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Radiology Dosimetry Methods and Applications

Understand radiation dosimetry calculations using the absorbed fraction method for determining cumulative activity and absorbed dose in various radiation therapy scenarios. Learn about radionuclide properties, uptake kinetics, and equilibrium dose constants for effective radiation treatment planning.

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Radiology Dosimetry Methods and Applications

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  1. Internal Radiation Dosimetry J.D. Kalen, Ph.D.

  2. Radiation Dose (Quantities and Units) • Radiation Dose (D) • The quantity of radiation energy deposited in an absorber/gm of absorber material • Units: rad; radiation absorbed dose • 1 rad = 100 ergs deposited/gm of absorber • SI units: gray (Gy): 1 Gy = 1 joule/kg absorber • note: 1 joule = 107 ergs 1Gy = 100 rads

  3. Calculation of Radiation Dose(Absorbed Fraction Method) 3 Step Process: 1) Amount of activity and time within the source organ 2) Amount of radiation emitted from the source organ; energy and emission frequency dependent 3) Fraction of energy absorbed by the target organ; dependent on a) characteristics of organ (tissue) b) positional relationship of source to target.

  4. Calculation of Radiation DoseCumulative Activity (A) ~ Cumulative Activity: The amount of radiation delivered to the organ and the length of time the activity is present within the organ. Units:(mCi-hr) ~ 8 A =  A(t) dt A(t) Activity (mCi) 0 time activity curve time (hr)

  5. ~ Cumulative Activity (A) • Four situations • Instantaneous uptake with physical decay • 90Y Microspheres (Unresectable Hepatocellular Carcinoma) • Instantaneous uptake with clearance by biologic excretion. • Radionuclide T1/2 >> Biologic T1/2 • Instantaneous uptake with clearance by biologic excretion and physical decay. • 131I (Hyperthyroidism and Thyroid Cancer) • 90Y (Zevalin) and 131I (Bexxar) radioimmunotherapy • Non-instantaneous uptake with clearance by biologic excretion and physical decay.

  6. ~ Cumulative Activity (A) Situation 1: Instantaneous uptake; no biologic excretion (Unresectable Hepatocellular Carcinoma) i.e.: 90Y Microspheres • MicroSphere Properties: • Glass sphere diameter: 20-30 mm • Trapped in the vasculature • 1 mg contains  22,000 – 73,000 spheres • 90Y Properties: • Pure β- emitter • Decays to 90Zr • T1/2 (hr): 64.1 • Eβ ave (MeV): 0.9348; Range (mm): 4

  7. ~ Cumulative Activity (A) Situation 1: Instantaneous uptake; no biologic excretion A(t) = A0 exp(-0.693*t/Tp) Activity (mCi) Tp = physical half-life of radionuclide A0 = initial activity present in organ time (hr) ~ 8  Semi-log A =A0exp(-0.693*t/Tp )dt 0 Activity (mCi) A = TpA0 = 1.44(A0Tp) 0.693 time (hr)

  8. Cumulative Activity Trap vs Shunt to Lungs inject 4 mCi of 99mTc MAA Shunt (F) = [Lungs/(Lungs + Liver)] x 100% =10%

  9. ~ Cumulative Activity (A) Situation 1: Example (90Y: Unresectable Hepatocellular Carcinoma) 90% retention in Liver (1-F) 10% shunting to the Lung (F) A(Liver) = 1.44(Tp)(1-F)(A0) = 1.44(64.16 hr)(0.9)[A0(Ci)] ~ ~ A(Lung) = 1.44(Tp)(F)(A0) = 1.44(64.16 hr)(0.1)[A0 (Ci)]

  10. Cumulative Activity Situation 2: Instantaneous uptake; biologic excretion no physical decay, or Tp(1/2) >> biologic excretion i.e. 131I (8.04 days) >> Tb ( few hrs); Decay fraction: (< 5%) Tb1 Semi-log f1 Tb2 f2 Activity Tb3 f3 time ~ A = 1.44 Tb1 f1 A0 + 1.44 Tb2 f2 A0 + 1.44 Tb3 f3 A0

  11. Cumulative Activity Situation 3: Instantaneous uptake Clearance by biologic and Physical decay Determine effective T1/2 Effective T1/2 = Te 1 Te = Tp Tb 1 + 1 = Te Tp Tb Tp + Tb ~ A = 1.44(Te)(A0) note: Te is always shorter than Tp and Tb

