Internal Radiation Internal Radiation Dosimetry (MIRD method)Dosimetry (MIRD method)

Candidate: Durgesh Kumar DwivediCandidate: Durgesh Kumar Dwivedi

Moderator: Dr. Chetan PatelModerator: Dr. Chetan Patel

Department of Nuclear Medicine, Department of Nuclear Medicine, AIIMS, New Delhi, IndiaAIIMS, New Delhi, India

IntroductionIntroduction

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

Because these radiation doses are received from Because these radiation doses are received from radioactive materials within the body, they are radioactive materials within the body, they are normally referred to as normally referred to as internal dosesinternal doses. These doses . These doses are calculated from standardized assumptions and are calculated from standardized assumptions and procedures.procedures.

Internal dose calculations in Internal dose calculations in nuclear medicinenuclear medicine normally use the techniques, equations, and normally use the techniques, equations, and resources provided by the resources provided by the Medical Internal Radiation Medical Internal Radiation Dose (MIRD)Dose (MIRD) Committee of the Society of Nuclear Committee of the Society of Nuclear Medicine. Medicine.

MIRD committee publicationsMIRD 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.

Radiation dose (D) and radiation Radiation dose (D) and radiation dose rate (dD/dt)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

Identify source (r) and target(k) organs

Determine à from time activity curve

Look up S factor using appropriate table

Determine dose deliver to target from sourceDsoucre to target= ÃÃ *s

Sum contributions of doses from all sources to the targetDk= i Dsoucre to target

Flow chart illustrating MIRD Flow chart illustrating MIRD methodologymethodology

Internal Radiation Dosimetry Internal Radiation Dosimetry MIRD SchemaMIRD Schema

Concept of Concept of Source Source and and Target Target Organ(s)Organ(s)

Target Organ

Source Organs

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

Target Organ

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.

Steps involve for calculating radiation dose to a target organ from source organ

1. Calculation of rate of energy emission by radionuclide in source organ.

2. Calculation of rate of energy absorption by radionuclide in target organ.

3. Calculation of average dose rate dD/dt.

4. Calculation of average dose D.

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,

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

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:

Step1: Energy emission from Step1: Energy emission from source organsource 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

Step 2: Rate of energy Step 2: Rate of energy absorption by target organabsorption by target organ

Define a term “Absorbed fraction”

Energy absorbed in target vol.(rk) from radiation ii (rkrh) = ------------------------------------------------------------------- Energy emitted in source vol. (rh) as radiation i

Rate of energy absorption by the

target From radiation i = 213niEii (rk, rh) (ergs/Ci*hr)

= 1.6*10-13 niEi i (rk, rh) Joules/Bq. sec

Target Organ

Source

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

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.

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)

Step 3: Dose rate in target Step 3: Dose rate in target OrganOrgan

Rate of energy absorption by the target from radiation iRate of energy absorption by the target from radiation i = 213n= 213niiEEiii i (r(rk, k, r rhh) (ergs/) (ergs/Ci*hr)Ci*hr)

Rate of energy absorption per gm of tissueRate of energy absorption per gm of tissue = 213= 213iinniiEEiii i (r(rk, k, r rhh) / (m) / (mkk*100) *100)

rad/ rad/ Ci/hrCi/hr where mwhere mkk is the mass of target organ in gm is the mass of target organ in gm

Thus, Thus, Dose rateDose rate = 2.13= 2.13iinniiEEiii i (r(rk, k, r rhh) / m) / mkk rad/ rad/ Ci*hrCi*hr

=1.6*10=1.6*10-13 -13 iinniiEEiii i (r(rk, k, r rhh) Gy/Bq.sec) Gy/Bq.sec

Dose rate Dose rate = = 2.132.13iinniiEEiii i (r(rk, k, r rhh)/ m)/ mkk rad/ rad/ Ci*hrCi*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)

By defining Δi =2.13 niEi , then dose rate will be:

dD/dt = [1/mk] i Δi 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] i Δi i (rk, rh) rad/hr

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] i Δi i (rk, rh) rad/hrThus 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 .

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 TT1/2(eff)1/2(eff)ffAoAo/m/mkk i Δi i (rk rh)

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.

Cumulated Activity Cumulated Activity ÃÃ

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 Ã

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

Situation 1:Situation 1:

uptake by organ is instantaneous, and there is no uptake by organ is instantaneous, and there is no biological excretionbiological excretion

A(t) = Ao e-0.693/Tp

Thus à ≈ Ao ∫e-0.693/Tpdt (0-∞)

= TpAo/0.693

= 1.44Tp Ao

Situation 2:Situation 2:Uptake is instantaneous, and clearance is by biologic Uptake is instantaneous, and clearance is by biologic

excretion onlyexcretion 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:

à ≈ Ao ∫f1 e-0.693/Tb1dt + Ao ∫f2 e-0.693/Tb2dt + …… (0-∞)

= 1.44 Tb1f1Ao + 1.44 Tb2f2Ao + …..

Situation 3:Situation 3:Uptake is instantaneous but clearance by both physical and Uptake is instantaneous but clearance by both physical and

biologic excretion are significantbiologic 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

Situation 4:Situation 4:Uptake is not instantaneous Uptake is not instantaneous

That is significant amount of physical decay occurs,

Cumulated Activity is then:

à ≈ 1.44 Ao Te (Tue/ Tu)

Tue is the effective uptake half- time

Tue = TuTp/ (Tu + Tp)

Average absorbed doseAverage 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

Dose reciprocity theoremDose reciprocity theorem

The specific absorbed fraction is 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.

