“…With the introduction of frequent imaging during the treatment process, such as cone-beam computed tomography (CT) systems (Jaffray et al 2002, Oldham et al 2005, Sykes et al 2005, CT-on-rails systems (Ma andPaskalev 2006, Zhang et al 2007) and proposed on-board magnetic resonance systems (Baldwin et al 2005, Fox et al 2006, Tomas et al 2006 coupled with the use of deformable image registration (DIR), determination of the accumulated dose for arbitrary tissue voxels over a course or fraction of therapy when tissues move with respect to each other is becoming clinically practical (Christensen et al 2001, Foskey et al 2005, Flampouri et al 2005, Schaly et al 2004, Yan et al 1997, 1999. For current DIR algorithms, the displacement vector fields (DVFs) of image registrations, which are used to map the patient dose from one instance of a patient's anatomy (e.g., the time of treatment) to a reference anatomic instance (e.g., the planning image set), are not without error (Wang et al 2005, Li et al 2005, Foskey et al 2005, Webb 2006).…”