  Motion information from 4D medical imaging offers critical insights into
dynamic changes in patient anatomy for clinical assessments and radiotherapy
planning and, thereby, enhances the capabilities of 3D image analysis. However,
inherent physical and technical constraints of imaging hardware often
necessitate a compromise between temporal resolution and image quality. Frame
interpolation emerges as a pivotal solution to this challenge. Previous methods
often suffer from discretion when they estimate the intermediate motion and
execute the forward warping. In this study, we draw inspiration from fluid
mechanics to propose a novel approach for continuously modeling patient
anatomic motion using implicit neural representation. It ensures both spatial
and temporal continuity, effectively bridging Eulerian and Lagrangian
specifications together to naturally facilitate continuous frame interpolation.
Our experiments across multiple datasets underscore the method's superior
accuracy and speed. Furthermore, as a case-specific optimization
(training-free) approach, it circumvents the need for extensive datasets and
addresses model generalization issues.
