Callaghan studied physics at the University of Limerick. She moved to Imperial College London for her graduate research, where she joined Joseph Hajnal and David Larkman at Hammersmith Hospital and earned her Ph.D. Her research considered image reconstruction using under-sampled datasets. She worked as a postdoctoral researcher at Imperial College London and Middlesex University, focusing on parallel transmit technology, lipid quantification in clinical populations and the use of nanotechnology in oncology.