Purpose: At our institute, a transit back-projection algorithm is used clinically to reconstruct in vivo patient and in phantom 3D dose distributions using EPID measurements behind a patient or a polystyrene slab phantom, respectively. In this study, an extension to this algorithm is presented whereby in air EPID measurements are used in combination with CT data to reconstruct 'virtual' 3D dose distributions. By combining virtual and in vivo patient verification data for the same treatment, patient-related errors can be separated from machine, planning and model errors. Methods and materials: The virtual back-projection algorithm is described and verified against the transit algorithm with measurements made behind a slab phantom, against dose measurements made with an ionization chamber and with the OCTAVIUS 4D system, as well as against TPS patient data. Virtual and in vivo patient dose verification results are also compared. Results: Virtual dose reconstructions agree within 1% with ionization chamber measurements. The average c-pass rate values (3% global dose/3 mm) in the 3D dose comparison with the OCTAVIUS 4D system and the TPS patient data are 98.5 +/- 1.9%(1SD) and 97.1 +/- 2.9%(1SD), respectively. For virtual patient dose reconstructions, the differences with the TPS in median dose to the PTV remain within 4%. Conclusions: Virtual patient dose reconstruction makes pre-treatment verification based on deviations of DVH parameters feasible and eliminates the need for phantom positioning and re-planning. Virtual patient dose reconstructions have additional value in the inspection of in vivo deviations, particularly in situations where CBCT data is not available (or not conclusive). (C) 2017 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.