Brachytherapy - source calibration - dose calculation algorithms

Firas Mourtada, Ph.D.Brachytherapy Section

Photon Energies

Isotope Energies(MeV)226 Ra 0.047 - 2.45 (ave 0.83)137Cs 0.662192Ir 0.136 - 1.06 (ave 0.38)198Au 0.412125I 0.0274 - 0.0355 (ave 0.028)103Pd 0.0201, 0.023 (ave 0.021)

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.

TG-43 Updates

Task Group 43

Incorporates latest dataIncorporates SI units– Becquerel (Bq)

• 1 Bq = 1dps = 2.7*10-11 Ci

– Air Kerma Strength (U)• 1U = 1μGy m2/hr = 1cGy cm2/hr

Becquerel

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

Task Group 43-updated

Point source

Line source

1) Air Kerma Strength

Sk = (dK(d)/dt)d2, U1 U = 1 μGy 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.

*Updated – 5 keV cutoff

Kerma

KineticEnergyReleased toMAterial

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)

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

SI unit“21st century Exposure”

Air Kerma Strength

K = X(W/e)[(μtr /ρ)/(μen /ρ)]μen /ρ = (μtr /ρ)(1-g)g = 0K = X(W/e)Sk = (dXd /dt)(W/e)d2

Sk = (dX(R/h)/dt) (0.876 cGy/R)(1m2)

TG43 updated

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 μGy - m2/hr or 1 cGy- cm2/hr

AAPM TG-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 μGy m2/hr = 7.227U

– 1U = 0.138 mg Ra (0.5mm Pt)

Air Kerma Strength Conversions

1 μGy 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 μGy/hrEuropean nomenclature for quantity numerically equal to Air Kerma Strength(μGy-m2/hr)RAKR times the duration of the implant is – Total Reference Air Kerma - μGy @ 1 m

“21st century mg-hrs”

2) Dose Rate Constant

Dose rate to water at a point along perpendicular bisector of source 1 cm from the source for source strength of 1U.

TG43- 1995 Dose Rate Constants

(Best seed)

*Λ-mc = (1.123 ±

0.001) cGy h-1 U-1

TG 43-updated Dose Rate Constants

Geometry Factor- old TG43

G(r,θ) = 1 / r2 point sourceG(r,θ) = β / (L r sin θ) line sourceL = active lengthβ = θ2 - θ1

Accounts for variation in relative dose due to distribution of activity within the source, ignoring photon absorption and scattering.

Derivation of Geometry Factor

TG43-Updated 2004

TG43 Source Geometry

Sievert Integral Source Geometry

Comparison Sievert to TG 43

point source geometry factor divided by 5 cm line source geometry factor

1

10

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

cm

ratio

of p

oint

to li

ne

0.010

0.100

1.000

10.000

100.000

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000

cm

geom

etry

fact

or

line = 5cm

point

Geometry Factor for point source vs 5 cm active length line sourceL= active length of 5 cm r = distance to calc point

r/L r(cm) line = 5cm point point/line =5 cm0.025 0.125 4.867 64.000 13.1510.050 0.250 2.354 16.000 6.7980.075 0.375 1.517 7.111 4.6890.100 0.500 1.099 4.000 3.6410.125 0.625 0.849 2.560 3.0170.150 0.750 0.682 1.778 2.6060.175 0.875 0.564 1.306 2.3150.200 1.000 0.476 1.000 2.1000.225 1.125 0.408 0.790 1.9360.250 1.250 0.354 0.640 1.8060.275 1.375 0.311 0.529 1.7020.300 1.500 0.275 0.444 1.6180.325 1.625 0.245 0.379 1.5470.350 1.750 0.219 0.327 1.4880.375 1.875 0.198 0.284 1.4380.400 2.000 0.179 0.250 1.3950.425 2.125 0.163 0.221 1.3580.450 2.250 0.149 0.198 1.3260.475 2.375 0.137 0.177 1.2980.500 2.500 0.126 0.160 1.2730.525 2.625 0.116 0.145 1.2510.550 2.750 0.107 0.132 1.2320.575 2.875 0.100 0.121 1.2150.600 3.000 0.093 0.111 1.1990.625 3.125 0.086 0.102 1.1860.650 3.250 0.081 0.095 1.1730.675 3.375 0.076 0.088 1.1620.700 3.500 0.071 0.082 1.1520.725 3.625 0.067 0.076 1.1420.750 3.750 0.063 0.071 1.1340.775 3.875 0.059 0.067 1.1260.800 4.000 0.056 0.063 1.1190.825 4.125 0.053 0.059 1.1120.850 4.250 0.050 0.055 1.1060.875 4.375 0.047 0.052 1.1010.900 4.500 0.045 0.049 1.0960.925 4.625 0.043 0.047 1.0910.950 4.750 0.041 0.044 1.0860.975 4.875 0.039 0.042 1.0821.000 5.000 0.037 0.040 1.078

