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

Transcription

1 Brachytherapy: Sources and Dose Calculations Kent A. Gifford, Ph.D. Source Construction Source characteristics Physical length Active length Linear intensity Filtration Activity 1

2 3/3/14 Sources: HDR/PDR Sources: LDR I Seed 2

3 3/3/14 Sources: fluence distribution Sources: radionuclides Nuclide Radium-226 Cobalt-60 Radon-222 Cesium-137 Palladium-103 Iodine-125 Cesium-131 Iridium-192 Energy (MeV) Half-life 1600 years 5.26 years 3.83 days 30 years 17 days 59.4 days 9.7 days days 3

4 Sources: appearance and size Cesium Pellet Cesium Walstram Cesium Tube Source Iridium Wire Gold (Au) Seeds Iodine Seeds Source Construction Iridium Wire Gold (Au) Seed Iodine Seed 4

5 Mean life N(t)/N 0 = e -1 = e -lt lt = 1 t = T av =1/l T av = T 1/2 /.693 = 1.44 T 1/2 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 5

6 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/T 1/2 ) is the % decay per time interval. Example: I-125 decay T 1/2 =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 6

7 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 226 Ra standards, quantified amount by expressing mass of sample in g or mg. 7

8 Activity 226 Ra alpha decays to 222 Rn, 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 222 Rn to 226 Ra 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 * alpha per second. 1 Ci defined as 3.7*10 10 disintegrations per second (d.p.s.). 8

9 Activity Later experiments established amount of radon in equilibrium with 1 g of radium gives 3.61 * d.p.s. Curie definition remains 3.7 *10 10 d.p.s. millicurie (mci) is 3.7 * 10 7 d.p.s. 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., 125 I, 103 Pd 9

10 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-cm 2 )/(mg-hr)] - Ra(0.5mm Pt) G = 7.71 [(R-cm 2 )/(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 10

11 Exposure Rate Constants Isotope G d (R-cm 2 /mci-hr) 226 Ra (0.5mmPt) Cs Ir Au I 1.51 * 103 Pd 1.48 * Implant Doses Permanent Implant D = (dd 0 /dt )T av Temporary Implant with T 1/2 >>T D = (dd 0 /dt ) T Temporary Implant with T 1/2 not >> T D = (dd 0 /dt ) T av [1 - exp(-t/t av )] millicuries destroyed 11

12 Temporary Implant T 1/2 not >>T D = (dd 0 /dt)[-{exp(-lt)}/{l}] T 0 D = (dd 0 /dt)[-{exp(-lt)/l} +{1/l}] D = ((dd 0 /dt) /l)[1-exp(-lt)] D = (dd 0 /dt) T av [1-exp(-lT)] D = (dd 0 /dt) T av [1-exp(-T/T av )] millicuries destroyed D = (dd 0 /dt) T av [1-exp(-lT)] D = (dd 0 /dt) T av - (dd 0 /dt) exp(-lt) T av D = (dd 0 /dt) T av - (dd T/dt) T av 12

13 Half -Value Layers Isotope HVL(mm of Pb) 226 Ra Cs Ir Au I Pd AAPM Task Group 43 Dosimetry of interstitial brachytherapy sources: Recommendations of the AAPM Radiation Therapy Committee Task Group 43, Med Phys 22, , Update of AAPM Task Group No. 43 Report: A revised AAPM protocol for brachytherapy dose calculations, Med Phys 31, ,

14 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 m 2 /hr = 1cGy cm 2 /hr Becquerel 1 Bq = 1 d.p.s. 1 Bq = 2.7*10-11 Ci = 2.7*10-8 mci SI unit 21st century Activity 14

15 Dose calculations- photon emitters (TG-43) Dose calculations: TG-43 MC calculations/measurements parameterized 2D dose calculation formalism Water D w,w 15

16 Dose calculations: TG-43 Reference media: 22 C, 760 mm Hg, 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 16

17 Dose calculations: TG-43 Air Kerma Strength S k = (dk(d)/dt)d 2, U 1 U = 1 mgy m 2 /h = 1cGy cm 2 /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. 17

