# 3 - Radiation Dose Calculations

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```					                          3 – Radiation Dose Calculations

1) Dosimetry

a) Definitions
i) D Dose
&
ii) D Dose rate

& D
D=
t

b) General Dose Calculations
i) Dose from a static radiation source
ii) Dose = Dose Rate × Time

&
D = D ⋅t

c) Gamma-Ray Constants for Isotopes – Г
i) R − cm 2 / mCi − hr

Isotope                   Г
(R/hr @ 1cm per mCi)
I-131                   2.2
Tc-99m                  0.78
F-18                    5.7
Tl-201                  0.46
Mo-99                   1.45
Cs-137                   3.3
Co-60                  13.2

d) Dose from a decaying radiation source

&
D=
D
λ
(1 − e )
− λt

2) External Dosimetry
a) Point-Source Geometry
i) Area of Sphere = 4πr2
ii) Inverse Square Law

& 2 & 2
D1d1 = D2 d s
2
&   & d
D2 = D1 1 2
d2
3) Plane-Source Geometry
a) Source approximates a thin disk

Dose rate (R/hr) at point Q:

&            r 2 + h2
D = Aa Γπ ln
h2

where:
Aa           – Activity per unit area (mCi/cm2)
Γ            – Gamma-ray constant (R/hr @ 1 cm per mCi)
h             – height (cm)

4) Internal Dosimetry
a) Effective Half-Life

λeffective = λbiological + λphysical

TPTB
T1/ 2 effective =
TP + TB

b) MIRD – Dose Rate from an Internally-Deposited Nuclide

& kA nEφ , where
D=
m
∑
Energy Absorbed
φ=                    , which for beta particles in tissue = 1
Energy Emitted
⎜ J/kg ⎟ ⋅ 1000⎜ kg ⎟
100⎜      ⎟       ⎜ ⎟
⎝      ⎠       ⎝ ⎠                              rad - g
k=                                                        = 2.13
1 ⎛ hr ⎞         1       ⎛ μCi ⎞       1      ⎛ MeV ⎞        μCi - hr - MeV
⎜        ⎟⋅         6 ⎜
⎜     ⎟⋅
⎟ 1.6 × 10 −13 ⎜ J ⎟
60 ⎝ minute ⎠ 2.22 × 10 ⎝ dpm ⎠                ⎝     ⎠

Most isotope data tables list Δ instead of k:

Δ = 2.13nE

c) Simplified Internal Dose Equation

&   Δφ
D=A
m

5) Internal Dosimetry Based on Intake
a) ALI – Annual Limit on Intake
i) SALI = 5 rem whole body
ii) NALI = 50 rem to target organ

6) Regulatory Definitions of Dose Equivalent
a) Effective Dose Equivalent (EDE) – correlates a dose to a specific tissue to
an equivalent risk factor from whole body dose.
b) Committed Dose Equivalent (CDE) – Dose to a tissue from internally
c) Committed Effective Dose Equivalent (CEDE) – CDE expressed in terms
of risk to the whole body.
d) Total Effective Dose Equivalent (TEDE) – Sum of EDE and CEDE.
e) Deep Dose Equivalent (DDE) – dose equivalent from penetrating
radiation, measured at a depth of 1 cm
f) Shallow Dose Equivalent (SDE) – 0.007 cm
g) Lens Dose Equivalent – 0.3 cm

7) Tissue Weighting Factors

Tissue                         wT
Breast                        0.15
Red Bone Marrow                    0.12
Lung                         0.12
Thyroid                        0.03
Bone Surfaces                     0.03
Remainder               0.3 for 6, 0.06 each
H = ∑ HT w T

H – Total Effective Dose Equivalent
HT – Tissue Dose Equivalent
wT – Tissue Weighting Factor

References

Bevelaqua, J., Contemporary Health Physics, Wiley-Interscience, 1995.

Cember, H., Introduction to Health Physics (2nd edition), Pergamon Press, 1988.

Loevinger, R., Budinger, T.F., Watson, E.E., MIRD Primer for Absorbed Dose
Calculations, Society of Nuclear Medicine, 1988.

& Sons, 1995.

US Nuclear Regulatory Commission, Code of Federal Regulations, Title 10, Part