Internal Dose Calculation
The removal of activity from a biological tissue proceeds two ways:
1. There is the radiological decay, characterized by the decay constant, λ, which we will now call λR
2. The removal from tissue due to chemical and biological processes – this proceeds with the same
stochastic pattern as radiological decay, characterized by another decay constant we will call λB
So:
− λ +λ
A ( t ) = A0 e − λRt e − λBt = A0 e ( R B )t
The sum of the radiological and biological decay constants therefore result in an effective
decay constant, λE, which we can convert into an effective half-life:
λE = λR + λ B
TE =
ln 2
λE
=
TR × TB
TR + TB
𝑡𝑡
𝐷𝐷 = 𝐷𝐷̇0 � 𝑒𝑒 −𝜆𝜆𝐸𝐸𝑡𝑡 𝑑𝑑𝑑𝑑 =
0
𝐷𝐷̇0
�1 − 𝑒𝑒 −𝜆𝜆𝐸𝐸 𝑡𝑡 �
𝜆𝜆𝐸𝐸
Material deposited in different parts of the body may be cleared at different rates:
𝐷𝐷̇10
𝐷𝐷̇20
𝐷𝐷̇𝑛𝑛0
−𝜆𝜆1𝐸𝐸 𝑡𝑡
−𝜆𝜆2𝐸𝐸 𝑡𝑡
𝐷𝐷 =
�1 − 𝑒𝑒
�+
�1 − 𝑒𝑒
�+ ⋯+
�1 − 𝑒𝑒 −𝜆𝜆𝑛𝑛𝐸𝐸 𝑡𝑡 �
𝜆𝜆1𝐸𝐸
𝜆𝜆2𝐸𝐸
𝜆𝜆𝑛𝑛𝐸𝐸
How do we find 𝐷𝐷̇0 ?
For charged particles:
𝐷𝐷̇0 =
𝐸𝐸�
𝑚𝑚
× 𝐴𝐴0
where E is the average energy released per decay, and m is the mass of the tissue volume.
For gamma rays?
ICRP 133:
Internal dose or Dose Commitment
𝑡𝑡+50
𝐻𝐻50,𝑇𝑇 = � 𝐻𝐻̇𝑇𝑇 (𝑑𝑑)𝑑𝑑𝑑𝑑
𝑡𝑡
T = tissue T
t = time
H50,T = Committed Dose Equivalent (CDE)
CEDE = H E ,50 (or E ) = ∑ wT H T ,50
T
Total Effective Dose Equivalent (TEDE).
Limits on Intake of Radioactivity
Annual Limit on Intake
(
I s Bq y
−1
)
0.05 Sv y −1
≤
∑ wT H 50,T (Sv / Bq)
(
I N Bq y
−1
)
0.5 Sv y −1
≤
H 50,T ( Sv / Bq )
T
Where
• I (Bq) is the annual intake of the specified radionuclide (by ingestion or inhalation).
o S = stochastic limit
o N = nonstochastic limit
• HT,50 per unit intake (Sv Bq-1) is the committed dose equivalent in tissue (T) from the
intake of unit activity of the nuclide by the specified route.
• If Is not exceeded, then stochastic limits met
• If In not exceeded, then nonstochastic limits met
• We select value of I which satisfies both inequalities to determine the limiting value.
CEDE =
Intake
Intake
× 0.05 Sv or CDET =
× 0.5 Sv
ALI S
ALI N
Derived Air Concentration
DAC ( Bq m3 ) =
ALI
( 2000 h y −1 )(1.2 m3 h−1 )
Dose Conversion Coefficients
•
Only consider stochastic effects (effective dose)
Committed Effective Dose = A (intake) x DCF (Sv/Bq)
MIRD Dose Models