NuTracker: a coordinate-based neural network representation of lung motion for intrafraction tumor tracking with various surrogates in radiotherapy

Objective. Tracking tumors and surrounding tissues in real-time is critical for reducing errors and uncertainties during radiotherapy. Existing methods are either limited by the linear representation or scale poorly with the volume resolution. To address both issues, we propose a novel coordinate-based neural network representation of lung motion to predict the instantaneous 3D volume at arbitrary spatial resolution from various surrogates: patient surface, fiducial marker, and single kV projection. Approach. The proposed model, namely NuTracker, decomposes the 4DCT into a template volume and dense displacement fields (DDFs), and uses two coordinate neural networks to predict them from spatial coordinates and surrogate states. The predicted template is spatially warped with the predicted DDF to produce the deformed volume for a given surrogate state. The nonlinear coordinate networks enable representing complex motion at infinite resolution. The decomposition allows imposing different regularizations on the spatial and temporal domains. The meta-learning and multi-task learning are used to train NuTracker across patients and tasks, so that commonalities and differences can be exploited. NuTracker was evaluated on seven patients implanted with markers using a leave-one-phase-out procedure. Main results. The 3D marker localization error is 0.66 mm on average and <1 mm at 95th-percentile, which is about 26% and 32% improvement over the predominant linear methods. The tumor coverage and image quality are improved by 5.7% and 11% in terms of dice and PSNR. The difference in the localization error for different surrogates is small and is not statistically significant. Cross-population learning and multi-task learning contribute to performance. The model tolerates surrogate drift to a certain extent. Significance. NuTracker can provide accurate estimation for entire tumor volume based on various surrogates at infinite resolution. It is of great potential to apply the coordinate network to other imaging modalities, e.g. 4DCBCT and other tasks, e.g. 4D dose calculation.