Physics and Radiobiology of Nuclear Medicine

(14.13)

Here,Teis the effective half-life of the radiopharmaceutical in hours (dis-
cussed in Chapter 3). If t=∞, that is, the radiopharmaceutical is completely
eliminated, then the exponential term e−let approaches zero and the
absorbed dose in Eq. (14.13) may be written as

Di(rad) =1.44(f·Ao/m)DiTefi(v←r) (14.14)

If the radionuclide has nradiations with energies E 1 ,E 2 ,...Enand frac-
tional abundances N 1 ,N 2 ,...Nnper disintegration, then the total dose D
can be obtained by summing Eq. (14.14) over all radiations. Thus,

(14.15)

This summation can also be applied to Eq. (14.12) for the dose rate Ri.The
total dose to the target from different sources of radiations can be calcu-
lated by summing Eq. (14.15) over all sources.
In the MIRD pamphlets, the values of Dihave been compiled on the basis
of various nuclear characteristics of the radionuclide in question. The fi
values have been calculated on the basis of different sizes and compositions
of the targets receiving the radiation dose and the radiation characteristics
of the radionuclide. In MIRD pamphlet no. 11, Eq. (14.15) has been sub-
stituted by

D(rad) = ·S (14.16)

where

=1.44 ×f·Ao×Te (14.17)

(14.18)

The quantity is called the cumulated activityand has the unit of mCi·hr.
The quantity Sis called the mean absorbed dose per cumulated activity
and has the unit of rad/mCi · hr. These two quantities are further discussed
next.

Factors Affecting
The cumulated activity in Eq. (14.17) is given as

=1.44f·AoTe

This is calculated on the assumption that the radiopharmaceutical localizes
in the organs instantaneously and cleared by both physical decay and bio-
logical elimination.

A ̃

A ̃

A ̃

A ̃

Smii

i

n

=

=

∑Df

1

A ̃

A ̃

DfAmioTreii

i

n

()rad =⋅()()←

=

(^144) ∑
1

. Δf 

=⋅ 144. ()fA m ToieΔ () 1 −e−letfi()←r

=⋅()fA moii()←r ()−e−

e

Δf et

l

^11 l

Dose Calculation 213