Does elastic tissue intrafraction motion with density changes forbid motion-compensated radiotherapy?

Intrafraction organ motion disturbs the otherwise highly conformal dose distributions planned for conformal radiotherapy and intensity-modulated radiotherapy. If the organ motions are rigid-body translations and preserve voxel density, techniques to make the beam follow the target by synchronous breathing can be arranged. Several potential difficulties disturb this oversimple statement and one of these is addressed in this paper. The effects of general elastic motion without preserving density are investigated. The effects are complex. Dose-space voxels disconnect from the planned irradiation bixel; voxels in a set aligned with a particular bixel cease to be so aligned even with a different bixel on elastic motion. Furthermore the density changes to conserve mass and this further perturbs the dose distribution. These effects are demonstrated here via simple examples but it may be impossible to make 'beam-breathing' strategies to compensate for them. Consequently understanding (and possibly ignoring) these second-order effects may be all that is possible.