Physics and Radiobiology of Nuclear Medicine

Here fi(v←r) is called the absorbed fractionand is defined as the ratio of
the energy absorbed by the target volume vfrom the ith radiation to the
energy emitted by the ith radiation from the source volume r. This is a crit-
ical factor that is difficult to evaluate, because the absorbed fraction fi
depends on the type and energy of the radiation, the shape and size of the
source volume, and the shape, composition, and distance of the target
volume. However, in the case of b-particles, conversion electrons,a-parti-
cles, and x- and g-rays of energies less than 11 keV, all of the energy emitted
by a radionuclide is absorbed in the volume rlarger than 1 cm. Then,fi
becomes 0, unless vand rare the same, in which case fi=1. For x- and g-
rays with energies greater than 11 keV, the value of fidecreases with
increasing energy and varies between 0 and 1, depending on the energy. The
values of fiare calculated by statistical Monte Carlo methods on the basis
of fundamental mechanisms of interaction of radiation with matter, and are
available in standard textbooks on radiation dosimetry, particularly the
medical internal radiation dose (MIRD) pamphlets published by the
Society of Nuclear Medicine.
The quantity 2.13NiEiis a constant for the ith radiation and is often
denoted by Di. Thus,

Di=2.13NiEi (14.10)

The quantity Diis called the equilibrium dose constantfor the ith radiation
and has the unit g · rad/(mCi · hr) based on the units chosen in Eq. (14.9). It
should be pointed out that since b-particles are emitted with a distribution
of energy, the average energy bof b-particles is used in the calculation of
Di. Thus, Eq. (14.9) becomes

Ri(rad/hr) =(A/m)Difi(v←r) (14.11)
The activity Awill change due to the physical decay and biological elim-
ination of the radiopharmaceutical, and therefore the dose rate will also
change. If Aois the initial administered activity, then the activity localized
in an organ is a fraction fof Ao. Assuming an effective exponential change
in Awith time, Eq. (14.11) can be written

Ri(rad/hr) =(f·Ao/m)Die−letfi(v←r) (14.12)

Here leis the effective decay constant of the radiopharmaceutical, and tis
the time over which the original activity has decayed.

Cumulative Radiation Dose

The cumulative radiation dose Dito the target due to the ith radiation of
the radionuclide during the period t=0 to tcan be obtained by integrating
Eq. (14.12). Thus,

DfAm redtioiiet

t

()rad =⋅()Δf()← ∫ −l

0

E

212 14. Internal Radiation Dosimetry