Mean dose per cumulated activity, Mean dose per cumulated activity, S factorS 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

Given the value of S and

cumulated activity Ã, the average dose to an organ is given by

D(rk rh) = Ã * S (rk rh)

Identify source (r) and target(k) organs

Determine à from time activity curve

Look up S factor using appropriate table

Determine dose deliver to target from sourceDsoucre to target= ÃÃ *s

Sum contributions of doses from all sources to the target Dk= i Dsoucre to target

Flow chart illustrating MIRD methodology

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)

Then the absorbed dose is calculated by multiplying the residence time ( or Ã) by appropriate S- values.

Dk = Ao ∑ h S (rk rh)

Problem: To calculate the radiation dose to the liver for an Problem: To calculate the radiation dose to the liver for an injection of 100 MBq of injection of 100 MBq of 99m99mTc- sulfur colloid. Assuming that 60% Tc- sulfur colloid. Assuming that 60% of the activity is trapped by the liver, 30% by the spleen, and of the activity is trapped by the liver, 30% by the spleen, and 10% by red bone marrow, with instantaneous uptake and no 10% by red bone marrow, with instantaneous uptake and no biologic excretion.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

ÃÃRM= 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.secS(RM to LI) = 8.93* 10-8 mGy/MBq.sec

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)

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.

In managing the therapy, It is In managing the therapy, It is ideal to:ideal to:

1.1. Acquire the time sequence quantitative data using diagnostic Acquire the time sequence quantitative data using diagnostic activities of therapeutic RP to determine the biodistribution activities of therapeutic RP to determine the biodistribution over the relevant time (using planar and tomographic over the relevant time (using planar and tomographic approaches).approaches).

2.2. Estimate the radiation dose to the tumor per unit administered Estimate the radiation dose to the tumor per unit administered activity using patient- specific biokinetic and anatomic data. activity using patient- specific biokinetic and anatomic data. SPECT and PET provide activity distribution in patientSPECT and PET provide activity distribution in patient

3.3. Predict the radiation dose to be delivered to the patient under Predict the radiation dose to be delivered to the patient under the therapy regimen through extrapolation of the diagnostic the therapy regimen through extrapolation of the diagnostic dose. However, the dose. However, the biokinetics for the diagnostic and therapy biokinetics for the diagnostic and therapy administered activities might not be identical.administered activities might not be identical.

4.4. Use more sophisticated dosimetry approach to therapy to Use more sophisticated dosimetry approach to therapy to evaluate individual patients response to therapy e.g. Tumor evaluate individual patients response to therapy e.g. Tumor control probability.control probability.

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 difficult to 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.

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.

Snapshot of ICRP methodSnapshot 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)

ICRP ICRP 6060 has recommended the weighting has recommended the weighting factors for different organs.factors for different organs.

ICRP has published a compendium of ICRP has published a compendium of Radiation Dose Estimates for Radiation Dose Estimates for radiopharmaceuticals(~120 RP), in ICRP radiopharmaceuticals(~120 RP), in ICRP 5353 and and 8080..

A comparison of ICRP and MIRD formulae shows that A comparison of ICRP and MIRD formulae shows that they are practically identical (leaving aside the they are practically identical (leaving aside the numerical factors which are involved in the numerical factors which are involved in the conversions):conversions):

Symbols used bySymbols used by ParametersParameters MIRDMIRD ICRPICRP Target region rk T

source region rh S

Absorbed fraction Фi(rk rh) AF for radiation i (T S)

Eqm absorbed dose Δi γiEi

constant for ith radn.

Cumulated activity à Usmean dose per Cum Act S(rk rh) SEE

or (T S)specific effective energy

ConclusionConclusion 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.

A Monte Carlo method is a technique that involves using A Monte Carlo method is a technique that involves using random numbers and probability to solve problems. The term random numbers and probability to solve problems. The term Monte Carlo Method was coined by S. Ulam and Nicholas was coined by S. Ulam and Nicholas Metropolis in reference to games of chance, a popular Metropolis in reference to games of chance, a popular attraction in Monte Carlo, Monacoattraction in Monte Carlo, Monaco

Monte Carlo simulation is a method for Monte Carlo simulation is a method for iterativelyiteratively evaluating a evaluating a deterministic model using sets of random numbers as inputs. deterministic model using sets of random numbers as inputs. This method is often used when the model is complex, This method is often used when the model is complex, nonlinear, or involves more than just a couple uncertain nonlinear, or involves more than just a couple uncertain parameters. parameters.

Monte CarloMonte Carlo simulation the simulation the five stepsfive steps listed below: listed below:

Step 1:Step 1: Create a parametric modelCreate a parametric model, y = , y = ff(x1, x2, ..., (x1, x2, ..., xxqq).).

Step 2:Step 2: Generate a set of random inputsGenerate a set of random inputs, x, xii1, x1, xii2, ..., 2, ..., xxiqiq..

Step 3:Step 3: Evaluate the modelEvaluate the model and store the results as y and store the results as yii..

Step 4:Step 4: RepeatRepeat steps 2 and 3 for steps 2 and 3 for ii = 1 to = 1 to nn..

Step 5:Step 5: Analyze the resultsAnalyze the results using histograms, summary using histograms, summary statistics, confidence intervals, etc.statistics, confidence intervals, etc.