Rotational kernels for conformal therapy

Conformal therapy treatment planning involves determining an irradiation strategy to deliver a dose distribution which is optimized for a given tumor volume. A technique proposed by Brahme restricts the search for the optimal treatment strategy to x-ray distributions in which points within the target volume are irradiated uniformly under rotation of the beam source around the patient. The dose distribution in this case may be calculated as a convolution of an irradiation weighting distribution with an invariant kernel. A procedure is described for calculating three-dimensional kernels to be used for clinical treatment planning with x rays produced by an electron accelerator. The convolution kernel is calculated as the sum of pencil beams irradiating the center of a cylindrical phantom uniformly from all angles. The shape of the kernel at points off the center of the phantom is investigated by means of numerical calculations which support the assumption that the kernel is invariant with respect to position within the phantom. The calculated kernels are verified by comparison with experimentally measured rotational arc dose distributions.