991)Slide50

Determination of Absorbed Dose

Calibration in water with ion chambersADCL-calibrated systemCylindrical-chamber reference point located upstream of the chamber center by 0.5 rcavReference conditions 100 cm SSD for a 1010 cm2

field Formalism:Slide51

Depth-Dose Distribution

Dose 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 correctionSlide52

Clinical aspects and dosimetrySlide53

Characteristics of clinical electron beams

X-Ray Contamination

Surface

Dose

Depth of 80% Dose

Depth of 50 % dose

Depth of

90% DoseSlide54

Characteristics of Clinical Electron BeamsSurface Dose:Surface dose

increases with increasing electron energy

From: KhanSlide55

Characteristics of Clinical Electron BeamsDepth of the 80% Dose:

Equal to approximately Enom/2.8 :

Depth of 90% is approximately Enom

/3.2

MDACC 21EXSlide56

Characteristics of clinical electron beamsPractical Range:

Equal to approximately 1/2 nominal energy:

Energy loss is about 2 MeV / cm

MDACC 21EXSlide57

Characteristics of clinical electron beamsX-Ray Contamination:

Increases with energy:Varies with accelerator design Defined as RP+2 cm

MDACC 21EXSlide58

Characteristics of clinical electron beams

Accelerator design variationsPenumbraX-ray Contamination

From: TapleySlide59

Characteristics of clinical electron beams

Penumbral Effects:Low energies show expansion of isodose valuesHigh energies show constriction of high isodose values with bowing of low values.Slide60

Electron Beam DosimetryIsodoses (6 MeV)Slide61

Electron Beam DosimetryIsodoses (20 MeV)Slide62

Electron Beam DosimetryPDD- effect of field size (6 MeV)Slide63

Electron Beam DosimetryPDD- effect of field size (20 MeV)Slide64

Electron Beam DosimetryBeam abutmentSlide65

Electron Beam DosimetryBeam abutment- electrons (6 & 20 MeV)Slide66

Electron Beam DosimetryBeam abutment- electrons (6 & 12 MeV)Slide67

Electron Beam DosimetryBeam abutment- electronsSlide68

Electron Beam DosimetryBeam abutment- photon & electron (6 MeV & 6 MV)Slide69

Electron Beam DosimetryBeam abutment- photon & electron (6 MeV & 18 MV)Slide70

Electron Beam DosimetryBeam abutment- photon & electron (IMC & tangents)Slide71

Electron Beam DosimetryObliquity Effects

Oblique incidence results in pdd shifts

From: KhanSlide72

Electron Beam DosimetryObliquity effectsSlide73

Electron Beam Dosimetry

Field Shaping:Lead and/or Cerrobend is normally usedThickness should be sufficient to stop electrons:

t

= mm Pb

E

0

= Nom E (MeV)Slide74

Electron Beam DosimetryContour Irregularities:Sharp contour irregularities result in hot and cold spots

Bolus:Place as close to skin as possibleUse tissue-equivalent materialBevel bolus to smooth sharp edges

From: KhanSlide75

Electron Beam DosimetryEffects of inhomogeneities:

CET - coefficient of equivalent thicknessThe CET of a material is approximately equal to its electron density relative to water

From: KhanSlide76

Electron Beam Dosimetry

CET:Sample calculation

1 cm

For Lung:

For Bone:

3 cm

·Slide77

Electron Beam DosimetryInternal Shielding:

Used to protect tissues beyond treatment volumeBackscattered electrons produce “dose enhancement”

From: Khan (Note E in M

eV)

A dose enhancement of about 50% could be expected in a 6-MeV electron beamSlide78

Electron Beam DosimetryInternal Shielding:

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

Electron energy at the scatterer

From: Khan Slide79

Electron BeamMonitor-Unit CalculationsElectron-beam monitor units (MU) are normally calculated to a point at d

max along the central axisA dose DRx that is prescribed to a point other than dmax, can be related to the d

max dose Ddmax through the precription isodose level %D: Slide80

Electron BeamMonitor-Unit CalculationsThe 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) Slide81

Electron BeamMonitor-Unit CalculationsFor an electron beam calibrated such that 1 MU = 1 cGy at 100 cm SSD for a 10

´10 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 SSDSlide82

Monitor-Unit CalculationsField-Size Corrections

OFFS:Field-size corrections generally account for the aperture produced by two devices:Cones or Applicators, and Customized InsertsThe field-size dependent output factor OF

FS can then be thought to consist of cone and insert output factors, OFCS and OFIS:Slide83

Monitor-Unit CalculationsField-Size Corrections -

OFCS, IS :When used separately, cone factors, OFCS, are normalized to the 10´10 (or 15

´15) cone, and insert factors, OFIS, are normalized to the open cone into which inserts are placedAlternatively, they can be combined into a single factor, OFCS, IS

,

that is normalized to the open 10

´

10 (or to the 15

´

15) cone :Slide84

Monitor-Unit CalculationsField-Size Corrections -

OFL´W :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 L´W:For example, the 4´12 output factor

OF

4

´

12

is the square-root of the product of the 4

´

4 output factor,

OF

4

´

4

, and the 12

´

12 output factor,

OF

12

´

12Slide85

Monitor-Unit CalculationsDistance (SSD) Corrections

FSSD:The variation of electron-beam output with distance does not follow a simple conventional inverse-square relationshipDue to attenuation and scattering in air and in beam collimation and shaping devicesDistance corrections take two forms:

Use of an “effective SSD” that can be used in an inverse-square fashionUse of an “air-gap factor” that can be used in addition to a conventional inverse-square factorSlide86

Monitor-Unit CalculationsDistance 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;

d

m

is the d

max

depthSlide87

Monitor-Unit CalculationsDistance Corrections -

SSDeff :The “effective SSD” is a virtual distance that is utilized so that an inverse-square approximation can be usedEffective SSDs vary with energy and field size as well as with electron collimation designSlide88

Monitor-Unit CalculationsDistance 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) SSDSlide89

Monitor-Unit CalculationsDistance 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:Slide90

Monitor-Unit CalculationsUse 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 Slide91

Electron Monitor-Unit Calculations - Sample ProblemsSlide92

Electron Monitor-Unit Calculations - Sample ProblemsSlide93

Electron Monitor-Unit Calculations - Sample ProblemsSlide94

Electron Monitor-Unit Calculations - Sample ProblemsSlide95

Electron Monitor-Unit Calculations - Sample ProblemsSlide96

Electron Monitor-Unit Calculations - Sample ProblemsSlide97

Electron Monitor-Unit Calculations - Sample ProblemsSlide98

Electron Monitor-Unit Calculations - Sample ProblemsSlide99

Electron MU Sample ProblemsSlide100

Electron MU Sample ProblemsSlide101

Electron MU Sample ProblemsSlide102

Electron MU Sample Problems