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.

翻译：胰腺疾病常呈现周期性及非周期性形变，因此难以通过高剂量放射进行治疗。然而，我们预期若能利用在照射过程中可捕捉器官二维切片的设备，这些困难有望被克服，治疗结果也可能得到改善。但由于仅能获取少量二维切片，需根据部分观测信息估计三维运动。本研究提出一种基于物理的框架，可根据一个或多个方向二维切片获取的运动信息估计器官三维运动（无论其周期与否），并构建回归模型以评估所提框架的精度，从而选择最优切片。通过切片间配准获取信息，并以周围器官为边界，该框架驱动物理模型进行三维运动估计。所提回归模型的R²分数大于0.9，均方根误差为0.357毫米。使用轴向切片时平均误差为5.11±1.09毫米，同时使用轴向、矢状及冠状切片时平均误差为2.13±0.598毫米。结果表明，该框架与体积配准效果相当，具有可行性。