Brachytherapy: Sources and Dose Calculations

Kent A. Gifford, Ph.D.

Source Construction

Source characteristics

Physical length

Active length

Linear intensity

Filtration

Activity

Sources: HDR/PDR

Sources: LDR 6711 125I Seed

Sources: fluence distribution

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

Cesium Pellet

Cesium Walstram

Cesium Tube Source

Iridium Wire

Gold (Au) Seeds Iodine Seeds

Sources: appearance and size

Gold (Au) Seed Iodine Seed

Iridium Wire

Source Construction

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

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.

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*

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”

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)]

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

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

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.

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

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)

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.

Kerma

Kinetic Energy Released to MAterial

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)

Kerma

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)

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

•  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

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.

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.

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.

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

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.

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.

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? Model based calculations

Linear Boltzmann Transport Equation (LBTE)

Collision Sources Streaming

Obeys conservation of particles

•  Streaming + collisions = production

Dose calculations: where are we going? Model based calculations-LBTE

Reactions

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)

Advanced Dose Calculations via Collapsed Cone

Dose calculations: where are we going? Model based calculations-CCC

Dprimary

Dscatter

Dresidual

Courtesy of MJ Price

Dtotal

Advanced Dose Calculations via Collapsed Cone

Dose calculations: where are we going? Model based calculations-CCC

Dprimary

Dscatter

Dresidual +

Courtesy of MJ Price

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

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