Collapsed cone convolution of radiant energy for photon dose calculation in heterogeneous media

A method for photon beam dose calculations is described. The primary photon beam is raytraced through the patient, and the distribution of total radiant energy released into the patient is calculated. Polyenergetic energy deposition kernels are calculated from the spectrum of the beam, using a database of monoenergetic kernels. It is shown that the polyenergetic kernels can be analytically described with high precision by (A exp( -ar) + B exp( -br)/r2, where A, a, B, and b depend on the angle with respect to the impinging photons and the accelerating potential, and r is the radial distance. Numerical values of A, a, B, and b are derived and used to convolve energy deposition kernels with the total energy released per unit mass (TERMA) to yield dose distributions. The convolution is facilitated by the introduction of the collapsed cone approximation. In this approximation, all energy released into coaxial cones of equal solid angle, from volume elements on the cone axis, is rectilinearly transported, attenuated, and deposited in elements on the axis. Scaling of the kernels is implicitly done during the convolution procedure to fully account for inhomogeneities present in the irradiated volume. The number of computational operations needed to compute the dose with the method is proportional to the number of calculation points. The method is tested for five accelerating potentials; 4, 6, 10, 15, and 24 MV, and applied to two geometries; one is a stack of slabs of tissue media, and the other is a mediastinum-like phantom of cork and water. In these geometries, the EGS4 Monte Carlo system has been used to generate reference dose distributions with which the dose computed with the collapsed cone convolution method is compared. Generally, the agreement between the methods is excellent. Deviations are observed in situations of lateral charged particle disequilibrium in low density media, however, but the result is superior compared to that of the generalized Batho method.