Brachytherapy: Sources and Dose Calculations Kent A. Gifford, Ph.D.

Source Construction Physical length Active length Linear intensity Source characteristics Physical length Active length Linear intensity Filtration Activity MDACC Brachytherapy Short Course 2003

Sources: HDR/PDR

Sources: LDR 6711 125I Seed MDACC Brachytherapy Short Course 2003

Sources: fluence distribution MDACC Brachytherapy Short Course 2003

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

Sources: appearance and size Cesium Walstram Cesium Tube Source Cesium Pellet Iridium Wire Gold (Au) Seeds Iodine Seeds

Source Construction Iridium Wire Gold (Au) Seed Iodine Seed

N(t)/N0 = e-1 = e-lt lt = 1 t = Tav =1/l Tav = T 1/2/.693 = 1.44 T 1/2 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 MDACC Brachytherapy Short Course 2003

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

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

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

Brachytherapy Source Strength Specification Mass- Early 20th century Activity- Early 20th century Apparent Activity- Mid 20th century Air Kerma Strength- Late 20th century

Mass Radium Mme. Curie prepared first 226Ra standards, quantified amount by expressing mass of sample in g or mg.

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.

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.).

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. MDACC Brachytherapy Short Course 2003

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

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)

mg-hours or mgRaeq-hours Number of mg or mgRaeq in implant times the duration of the implant in hours

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* MDACC Brachytherapy Short Course 2003

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” MDACC Brachytherapy Short Course 2003

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)] MDACC Brachytherapy Short Course 2003

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 MDACC Brachytherapy Short Course 2003

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 MDACC Brachytherapy Short Course 2003

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. MDACC Brachytherapy Short Course 2003

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 MDACC Brachytherapy Short Course 2003

Becquerel 1 Bq = 1 d.p.s. 1 Bq = 2.7*10-11 Ci = 2.7*10-8 mCi SI unit “21st century Activity”

Dose calculations- photon emitters (TG-43) MDACC Brachytherapy Short Course 2003

Dose calculations: TG-43 MC calculations/measurements parameterized 2D dose calculation formalism Water Dw,w

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

Dose calculations: TG-43 Dimensions in cm

Dose calculations: TG-43

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. MDACC Brachytherapy Short Course 2003

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

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) MDACC Brachytherapy Short Course 2003

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

Air Kerma Strength = 7.227 cGy cm2/hr = 7.227 mGy m2/hr 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)

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 MDACC Brachytherapy Short Course 2003

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”

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. MDACC Brachytherapy Short Course 2003

Geometry Factor L = active length b = q2 - q1 in radians 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. MDACC Brachytherapy Short Course 2003

Derivation of Geometry Factor MDACC Brachytherapy Short Course 2003

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. MDACC Brachytherapy Short Course 2003

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 MDACC Brachytherapy Short Course 2003

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. MDACC Brachytherapy Short Course 2003

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. MDACC Brachytherapy Short Course 2003

Dose calculations: where are we going? Model based dose calculations

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

Dose calculations: where are we going Dose calculations: where are we going? Model based calculations-Acuros Linear Boltzmann Transport Equation (LBTE) Sources Collision Streaming ↑direction vector ↑Angular fluence rate ↑position vector ↑particle energy ↑macroscopic total cross section ↑scattering source extrinsic source ↑ Obeys conservation of particles Streaming + collisions = production

Dose calculations: where are we going Dose calculations: where are we going? Model based calculations-Acuros Reactions ↑reaction rate scalar fluence rate↑ ↑macroscopic cross-section of type whatever

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)

Dose calculations: where are we going? Model based calculations-CCC Advanced Dose Calculations via Collapsed Cone Dresidual Dscatter Dprimary Courtesy of MJ Price

Dose calculations: where are we going? Model based calculations-CCC Advanced Dose Calculations via Collapsed Cone + Dresidual Dtotal Dscatter Dprimary Courtesy of MJ Price

Dose calculations: where are going? Clinical effects summary Treatment type Estimated effect on absorbed dose 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

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.

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.

Problems 3. Convert 55 mg Ra eq of Cs-137 to: a. mCi of Cs-137 b. U