Fig. 1.

Geometry used for calculation of the absorbed fractions. The homogeneous unit density sphere (center C, radius R) represents a soft tumor tissue, containing a spherically symmetric distribution of radioactivity given by Eqs. (3)–(5). Located at a distance s from the center of the tumor is an arbitrary source point P. The variable x represents the distance traveled by radiation emanating from the source point. The annular region between the radii r₁, and r₂ is an example of the 25 target regions in which the dose rates are calculated. The fraction of energy emitted from all source points in the entire sphere and absorbed in each target region is calculated using Eq. (8) for photons, and Eq. (12) for electrons and for β particles (see text, Sec. II E).