(If you can’t afford a CT scanner, there’s a nice (enormous) poster of all the parts inside a Curta, which makes a good gift!)
Wikipedia has a History of computed tomography page, from which we learn that EMI’s first successful experiment, in 1971, took 9 days of exposures in 160 traverse and 2.5 hours of processing on an ICL 1905 mainframe. The first brain scan was done later the same year:
Early scan data were actually taken back to EMI on tape for processing overnight which took 20 min per image on an ICL 1905 computer. In production this was done on a minicomputer which fortuitously had emerged at the right time. Images were taken back the next day on tape to Atkinson Morley’s Hospital to be displayed. The early images were displayed in three ways; paper printout, cathode ray tube (CRT) display or as a Polaroid picture of the CRT display.
(Fair use excerpts from Beckmann, E. C. (2006). CT scanning the early days. The British Journal of Radiology, 79(937), 5–8. doi:10.1259/bjr/29444122)