1 Physics of Electron Beam Radiation Therapy Physics of Electron ...

Physics of Electron Beam Radiation Therapy George George Starkschall, Starkschall, Ph.D. Ph.D. Department Department of of Radiation Radiation Physics Physics U.T. U.T. M.D. M.D. Anderson Anderson Cancer Cancer Center Center

Why use electrons? •• Electron Electron beam beam characteristics: characteristics: –– Rapid Rapid rise rise to to 100% 100% –– Region Region of of uniform uniform dose dose –– Rapid -off fall Rapid dose dose fallfall-off

AAPM TG-21 Med Phys 10(6), 741-771 (1983)

Why use electrons? •• Tumors Tumors that that can can be be treated treated with with electrons electrons –– Superficial Superficial tumors tumors –– Lymph Lymph node node boosts boosts –– Chest Chest walls walls –– CNS CNS –– TSI TSI AAPM TG-21 Med Phys 10(6), 741-771 (1983)

1

Review electron interactions • Long-range interactions with orbital Long Long-range electrons –– Excitation Excitation and and ionization ionization

• Long-range interactions with atomic Long Long-range nuclei –– Bremsstrahlung -rays) (x Bremsstrahlung (x(x-rays)

Review electron interactions • Characteristics of energy deposition –– Continuous Continuous loss loss of of energy energy –– approx approx 22 MeV/cm MeV/cm (in (in water) water) –– Multiple Multiple Coulomb Coulomb scatter scatter –– spreading spreading out out of of dose dose distribution distribution at at depth depth

• Electron interactions interactions result result in in reductions reductions in beam energy

Specification of electron energy •• (E (Epp))00 (most (most probable probable energy energy at at phantom phantom surface) surface) •• E E00 (mean (mean energy energy at at phantom phantom surface) surface) •• E (mean energy energy at at Ezz (mean depth depth z) z)

From: Khan

2

Specification of electron energy • (Epp)00 – most probable energy at phantom surface

(E ) (MeV ) = 0.22 + 1.98R p 0

p

+ 0.0025 R p2

• Rpp – practical range (expressed in cm)

Specification of electron energy • E00 – mean energy at phantom surface

E 0 ( MeV ) = 2.33R50 • R50 – depth at which dose is 50% 50% of of 50 maximum dose (expressed in cm)

Specification of electron energy • Ezz – mean energy at depth z

⎛ z ⎞⎟ E z = E 0 ⎜1 − ⎜ R ⎟ p ⎠ ⎝ •• Note Note that that energy energy decreases decreases linearly linearly with with depth depth

3

Electron energy measurement E nom inal (MeV) 6 9 12 16 20

(E p ) 0 (MeV) 6.06 8.86 12.11 15.90 20.17

Eo (MeV) 5.43 8.22 11.46 15.21 18.92 Varian Clinac 2100C

–– Average E00): ((E Average Energy Energy (E ):

Ε 0 = ( 2 .33 ) R 50

): –– Most Ep0 ((E Most Probable Probable Energy Energy (E p0):

Ε p 0 = 0.22 + 1.98 × Rp + 0.0025 × Rp 2 –– Energy Ezz)) at ((E Energy (E at depth depth zz

E z = E 0 ( 1- z

Rp

)

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

Properties of depth dose distributions Depth Doses for Varian 21EX 25 x 25 cone

6 MeV 9 MeV 12 MeV 16 MeV 20 MeV

100

80

% Depth Dose

• Characterized by uniform irradiation to specified depth, followed by sharp fall-off fall fall-off

60

40

20

0

0

2

4

6

8

10

12

Depth (cm)

Clinical consequence Depth Doses for Varian 21EX 25 x 25 cone


100

80

% Depth Dose

• Deliver uniform dose to superficial tumor (e.g., nodes, chest wall), with sparing of distal tissue

60

40

20

0

0

2

4

6

8

10

12

Depth (cm)

4

Regions of electron depth dose distributions

––

Surface Surface dose dose increases increases with with increase increase in in energy energy

Depth Doses for Varian 21EX 25 x 25 cone


100

80

% Depth Dose

1. 1. Shallow Shallow depths depths --build-up region build build-up region caused side caused by by sideside-scattered scattered electrons electrons

60

40

20

0

0

2

4

6

8

10

12

Depth (cm)

Increase surface dose with increased energy

Increase surface dose with increased energy •• Lower Lower energies energies –– Electrons Electrons scattered scattered through through larger larger angles angles –– Dose Dose builds builds up up more more rapidly rapidly over over shorter shorter distance distance –– Ratio Ratio of of surface surface dose dose to to maximum maximum dose dose less less

