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Chapter 14

Electron Beam Therapy

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1. In early days, betatrons were used to produce electron beams, in modern times, linacs are used to produce electron beams.

2. Clinically useful energies are between 6 and 20-MeV.

3. Used for treating superficial tumors (skin, chestwall, boost to nodes, head/neck).

4. Relatively uniform dose in the target, fast dose drop off beyond the electron range.

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14.1 Electron Interactions

Electrons interact with atoms by different processes through the Coulomb force. These processes are (1) inelastic collisions with atomic electrons (ionization/excitation); (2) inelastic collisions with nuclei (bremsstrahlung); (3) elastic collisions with atomic electrons; (4) elastic collisions with nuclei (no energy loss, large angle deflection).

In inelastic collisions, some of the kinetic energy is lost in producing ionization or converted to other forms of energy.

In elastic collisions, kinetic energy is not lost but it may be redistributed among the emerging particles.

In low-Z media (water, tissue), electrons lose energy through ionization and excitation.

In high-Z media (tungsten, lead), bremsstrahlung is important.

In ionization, if the ejected electron is energetic enough to cause further ionization, it is called secondary electron or -ray. (note: by definition, the energy of the -ray is < ½ of the incident electron energy)

Electrons continuously lose its energy traveling through the medium.

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14.1 Electron Interactions – A. Rate of Energy Loss

colS

radS

2 MeV/cm

kge

kge

S

leade

watere

ecol

/1038.2

/1034.3

density)(electron

26

26

MeV-1 ~ minimumcolS

electronsenergy -high

material, Z-high

for efficient more

production lungbremsstrah

2EZS rad

radcoltot SSS

5

14.1 Electron Interactions – A. Rate of Energy Loss (polarization or density effect)

mediumdensegas SS

Because of polarization of the condensed medium. Atoms close to the incident electron track screen those remote from the track.

The ratio of (S/)water to (S/)air varies with energy, therefore, the conversion from dose-to-air(in chamber) to dose-to-water(phantom) varies with depth (because electron energy decreases with depth by ~ 2-MeV/cm in water).

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14.1 Electron Interactions – A. Rate of Energy Loss (absorbed dose)

(E>energy carried away by -ray

Local energy deposition due to ionization and excitation

(unrestricted) Stopping power (S/) refers to the energy lost by a charged particle to the medium.

Restricted stopping power (L/)col,

(linear energy transfer LET) refers to energy absorbed by the medium. (collisions in which energy loss < )

dEL

EDcol

E

,

0

)(

SL

col ,

7

14.1 Electron Interactions – B. Electron Scattering

l

θ

When an electron pencil beam passes through a medium, it suffers multiple scattering, resulting in spread in both lateral position and direction. The spread in approximately Gaussian.

2222

2

/angle. scattering squaremean theis where

:power scatteringangular mass the

EZ

l

High-Z materials are used for electron scattering foil to spread out the electron beam. (recall that photon beam is spread out by the production of bremsstrahlung itself.)

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14.2 Energy Specification and Measurement

Electron energy

Ele

ctro

n flu

ence

Accelerator tube

Scattering foil

phantom

At exit window, nearly monoenergetic

At patient surface, energy degraded and spread due to collision with scattering foil, air

Emax(0) Ea

Ep(0)

E(0)

z

At depth z, further energy degradation and spread

Ep(z)

Electron beam

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14.2 Energy Specification and Measurement

depth

Per

cent

dep

th d

ose

100

50

R50 Rp

Rp : practical range

Most probable energy Ep:

Ep(0)=C1+C2Rp+C3Rp2

for water

C1 = 0.22 MeV

C2 = 1.98 MeV/cm

C3 = 0.0025 MeV/cm2

Mean energy at surface E(0):

E(0)=C4×R50

for water, C4 ~ 2.33 MeV/cm

Energy at depth:

p

ppp

R

zEzE

R

zEzE

1)0()(

1)0()(

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14.3 Determination of Absorbed Dose

Absolute dose can be measured with:

ionization chamber

calorimetry

Fricke dosimetry

Relative dose can be measured with:

film: energy independence for electron beam

TLD

diode: often used for electron beam measurement.

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14.3 Determination of Absorbed Dose – output calibration

For photon beams, the output varies smoothly with field size.

For electron beams, the output does NOT vary smoothly with field size. This is because each applicator has its own collimator setting. For example, the output of a 10x10 applicator with a 10x10 insert may be different from that of a 15x15 applicator with a 10x10 insert.

Thus, for electron beams, it is important to measure the output of every applicator and every insert in clinical use. Do not assume that the output very smoothly with field size, especially when different applicators are involved.

For elongated or irregularly-shaped cutouts, the output should be individually measured.

