Basic Physics Concepts

Firas Mourtada, Ph.D. D. ABR

Associate Professor

MD Anderson Cancer Center

Radioactive Decay

dN/dt = -N

dN/N = -dt

N(t) = N0e-t

N0 = initial number

N(t) = number at time t

= decay constant

Half - life

N(t)/N0 = 0.5 = e-t

ln(0.5) = -t

t = T1/2 = 0.693/

half-life of 198Auhalf life 2.7 days

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Decay of Au198Half-life = 2.7 days

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Decay of Au198Half-life = 2.7 days

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Half - Lives

Isotope Half - Life226Ra 1620 years137Cs 30 years198Au 2.7 days192Ir 73.83 days125I 59.4 days103Pd 16.97 days

Mean life

N(t)/N0 = e-1 = e-t

t = 1

t = Tav =1/

Tav = T 1/2/.693 = 1.44 T 1/2

Au198 half-life vs mean lifeHalf-life = 2.7 days

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Brachytherapy Source Strength Specification

Sealed photon source Encapsulated so radioactive material can not be

lost from physical or chemical stress under foreseeable circumstances. Usually double metal wall encapsulation, prevents escape of radioactive material and absorbs unwanted betas.

All brachytherapy sources are sealed sources except 192Ir wire or hairpins, which have core exposed when cut. ISO considers 192Ir wire or hairpins to be a closed source.

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.

222Radon 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.

Roughly, conversion is 27 mCi per 1 GBq

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

Post WWII, other reactor produced isotopes began to be used as radium substitutes in radiotherapy.

Source strength was expressed in mCi, but also needed a method to take advantage of clinical experience with radium.

Used mgRaeq.

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 () is = 8.25 [(R-cm2)/(mg-hr)] - Ra(0.5mm Pt)

= 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

Source Specification

Activity - mCi - 3.7 x 107 d.p.s.

Apparent activity - activity of a bare point source that produces same exposure rate at calibration distance as the specified source.

mg Ra eq - amount of 226Ra that produces same exposure rate at calibration distance as specified isotope

Exposure Rate Constants

Isotope (R-cm2/mCi-hr)226Ra (0.5mmPt) 8.25137Cs 3.3192Ir 4.69198Au 2.38125I 1.51103Pd 1.48

Conversion - mCi to mg Ra eq

# of mg Ra eq = (x/Ra) * # of mCix

Conversion - mCi to mg Ra eq

Examples137Cs

# of mg Ra eq = (/) * # of mCi137Cs

= 0.4 * # of mCi137Cs

192Ir

# of mg Ra eq = (/) * # of mCi192Ir

= 0.569* # of mCi192Ir

1 mCi of 137Cs-dN / dt = 3.7 * 107 dps = NN = 3.7*107 dps / = 0.693 / T1/2 = 0.693 / (30 y * * 107 s/y) = 7.36 *10-10 s-1

N = 5.03 * 1016 atoms of 137Cs

A0 = 6.023 * 1023 atoms per 137 g (1 mole) of 137CsMass of 1mCi =

(5.03 * 1016 / 6.02 * 1023)*137 = 10 g

Dose Rate Calculation - Seeds

dD/dt = A f Btiss Bw Bs an /d2

activityexposure rate constantf = f-factor - R to cGy conversion factorBtiss = attenuation and scattering in tissue

w, s = attenuation and scattering for source encapsulation and self attenuation

an= anisotropy factord = distance to calculation point

Attenuation and Scattering Functions

TissueBtiss = 1+k(d)k

Btiss = + d + d2 +d3

WallBw = exp(-wtw)

SourceBs = exp(-sts)

Meisberger Coefficients

Ratio of in-water exposure to in-air exposure - Tissue attenuation/scattering

Meisberger, L.L., Keller, R., Shalek, R.J., The effective attenuation in water of gold-198, iridium-192, cesium-137, radium-226, and cobalt-60, Radiology 90, 953, 1968.

