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

2. Source Construction Physical length Active length Linear intensity
Source characteristics
Physical length
Active length
Linear intensity
Filtration
Activity
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3. Sources: HDR/PDR

4. Sources: LDR I Seed
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5. Sources: fluence distribution
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6. Sources: radionuclides
Nuclide Energy (MeV) Half-life
Radium years
Cobalt years
Radon days
Cesium years
Palladium days
Iodine days
Cesium days
Iridium days

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

8. Source Construction
Iridium Wire
Gold (Au) Seed
Iodine Seed

9. 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
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10. 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

11. 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

12. 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

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

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

15. 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.

16. 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.).

17. 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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18. 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

19. 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)

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

21. Exposure Rate Constants
Isotope Gd(R-cm2/mCi-hr) 226Ra (0.5mmPt) Cs Ir Au I 1.51* 103Pd 1.48*
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22. 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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23. 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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24. 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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25. Half -Value Layers
Isotope HVL(mm of Pb) 226Ra Cs Ir Au I Pd 0.008
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26. AAPM Task Group 43
Dosimetry of interstitial brachytherapy sources: Recommendations of the AAPM Radiation Therapy Committee Task Group 43, Med Phys 22, , 1995.
Update of AAPM Task Group No. 43 Report: A revised AAPM protocol for brachytherapy dose calculations, Med Phys 31, , 2004.
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27. 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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28. Becquerel 1 Bq = 1 d.p.s. 1 Bq = 2.7*10-11 Ci = 2.7*10-8 mCi SI unit
“21st century Activity”

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

31. 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

32. Dose calculations: TG-43
Dimensions in cm

33. Dose calculations: TG-43

34. 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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35. 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

36. 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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37. 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

38. 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
= cGy cm2/hr = mGy m2/hr
= 7.227U
1U = mg Ra (0.5mm Pt)

39. Air Kerma Strength Conversions
1 mGy m2/h = mCi for 137Cs = mCi for 192Ir = mCi for 198Au = mCi for 125I = mCi for 103Pd
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40. 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”

41. 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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42. Geometry Factor L = active length b = q2 - q1 in radians
GP(r,q) = 1 / r 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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43. Derivation of Geometry Factor
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44. 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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45. 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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46. 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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47. 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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48. Dose calculations: where are we going?
Model based dose calculations

49. 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

50. 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

51. 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

52. 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)

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

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

55. Dose calculations: where are going? Clinical effects summary
Treatment type
Estimated effect on absorbed dose
Low-energy Eye plaques
% 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)
% overestimation adjacent to shielding (direction, shielding material, isotope)
Adapted from MJ Price

56. 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.

57. 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.

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