  12. Cumulative Activity Situation 3: Instantaneous uptake 131I (Hyperthyroidism) 131I Tp (days): 8.04 Tb (days): 13.22 Te = Tp Tb = 5 days Tp + Tb ~ A = 1.44(Te)(A0)

  13. Cumulative Activity Situation 3: Uptake is NOT Instantaneous significant amount of physical decay occurs during uptake process. A(t) = A0(1-e-0.693t/T(u,e)) Activity ~ A = 1.44 Ao Te Tue Tu Tue = effective uptake Tu = uptake half-life Te = effective excretion time

  14. Equilibrium Absorbed Dose Constant (D) Step 2: Determine amount of radiation emitted by source organ* g-rad Di = 2.13 Ni Ei mCi-hr Ei = ave. energy (MeV) of the ith emission Ni = # emitted per disintegration Dtotal = SiDi = D1+ D2+ … + Dn Dtotal is obtained from tables *the energy emitted per nuclear disintegration: 1 MeV/dis = 2.13 g-rad/(mCi-hr)

  15. Equilibrium Absorbed Dose Constant (D) Step 2: Example (90Y) 90Y emits b particles: 100% of its disintegrations with Eb ave= 0.9348 MeV. Di = 2.13 Ni Ei Dtotal = SiDi = Dβ g-rad Dtotal = Db = 2.13 (1.0) 0.9348 = 1.99 mCi-hr

  16. Equilibrium Absorbed Dose Constant (D) Step 2: Example (131I) 131I emits b, particles Di = 2.13 Ni Ei Dtotal = SiDi = Dβ1 +D β2 + …+ D βn + D1+D2+ …+Dn Db1 = 2.13 (0.0213) 0.069 = 0.003 Db4 = 2.13 (0.894) 0.192 = 0.365 Dg14 = 2.13 (0.812) 0.364 = 0.629 Dg7 = 2.13 (0.0606) 0.284 = 0.036 Dg17 = 2.13 (0.0727) 0.637 = 0.098 g-rad = 1.133 mCi-hr

  17. Equilibrium Absorbed Dose Constant (D) Step 2: Example g-rad Dtotal mCi-hr ~ A is the cumulated activity (mCi-hr) Dis the total energy emitted per mCi-hr ~ A x D = total energy emitted (g-rad) or (ergs) 1 g-rad = 1 erg

  18. Absorbed Fraction (f) Step 3: Determine the fraction of radiation emitted by the source organ that is absorbed by the target organ. Absorbed Fraction f is dependent on: 1) type and energy of the emission 2) anatomical relationship of target-source pair ~ Total energy absorbed (g-rad) = A Si fiDi Average absorbed Dose (rad) = ASi fiDi ~ mt

  19. Average Absorbed Dose (D) Average absorbed Dose (rad) = ASi fiDi ~ mt mt: organ mass “average female/male” fi: fraction of energy delivered to target organ from all source organs Di: amount of energy emitted from source organ f is complicated for energies > 10 keV (penetrating; g-rays) f < 10 keV (non-penetrating radiation; b, x-rays)

  20. Average Absorbed Dose (D) Energies < 10 keV (non-penetrating radiation) f = 0 for (penetrating radiation) f = 1 for (non-penetrating radiation): source and target organs are the same radiation is locally absorbed within the source organ ~ Average absorbed Dose (rad) = ASi fiDi mt f = 1 ~ <D> (rad) = ASi Dnp mt

  21. Average Absorbed Dose (D) Example: (non-penetrating radiation) Compute absorbed dose delivered to the Liver. 90Y emits b particles: 100% of its disintegrations with Ebave = 0.9348 MeV. Di = 2.13 Ni Ei Dtotal = SiDi = Dβ= Dnp g-rad Dtotal = Db = 2.13 (1.0) 0.9348 = 1.99 mCi-hr Dtotal = Db=1.6x10-13 NiEi kg-Gy Bq-Sec =1.49x10-13

  22. Average Absorbed Dose (D) Example: (non-penetrating radiation): 90Y Compute absorbed dose delivered to the Liver.

  23. Average Absorbed Dose (D) Example: (non-penetrating radiation): 90Y Compute Activity to be delivered based on Dose to the Organ.

