Concepts & Quantities & Formalism for the dosimetry of internal radiation exposure by radioactive substances

1. MIRD schema
 General formalism for calculation of absorbed
doses from internal radio nuclides
– Loevinger & Berman 1976
 Medical Internal Radiation Dose Committee
of the Society of Nuclear Medicine
– MIRD pamphlets

Anthropomorphic phantom / Reference man 70kg
– Snyder et al. 1975
– Loevinger et al.1991

ICRU report 67, 2002
Chris J. Huyskens @2006

2. MIRD schema
 Basic concepts for dosimetry
 Source  Target model
 absorbed fraction in target
 conventions for notations
 multiple source  single target
 application for internal dosimetry
– in nuclear medicine
– radiological protection
 strengths and limitations
Chris J. Huyskens @2006

3. MIRD

basic concepts
Absorbed dose rate to target ‘tissue’
from nuclear transformations in a ‘source’ tissue
 = N E A φ
D
m
 Absorbed fraction φ of the energy emitted by
radioactivity in the source region that is absorbed
in the target region

Mean energy emitted per nuclear transition
∆ = N .E
Chris J. Huyskens @2006

4. MIRD
basic concepts
 The specific absorbed fraction is defined as the
absorbed fraction per unit mass of the target
region
φ
Φ =
m
 Cumulated activity represents the total number
of radioactive transformations in the source
region over time of interest
 time integral of the activity
t2
~
Α = ∫ Α ( t )d t
t1
Chris J. Huyskens @2006

5. MIRD
mean absorbed dose
 the mean absorbed dose to the target volume
from nuclear transitions in the source region
results from integration of the absorbed dose
rate over the time interval
D =
t2
∫
t1
A (t)∆φ
dt
m
~
A∆φ
D =
m
~
D = Α∆Φ
~
D = AS
Chris J. Huyskens @2006

6. MIRD
basic assumptions for φ

for non penetrating radiations / beta
– if source and target is the same then φ = 1
– if source and target is different then φ = 0

for penetrating radiations / photons
– for all source – target combinations 0 < φ < 1
Chris J. Huyskens @2006

7. MIRD
(specific) absorbed fraction
 Absorbed fraction φ of the energy emitted by
radioactivity in the source region that is absorbed
in the target region
 The specific absorbed fraction is defined as the
absorbed fraction per unit mass of the target
φ
region
Φ =
m
 Reciprocity theorem : for any pair of regions, the
specific absorbed fraction is independent of which
region is designated as source or as target region
 this implies
Φ i (rk ↔ rh ) = Φ 1 (rk ← rh ) = Φ i (rh ← rk
Chris J. Huyskens @2006
)

8. MIRD
specific absorbed dose in target
 absorbed dose in target region per unit
cumulated activity in source region
 absorbed dose in target region per
transformation in source region
φ
S = ∆Φ = ∆
m
 mean absorbed dose in target region
~
D = AS
 mean absorbed dose per unit administered
activity Ao
D
A
= τS
0
Chris J. Huyskens @2006

9. MIRD cumulated activity
 the activity in the source region is represented by
the sum of exponentials for each biological
process j that contributes to deposit and/or
clearance of radioactive material in source region.
−λt
A (t) = e
∑
A j e
− λ jt
j
 the cumulated activity follows from integrating A(t)
over time interval t1 –t2
~
A =
∑
j
A
j
λ + λ
(e
− ( λ + λ j ) t1
j
Chris J. Huyskens @2006
−e
− (λ + λ j )t2
)

10. MIRD
residence time in source region
 residence time in source region is defined as
~
A
τ =
A0
 encompasses the uptake of radioactivity in the
source region relative to the administered
activity Ao
 not to be confused with the mean lifetime of the
radioactivity
 Residence time for radio nuclides
– Loevinger et al.1991
Chris J. Huyskens @2006

11. MIRD half-time / half live
 physical half - life / physical decay constant
T = (ln 2 ) λ
 biologic half- time of biologic component j
T bj = (ln 2 ) / λ
j.
 effective half - time for biologic component j
(
T e, j = (ln 2 ) / λ + λ
j
)
1
Te,j
1
1
= +
= λ + λ j = λe,j
T
Tj
Chris J. Huyskens @2006

12. MIRD

multiple source h / single target k
mean absorbed dose in target region
D k =
∑
h

~
A h S (rk ← rh )
specific absorbed dose in target region
– mean absorbed dose per transformation in
source region
– mean absorbed dose per unit cumulated
activity in source region
S (rk ← rh ) =
∑
∆ iΦ i (rk ← rh ) =
i
∑
i
Chris J. Huyskens @2006
∆ iφ i (rk ← rh )
mk

13. MIRD
anthropomorphic phantom
Assumptions in constructing the MIRD phantom
 major organs are taken as source and target
regions
 target region is radio sensitive (part of) organ
 radioactivity uniformly distributed in the source
organs
 source and target regions homogeneous in
composition
 a single 70-kg phantom to represent all persons
– Snyder phantom
Chris J. Huyskens @2006

14. MIRD  symbols & conventions  ICRP mean absorbed dose (Dk) in target organ (k)
- committed equivalent dose (HT) in target organ (T)
- committed effective dose
 source region (h) & target region (k)
- source organ (S) & target organ (T)
 absorbed fraction Φ(rk rh)
- absorbed fraction AF(TS)
 mean absorbed dose per unit cumulated activity S(rkrh)
- specific effective energy SEE(TS)
 cumulated activity in source region
- committed number of transformations in source organ
Chris J. Huyskens @2006

15. MIRD
source  target model
Chris J. Huyskens @2006
ICRP

16. MIRD  symbols & conventions  ICRP
 MIRD : mean absorbed dose in target region
D k =
~
A h S (rk ← rh )
∑
h
S (rk ← rh ) =
∑
∆ iΦ i (rk ← rh ) =
i
∑
i
∆ iφ i (rk ← rh )
mk
 ICRP : committed equivalent dose in target organ
H
T
=
∑
i
U
Si
S E E (T ← si )
Chris J. Huyskens @2006

17. MIRD formalism
strengths
 The utility of the MIRD formalism lies in its
simplicity and generality
 clear separation of physics and biology:
– physical aspects: embedded in S values
– biologic aspects: embedded in cumulated
activity & residence time
 the organ S-values are published in MIRD
pamphlets
 ICRP: SEE values are based on revised values
for the absorbed fraction AF
– Cristy & Eckerman, 1987, 1993
Chris J. Huyskens @2006

18. MIRD
strengths
 advanced -dedicated- internal dosimetry based
on MIRD formalism for:
– complex composition and geometry of the
source & target regions
– non uniform distribution of radioactive
material in source region
– temporal dependence of the mass of organs
 The MIRD schema can accommodate a wide
variety of radio nuclide dosimetry applications
– nuclear medicine diagnostics & therapy
– internal contamination in radiation protection
Chris J. Huyskens @2006

19. Chris J. Huyskens @2006

20. MIRD
D =
t2
∫
t1
A (t)∆φ
dt
m
~
D = Α∆Φ
t2
~
Α = ∫ Α ( t )d t
mean absorbed dose
D = A~ . S
φ
Φ =
m
∆ = N .E
t1
Chris J. Huyskens @2006
D
= τ.S
A0
~
A ∆φ
D =
m