Internal Radiation Dosimetry (MIRD method)

1. Internal Radiation Dosimetry (MIRD method) Candidate: Durgesh Kumar Dwivedi Moderator: Dr. Chetan Patel Department of Nuclear Medicine, AIIMS, New Delhi, India

2. Introduction Calculation of radiation energy deposited by internal radionuclide is the subject of internal radiation dosimetry.

3. Because these radiation doses are received from radioactive materials within the body, they are normally referred to as internal doses. These doses are calculated from standardized assumptions and procedures. • Internal dose calculations in nuclear medicine normally use the techniques, equations, and resources provided by the Medical Internal Radiation Dose (MIRD) Committee of the Society of Nuclear Medicine.

4. MIRD committee publications • MIRD committee of SNM has published many useful reports and other aids to calculating absorbed dose estimates in nuclear medicine applications. • The aim of this committee is to develop a dosimetry system (now called MIRD schema) for diagnostic nuclear medicine. However, the methods have also applied to radionuclide therapy. • First, there is a series of technical reports, called MIRD pamphlets, which contain much useful and varied information about dose models and data. • There is also series of reports that detail metabolic models and dose estimate reports (DERs) published by MIRD.

5. Radiation dose (D) and radiation dose rate (dD/dt) • The energy absorbed from radiation per unit mass of a substance is called radiation absorbed dose. • Radiation dose rate is the absorbed dose per unit time,designated by D’ . unit is rads/minute

6. Flow chart illustrating MIRD methodology

7. Internal Radiation Dosimetry MIRD Schema Concept of Source and Target Organ(s)

8. Target Organ Source Organs TargetOrgan In MIRD schema the body is considered as a combination of Sourceorgans (i.e dose with significant uptake of radiopharmaceutical) and Target organs (i.e. those being irradiated by source organs)

9. Source and target may be the same organ. In general, organs other than the target organ is considered to be source organ if they contain concentrations of radioactivity that exceed the average concentration in the body. • MIRD method allows one to calculate radiation dose to a target organ from radioactivity in one or more source organs in the body.

10. Steps involve for calculating radiation dose to a target organ from source organ • Calculation of rate of energy emission by radionuclide in source organ. • Calculation of rate of energy absorption by radionuclide in target organ. • Calculation of average dose rate dD/dt. 4. Calculation of average dose D.

11. Dose rate • Dose rate is the amount of energy absorbed per unit time per unit mass of material, it varies directly with the activity per unit mass of absorbing material and the amount of energy released (emitted) per nuclear transition. In the example of a huge volume of tissue, all of the energy emitted is absorbed; therefore, if we know the energy emitted per unit time, we know the energy absorbed per unit time, expressed as follows: • Since activity is the number of transitions per unit time,

12. If all of the energy emitted is absorbed in the material, • The terms that represent the components of dose rate can be replaced by the symbols used in the MIRD schema: D’ = absorbed dose rate, A = amount of activity, m = tissue mass, and E = the average energy emitted per nuclear

13. where k is the constant that will yield the dose rate in the desired units. For example, to calculate dose rate in rad per hour if A is in microcuries (µCi), m is in grams (g), and E is in megaelectron volts (MeV) per transition, k has a value of 2.13, derived as follows:

14. Step1: Energy emission from source organ One microcurie (3.7*104decay/s) of radionuclide will emit energy at rate of 3.7*104 * E MeV/s Rate of energy emission = 3.7 * 104 * 1.6 * 10-6 *3600 * E ergs/hr*Ci = 213 E ergs/hr*Ci = 213 E ergs/1.332*108 Bq*sec = 1.6*10-6 E ergs/Bq*sec For more than one type of radiation with different abundance = 213 i niEi ergs/hr*Ci = 1.6*10-6 niEi ergs/Bq *sec = 1.6*10-13 niEi Joules/Bq. sec Source organ

15. Step 2: Rate of energy absorption by target organ Define a term “Absorbed fraction” Energy absorbed in target vol.(rk) from radiation i i (rkrh)= ------------------------------------------------------------------- Energy emitted in source vol. (rh) as radiation i Rate of energy absorption by the target From radiation i = 213niEii (rk,  rh) (ergs/Ci*hr) = 1.6*10-13 niEi i (rk,  rh) Joules/Bq. sec Source TargetOrgan

16. Absorbed fraction, Ф cont… • Fraction of energy emitted by the source organ that is absorbed by the target organ is given by absorbed fraction Ф . • It depends upon • A) amount of radiation reaching target organ • B) distance attenuation b/w source and target organ • C) volume and composition of source and target

17. The notation Фi(rk rh) is used to indicate absorbed fraction for energy delivered from a source organ (rh) to a target organ (rk) • ∑i is the sum of all terms when i changes from 1 to n.