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14.3 Determination of Absorbed Dose – depth dose distribution

If ion chamber is used to measure electron beam depth doses, the conversion from depth-ionization to depth-dose involves the water-to-air stopping power ratio, which is depth-dependent. In addition, if the chamber is cylindrical, the measured depth-dose curve needs to be shifted to account for the effective point of measurement.

If diode is used, the diode response is taken as the depth-dose, no correction is needed.

Med Phys 14, 1060 (1987)

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Med Phys 14, 1060 (1987)

14.3 Determination of Absorbed Dose – film dosimetry

Med Phys 16, 911 (1989)

Energy independence for electron relative dose measurement. The optical density can be taken as proportional to dose without correction.

14

Med Phys 16, 911 (1989)

14.3 Determination of Absorbed Dose – film dosimetry

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14.3 Determination of Absorbed Dose – film dosimetry

Air gaps adjacent to film

Film sticking out the phantom

Film recess inside the phantom

Things to avoid with film dosimetry

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14.3 Determination of Absorbed Dose – phantom

Water is the standard phantom.

Water-equivalent Plastic phantom (polystyrene, electron solid-water): same electron density (# electrons/cc), same effective-Z → same linear stopping power S, same linear angular stopping power.

Depth-dose measured in plastic phantom converted to depth-dose in water:

med

water

medeffmedw

watermed

watermedmedmedww

R

Rddd

SdDdD

50

50

)()(

waterPolystyrene

(clear)Polystyrene

(white)Acrylic

Electron solid water

1.000 1.045 1.055 1.18 1.04

eff 1.000 0.975 0.99 1.15 1.00

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14.4 Characteristics of Clinical Electron BeamsCentral axis depth dose curves

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18Modest skin sparing ↑energy ↑skin dose

Relatively uniform dose

Rapid dose drop-off for low energy electron beams, but disappears for high-energy electron beams

Bremsstrahlung x-ray contamination

The choice of beam energy is much more critical for electrons than for photons.

R80(cm) ~ E(MeV)/2.8R90(cm) ~ E(MeV)/3.2

increases with energy

dmax increases with energy for low-energy electrons, ~ 2.5cm for high-energy electrons (12-20 MeV)

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14.4 Characteristics of Clinical Electron BeamsCentral axis depth dose curves – buildup region

Lower energy electrons scatter more and through larger angles, causing more rapid buildup, thus, the difference between the surface dose and maximum dose is larger.

Higher energy electrons scatter less and through smaller angles, causing less rapid buildup (in the extreme case, if there is no scatter, there will be no buildup).

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14.4 Characteristics of Clinical Electron BeamsIsodose curves

Different machines → different collimation systems (scattering foil, monitor chamber, jaws, cones, air-gap to surface) → dose distribution

For low energy electron beams, isodose curves bulging out for all dose levels

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14.4 Characteristics of Clinical Electron BeamsIsodose curves

But bulge out for low dose levels

For high energy electron beams, isodose curves constrict for high dose levels

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14.4 Characteristics of Clinical Electron BeamsField flatness and symmetry

)maxd (e.g.depth reference aat plane reference aon

uniformindex

uniformindex

7.0A

A

A

A

50%

90%

edgegeometric

90%

or

axiscentralDD %103max

%22)()(

)()(

pDpD

pDpDsymmetry

＋ ●●

+p-p

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14.4 Characteristics of Clinical Electron BeamsBeam collimation

Dual scattering foil system

applicator

Collimator jaws open to a fixed predetermined size for a given electron energy and applicator size (do NOT change it !)

Variation of output with collimator jaws opening

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14.4 Characteristics of Clinical Electron BeamsField size dependence

Output increases smoothly with field size (as defined by the insert with collimator jaws size fixed) due to increased phantom scatter and in-air scatter.

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14.4 Characteristics of Clinical Electron BeamsField size dependence

The PDD increases with field size until it exceeds the lateral range of the electrons, then the PDD is almost constant with field size.

The depth of maximum dose, dmax, also increases field size until the lateral range is reached.

The output and PDD for small field electron beams need to be individually measured.

Small field size, PDD increases significantly with field size

large field size, PDD nearly constant

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14.4 Characteristics of Clinical Electron BeamsField equivalence and square root method

For large fields (>10x10), the PDDs are nearly the same, thus, they are all equivalent.

For small circular fields, the equivalent field radius, Requiv, to a 2ax2a square field is: Requiv ~ 1.116a.

For small rectangular fields XxY, as a result of Gaussian pencil beam distribution, the PDD is related to that of square fields by:

YYXXYX DDD ,,,

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g

f < 100 cm

14.4 Characteristics of Clinical Electron Beams

IQdmax

Electron source (virtual source)

g

IIsloped

slopef

df

g

I

Ior

df

gdf

I

I

gm

mgm

m

g

11

1

0

02

0

Virtual source

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14.4 Characteristics of Clinical Electron BeamsX-ray contamination

6-12 MeV 0.5-1%

12-15 MeV 1-2%

15-20 MeV 2-5%

Dose due to x-ray contamination generated in the collimating system and in phantom

Dose due to x-ray contamination generally is not a concern, except for total skin electron therapy (TSET) in which the entire body is irradiated (six directions, thus, the x-ray contamination dose is increased 6-times).