5

Increase surface dose with increased energy •• Higher Higher energies energies –– Electrons Electrons scattered scattered through through smaller smaller angles angles –– Dose Dose builds builds up up more more slowly slowly over over longer longer distance distance –– Ratio Ratio of of surface surface dose dose to to maximum maximum dose dose greater greater

Regions of electron depth dose distributions Depth Doses for Varian 21EX 25 x 25 cone


100

80

% Depth Dose

2. R egion of sharp Region dose falloff begins at approximately 90% dose

60

40

20

0

0

2

4

6

8

10

12

Depth (cm)

Region of sharp dose falloff Depth Doses for Varian 21EX 25 x 25 cone


100

80

% Depth Dose

• Select electron energy so that 90% or 80% isodose encloses target volume

60

40

20

0

0

2

4

6

8

10

12

Depth (cm)

6


• Depth of 80% central-axis central central-axis dose easy to estimate

80

% Depth Dose

d 80 (cm ) ≈ 13 E (MeV ) .


100

60

40

20

0

0

2

4

6

8

10

12

Depth (cm)

Region of sharp dose falloff •• Depth Depth of of the the 80% 80% Dose: Dose: –– Equal Equal to to approximately approximately 1/3 1/3 nominal nominal energy: energy: E nom inal

E nom / 3

Actual

6 9 12 16 20

2.0 3.0 4.0 5.3 6.7

1.99 3.08 4.26 5.70 6.96

Varian 2100C

–– Depth Depth of of 90% 90% is is approximately approximately 1/4 1/4 nominal nominal energy energy



100

80

% Depth Dose

• Slope of falloff becomes more gradual with increasing energy

60

40

20

0

0

2

4

6

8

10

12

Depth (cm)

7

Regions of electron depth dose distributions Depth Doses for Varian 21EX 25 x 25 cone


100

80

% Depth Dose

3. At end of falloff region, beyond range of electrons, tail is due to bremsstrahlung

60

40

20

0

0

2

4

6

8

10

12

Depth (cm)

Region of bremsstrahlung tail Depth Doses for Varian 21EX 25 x 25 cone

• Magnitude of tail increases with increasing energy


100

% Depth Dose

80

–– Typically Typically around around 5% 5% of of maximum maximum dose dose

60

40

20

0

0

2

4

6

8

10

12

Depth (cm)

Region of bremsstrahlung tail •• X -Ray Contamination: X-Ray Contamination: –– Increases Increases with with energy: energy: Enom

X-ray %

6 9 12 16 20

1.3% 1.6% 2.1% 3.7% 4.9%

Varian 2100C

–– Varies Varies with with accelerator accelerator design design

8

Region of bremsstrahlung tail

R p (cm ) ≈ 12 E (MeV ) .

Depth Doses for Varian 21EX 25 x 25 cone


100

80

% Depth Dose

• Practical range of electrons can be estimated using approximate relation

60

40

20

0

0

2

4

6

8

10

12

Depth (cm)

Region of bremsstrahlung tail •• Practical Practical Range: Range: –– Equal Equal to to approximately approximately 1/2 1/2 nominal nominal energy: energy: Enominal

Enom / 2

6 9 12 16 20

Rp

3.0 4.5 6.0 8.0 10.0

2.97 4.35 5.95 7.95 10.09 Varian 2100C

–– Energy Energy loss loss is is about about 22 MeV MeV // cm cm

Field-size dependence Depth Doses for 21 EX 20 MeV electrons

3x3 4x4 5x5 6x6 8x8 10 x 10

100

80

% Depth Dose

• Note increase in penetration with field size until lateral equilibrium is reached

60

40

20

0 0

2

4

6

8

10

12

14

Depth (cm)

9

Choice of energy and field size • Choose field size and energy so that target volume lies entirely within 90% isodose curve –– Need Need to to provide provide sufficient sufficient margin margin to to enclose enclose target target volume volume –– base base on on isodose isodose curves curves

Oblique Incidence • Isodose lines track skin surface • Central axis has approximately same depth dose as normal incidence beam

Oblique Incidence •• Modifications Modifications •• Inverse Inverse square square correction correction •• Changes Changes in in side side scatter scatter •• ↑↑ scatter scatter at at R R100 100 •• Shift toward surface Shift R R100 100 toward surface •• ↓↓ beam beam penetration penetration

10

Matching Fields Max doses 100 MU 16 MeV e-• No gap - 147 cGy • 1 cm gap gap - 103 cGy cGy • 0.5 cm gap - 120 cGy

