Kinematics method of population-based planning target volume to improve coverage and pharyngeal constrictor sparing in oropharyngeal cancer

Background: ICRU-83 notes the lack of methods to consider rotational displacements in planning target volume (PTV) construction. Probabilistic PTVs have been constructed that treat the rotational and translational components independently, but for off-axis (e.g., about the spine) rotations, the components are not independent. Purpose: A new method was developed to incorporate the correlations into PTV construction using Euler angles or quaternions to express the displacements and tested using treatment imaging records. Methods: Ten cases of oropharyngeal cancer with cone beam computed tomography (CBCTs) at approximately weekly intervals were studied. Principal Component Analysis (PCA) was used to form a covariance matrix of displacements from which confidence ellipsoids were derived. A one-out method was used to form a test series consisting of PTVs formed from population records of nine cases and tested against displacements recorded for the excluded case. Motions of a defined C1 landmark were examined on the transaxial plane and applied to the clinical target. A Rotational and Translational Confidence Limit (RTCL) technique treating components independently was compared to a PCA method that considered their covariance and to a simple 3 mm rolling ball expansion. Results: The PCA method spared more of the constrictors than did the RTCL method in 5/10 of cases (median relative difference 50%) and in none of these was there a higher percentage of target boundary points that fell outside the PTV twice or more. In two cases, the RTCL method performed better, but in one with poorer target coverage. A 3 mm expansion inadequately covered the target in most cases. Conclusion: A previous assumption of rotational and translational independence is not valid for off-center rotations produced by curving of the spine. Allowing for the covariance of component shifts produces a PTV that more closely tracks the clinical target volume (CTV) pose over the course of treatment, providing better coverage and sparing the constrictors.