Physics and Radiobiology of Nuclear Medicine

Dose Calculation

The radiation absorbed dose depends on a number of factors: (1) the
amount of radioactivity administered; (2) the physical and biological half-
lives of the radioactivity; (3) the fractional abundance of the radiation in
question from the radionuclides; (4) the biodistribution of radioactivity in
the body; and (5) the fraction of energy released from the source organ that
is absorbed in the target volume, which is related to the shape, composi-
tion, and location of the target. The physical characteristics of a radionu-
clide are well established. Information concerning the biodistribution of
ingested radioactivity can be obtained from various experimental studies in
humans and animals. The factors 4 and 5 are variable from one individual
to another and, therefore, they are approximated for a “standard” or
“average” 70-kg man.
Radiopharmaceuticals administered to patients are distributed in differ-
ent regions of the body. A region of interest for which the absorbed dose
is to be calculated is considered the “target,” whereas all other regions con-
tributing to the radiation dose to the target are considered “sources.” The
source and the target become the same when the radiation dose due to the
radioactivity in the target itself is calculated.

Radiation Dose Rate

Suppose a source volume rcontains A mCi of a radiopharmaceutical emit-
ting several radiations. If the ith radiation has energy Eiand a fractional
abundance Niper disintegration, then the energy absorbed per hour (dose
rate) by a target of mass mand volume vfrom the ith radiation emitted by
the source volume ris given by

Ri(rad/hr) =A/m(mCi/g)NiEi(MeV/disintegration)

×[3.7 × 104 disintegrations/(s ·mCi)]

×(1.6 × 10 −^6 erg/MeV)

×(0.01 g · rad/erg)

×(3600 s/hr)

=2.13(A/m)NiEi

The above equation is valid for nonpenetrating radiations only, meaning all
energy is absorbed in the absorber. For penetrating radiations, total or part
of the radiation energy may be absorbed in the absorbing material. If the
target and the source are not the same, then a factor must be introduced to
account for the partial absorption, if any, of the radiation energy. Thus,

Ri(rad/hr) =2.13(A/m)NiEifi(v←r) (14.9)

Dose Calculation 211