Adjoint-based methods reconstruct unknown boundary conditions and calibrate model parameters by minimizing the mismatch between simulations and observations through gradient-based optimization. Previous studies solved adjoint equations backwards in time and space to efficiently compute sensitivities of an objective function with respect to inlet discharge conditions in free-surface channel flows, enabling accurate recovery of upstream information from downstream measurements. Here, this methodology is extended for the first time to hemodynamics, allowing the reconstruction of inlet flow rate boundary conditions in one-dimensional arterial networks and the simultaneous calibration of outlet Windkessel parameters. A peripheral arterial pressure signal is used as reference data, aiming to make the approach applicable in realistic clinical scenarios where direct intra-thoracic flow rate measurements are unavailable or difficult to obtain non-invasively. This framework provides physiologically meaningful estimates of cardiovascular parameters, improves patient-specific modelling, and enhances the predictive capability of arterial flow simulations, supporting diagnosis and personalized assessment of vascular health.