A novel proposition of radiation energy conservation in radiation dose deformation using deformable image registration

Objective. The purpose of this study is to analytically derive and validate a novel radiation energy conservation principle for dose mapping via deformable image registration (DIR). Approach. A radiation energy conservation principle for the DIR-based dose-deforming process was theoretically derived with a consideration of the volumetric Jacobian and proven using synthetic examples and a patient case. Furthermore, an energy difference error was proposed that can be used to evaluate the DIR-based dose accumulation uncertainty. For the analytical validation of the proposed energy conservation principle, a synthetic isotropic deformation was considered, and artificial deformation uncertainties were introduced. For the validation with a patient case, a ground truth set of computed tomography images and the corresponding deformation was generated. Radiation energy calculation was performed using both the ground truth deformation and another deformation with uncertainty. Main results. The suggested energy conservation principle was preserved with uncertainty-free deformation, but not with error-containing deformations using both the synthetic examples and the patient case. For a synthetic example with a tumor volume reduction of 27.1% (10% reduction in length in all directions), the energy difference error was calculated to be -29.8% and 37.2% for an over-deforming and under-deforming DIR uncertainty of 0.3 cm. The energy difference error for the patient case (tumor volume reduction of 37.6%) was 2.9% for a displacement vector field with a registration error of 2.0 +/- 3.2 mm. Significance. A novel energy conservation principle for DIR-based dose deformation and the corresponding energy difference error were mathematically formulated and successfully validated using simple synthetic examples and a patient example. With a consideration of the volumetric Jacobian, this investigation proposed a radiation energy conservation principle which can be met only with uncertainty-free deformations.