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14.5 Treatment Planning Choice of energy and field size

Choice of beam energy is dictated by the depth of the prescribed level, typically, 80-90%, (thus ~ E(MeV)/3 in cm). Similarly, the choice of field size depends on the constriction of the isodose curve of the dose level. (the margin between 90% and geometric field edge typically > 0.5 cm)

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14.5 Treatment Planning Correction for air gaps and beam obliquity

Dose affected by air-gap (inverse square) and obliquity

dmax shifts toward the surface with increasing incident angle

Decreased penetration with increasing incident angle

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Effect of oblique incidence

d

d’

Increased dose at shallow depth due to greater side scatter from neighboring pencil beams traversing through a larger depth (d’ > d)

Decreased dose at larger depth due to lack of side scatter since it is beyond the range of neighboring pencil beams

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g

d

d

f

f = effective SSD (surface-to-virtual source distance)

θ

D(f+g,d)

D0(f,d)

),(),(),(2

0 dOFdgf

dfdfDdgfD

Obliquity factor

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Obliquity factor

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14.5 Treatment Planning Irregular surface

High dose due to extra scatterLow dose due to loss of scatter

High dose due to extra scatter

Low dose due to loss of scatter

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14.5 Treatment Planning Tissue inhomogeneity

d

ze

) thicknessequivalent ofnt (coefficie

)1(

)(

CET

zd

zzdd

e

e

eeff

D2

),,(

df

dfAdfPDDD eff

eff

A

fAn approximation:

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Homogeneous water phantom

Lung inhomogeneity

Without lung inhomogeneity correction

With lung inhomogeneity correction

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Small inhomogeneity

M’

M

Material M’ has greater scattering power than material M

Cold spot

hot spot

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14.5 Treatment Planning Use of bolus and absorbers

Bolus is used to (a) flatten out an irregular surface, (b) reduce penetration in parts of the field, and (c) increase surface dose

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14.5 Treatment Planning

Problems of adjacent fields

Big gap, cold spot

Small gap, hot spot

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14.5 Treatment Planning Problems of adjacent fields

9-MeV e- SSD = 100

6-MV x-ray SSD = 100

9-MeV e- SSD = 120

6-MV x-ray SSD = 100

Increased SSD leads to wider e-beam penumbra, resulting in larger areas of hot/cold spots

(due to setup clearance)

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14.6 Field Shaping

Electron beam can be shaped by cutouts made of cerrobend or lead, placed at the applicator (cone) or directly on the skin.

Shielding thickness to achieve transmission < 5%

Shielding too thin (e.g. eye shield), causing dose buildup at depth immediately under shield

External shielding

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14.6 Field Shaping

Lead thickness (in mm) required to stop primary electrons (transmitted dose due to bremsstrahlung photons generated in the shield) ~ MeV/2. For cerrobend, increase the thickness by 20%.

Shielding thickness vs electron energy

Measurement of transmission curves

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14.6 Field Shaping Effect of blocking on dose rate

Output ratio = 1 / output-factor

Blocked field < electron lateral range (~ Rp/2)

When in doubt, individual dosimetry (output, depth-dose, isodose distribution) should be made for irregularly-shaped cutouts.

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14.6 Field Shaping Internal shielding (e.g. protection of eye in the treatment of eyelid)

D

D’

Dose enhancement at the interface due to extra backscatter from the lead shield = D’/D

~30-60% enhancement

Lower energy, more scatter

Energy (MeV)

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14.6 Field Shaping Internal shielding

No lead shield

Range of backscattered

electrons 1-2 cm in water

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A thin layer of low-Z material (e.g.wax) can be placed in front of the lead shield to reduce backscatter

14.6 Field Shaping Internal shielding

Incident primary electrons

Depth in polystyrene upstream from the interface

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14.6 Field Shaping Internal shielding - example

9-MeV electrons

Oral structure ch

eek

2 cm

(a) Energy immediately beyond cheek ~ 9-MeV – 2-MeV/cm x 2cm = 5 MeV

(b) Backscatter from 5-MeV electrons on lead ~ 56%

(c) Depth upstream from the interface to reach 10% dose is ~ 10 mm in polystyrene, or about 4mm of aluminum

aluminum

Pb shield

To protect oral structure, lead shield thickness ~ 5 MeV/2 = 2.5 mm

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14.7 Electron Arc Therapy

Suitable for treating superficial tumors along curved surfaces.

