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Biological experiments based on organ-on-chips (OOCs) exploit light Time-Lapse Microscopy (TLM) for a direct observation of cell movement that is an observable signature of underlying biological processes. A high spatial resolution is essential to capture cell dynamics and interactions from recorded experiments by TLM. Unfortunately, due to physical and cost limitations, acquiring high resolution videos is not always possible. To overcome the problem, we present here a new deep learning-based algorithm that extends the well known Deep Image Prior (DIP) to TLM Video Super Resolution (SR) without requiring any training. The proposed Recursive Deep Prior Video (RDPV) method introduces some novelties. The weights of the DIP network architecture are initialized for each of the frames according to a new recursive updating rule combined with an efficient early stopping criterion. Moreover, the DIP loss function is penalized by two different Total Variation (TV) based terms. The method has been validated on synthetic, i.e., artificially generated, as well as real videos from OOC experiments related to tumor-immune interaction. Achieved results are compared with several state-of-the-art trained deep learning SR algorithms showing outstanding performances., Paper submitted to a peer-reviewed journal