Brachytherapy Dose Calculation Formalism, Dataset Evaluation
Brachytherapy: Sources and Dose Calculations …KG)MedPhysIII_2_201… · Brachytherapy: Sources...
Transcript of Brachytherapy: Sources and Dose Calculations …KG)MedPhysIII_2_201… · Brachytherapy: Sources...
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Brachytherapy: Sources and Dose Calculations
Kent A. Gifford, Ph.D.
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Source Construction
Source characteristics
Physical length
Active length
Linear intensity
Filtration
Activity
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Sources: HDR/PDR
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Sources: LDR 6711 125I Seed
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Sources: fluence distribution
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Sources: radionuclides
Nuclide Energy (MeV) Half-life
Radium-226 0.24 - 2.2 1600 years Cobalt-60 1.25 5.26 years Radon-222 0.78 3.83 days Cesium-137 0.662 30 years Palladium-103 0.021 17 days Iodine-125 0.028 59.4 days Cesium-131 0.0304 9.7 days Iridium-192 0.380 73.83 days
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Cesium Pellet
Cesium Walstram
Cesium Tube Source
Iridium Wire
Gold (Au) Seeds Iodine Seeds
Sources: appearance and size
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Gold (Au) Seed Iodine Seed
Iridium Wire
Source Construction
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Mean life
N(t)/N0 = e-1 = e-lt
lt = 1 t = Tav =1/l Tav = T 1/2/.693 = 1.44 T 1/2
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Half-life, rule of 72
Rule used in finance to estimate growth - amount of time to double investment - rate of return to double investment in given time
Can be applied to exponential growth or decay
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Half-life, rule of 72
Doubling time estimated by (72/rate of return)
Example: Savings account pays 6%/yr. How long to
double? 72/(6%/yr)=12 years Exact: (1.06)12=2.01
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Half-life, rule of 72
Application to radioactive decay: (72/T1/2) is the % decay per time interval.
Example: I-125 decay T1/2=59.4 days How much of initial sample is left after 5
days? 72/59.4=1.2%/day, 5days*1.2%/days, 94%
remains
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Brachytherapy Source Strength Specification
• Mass- Early 20th century
• Activity- Early 20th century
• Apparent Activity- Mid 20th century
• Air Kerma Strength- Late 20th century
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Mass
• Radium – Mme. Curie prepared first 226Ra standards,
quantified amount by expressing mass of sample in g or mg.
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Activity
• 226Ra alpha decays to 222Rn, all photons are emitted by radon or radon daughter products.
• Radon seeds produced by collecting radon gas from decay of radium and encapsulating in gold tubing.
• Method needed to permit correlation of 222Rn to 226Ra clinical experience.
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Activity
• Defined 1 Curie (Ci) to be the amount of radon in equilibrium with 1 g of radium.
• A 1 Ci radon seed has same activity as 1 g of radium.
• Early experiments indicated 1 Ci of radon emitted 3.7 * 1010 alpha per second.
• 1 Ci defined as 3.7*1010 disintegrations per second (d.p.s.).
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Activity
• Later experiments established amount of radon in equilibrium with 1 g of radium gives 3.61 * 1010 d.p.s.
• Curie definition remains 3.7 *1010 d.p.s.
• milliCurie (mCi) is 3.7 * 107 d.p.s.
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Apparent Activity
• Apparent activity - activity of a bare source that produces the same exposure rate at calibration distance as the specified source.
• Expressed in mCi for brachytherapy. • Particularly useful for low energy
photon sources, e.g., 125I, 103Pd
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mgRaeq
• mgRaeq yields same exposure rate at calibration distance as 1 mg Ra encapsulated by 0.5mm Pt.
• The exposure rate at 1 cm from 1 mg Ra(0.5mm) is 8.25R/hr.