18 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)[(m tr /r)/(m en /r)] m en /r = (m tr /r)(1-g) g = 0 K = X(W/e) S k = (dx d /dt)(w/e)d 2 S k = (dx(r/h)/dt) (0.876 cgy/r)(1m 2 ) 18

19 Air Kerma Strength Product of air kerma rate times distance squared, usually 1 m, to point of specification. S k = (dk(r)/dt)*r 2, units are in U 1U = 1 mgy - m 2 /hr or 1 cgy- cm 2 /hr AAPM task group 43 protocol specifies air kerma strength on perpendicular bisector of source at 1cm Air Kerma Strength 1U = (dk(r)/dt)*r 2 1U = (dx(r)/dt)*(w/e)*r 2 1U = (dx(r)/dt)*(0.876 cgy/r)*r 2 Example Ra 1mg 226 Ra(0.5mm Pt) = [8.25 (R-cm 2 /mg-hr)]*(0.876 cgy/r)*r 2 = cgy cm 2 /hr = mgy m 2 /hr = 7.227U 1U = mg Ra (0.5mm Pt) 19

20 Air Kerma Strength Conversions 1 mgy m 2 /h = mci for 137 Cs = mci for 192 Ir = mci for 198 Au = mci for 125 I = mci for 103 Pd 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-m 2 /hr) RAKR times the duration of the implant is Total Reference Air Kerma - 1 m 21st century mg-hrs 20

21 Dose Rate Constant L = (dd(r 0, q 0 )/dt)/s k Dose rate to water at a point along perpendicular bisector of source 1 cm from the source for source strength of 1U. Geometry Factor G P (r,q) = 1 / r 2 point source G L (r,q) = b / (L r sin q) line source if q not 0 o G L (r,q) = 1/(r 2 -L 2 /4) line source if q = 0 o L = active length b = q 2 - q 1 in radians Accounts for variation in relative dose due to distribution of activity within the source, ignoring photon absorption and scattering. 21

22 3/3/14 Derivation of Geometry Factor 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. 22

23 Anisotropy Function F(r,q) = (dd(r,q)/dt) G(r,q 0 )/ (dd(r,q 0 )/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 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, f an (r). Valid for randomly oriented point sources. 23

24 Anisotropy Constant Anisotropy factor, f an (r), averaged over distance yields anisotropy constant f an. Used at all distance and angles for point sources considered in Task Group 43 report. Anisotropy constant not recommended by TG43 update. Dose calculations: where are we going? Model based dose calculations 24

25 Dose calculations: where are we going? Model based calculations-acuros - Solves time-independent LBTE equation nonanalytically 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? Model based calculations-acuros Linear Boltzmann Transport Equation (LBTE) direction Angular position vector particle fluence vector macroscopic energy rate total extrinsic cross section scattering source source Streaming Collision Sources Obeys conservation of particles Streaming + collisions = production 25

26 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) 26

27 Dose calculations: where are we going? Model based calculations-ccc Advanced Dose Calculations via Collapsed Cone Dresidua l Dscatter Courtesy of MJ Price Dprimary Dose calculations: where are we going? Model based calculations-ccc Advanced Dose Calculations via Collapsed Cone Dresidual + Dscatter Dtotal Dprimary Courtesy of MJ Price 27

28 Dose calculations: where are going? Clinical effects summary Low-energy Eye plaques High-energy Breast brachytherapy Low-energy Breast brachytherapy High-energy Prostate brachytherapy Low-energy Prostate brachytherapy GYN brachytherapy (unshielded) GYN brachytherapy (shielded) 10-30% underestimation (TG-129) 4-7 % overestimation (skin & rib) 3-5 % underestimation Negligible 5-10% underestimation +1.5 to -5%, (applicator attenuation) 30-50% overestimation adjacent to shielding (direction, shielding material, isotope) Adapted from MJ Price Problems 1. Calculate time of removal of temporary implant of 103 Pd. Prescription is 100 Gy. Initial dose rate at prescription point is 80 cgy/hr. Insertion time is Today at 2:00 PM. 28

29 Problems 2. Estimate exposure rate at the foot of the bed (1m) from a patient who received a tandem and ovoid implant loaded 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 29