18. In most problem encountered in nuclear medicine, the radioactivity is distributed within target volume T itself. In that case absorbed fraction is self absorbed fraction. • Determination of Ф requires Computational techniques. • The maximum value of Ф can only be 1 (i.e. all energy is absorbed in target) (For alpha, beta particles) . • The min. value of Ф is 0 (No absorption). (0<= Ф<=1)

19. Step 3: Dose rate in target Organ Rate of energy absorption by the target from radiation i = 213niEii (rk,  rh) (ergs/Ci*hr) Rate of energy absorption per gm of tissue = 213iniEii (rk,  rh) / (mk*100) rad/ Ci/hr where mk is the mass of target organ in gm Thus, Dose rate = 2.13iniEii (rk,  rh) / mk rad/ Ci*hr =1.6*10-13 iniEii (rk,  rh) Gy/Bq.sec

20. Dose rate = 2.13iniEii (rk,  rh)/ mk rad/ Ci*hr • By defining Δi =2.13 niEi • Equilibrium Absorbed Dose Constant, Δ • Energy emitted per unit of activity*time (later given as cumulated activity) is given by Equilibrium Absorbed Dose Constant, Δ Where, Ei is avg energy (in MeV) of ith emission and Ni is relative frequency of that emission by the radionuclide. • In traditional unit; Δi = 2.13 Ni EI (rad.gm/ µCi. hr) =213 Ni EI (ergs / µCi. hr) • Δi = 1.6 * 10-13 Ni EI (Gy.kg/ Bq.sec )(In SI unit)

21. By defining Δi =2.13 niEi , then dose rate will be: dD/dt = [1/mk] iΔi i (rk,  rh) rad/ Ci*hr • If the source organ contains A(t) Ci at time t, then dose rate dD/dt = [A(t)/mk] iΔi i (rk,  rh) rad/hr

22. Step 4: Average dose, D • The radioactivity A(t) localized in an organ is generally a fraction (f) of the administered activity Ao, and is being eliminated with T1/2(eff) i.e. A(t) = f Ao e(-0.693/ T1/2(eff) • Since dD/dt = [A(t)/mk] iΔi i (rk,  rh) rad/hr Thus the dose rate is continuously decreasing with time The total dose to the pt from t=o to the time when dose rate has finally reduced to 0 .

23. Avg dose D= ∫ dD/dt dt (0-∞) • This leads to (rad) • From this, it is evident to minimize the radiation dose to the patient, smaller the Ao, with shorter T1/2(eff) and radionuclide with smaller absorbed fraction are desired. D(rk  rh) = 1.44 T1/2(eff)fAo/mkiΔii (rk  rh)

24. Above equations assume that the uptake in the organ is instantaneous, this does not have to be so , above equation can not be used to describe the time behavior of radioactivity in blood or in organs one and two. • For these exact time activity curve should be used to calculate Cumulated activity Ã.

25. Cumulated Activity à • Radiation dose delivered to target organ depends upon: a) Amount of activity present in source organ b) Time for which activity is present Product of above two factors is Cumulated Activity à SI unit for à is Bq*sec Mathematically: Time activity curve can be quiet complex and thus above equation may be difficult to analyze. However, certain assumptions can be made to simplify

26. Situation 1:uptake by organ is instantaneous, and there is no biological excretion • A(t) = Ao e-0.693/Tp • Thus à ≈ Ao ∫e-0.693/Tpdt (0-∞) = TpAo/0.693 = 1.44Tp Ao

27. Situation 2:Uptake is instantaneous, and clearance is by biologic excretion only • In this situation, biologic excretion must be carefully analyzed. It can be set of exponential excretion, with a fraction f1 of initial activity Ao excreted by biologic half life Tb1 , a fraction f2 with half life Tb2 the cumulated activity then is given by: Ã ≈ Ao ∫f1e-0.693/Tb1dt + Ao ∫f2e-0.693/Tb2dt + …… (0-∞) = 1.44 Tb1f1Ao + 1.44 Tb2f2Ao + …..

