Physics of Electron Beam Radiation Therapy. Why use electrons? Why use electrons?

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1 Physics of Electron Beam Radiation Therapy George Starkschall, Ph.D. Department of Radiation Physics U.T. M.D. Anderson Cancer Center Why use electrons? Electron beam characteristics: Rapid rise to 1% Region of uniform dose Rapid dose fall-off AAPM TG-21 Med Phys 1(6), (1983) Why use electrons? Tumors that can be treated with electrons Superficial tumors Lymph node boosts Chest walls CNS TSI AAPM TG-21 Med Phys 1(6), (1983) 1

2 Review electron interactions Long-range interactions with orbital electrons Excitation and ionization Long-range interactions with atomic nuclei Bremsstrahlung (x-rays) Review electron interactions Characteristics of energy deposition Continuous loss of energy approx 2 MeV/cm (in water) Multiple Coulomb scatter spreading out of dose distribution at depth Electron interactions result in reductions in beam energy Specification of electron energy (E p ) (most probable energy at phantom surface) E (mean energy at phantom surface) E z (mean energy at depth z) From: Khan 2

3 Specification of electron energy (E p ) most probable energy at phantom surface 2 ( E ) MeV ) = R +.25R p ( p p R p practical range (expressed in cm) Specification of electron energy E mean energy at phantom surface E ( MeV ) = 2. 33R R 5 depth at which dose is 5% of maximum dose (expressed in cm) 5 Specification of electron energy E z mean energy at depth z z E z E 1 R = p Note that energy decreases linearly with depth 3

4 Electron energy measurement Average Energy (E( ): Ε = ( ) R E nominal (MeV) (Ep) (MeV) Eo (MeV) Varian Clinac 21C Most Probable Energy (E( p ): 2 Ε p = Rp Rp Energy (E( z ) at depth z Ez = E ( 1- z ) Rp AAPM TG-25 Med Phys 18(1), (1991) Properties of depth dose distributions Characterized by uniform irradiation to specified depth, followed by sharp fall-off MeV 8 2 MeV Clinical consequence Deliver uniform dose to superficial tumor (e.g., nodes, chest wall), with sparing of distal tissue MeV 8 2 MeV

5 Regions of electron depth dose distributions 1. Shallow depths -- build-up up region caused by side- scattered electrons Surface dose increases with increase in energy MeV 8 2 MeV Increase surface dose with increased energy Increase surface dose with increased energy Lower energies Electrons scattered through larger angles Dose builds up more rapidly over shorter distance Ratio of surface dose to maximum dose less 5

6 Increase surface dose with increased energy Higher energies Electrons scattered through smaller angles Dose builds up more slowly over longer distance Ratio of surface dose to maximum dose greater Regions of electron depth dose distributions 2. Region of sharp dose falloff begins at approximately 9% dose MeV 8 2 MeV Region of sharp dose falloff Select electron energy so that 9% or 8% isodose encloses target volume MeV 8 2 MeV

7 Region of sharp dose falloff Depth of 8% central-axis axis dose easy to estimate 1 ( cm) 3 ( MeV) d. 8 E MeV 8 2 MeV Region of sharp dose falloff Depth of the 8% Dose: Equal to approximately 1/3 nominal energy: Enominal E nom / 3 Actual Varian 21C Depth of 9% is approximately 1/4 nominal energy Region of sharp dose falloff Slope of falloff becomes more gradual with increasing energy MeV 8 2 MeV

8 Regions of electron depth dose distributions 3. At end of falloff region, beyond range of electrons, tail is due to bremsstrahlung MeV 8 2 MeV Region of bremsstrahlung tail Magnitude of tail increases with increasing energy Typically around 5% of maximum dose MeV 8 2 MeV Region of bremsstrahlung tail X-Ray Contamination: Increases with energy: Enom X-ray % 6 1.3% 9 1.6% % % 2 4.9% Varian 21C Varies with accelerator design 8

