A Dual Quaternion Based Method for Estimating Margins for Planning Target Volumes in Radiotherapy

This objective of this paper is to develop a dual quaternion based method for estimating target volumes in radiation therapy for head and neck cancer. Inaccuracies in radiation targeting are responsible for incidental exposure of healthy adjacent tissues, causing significant morbidity and mortality. This paper focuses on inaccuracies incurred when a tumor is displaced during treatment. To address this problem, the clinical target must be expanded to cover the region through which the tumor might move. The resulting expanded target is known as the Planning Target Volume (PTV). In the current practice, the rotational components of displacements are neglected, producing planning target volumes that either miss the true target motion or are larger than needed to cover the target path. By using the dual quaternion based kinematic formulation, this paper represents and captures both translational and rotational inaccuracies. It then presents a framework for calculating the PTV swept out by the target as it shifts within its range of translations and rotations.