• Exposure Rate constant (G) is G = 8.25 [(R-cm2)/(mg-hr)] - Ra(0.5mm Pt)
G = 7.71 [(R-cm2)/(mg-hr)] - Ra(1.0mm Pt)
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mg-hours or mgRaeq-hours
• Number of mg or mgRaeq in implant times the duration of the implant in hours
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Exposure Rate Constants
Isotope Gd(R-cm2/mCi-hr) 226Ra (0.5mmPt) 8.25 137Cs 3.26 192Ir 4.69 198Au 2.38 125I 1.51* 103Pd 1.48*
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Implant Doses
• Permanent Implant • D = (dD0/dt )Tav
• Temporary Implant with T1/2>>T • D = (dD0/dt ) T
• Temporary Implant with T1/2 not >> T • D = (dD0/dt ) Tav[1 - exp(-T/Tav)] – “milliCuries destroyed”
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Temporary Implant T1/2 not >>T
D = (dD0/dt)[-{exp(-lt)}/{l}]0t
D = (dD0/dt)[-{exp(-lT)/l} +{1/l}] D = ((dD0/dt) /l)[1-exp(-lT)] D = (dD0/dt) Tav[1-exp(-lT)] D = (dD0/dt) Tav[1-exp(-T/Tav)]
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milliCuries destroyed
D = (dD0/dt) Tav[1-exp(-lT)]
D = (dD0/dt) Tav- (dD0/dt) exp(-lT) Tav
D = (dD0/dt) Tav - (dDT/dt) Tav
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Half -Value Layers
Isotope HVL(mm of Pb) 226Ra 8.0 137Cs 5.5 192Ir 2.5 198Au 2.5 125I 0.025 103Pd 0.008
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AAPM Task Group 43
• Dosimetry of interstitial brachytherapy sources: Recommendations of the AAPM Radiation Therapy Committee Task Group 43, Med Phys 22, 209 - 234, 1995.
• Update of AAPM Task Group No. 43 Report: A revised AAPM protocol for brachytherapy dose calculations, Med Phys 31, 633 - 674, 2004.
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Task Group 43
• Incorporates latest data • Incorporates SI units
– Becquerel (Bq) • 1 Bq = 1dps = 2.7*10-11 Ci
– Air Kerma Strength (U) • 1U = 1mGy m2/hr = 1cGy cm2/hr
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Becquerel
• 1 Bq = 1 d.p.s. • 1 Bq = 2.7*10-11 Ci = 2.7*10-8 mCi • SI unit • “21st century Activity”
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Dose calculations- photon emitters (TG-43)
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Dose calculations: TG-43
• MC calculations/measurements parameterized
• 2D dose calculation formalism • Water Dw,w
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Dose calculations: TG-43
• Reference media: Water @ 22°C, 760 mm Hg, air @ 40% rel. humidity
• Collisional kerma approximates dose • 30 cm diameter water sphere • Voxels small enough to minimize volume
averaging (< 1%) • Histories: k=1 ≤ 2%, ≤ 1% for Sk • Calculate dose: 0.5 cm ≤ r ≤ 10 cm
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Dose calculations: TG-43
Dimensions in cm
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Dose calculations: TG-43
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Air Kerma Strength
Sk = (dK(d)/dt)d2, U 1 U = 1 mGy m2/h = 1cGy cm2/h
Brachytherapy source strength specified in terms air kerma rate at a point in air along the perpendicular bisector of the source. Product of air kerma rate times distance (usually 1 meter) to point.
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Kerma
Kinetic Energy Released to MAterial
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Kerma
• Indirectly ionizing radiations (photons and neutrons) deposit energy through two step process – 1st step, photon or neutron releases kinetic
energy to medium through interactions with electrons (photons) or nuclei (neutrons), kerma
– 2nd step, kinetic energy released is deposited downstream (collisional kerma), dose, or re-irradiated as bremsstrahlung (radiative kerma)
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Kerma
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Air Kerma
• Kerma created by photons interacting with air.
• At brachytherapy energies, amount of energy re-irradiated as bremsstrahlung is essentially zero.
• Air Kerma – K = X*(W/e)
• X = exposure • (W/e) = average energy to create an ion pair
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Air Kerma Strength
K = X(W/e)[(mtr/r)/(men/r)] men/r = (mtr/r)(1-g) g = 0 K = X(W/e) Sk = (dXd/dt)(W/e)d2
Sk = (dX(R/h)/dt) (0.876 cGy/R)(1m2)
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Air Kerma Strength
• Product of air kerma rate times distance squared, usually 1 m, to point of specification.
• Sk = (dK(r)/dt)*r2, units are in U • 1U = 1 mGy - m2/hr or 1 cGy- cm2/hr
• AAPM task group 43 protocol specifies air kerma strength on perpendicular bisector of source at 1cm
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Air Kerma Strength
• 1U = (dK(r)/dt)*r2 • 1U = (dX(r)/dt)*(W/e)*r2 • 1U = (dX(r)/dt)*(0.876 cGy/R)*r2 • Example - 226Ra
– 1mg 226Ra(0.5mm Pt) = [8.25 (R-cm2/mg-hr)]*(0.876 cGy/R)*r2 = 7.227 cGy cm2/hr = 7.227 mGy m2/hr = 7.227U
– 1U = 0.138 mg Ra (0.5mm Pt)
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Air Kerma Strength Conversions
1 mGy m2/h = 0.348 mCi for 137Cs = 0.243 mCi for 192Ir = 0.486 mCi for 198Au = 0.787 mCi for 125I = 0.773 mCi for 103Pd
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Total Reference Air Kerma - TRAK
• Reference Air Kerma Rate is air kerma rate at 1 m in units of mGy/hr
• European nomenclature for quantity numerically equal to Air Kerma Strength(mGy-m2/hr)
• RAKR times the duration of the implant is • Total Reference Air Kerma - mGy @ 1 m
• “21st century mg-hrs”
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Dose Rate Constant
L = (dD(r0, q0)/dt)/Sk
Dose rate to water at a point along perpendicular bisector of source 1 cm from the source for source strength of 1U.
