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Basic Physics Concepts

Basic Physics Concepts. Firas Mourtada, Ph.D. D. ABR Associate Professor MD Anderson Cancer Center. Radioactive Decay. dN/dt = - l N dN/N = - l dt N(t) = N 0 e - l t N 0 = initial number N(t) = number at time t l = decay constant. Half - life. N(t)/N 0 = 0.5 = e - l t

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Basic Physics Concepts

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  1. Basic Physics Concepts Firas Mourtada, Ph.D. D. ABR Associate Professor MD Anderson Cancer Center

  2. Radioactive Decay dN/dt = -lN dN/N = -ldt N(t) = N0e-lt N0 = initial number N(t) = number at time t l = decay constant

  3. Half - life N(t)/N0 = 0.5 = e-lt ln(0.5) = -lt t = T1/2 = 0.693/l

  4. Half - Lives IsotopeHalf - Life 226Ra 1620 years 137Cs 30 years 198Au 2.7 days 192Ir 73.83 days 125I 59.4 days 103Pd 16.97 days

  5. 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

  6. 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.

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

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

  9. 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.

  10. 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.).

  11. 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

  12. 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

  13. 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.

  14. 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)

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

  16. 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

  17. Exposure Rate Constants Isotope Gd(R-cm2/mCi-hr) 226Ra (0.5mmPt) 8.25 137Cs 3.3 192Ir 4.69 198Au 2.38 125I 1.51 103Pd 1.48

  18. Conversion - mCi to mg Ra eq # of mg Ra eq = (Gx/GRa) * # of mCix

  19. Conversion - mCi to mg Ra eq Examples 137Cs # of mg Ra eq = (3.3/8.25) * # of mCi137Cs = 0.4 * # of mCi137Cs 192Ir # of mg Ra eq = (4.69/8.25) * # of mCi192Ir = 0.569* # of mCi192Ir

  20. 1 mCi of 137Cs -dN / dt = 3.7 * 107 dps = lN N = 3.7*107 dps / l l = 0.693 / T1/2 = 0.693 / (30 y * p * 107 s/y) l = 7.36 *10-10 s-1 N = 5.03 * 1016 atoms of 137Cs A0 = 6.023 * 1023 atoms per 137 g (1 mole) of 137Cs Mass of 1mCi = (5.03 * 1016 / 6.02 * 1023)*137 = 10 mg

  21. Dose Rate Calculation - Seeds dD/dt = A G f Btiss Bw Bs fan /d2 A = activity G = exposure rate constant f = f-factor - R to cGy conversion factor Btiss = attenuation and scattering in tissue Bw, Bs = attenuation and scattering for source encapsulation and self attenuation fan= anisotropy factor d = distance to calculation point

  22. Attenuation and Scattering Functions Tissue Btiss = 1+ka(md)kb Btiss = a + bd + gd2 +Dd3 Wall Bw = exp(-mwtw) Source Bs = exp(-msts)

  23. 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.

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

  25. Quantization Method

  26. Quantization Method

  27. Dose Rate Calculation - Linear Sources Sievert Integral L = active length y = perpendicular distance from source to calculation point m = effective attenuation coefficient of wall q= as defined in diagram

  28. Sievert Integral Source Geometry

  29. Away & Along Tables Young - Batho Shalek - Stovall Krishnaswamy

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

  31. Young-Batho Source Geometry

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

  33. Shalek & Stovall Example

  34. Krishnaswamy, Radiology 105, 181, 1972.

  35. ACR Standardswww.acr.org

  36. 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

  37. 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”

  38. 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)]

  39. 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

  40. Radiation Protection Time Distance Shielding

  41. Time Dose is proportional to exposure time Half the time equals half the dose

  42. Distance For radiation protection purposes can assume dose follows inverse square law. Dose at 1 cm = 4 * Dose @ 2cm = 0.25 Dose @ 0.5cm

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