Portable surrogate-free 4D MRI from standard fast multi-slice 2D MRI via implicit neural representations

Four-dimensional MRI (4D MRI) characterizes respiratory organ motion, yet existing reconstruction pipelines are tightly coupled to specific acquisition platforms (e.g., non-Cartesian trajectories with self-gating, vendor-specific navigators, or external respiratory hardware), limiting broad adoption across diverse clinical and research settings, including low-field, open-bore, and non-supine imaging. We present SIMPLE-4D (Surrogate-free, IMplicit, PortabLE 4D MRI), a software-first portable workflow that operates entirely on reconstructed slices from standard fast multi-slice 2D MRI and requires no pulse-sequence modification, no non-Cartesian trajectory, no navigator, and no external hardware. SIMPLE-4D combines an acquisition-agnostic front end consuming standard 2D protocols, a surrogate-free variational motion encoder that extracts a compact motion code directly from each 2D slice, and a physics-aware continuous spatio-temporal reconstruction based on a hash-encoded implicit neural representation (INR) with a SIREN deformation network producing bidirectional cycle-consistent DVFs and motion-dependent Gauss-Legendre thick-slice quadrature. Bidirectionality yields a complete inter-frame motion model by composition, supporting downstream tasks such as dose accumulation without retraining. We validate the identical pipeline on two contrasting datasets: a 1.5 T clinical bSSFP dataset (5 volunteers, 3 sessions each) and a 0.5 T open-bore HASTE dataset (5 volunteers, supine and upright). To our knowledge, this is the first per-frame 4D volumetric respiratory MRI reconstruction on a weight-bearing upright open-bore low-field scanner from reconstructed 2D Cartesian slices alone. On low-field data the INR template additionally acts as an implicit denoiser, yielding +132% SNR. Systematic ablations isolate each component's contribution.