Internal Radiation
Dosimetry (MIRD method)
Candidate: Durgesh Kumar Dwivedi
Moderator: Dr. Chetan Patel
Department of Nuclear Medicine,
AIIMS, New Delhi, India
Introduction
Calculation of radiation energy deposited
by internal radionuclide is the subject of
internal radiation dosimetry.

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.
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.
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
Flow chart illustrating MIRD
methodology
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 source
Dsoucre to target= Ã *s
Sum contributions of doses from all sources to the target
Dk= i Dsoucre to target
Internal Radiation Dosimetry
MIRD Schema
Concept of Source and Target
Organ(s)
Source Organs
Target Organ
In MIRD schema the body is considered as a combination of
Source organs (i.e dose with significant uptake of
radiopharmaceutical) and Target organs (i.e. those being
irradiated by source organs)

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
source organ
One microcurie (3.7*104decay/s) of
radionuclide will emit energy at rate
of 3.7*104 * E MeV/s
Source organ
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
Step 2: Rate of energy
absorption by target organ
Define a term “Absorbed fraction”
i (rkrh) =
Source
Target Organ
Energy absorbed in target vol.(rk) from radiation i
------------------------------------------------------------------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
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
notation Фi (rk
r h)
is used to
indicate absorbed fraction for energy
delivered from a source organ (rh) to a
target organ (rk)
 The
 ∑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
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)
of
Ф
requires
Computational
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
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)

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/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 .

Avg dose D= ∫ dD/dt dt (0-∞)

This leads to
D(rk  rh) = 1.44 T1/2(eff)fAo/mk i Δi i (rk  rh)
(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.
 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 Ã

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:
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
= TpAo/0.693
= 1.44Tp Ao
(0-∞)
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:
à ≈ Ao ∫f1 e-0.693/Tb1dt + Ao ∫f2 e-0.693/Tb2dt + …… (0-∞)
= 1.44 Tb1f1Ao + 1.44 Tb2f2Ao + …..
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
Situation 4:
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 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 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.
i.e
Фi (rk
Фi (rh
mh
rh) =
rk) =
Фi (rh
Фi (rk
mk
Фi (rh
rk) = (mh/mk) * Фi (rk
rk)
rh)
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,
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
Unit of S-factor is Gy/Bq.s
rk)
Δi

Given the value of S and
Ã,
the average dose to
an organ is given by
cumulated
activity
Flow chart illustrating MIRD
methodology
Identify source (r) and target
(k) organs
Determine à from time activity curve
Look up S factor using appropriate table
D(rk
rh) = Ã * S (rk
rh)
Determine dose deliver to target from source
Dsoucre to target= Ã *s
Sum contributions of doses from all sources to the target
Dk= i Dsoucre to target

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 =


D/ Ao =
Ao S
* 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
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
S(SP to LI) = 7.20* 10-8 mGy/MBq.sec
S(RM to LI) = 8.93* 10-8 mGy/MBq.sec
(Self + Cross)


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 PatientSpecific 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
ideal to:
1.
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).
2.
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
3.
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.
4.
Use more sophisticated dosimetry approach to therapy to
evaluate individual patients response to therapy e.g. Tumor
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 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
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.
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
 Parameters
MIRD
ICRP
Target region
rk
T
source region
rh
S
Absorbed fraction
for radiation i
Фi(rk
Eqm absorbed dose
constant for ith radn.
Δi
γiEi
Cumulated activity
mean dose per Cum Act
or
specific effective energy
Ã
S(rk
Us
SEE
(T
r h)
r h)
AF
(T
S)
S)
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.

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.

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.