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Abstract: Purpose. Localizing structures and estimating the motion of a specific target region are common problems for navigation during surgical interventions. Optical coherence tomography (OCT) is an imaging modality with a high spatial and temporal resolution that has been used for intraoperative imaging and also for motion estimation, for example, in the context of ophthalmic surgery or cochleostomy. Recently, motion estimation between a template and a moving OCT image has been studied with deep learning methods to overcome the shortcomings of conventional, feature\-based methods. Methods. We investigate whether using a temporal stream of OCT image volumes can improve deep learning\-based motion estimation performance. For this purpose, we design and evaluate several 3D and 4D deep learning methods and we propose a new deep learning approach. Also, we propose a temporal regularization strategy at the model output. Results. Using a tissue dataset without additional markers, our deep learning methods using 4D data outperform previous approaches. The best performing 4D architecture achieves an correlation coefficient (aCC) of 98.58\% compared to 85.0\% of a previous 3D deep learning method. Also, our temporal regularization strategy at the output further improves 4D model performance to an aCC of 99.06\%. In particular, our 4D method works well for larger motion and is robust towards image rotations and motion distortions. Conclusions. We propose 4D spatio\-temporal deep learning for OCT\-based motion estimation. On a tissue dataset, we find that using 4D information for the model input improves performance while maintaining reasonable inference times. Our regularization strategy demonstrates that additional temporal information is also beneficial at the model output.