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Geometry Factor
GP(r,q) = 1 / r2 point source GL(r,q) = b / (L r sin q) line source if q not 0o GL(r,q) = 1/(r2-L2/4) line source if q = 0o L = active length b = q2 - q1 in radians
Accounts for variation in relative dose due to distribution of activity within the source, ignoring photon absorption and scattering.
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Derivation of Geometry Factor
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Radial Dose Function
g(r) = (dD (r,q0)/dt)GX(r0,q0)/ (dD(r0,q0)/dt)GX(r,q0)
X is P or L depending if a point or line source geometry function
Accounts for the effects of absorption and scatter in tissue in the transverse plane of the source. Similar in concept to Meisberger technique, but radial dose function is normalized at 1 cm.
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Anisotropy Function
F(r,q) = (dD(r,q)/dt) G(r,q0)/ (dD(r,q0)/dt) G(r,q)
Accounts for anisotropy of dose distribution around the source, including effects of absorption and scatter in medium, i.e., self filtration in source, oblique filtration in walls, scattering and absorption in tissue
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Anisotropy Factor
The ratio of dose rate at distance r, averaged with respect to solid angle, to dose rate on perpendicular bisector at same distance, fan(r). Valid for randomly oriented point sources.
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Anisotropy Constant
Anisotropy factor, fan(r), averaged over distance yields anisotropy constant fan. Used at all distance and angles for point sources considered in Task Group 43 report. Anisotropy constant not recommended by TG43 update.
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Dose calculations: where are we going?
Model based dose calculations
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Dose calculations: where are we going? Model based calculations-Acuros
- Solves time-independent LBTE equation non-analytically – Varian/Gamma med Ir-192 HDR/PDR sources – Transports with materials chosen from library
and based on mass density – Can account for applicator attenuation from
Varian applicator library
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Dose calculations: where are we going? Model based calculations
Linear Boltzmann Transport Equation (LBTE)
Collision Sources Streaming
Obeys conservation of particles
• Streaming + collisions = production
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Dose calculations: where are we going? Model based calculations-LBTE
Reactions
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Dose calculations: where are we going? Model based calculations-Acuros
• Angular discretization-discrete ordinates method
• Energy discretization-multigroup method
• Spatial discretization-variable Cartesian mesh
• Transports in medium and converts to dose to water (Dw,m)
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Advanced Dose Calculations via Collapsed Cone
Dose calculations: where are we going? Model based calculations-CCC
Dprimary
Dscatter
Dresidual
Courtesy of MJ Price
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Dtotal
Advanced Dose Calculations via Collapsed Cone
Dose calculations: where are we going? Model based calculations-CCC
Dprimary
Dscatter
Dresidual +
Courtesy of MJ Price
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Dose calculations: where are going? Clinical effects summary
Low-energy Eye plaques 10 - 30% underestimation (TG-129)
High-energy Breast brachytherapy 4-7 % overestimation (skin & rib)
Low-energy Breast brachytherapy 3-5 % underestimation
High-energy Prostate brachytherapy Negligible
Low-energy Prostate brachytherapy 5 - 10% underestimation
GYN brachytherapy (unshielded) +1.5 to -5%, (applicator attenuation)
GYN brachytherapy (shielded) 30 - 50% overestimation adjacent to
shielding (direction, shielding material, isotope)
Adapted from MJ Price
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Problems
1. Calculate time of removal of temporary implant of 103Pd. Prescription is 100 Gy. Initial dose rate at prescription point is 80 cGy/hr. Insertion time is Today at 2:00 PM.
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Problems
2. Estimate exposure rate at the foot of the bed (1m) from a patient who received a tandem and ovoid implant loaded 15-15-10 mgRaeq in the tandem and 15 mgRaeq in each ovoid.
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Problems
3. Convert 55 mg Ra eq of Cs-137 to: a. mCi of Cs-137
b. U