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) = N 0 e - t N 0 = initial number N(t) = number at time t = decay constant

Half - life N(t)/N 0 = 0.5 = e - t ln(0.5) = - t t = T 1/2 = 0.693/

Half - Lives IsotopeHalf - Life 226 Ra1620 years 137 Cs30 years 198 Au2.7 days 192 Ir73.83 days 125 I59.4 days 103 Pd16.97 days

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

Brachytherapy Source Strength Specification 4 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 192 Ir wire or hairpins, which have core exposed when cut. ISO considers 192 Ir wire or hairpins to be a closed source.

Brachytherapy Source Strength Specification 4 Mass-Early 20th century 4 Activity-Early 20th century 4 Apparent Activity-Mid 20th century 4 Air Kerma Strength-Late 20th century

Mass 4 Radium –Mme. Curie prepared first 226 Ra standards, quantified amount by expressing mass of sample in g or mg.

Activity 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. 4 Method needed to permit correlation of 222 Rn to 226 Ra clinical experience.

Activity 4 Defined 1 Curie (Ci) to be the amount of radon in equilibrium with 1 g of radium. 4 A 1 Ci radon seed has same activity as 1 g of radium. 4 Early experiments indicated 1 Ci of radon emitted 3.7 * alpha per second. 4 1 Ci defined as 3.7*10 10 disintegrations per second (d.p.s.).

Activity 4 Later experiments established amount of radon in equilibrium with 1 g of radium gives 3.61 * d.p.s. 4 Curie definition remains 3.7 *10 10 d.p.s. 4 milliCurie (mCi) is 3.7 * 10 7 d.p.s. Roughly, conversion is 27 mCi per 1 GBq

Apparent Activity 4 Apparent activity - activity of a bare source that produces the same exposure rate at calibration distance as the specified source. 4 Expressed in mCi for brachytherapy. 4 Particularly useful for low energy photon sources, e.g., 125 I, 103 Pd

mgRaeq 4 Post WWII, other reactor produced isotopes began to be used as radium substitutes in radiotherapy. 4 Source strength was expressed in mCi, but also needed a method to take advantage of clinical experience with radium. 4 Used mgRaeq.

mgRaeq 4 mgRaeq yields same exposure rate at calibration distance as 1 mg Ra encapsulated by 0.5mm Pt. 4 The exposure rate at 1 cm from 1 mg Ra(0.5mm) is 8.25R/hr.  Exposure Rate constant (  ) is  = 8.25 [(R-cm 2 )/(mg-hr)] - Ra(0.5mm Pt)  = 7.71 [(R-cm 2 )/(mg-hr)] - Ra(1.0mm Pt)

mg-hours or mgRaeq-hours 4 Number of mg or mgRaeq in implant times the duration of the implant in hours

Source Specification Activity - mCi x 10 7 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 226 Ra that produces same exposure rate at calibration distance as specified isotope

Exposure Rate Constants Isotope   (R-cm 2 /mCi-hr) 226 Ra (0.5mmPt) Cs Ir Au I Pd1.48

Conversion - mCi to mg Ra eq # of mg Ra eq = (  x /  Ra ) * # of mCi x

Conversion - mCi to mg Ra eq Examples 137 Cs # of mg Ra eq = (  /  ) * # of mCi 137Cs = 0.4 * # of mCi 137Cs 192 Ir # of mg Ra eq = (  /  ) * # of mCi 192Ir = 0.569* # of mCi 192Ir

1 mCi of 137 Cs -dN / dt = 3.7 * 10 7 dps = N N = 3.7*10 7 dps / = / T 1/2 = / (30 y *  * 10 7 s/y) = 7.36 * s -1 N = 5.03 * atoms of 137 Cs A 0 = * atoms per 137 g (1 mole) of 137 Cs Mass of 1mCi = (5.03 * / 6.02 * )*137 = 10  g

Dose Rate Calculation - Seeds dD/dt = A  f B tiss B w B s  an /d 2  activity  exposure rate constant f = f-factor - R to cGy conversion factor B tiss = attenuation and scattering in tissue  w,  s = attenuation and scattering for source encapsulation and self attenuation  an = anisotropy factor d = distance to calculation point

Attenuation and Scattering Functions Tissue B tiss = 1+k  (  d) k  B tiss =  +  d +  d 2 +  d 3 Wall B w = exp(-  w t w ) Source B s = exp(-  s t s )

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.

Dose Rate Calculation - Linear Sources Quantization Method - divide source into multiple point sources

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

Sievert Integral Source Geometry

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 Standards

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 4 Permanent Implant –D = (dD 0 /dt ) T av 4 Temporary Implant with T 1/2 >>T –D = (dD 0 /dt ) T 4 Temporary Implant with T 1/2 not >> T –D = (dD 0 /dt ) T av [1 - exp(-T/T av )] –“milliCuries destroyed”

Temporary Implant T 1/2 not >>T D = (dD 0 /dt ) [-{exp(- t)}/{ }] 0 t D = (dD 0 /dt ) [-{exp(- T)/ } +{1/ }] D = ((dD 0 /dt ) / )[1-exp(- T)] D = (dD 0 /dt )  T av [1-exp(- T)] D = (dD 0 /dt )  T av [1-exp(-T/T av )]

milliCuries destroyed D = (dD 0 /dt )  T av [1-exp(- T)] D = (dD 0 /dt )  T av - (dD 0 /dt )  exp(- T) T av D = (dD 0 /dt )  T av - (dD T /dt ) T av

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 * 2cm = cm

Photon Energies IsotopeEnergies(MeV) 226 Ra (ave 0.83) 137 Cs Ir (ave 0.38) 198 Au I (ave 0.028) 103 Pd0.0201, (ave 0.021)

Half -Value Layers IsotopeHVL(mm of Pb) 226 Ra Cs Ir Au I Pd0.008

Radiation Protection Example 125 I Calculation Assume 125 I prostate implant 10 cm to patient surface, 50 mCi total activity, tissue attenuates 95% of dose at 10 cm (5% transmission). (dX surface /dt) = 1.51 * 50 * (1/10) 2 * 0.05 =38 mR/hr (dX 1m /dt) = 38 mR/hr * (10/100) 2 = 0.4 mR/hr