9 Region of bremsstrahlung tail Practical range of electrons can be estimated using approximate relation ( cm) ( MeV) R p. 21 E MeV 8 2 MeV Region of bremsstrahlung tail Practical Range: Equal to approximately 1/2 nominal energy: E nominal E nom / 2 R p Energy loss is about 2 MeV / cm Varian 21C Field-size dependence Note increase in penetration with field size until lateral equilibrium is reached Depth Doses for 21 EX 2 MeV electrons 3 x 3 4 x 4 5 x 5 6 x 6 8 x 8 1 x

10 Choice of energy and field size Choose field size and energy so that target volume lies entirely within 9% isodose curve Need to provide sufficient margin to enclose target volume base on isodose curves Isodose lines track skin surface Central axis has approximately same depth dose as normal incidence beam Oblique Incidence Modifications Oblique Incidence Inverse square correction Changes in side scatter scatter at R 1 Shift R 1 toward surface beam penetration 1

11 Matching Fields Max doses 1 MU e - No gap cgy 1 cm gap - 13 cgy.5 cm gap - 12 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 out hot and cold spots 11

12 Heterogeneities Affect central-axis axis depth dose based on density-weighted depth Affect electron scatter Increase (decrease) in scatter from heterogeneity gives rise to hot and cold spots adjacent to heterogeneity boundary Heterogeneities Surface irregularities Produce hot and cold spots due to scatter Force tapering using bolus If bolus is used, edges should be tapered 12

13 Surface irregularities Another consequence: Surface irregularities or may cause high dose gradients in the vicinity of d 1, making that point unsuitable for dose prescription. Dose prescription How to prescribe dose, or 9% is 9% of what? Dose reference point is d 1 for beam perpendicularly incident on water phantom at same SSD This point is well-defined and in a region of low dose gradient Monitor unit setting The monitor unit setting (U) on a linear accelerator is determined by the equation: monitor unit setting = D U = D given dose given dose output max max U 13

14 Given Dose Output (cgy MU -1 ) D max /U Definition: The given dose output is the dose per monitor unit to muscle delivered to a point on the central axis at depth d max in a water phantom. Given Dose Output (cgy MU -1 ) D max /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(C s,i eq ) Note: This is for fixed cone applicators. Other formalisms hold for variable applicators. Definition: The output factor is the ratio of the output (dose per monitor unit) in water for an SSD equal to the source-isocenter distance and a depth equal to d max on central axis for a specified cone and equivalent insert size to the calibration dose output. 14

15 Output Factor OF(C s,i eq ) Square root method (used with almost all current electron linear accelerators, including all accelerators presently at MDACC): output factor [ output factor output factor ] = length length width width 1 [ s iso iso s iso iso ]2 ( C, X, Y ) = OF( C, X, X ) OF( C, Y, Y ) OF s iso iso 1 2 Inverse Square Factor - ISF Source of Data: The inverse square factor is computed according to the following equation: calibration output distance inverse square factor = treatment output distance ISF ( SSD, d ) max SAD + d = SSD + d max max 2 2 Source-Skin Distance (cm) SSD Definition: The source-skin skin distance is the distance from the virtual radiation source to a point defined on the patient's skin surface, projected onto the central axis Note that virtual source position may not coincide with nominal source position Often nominal source position used to avoid confusion 15

16 Air Gap Factor f air Definition: The air gap factor is the ratio of the output measured at a specified SSD to the inverse-square-predicted square-predicted output for that SSD It corrects for the loss of side-scatter scatter equilibrium, collimator scatter, other scatter effects, and, when appropriate, utilization of a nominal SSD Air Gap Factor f air The air gap factor is then determined by the following equation: air gap factor [ air gap factor air gap factor ] = length length width width 1 air ( X iso, Yiso, g) = [ f air ( X iso, X iso, g) f air ( Yiso, Yiso, g) ]2 f 1 2 Skin collimation factor SCF Definition: The skin collimation factor is a correction to the output factor that results from a shift of the d max depth toward the patient surface that can occur when skin collimation is included in an electron field 16