Motivated by the application of respiratory surface electromyography,we propose [1] a motion interpolation framework for computing a time-continuous model of the respiratory cycle based on end-inspiratory and end-expiratory 3D MRI images in the form of a dense deformation map ϕ : ℝ3 × [0, 1] → ℝ3. The challenge is to incorporate the sliding motion occurring in the pleural cavity, while simultaneously enabling accurate motion interpolation. Such a combination has not been addressed in previous works [2]. To facilitate sliding motion along predefined surfaces, we require an interior local volume Ωloc whose motion is assumed to differ from its surroundings in a sliding fashion. We then obtain ϕ as the composition := ϕloc ◦ ϕglob, where the global diffeomorphism ϕglob aligns structures outside Ωloc, followed by a local deformation ϕloc which diffeomorphically aligns the structures inside Ωloc. The result is a dense, piecewise diffeomorphic deformation map with sliding motion along the boundaries of Ωloc. We model both deformations ϕloc and ϕglob via stationary velocity fields, each parameterized by a neural implicit representation. To enforce invariance of Ωloc under the local deformation ϕloc, we propose a hybrid technique of restricting the velocity field and employing a soft penalty. We validate our approach for registration and motion interpolation experimentally on real-world data.