  Pancreatic diseases are difficult to treat with high doses of radiation, as
they often present both periodic and aperiodic deformations. Nevertheless, we
expect that these difficulties can be overcome, and treatment results may be
improved with the practical use of a device that can capture 2D slices of
organs during irradiation. However, since only a few 2D slices can be taken,
the 3D motion needs to be estimated from partially observed information. In
this study, we propose a physics-based framework for estimating the 3D motion
of organs, regardless of periodicity, from motion information obtained by 2D
slices in one or more directions and a regression model that estimates the
accuracy of the proposed framework to select the optimal slice. Using
information obtained by slice-to-slice registration and setting the surrounding
organs as boundaries, the framework drives the physical models for estimating
3D motion. The R2 score of the proposed regression model was greater than 0.9,
and the RMSE was 0.357 mm. The mean errors were 5.11 $\pm$ 1.09 mm using an
axial slice and 2.13 $\pm$ 0.598 mm using concurrent axial, sagittal, and
coronal slices. Our results suggest that the proposed framework is comparable
to volume-to-volume registration, and is feasible.