  24. Average Absorbed Dose (D) Example: (non-penetrating radiation) 131I Di = 2.13 Ni Ei Dtotal = SiDi = Dβ1 +D β2 + …+ D βn + D1+D2+ …+Dn Db1 = 2.13 (0.0213) 0.069 = 0.003 Db4 = 2.13 (0.894) 0.192 = 0.365 Dg14 = 2.13 (0.812) 0.364 = 0.629 Dg7 = 2.13 (0.0606) 0.284 = 0.036 Dg17 = 2.13 (0.0727) 0.637 = 0.098 Dt = 1.133 g-rad mCi-hr Dnp = 0.368

  25. Mean Dose per Cumulated Activity (S) [for penetrating radiation: -rays] Average absorbed Dose (rad) = ASi fiDi ~ mt Non-penetrating radiation: fi=1 Source and target organs: same Penetrating radiation: fi=0 Source and target organs: Different Source/ Target target target

  26. Mean Dose per Cumulated Activity (S) [for penetrating radiation: -rays] S = 1 Si fiDi rad mCi-hr mt F = f specific absorbed fraction mt S = Si FiDi

  27. Average Dose to an Organ (D) _ ~ D = A x S ~ A : Cumulative Activity (mCi-hr) (calculate) S: Mean dose per cumulated Activity (rad/ mCi-hr) (look-up table) D: Average dose (rad)

  28. Mean Dose per Cumulated Activity (S) Source Organs S(rad/ mCi-hr) for I131 Target Organs

  29. 123I Whole Body Scan Source Target

  30. Average Dose to an Organ (D) Example: A patient is to be treated with 131I for Hyperthyroidism. It is determined by prior studies with a tracer dose of 131I that the thyroidal uptake is 60%, and the effective half-life of iodine in the thyroid gland is 5 days. Assume instantaneous uptake (Tu << Tp = 8 days).

  31. Average Dose to an Organ (D) Te = Tp Tb Tp + Tb ~ A = 1.44(Te)(A0) Te = 5 days = 120 hrs ~ A = 1.44(120 hr)(0.6)(1,000 mCi) = 103,680 mCi-hr/mCi administered

  32. S-factor assumes 20 gm Average Dose to an Organ (D) S(Thy Thy) = 2.2 x 10-2 rad/(mCi-hr) _ ~ D = A x S D = 103,680 mCi-hr/mCi admin. x 2.2 x 10-2 rad/(mCi-hr) = 2,280 rad/mCi administered Note: Inspection of the S table for 131I reveals that in comparison to the Thyroid as the source organ, all other organs produce a much smaller S value.

  33. Thyroid Mass Collimator: Pinhole Matrix: 128 x 128 Calibrate Pixel: 0.06 cm2/pixel ROI: 405 pixels Mass: [(# pixels)(Pixel Cal)1.26](0.86) Mass: 48 g

  34. MIRD D = A x S A = 1.44 x Ag (Ci) x T1/2(hr) S = (1/mnorm) i I (g-rad /Ci-hr) Mnorm = 20 g Internal Dosimetry Isotope: 131I Thyroid Uptake: 60% A0 = 1,000 Ci T1/2 eff = 5 days Thyroid Mass = 48 g

  35. MIRD D = A x S A = 1.44 x Ag (Ci) x T1/2(hr) A = 103,680 (Ci-hr) S = (1/mnorm) i I (g-rad/Ci-hr) S = 0.022 g-rad/Ci-hr D = 2,280.9 rad (Mnorm = 20 g) D = A x S x (20/48) D = 950 rad/Ci administered note 1 rad = 1 rem in tissue D = 950 rem/Ci administered Internal Dosimetry Isotope: 131I Thyroid Uptake: 60% A0 = 1,000 Ci T1/2 eff = 5 days Thyroid Mass = 48 g • Dose (rem) = Dose (rad) x RBE • RBE = relative biologic effectiveness ; effect of different radiation on biologic material. • RBE (, , x-ray) = 1 ; RBE () = 20

  36. MIRD D = A x S A = 1.44 x Ag (Ci) x T1/2(hr) S = (1/mnorm) i I (g-rad/Ci-hr) S = 0.022 g-rad/Ci-hr D = A x S x (20/Measured Thyroid Mass) Internal Dosimetry

  37. MIRD D = A x S S = 0.022 g-rad/Ci-hr D = (A0)(1.44)(% Uptake)(Teff)(S)(20g/Measured Thyroid Mass) Internal Dosimetry Uptake Probe Image: Pinhole