Meisberger ratio = A + Br + Cr^2 + Dr^3, r distance in cm from source to point of calculation

Cs137 Ir192 Au198 Ra226A 1.009100000 1.012800000 1.036000000 1.000500000B -0.009015000 0.005019000 -0.008134000 -0.004423000C -0.000345900 -0.001178000 0.001111000 -0.001707000D -0.000028170 -0.000020080 -0.000159700 0.000074480

r(cm) Cs137 Ir192 Au198 Ra2260.50000 1.00450 1.01501 1.03219 0.997871.00000 0.99971 1.01662 1.02882 0.994441.50000 0.99470 1.01761 1.02576 0.990282.00000 0.98946 1.01797 1.02290 0.985422.50000 0.98396 1.01767 1.02011 0.979943.00000 0.97818 1.01671 1.01729 0.973883.50000 0.97210 1.01508 1.01429 0.967304.00000 0.96570 1.01274 1.01102 0.960264.50000 0.95896 1.00970 1.00734 0.952825.00000 0.95186 1.00594 1.00314 0.94502

Meisberger Ratio

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Cs137

Ir192

Au198

Ra226

Dose Rate Calculation - Linear Sources

Quantization Method - divide source into multiple point sources

Quantization Method

Quantization Method

Dose Rate Calculation - Linear Sources

Sievert Integral

L = active length

y = perpendicular distance from source to calculation point

= effective attenuation coefficient of wall

= as defined in diagram

2

1

dsec)texp(}Ly/)BBA{(dt/)y,x(dD stiss

Sievert Integral Source Geometry

% difference between 1.5cm Ra source and point Ra source

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dist(cm) 1.5 cm AL point % diff0.25 50.67 126.23 59.86%0.50 20.26 31.51 35.71%0.75 10.84 13.98 22.48%1.00 6.67 7.85 15.05%1.50 3.20 3.47 7.91%2.00 1.85 1.95 4.89%2.50 1.20 1.24 3.06%3.00 0.83 0.85 2.85%3.50 0.61 0.62 2.16%4.00 0.47 0.47 0.81%4.50 0.37 0.37 0.40%5.00 0.30 0.30 -0.52%

cGy/mg-hr

Away & Along Tables

Young - Batho

Shalek - Stovall

Krishnaswamy

Young and Batho,British Journal of Radiology, 37, 38, 1962.

Young-Batho Source Geometry

Shalek and Stovall, American Journal of Roentgenology, Radium Therapy and Nuclear Medicine, CII, 662, 1968.

Shalek & Stovall Example

Krishnaswamy, Radiology 105, 181, 1972.

ACR Standardswww.acr.org

ACR Standard on Brachy Physics Manually-Loaded Temporary Implants Section IV.C.3.

An additional and independent method should be used to validate the dose calculation results of the computerized planning systems. This validation should be consistent with the written prescription and completed before 50% of the dose is delivered.

End of Lecture 1

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(-t)}/{}]0t

D = (dD0/dt)[-{exp(-T)/} +{1/}]

D = ((dD0/dt) /)[1-exp(-T)]

D = (dD0/dt)Tav[1-exp(-T)]

D = (dD0/dt)Tav[1-exp(-T/Tav)]

t

00 dt)texp()dt/dD(D

milliCuries destroyed

D = (dD0/dt)Tav[1-exp(-T)]

D = (dD0/dt)Tav- (dD0/dt)exp(-T) Tav

D = (dD0/dt)Tav - (dDT/dt) Tav

Radiation Protection

Time

Distance

Shielding

Time

Dose is proportional to exposure time

Half the time equals half the dose

Distance

For radiation protection purposes can assume dose follows inverse square law.

Dose at 1 cm = 4 * Dose @ 2cm

= 0.25 Dose @ 0.5cm

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)

Half -Value Layers

Isotope HVL(mm of Pb)226Ra 8.0137Cs 5.5192Ir 2.5198Au 2.5125I 0.025103Pd 0.008

Radiation Protection Example 125I CalculationAssume 125I prostate implant 10 cm to patient

surface, 50 mCi total activity, tissue attenuates 95% of dose at 10 cm (5% transmission).

(dXsurface /dt) = 1.51 * 50 * (1/10)2 * 0.05 =38 mR/hr

(dX1m/dt) = 38 mR/hr * (10/100)2 = 0.4 mR/hr