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Internal Radiation Dosimetry

Internal Radiation Dosimetry. J.D. Kalen, Ph.D. Radiation Dose (Quantities and Units). Radiation Dose (D) The quantity of radiation energy deposited in an absorber/gm of absorber material Units: rad; r adiation a bsorbed d ose 1 rad = 100 ergs deposited/gm of absorber

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Internal Radiation Dosimetry

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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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