Calibration of arc therapy beams

angle. i at the correction sqaure inverse Inv(i)

angle i at the chart) isodose (from P todose (P)D

min / rotations ofnumber n

(MU/min) rate dose

)()(2

)(

th

thi

0

1

0

D

where

iInvPDn

DPD

n

iiarc

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14.7 Electron Arc Therapy Treatment planning

Beam energy

Dose increased at larger depth

Dose decreased at shallow depth

‘velocity effect’ (?)The effect depends on the field width and arc-size, i.e., the range of angles a given point is irradiated (exposed), it has nothing to do with the rotation speed.

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14.7 Electron Arc Therapy Treatment planning

Scanning field width:

Smaller field width →

Lower dose rate (greater MU) →

Greater x-ray contamination dose (at the isocenter)

Smaller field width →

~Normal incidence at all angles (less surface curvature/obliquity effect)

Typically, field width 4 – 8 cm at isocenter.

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14.7 Electron Arc Therapy

Location of isocenter:

Approximately equi-distance from the contour surface from all angles, and

The depth of isocenter > electron range, so that dose from primary electrons is not accumulated (but dose from contaminated bremsstrahlung x-rays cannot be avoided).

Treatment planning

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14.7 Electron Arc Therapy Treatment planning

Field shaping

Gradual dose falloff at both ends of the arc

Use surface shield to better define the dose distribution

Isodose distribution calculated by computer treatment planning system

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14.8 Total Skin Irradiation

Stanford technique

2-9 MeV electron beams are useful for treating superficial lesions covering a large areas of the body (e.g. mycosis fungoides)

A. Translational technique

B. Large field technique

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14.8 Total Skin Irradiation Field flatness

3 weighted fields

Arc field vs stationary field

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14.8 Total Skin Irradiation X-ray contamination

X-ray contamination along the beam central-axis

Reduce x-ray contamination by angling the central axis away from the patient

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14.8 Total Skin Irradiation Field arrangement

15°15°

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14.8 Total Skin Irradiation Dose distribution

The depth-dose curve and dmax shift toward the surface, due to oblique incident angles.

With the 6-field technique, dose uniformity of ±10% can be achieved in general, except in areas with large surface irregularities (e.g. inner thigh) where supplementary irradiation may be needed.

Bremsstrahlung dose in patient midline is approximately doubled due to the opposed beam arrangement.

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14.8 Total Skin Irradiation Modified Stanford technique (dual field angle)

~ 400 cm

10-15°

10-15°

films

Plastic screen

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14.8 Total Skin Irradiation Modified Stanford technique (calibration)

Single Dual-angle field

polystyrene

Parallel plate chamber

replion

poly

air

gasPTpolyP PPL

NCMD

,

=1 for parallel-plate chamber

waterpoly

water

poly

polyPwaterPS

DD

=1 P at surface

P

59

14.8 Total Skin Irradiation Modified Stanford technique (treatment skin dose)

Dual-angle field

All 6 fields

Total skin dose from all 6 dual-angle fields:

BDD polyPpolyS

BDD waterPwaterS 2.5 ~ 3.0

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14.8 Total Skin Irradiation Modified Stanford technique (in-vivo dosimetry)

Although an overall surface dose uniformity of ±10% can be achieved, there are localized regions of extreme non-uniformity of dose on the patient’s skin. (e.g. sharp body projections, curved surfaces,…)

TLDs are most often used for in-vivo dosimetry.

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r

14.9 Treatment Planning Algorithms

Pencil beam based on multiple scattering theory

)()(),(

)(/)(),0(

)(),0()(

2),0(2),(

22

),0(),(

2

)(

2

2

0

)(

0

222

)(

22

22

22

z

ezDzrd

zzDzd

zzdzD

rdrezdrdrzrd

ezdzrd

r

zr

p

rp

rp

r

zrp

rp

yxr

zrpp

r

r

r

x

y

Dose due to an infinite field size beam

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14.9 Treatment Planning AlgorithmsPencil beam based on multiple scattering theory

xt

rrrr

p

yx

z

yx

p

dtexerf

z

yberf

z

yberf

z

xaerf

z

xaerf

zDzyxD

dydxzyyxxdzyxD

z

ezDzyxd

yx

0

2,

)(2

2

2,

22

2)(

where

)()()()(4

)(),,(

:2b2a size fieldr rectangulafor

''),','(),,(

)(2)(),,(

63

14.9 Treatment Planning AlgorithmsPencil beam based on multiple scattering theory (lateral spread parameter, )

')')('()'(2

1)(

:equation Eyges

2

0'

22 dzzzzz

lz

z

zx

Modified Eyges equation

Mass angular scattering power

64

14.9 Treatment Planning AlgorithmsPencil beam based on multiple scattering theory (implementation)

For more accurate electron-beam dose calculation, Monte Carlo methods are available on modern-day commercial treatment planning systems.