  38. Internal Dosimetry Dose: Diffuse Goiter: 10,000 rad Uni-nodular Goiter: 25,000 rad Multi-nodular Goiter: 15,000 rad Ablate: 30,000 rad A0(Ci) = (D rads)(Measured Thyroid Mass/20g) (1.44)(% Uptake)(Teff hrs)(0.022 g-rad/Ci-hr)

  39. Average Dose to an Organ (D) Example: Calculate the radiation dose to the Liver for an injection of 3 mCi of 99mTc sulfur colloid. Assume 60% of the activity is trapped by the liver, 30% by the spleen, and 10% by the red bone marrow, with instantaneous uptake and no biologic excretion. ~ A = 1.44(Tp)(A0) ~ ALIVER = 1.44 (6 hr)(0.6)(3,000 mCi) = 15,600 mCi-hr ~ Aspleen = 1.44 (6 hr)(0.3)(3,000 mCi) = 7,780 mCi-hr ~ Arbm = 1.44 (6 hr)(0.1)(3,000 mCi) = 2,590 mCi-hr

  40. Average Dose to an Organ (D) S Values: S(Liver Liver) = 4.6 x 10-5 rad/mCi-hr S(Liver Spleen) = 9.8 x 10-7 rad/mCi-hr S(Liver RBM) = 9.2 x 10-7 rad/mCi-hr ~ D = A x S D(Liver Liver) = (15,600 mCi-hr) x (4.6 x 10-5 rad/mCi-hr) D(Liver Spleen) = (7,780 mCi-hr) x (9.8 x 10-7 rad/mCi-hr) D(Liver RBM) = (2,590 mCi-hr) x (9.2 x 10-7 rad/mCi-hr) D(total) = 0.718 + 0.0076 + 0.0024 = 0.728 rad

  41. Comparisons Tc99m Inject: 5,000 uCi T1/2: 6.03 hr A = 1.44 A0 Tp = 43,416 uCi-hr I131 Inject: 100 uCi T1/2: 8 days A = 1.44 A0 Tp = 27,648 uCi-hr I123 Inject: 300 uCi T1/2: 13.2 hr A = 1.44 A0 Tp = 5,702 uCi-hr Activity (uCi) Time (hr)

  42. Comparisons Tc99m I131 Source Organs Source Organs Target Organs

  43. Comparisons

  44. Cumulative Activity: Comparison ~ A = 1.44 Ao Te Tue = 1.44 Ao Te TuTp = 1.44 Ao TeTp Tu Tu(T u+T p) (T u+T p) Tue = Tu Tp Tu + Tp Activity Tue = effective uptake Tu = uptake half-life Te = effective excretion time

  45. Cumulative Activity Example: A radioactive (10 mCi) gas Tp(1/2) (20 sec) is injected in an intravenous solution. The lung uptake is Tu (30 sec) and is excreted (by exhalation) with a biologic Tb(1/2) (10 sec). Effective Uptake =Tue = Tu Tp = 30(20) = 12 sec. Tu + Tp 30 + 20 Effective Excretion =Te = Te Tp = 10(20) = 6.7 sec. 10 + 20 Te + Tp

  46. Cumulative Activity Situation 3: Example Te = 6.7 sec Tue = 12 sec Tu = 30 sec ~ A = 1.44 Ao Te Tue = 1.44 (10 mCi) 6.7 sec (12 sec) Tu 30 sec = 38.6 mCi-sec = 10.7 mCi-hr = 26.8 mCi-hr (Instantaneous Uptake)

  47. Cumulative Activity: Comparison ~ A = = 1.44 Ao TeTp (T u+T p) 26.8 mCi-hr: D(rad)= 2.5 x D(non-instantaneous uptake) Activity 10.7 mCi-hr time

  48. Medical Internal Radiation Dose • MIRD Limitations • Activity is uniformly distributed within a standard size organ • Absorbed Fraction f is based on standard models of human anatomy. • Calculation of Cumulated activity. • First based on animal studies • Different between disease states; uptake and decay

  49. Medical Internal Radiation Dose • MIRD • New techniques are developed • Actual distribution of activity is becoming available • Easy to implement

  50. MIRD-Summary Organ-specific Length of time and the amount of the radiopharmaceutical is within the organ. Obtained using Nuclear Medicine Techniques.

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