5 cm Active Length Source Geometry Factor

1.025 5.125 0.035 0.038 1.0751.050 5.250 0.034 0.036 1.0711.075 5.375 0.032 0.035 1.0681.100 5.500 0.031 0.033 1.0651.125 5.625 0.030 0.032 1.0631.150 5.750 0.029 0.030 1.0601.175 5.875 0.027 0.029 1.0581.200 6.000 0.026 0.028 1.0551.225 6.125 0.025 0.027 1.0531.250 6.250 0.024 0.026 1.0511.275 6.375 0.023 0.025 1.0491.300 6.500 0.023 0.024 1.0481.325 6.625 0.022 0.023 1.0461.350 6.750 0.021 0.022 1.0441.375 6.875 0.020 0.021 1.0431.400 7.000 0.020 0.020 1.0411.425 7.125 0.019 0.020 1.0401.450 7.250 0.018 0.019 1.0381.475 7.375 0.018 0.018 1.0371.500 7.500 0.017 0.018 1.0361.525 7.625 0.017 0.017 1.0351.550 7.750 0.016 0.017 1.0341.575 7.875 0.016 0.016 1.0331.600 8.000 0.015 0.016 1.0321.625 8.125 0.015 0.015 1.0311.650 8.250 0.014 0.015 1.0301.675 8.375 0.014 0.014 1.0291.700 8.500 0.013 0.014 1.0281.725 8.625 0.013 0.013 1.0271.750 8.750 0.013 0.013 1.0271.775 8.875 0.012 0.013 1.0261.800 9.000 0.012 0.012 1.0251.825 9.125 0.012 0.012 1.0251.850 9.250 0.011 0.012 1.0241.875 9.375 0.011 0.011 1.0231.900 9.500 0.011 0.011 1.0231.925 9.625 0.011 0.011 1.0221.950 9.750 0.010 0.011 1.0221.975 9.875 0.010 0.010 1.0212.000 10.000 0.010 0.010 1.020

2.025 10.125 0.010 0.010 1.0202.050 10.250 0.009 0.010 1.0202.075 10.375 0.009 0.009 1.0192.100 10.500 0.009 0.009 1.0192.125 10.625 0.009 0.009 1.0182.150 10.750 0.009 0.009 1.0182.175 10.875 0.008 0.008 1.0172.200 11.000 0.008 0.008 1.0172.225 11.125 0.008 0.008 1.0172.250 11.250 0.008 0.008 1.0162.275 11.375 0.008 0.008 1.0162.300 11.500 0.007 0.008 1.0162.325 11.625 0.007 0.007 1.0152.350 11.750 0.007 0.007 1.0152.375 11.875 0.007 0.007 1.0152.400 12.000 0.007 0.007 1.0142.425 12.125 0.007 0.007 1.0142.450 12.250 0.007 0.007 1.0142.475 12.375 0.006 0.007 1.0132.500 12.500 0.006 0.006 1.0132.525 12.625 0.006 0.006 1.0132.550 12.750 0.006 0.006 1.0132.575 12.875 0.006 0.006 1.0122.600 13.000 0.006 0.006 1.0122.625 13.125 0.006 0.006 1.0122.650 13.250 0.006 0.006 1.0122.675 13.375 0.006 0.006 1.0122.700 13.500 0.005 0.005 1.0112.725 13.625 0.005 0.005 1.0112.750 13.750 0.005 0.005 1.0112.775 13.875 0.005 0.005 1.0112.800 14.000 0.005 0.005 1.0112.825 14.125 0.005 0.005 1.0102.850 14.250 0.005 0.005 1.0102.875 14.375 0.005 0.005 1.0102.900 14.500 0.005 0.005 1.0102.925 14.625 0.005 0.005 1.0102.950 14.750 0.005 0.005 1.0102.975 14.875 0.004 0.005 1.0093.000 15.000 0.004 0.004 1.009

Radial Dose Function

Accounts for the effects of absorption and scatter in tissue along the perpendicular bisector of the source. Similar in concept to Meisberger technique, but radial dose function is normalized at 1 cm.

TG43, 1995

TG 43 Point Source Radial Dose Functions

normalized at 1 cm

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

Distance(cm)

g(r)

I-125(6711)

I-125(6702)

Pd-103

Ir -192

Relative Dose vs DistanceAll isotopes normalized at 1 cm

0.001

0.01

0.1

1

10

100

0.0 2.0 4.0 6.0 8.0 10.0

distance(cm)

rela

tive

dose

I-125(6711)I-125(6702)Pd-103Ir -192inv sq

TG43- radial dose functions

TG43-update g(r) consensus data

Anisotropy Function

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

Unity along bisectorDecreases as– r decreases– theta approaches 0 or 180 deg.– Encapsulation thickness increases– Photon energy decreases

May exceed unity for right-cylinder sources coated w/ low E photon source– Due to screening of photons by active core at angles

towards the transverse plane

Anisotropy Function Behavior

TG43, 1995

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, φan (r). Valid for randomly oriented point sources.

TG43-update Anisotropy Factor

Recommended for higher accuracy at <1cm

Anisotropy Constant

Anisotropy factor, φan (r), averaged over distance yields anisotropy constant φan . Used at all distances and angles for point sources considered in Task Group 43 report.

No longer recommended per TG43-update

Anisotropy Factor Data- example

TG43-updated

Dose rate results- TG43 Update

Error Propagation Analysis – TG43-update

1D or 2D Anisotropy uncertainty analysis not available

MC onlyExperimental+MC

Experimental+MCVendor-suppliedNot better than 3%

6-7% total dose uncertaintyHowever,

Law of Propagation of Uncertainty (LPU)

Covariance is zero

B-type B-type A-type

LPU for Dose Rate Constant Uncertainty Estimation

Source Specification

mg Ra eq

Activity - mCi

Apparent activity - mCi

Air Kerma Strength - U

TG-32