Matching Fields • Electron dose spreads with depth due to scattering ⇒ hot spots and/or cold spots in region of overlap, depending on amount of field separation

Matching Fields • To mitigate problem: move electron field junction several times during course of treatment –– Smears Smears out out hot hot and and cold cold spots spots

11

Heterogeneities • Affect -axis depth central Affect centralcentral-axis depth dose dose –– based based on on density-weighted depth density density-weighted • Affect electron scatter

Heterogeneities •• Increase Increase (decrease) (decrease) in in scatter scatter from from heterogeneity heterogeneity gives gives rise rise to to hot hot and and cold cold spots spots adjacent adjacent to to heterogeneity heterogeneity boundary boundary

Surface irregularities • Produce hot and cold spots due to scatter –– Force Force tapering tapering using using bolus bolus –– If If bolus bolus is is used, used, edges edges should should be be tapered tapered

12

Surface irregularities •• Another Another consequence: consequence: Surface Surface irregularities irregularities or or may may cause cause high high dose dose gradients gradients in in the the vicinity vicinity of of , making that point unsuitable for dose d d100 100, making that point unsuitable for dose prescription. prescription.

Dose prescription •• How How to to prescribe prescribe dose, dose, or or 90% 90% is is 90% 90% of of what? what? •• Dose for beam Dose reference reference point point is is d d100 100 for beam perpendicularly perpendicularly incident incident on on water water phantom phantom at at same same SSD SSD –– This -defined and well This point point is is wellwell-defined and in in aa region region of of low low dose dose gradient gradient

Monitor unit setting • The monitor unit setting (U) on a linear accelerator is determined by the equation:

given dose given dose output Dmax U = Dmax U

monitor unit setting =

13

Given Dose Output (cGy MU-1) – Dmax/U • Definition: The given dose output is the dose per monitor unit to muscle delivered to a point on the central axis at depth dmax max in a water phantom.

Given Dose Output (cGy MU-1) – Dmax/U • Source of Data: The given dose output is calculated using the formula given dose output = calibration dose output × output factor × inverse square factor × air gap factor × skin collimation factor

Output Factor – OF(Cs,Ieq) •• Note: Note: This This is is for for fixed fixed cone cone applicators. applicators. Other Other formalisms formalisms hold hold for for variable variable applicators. applicators.

• Definition: The output factor is the ratio of the output (dose per monitor unit) in water for an SSD equal -isocenter source equal to to the the sourcesource-isocenter distance and a depth equal to dmax on max central axis for a specified cone and equivalent insert size to the calibration dose output.

14

Output Factor – OF(Cs,Ieq) • Square root method (used with almost all current electron linear accelerators, including all accelerators presently at MDACC):

[

output factor = output factorlength × length × output factorwidth × width

]

1 2

OF (Cs , X iso , Yiso ) = [OF (Cs , X iso , X iso )× OF (Cs , Yiso , Yiso )]2 1

Inverse Square Factor - ISF • Source of of Data: Data: The inverse square factor is computed according to the following equation: ⎡ calibration output distance ⎤ inverse square factor = ⎢ ⎥ ⎣ treatment output distance ⎦ ⎡ SAD + d max ⎤ ISF (SSD, d max ) = ⎢ ⎥ ⎣ SSD + d max ⎦

2

2

Source-Skin Distance (cm) – SSD • Definition: -skin distance source Definition: The The sourcesource-skin distance is is the the distance from the virtual radiation source to a point defined on the patient's skin surface, projected onto the central axis –– Note Note that that virtual virtual source source position position may may not not coincide coincide with with nominal nominal source source position position –– Often Often nominal nominal source source position position used used to to avoid avoid confusion confusion

15

Air Gap Factor – fair • Definition: The The air air gap gap factor factor is the ratio ratio of of the output measured at a specified SSD to the inverse-squareinverse square-predicted output for inverse-square-predicted that SSD –– It -scatter side It corrects corrects for for the the loss loss of of sideside-scatter equilibrium, equilibrium, collimator collimator scatter, scatter, other other scatter scatter effects, effects, and, and, when when appropriate, appropriate, utilization utilization of of aa nominal nominal SSD SSD

Air Gap Factor – fair • The air gap factor is then determined by the following equation:

[

air gap factor = air gap factorlength×length × air gap factorwidth×width

]

1 2

f air ( X iso , Yiso , g ) = [ f air ( X iso , X iso , g ) × f air (Yiso , Yiso , g )]2 1

Skin collimation factor – SCF • Definition: The skin collimation factor is a correction to the output factor that results depth toward the from a shift of the dmax max patient surface that can occur when skin collimation is included in an electron field

16