28. Situation 3:Uptake is instantaneous but clearance by both physical and biologic excretion are significant • In this case total clearance is described by Single term Effective half life Te Te = TpTb/ (Tp+Tb) Then à ≈ 1.44 Te Ao

29. Situation 4:Uptake is not instantaneous • That is significant amount of physical decay occurs, Cumulated Activity is then: Ã ≈ 1.44 Ao Te (Tue/ Tu) Tue is the effective uptake half- time Tue = TuTp/ (Tu + Tp)

30. Average absorbed dose • The energy absorbed by the target organ divided by the target mass mk gives average absorbed dose in Grays. • Avg absorbed dose Ď (rk rh) = (Ã/ mk) ∑i Фi (rk rh) Δi

31. Dose reciprocity theorem • The specific absorbed fractionis given by Ф = Ф/mt This theorem states that for a given organ pair the specific absorbed fraction is same regardless of which organ is the source and which is target. Фi (rk rh) = Фi (rh rk) i.e Фi (rh rk) = Фi (rk rh) mh mk Фi (rh rk) = (mh/mk) * Фi (rk rh) This is useful when tables for Ф are not available for all source target organ pairs . If we know one we can calculate for other.

32. Mean dose per cumulated activity, S factor • Most of the quantities we need for the estimation of dose are either physical or anatomical. A convenient quantity has been introduced for making the dose calculations simple. The quantity is called S- factor and is defined as: S (rk rh) = (1/mk) ∑i Фi (rh rk) Δi Unit of S-factor is Gy/Bq.s

33. Flow chart illustrating MIRD methodology • Given the value of S and cumulated activityÃ, the average dose to an organ is given by D(rk rh) = Ã * S (rk rh)

34. If the area under the time activity curve for a source organ (Ã) may be normalized to the amount of activity administered, this has been defined by the MIRD as the source organ “residence time” = Ã/Ao The MIRD concept of residence time has often caused confusion because of its apparent units of time (even though it really expresses the number of nuclear transitions that occur in a source region). Nonetheless, this definition can be used to write Dose Equation as: D = Ao S D/ Ao = * S (mGy/ MBq)

35. Then the absorbed dose is calculated by multiplying the residence time ( or Ã) by appropriate S- values. Dk = Ao∑ h S (rk rh)

36. Problem: To calculate the radiation dose to the liver for an injection of 100 MBq of 99mTc- sulfur colloid. Assuming that 60% of the activity is trapped by the liver, 30% by the spleen, and 10% by red bone marrow, with instantaneous uptake and no biologic excretion. • Solution: 3 source organs; cumulated act. Ã= 1.44Tp Ao ÃLI = 1.44* 6hr* 0.60* 100MBq= 1.87*106 MBq. Sec Ãsp = 1.44*6.0*0.3*100MBq. = 9.33*105MBq. Sec ÃRM= 1.44*6.0*0.10*100MBq = 3.11* 105 MBq.sec Values of S for 99mTc are: S(LI to LI) = 3.23* 10-6 mGy/MBq.sec (Self + Cross) S(SP to LI) = 7.20* 10-8 mGy/MBq.sec S(RM to LI) = 8.93* 10-8 mGy/MBq.sec

37. Thus the absorbed doses are: • Since D (rk rh) = Ã * S (rk rh) D(LI to LI) = (1.87*106 MBq. Sec)*(3.23* 10-6 mGy/MBq.sec) = 6.04 mGy D(SP to LI) = (9.33*105MBq. Sec)*(7.20* 10-8 mGy/MBq.sec) = 6.72* 10-2 mGy D(RM to LI) = (3.11* 105 MBq.sec )*(8.93* 10-8 mGy/MBq.sec) = 2.78*10-2 mGy The avg total dose to liver is D = 6.04+ 6.72*10-2 2.78* 10-2 mGy = 6.14mGy (~ 0.6 rads)

38. Current trends in Patient-Specific dosimetry • Radionuclide therapy based on patient-specific dosimetry offers the potential for optimizing the dose delivered to the target tumor through utilization of measured radiopharmaceuticals kinetics specific to the individual. • Kinetic data is obtained for organs which concentrate the radiopharmaceuticals (Source organ), the whole body, and for all excretion pathways (i.e. temporal sampling of blood, excreta, tumor). • As the use of radiopharmaceuticals in therapy is increasing, it is important that internal emitter therapy achieve a higher level of quality.

