nuclear particles are about as invasive as it gets, wandering right through our cell walls; a very intimate form of turf violation
PET scanning is non-invasive, but it does involve exposure to ionizing radiation. The total dose of radiation is small, however, usually around 7 mSv. This can be compared to 2.2 mSv average annual background radiation in the UK, 0.02 mSv for a chest X-Ray, up to 8 mSv for a CT scan of the chest, 2-6 mSv per annum for aircrew, and 7.8 mSv per annum background exposure in Cornwall (Data from UK National Radiological Protection Board). (wiki)
