True three-dimensional dose computations for megavoltage x-ray therapy: a role for the superposition principle

The objective of radiation therapy is to concentrate a prescribed radiation dose accurately within a target volume in the patient. Major advances in imaging technology have greatly improved our ability to plan radiation treatments in three dimensions (3D) and to verify the treatment geometrically, but there is a concomitant need to improve dosimetric accuracy. It has been recommended that radiation doses should be computed with an accuracy of 3% within the target volume and in radiosensitive normal tissues. We review the rationale behind this recommendation, and describe a new generation of 3D dose algorithms which are capable of achieving this goal. A true 3D dose calculation tracks primary and scattered radiations in 3D space while accounting for tissue inhomogeneities. In the past, dose distributions have been computed in a 2D transverse slice with the assumption that the anatomy of the patient dose not change abruptly in nearby slices. We demonstrate the importance of computing 3D scatter contributions to dose from photons and electrons correctly, and show the magnitude of dose errors caused by using traditional 2D methods. The Monte Carlo technique is the most general and rigorous approach since individual primary and secondary particle tracks are simulated. However, this approach is too time-consuming for clinical treatment planning. We review an approach that is based on the superposition principle and achieves a reasonable compromise between the speed of computation and accuracy in dose. In this approach, dose deposition is separated into two steps. Firstly, the attenuation of incident photons interacting in the absorber is computed to determine the total energy released in the material (TERMA). This quantity is treated as an impulse at each irradiated point. Secondly, the transport of energy by scattered photons and electrons is described by a point dose spread kernel. The dose distribution is the superposition of the kernels, weighted by the magnitude of the TERMA impulse for all interaction sites. In this review, we demonstrate the capabilities of the superposition method, particularly for situations of charged particle disequilibrium, and we report on the progress made by several research groups in adapting this method to clinical treatment planning. In the future, the superposition method will have a significant role in dose optimization for conformal irradiation techniques because of its close correspondence to image reconstruction by filtered back-projection.