39. In managing the therapy, It is ideal to: • Acquire the time sequence quantitative data using diagnostic activities of therapeutic RP to determine the biodistribution over the relevant time (using planar and tomographic approaches). • Estimate the radiation dose to the tumor per unit administered activity using patient- specific biokinetic and anatomic data. SPECT and PET provide activity distribution in patient • Predict the radiation dose to be delivered to the patient under the therapy regimen through extrapolation of the diagnostic dose. However, the biokinetics for the diagnostic and therapy administered activities might not be identical. • Use more sophisticated dosimetry approach to therapy to evaluate individual patients response to therapy e.g. Tumor control probability.

40. Limitation of the MIRD method • Since accurate determination of anatomical size of organ and its geometrical relationship with organs of interest and also biological data (extrapolated from animal data) can’t be precisely determined in routine practice, it is difficultto calculate the dose with great accuracy. • MIRD provides dose to the target organ as an average, without permitting the determination of a maximum and minimum within each target organ.

41. Software packages for dosimetry of internal emitters • Number of software packages were developed for S-value based dose assessment of internal emitters. • Most widely used of these , MIRDOSE3, incorporate S factors for 223 radionuclide. • The MIRDOSE code has been rewritten in JAVA for grater computer platform and renamed : Organ Level Internal Dose Assessment (OLINDA). For more than 800 radionuclide. It has been deployed on RAdiation Dose Assessment Resource (RADAR) website for nuclear medicine studies. • MABDOSE another package (University of Colorado), allows with simplified anatomic details.

43. Snapshot of ICRP method • ICRP has developed equations for internal dosimetry system which is identical to MIRD equation, simply with different names for the factors. • In ICRP 30 system, the cumulated dose equivalent is given by: H= 1.6* 10-10∑s Us SEE(T S) (In sieverts)

44. ICRP 60 has recommended the weighting factors for different organs. • ICRP has published a compendium of Radiation Dose Estimates for radiopharmaceuticals(~120 RP), in ICRP 53 and 80.

45. A comparison of ICRP and MIRD formulae shows that they are practically identical (leaving aside the numerical factors which are involved in the conversions): Symbols used by • ParametersMIRDICRP Target region rkT source region rhS Absorbed fraction Фi(rk rh) AF for radiation i (T S) Eqm absorbed dose ΔiγiEi constant for ith radn. Cumulated activity ÃUs mean dose per Cum Act S(rk rh) SEE or (T S) specific effective energy

46. Conclusion • Internal radiation dosimetry has been established for nearly 3 decades. • A variety of models representing the body and various organs have been well established, and facilitated in various software applications, so that to calculate doses in our routine. • 3D distribution of dose for individual patients and more realistic phantoms must be more sharpened. • The area of radiobiology for internal emitters is not very well developed at present.

47. Thank You

49. A Monte Carlo method is a technique that involves using random numbers and probability to solve problems. The term Monte Carlo Method was coined by S. Ulam and Nicholas Metropolis in reference to games of chance, a popular attraction in Monte Carlo, Monaco • Monte Carlo simulation is a method for iteratively evaluating a deterministic model using sets of random numbers as inputs. This method is often used when the model is complex, nonlinear, or involves more than just a couple uncertain parameters.

50. Monte Carlo simulation the five steps listed below: • Step 1:Create a parametric model, y = f(x1, x2, ..., xq). • Step 2:Generate a set of random inputs, xi1, xi2, ..., xiq. • Step 3:Evaluate the model and store the results as yi. • Step 4:Repeat steps 2 and 3 for i = 1 to n. • Step 5:Analyze the results using histograms, summary statistics, confidence intervals, etc.