3D conformal intensity-modulated radiotherapy planning: interactive optimization by constrained matrix inversion

Abstract

Background and purpose: This paper presents a method for interactive optimization of 3D conformal intensity-modulated radiotherapy plans employing a quadratic objective that also contains dose limitations in the organs at risk. This objective function is minimized by constrained matrix inversion (CMI) that follows the same approach as the gradient technique using matrix notation. Materials and methods: Sherouse's GRATIS™ radiotherapy design system is used to determine the outlines of the target volume and the organs at risk and to input beam segments which are given by the beam segmentation technique. This technique defines the beam incidences and the beam segmentation. The weights of the segments are then calculated using a quadratic objective function and CMI. The objective function to be minimized consists of two components based on the planning target volume (PTV) and the organ at risk (OAR) with an importance factor w associated with the OAR. Results: Optimization is tested for concave targets in the head and neck region wrapping around the spinal cord. For a predefined w-value, segment weights are optimized within a few seconds on a DEC Alpha 3000. In practice, 5–10 w-values have to be tested, making optimization a less than 5 min procedure. This optimization procedure predicts the possibility of target dose escalation for a tumour in the lower neck to 120–150 Gy without exceeding the spinal cord tolerance, whereas human planners could not increase the dose above 65–80 Gy. Conclusions: Treatment plans optimized using a quadratic objective function and the CMI algorithm are superior to those which are generated by human planners. The optimization algorithm is very fast and allows interactive use. Quadratic optimization by CMI is routinely used by clinicians at the Division of Radiotherapy, U.Z.-Gent.