Space and time

(1) Positron emission tomography (PET) builds a three-dimensional map of where a radioactive tracer collects in the body. The most common tracer is a sugar labelled with fluorine-18, which decays by β⁺ emission with a half-life of 110 minutes. (2) Because fluorine-18 decays so quickly, it is made in a cyclotron close to the hospital. A typical dose leaves the cyclotron at 08:00 with an activity of 2.0 GBq and is injected about two hours later. (3) Each positron travels about a millimetre through tissue before it meets an electron. The pair annihilates, producing two gamma photons, each of energy 511 keV, which travel in almost exactly opposite directions. (4) A ring of detectors surrounds the patient. When two detectors on opposite sides register photons within a few nanoseconds of each other, the annihilation must have happened somewhere on the line joining them. Modern scanners also measure the tiny difference in arrival times to locate the event along that line. (5) A scan typically collects about 4 × 10⁸ such coincidences in 20 minutes. Like all counting experiments, the image is noisy: the uncertainty in N counts is about √N. (6) A PET scan gives the patient an effective dose of about 7 mSv, compared with an average background dose in the UK of 2.7 mSv per year. The commonly used risk estimate is a 5% chance of a fatal cancer per sievert. (7) PET shows what tissues are doing (for example, fast-growing tumours take up more sugar), while X-ray CT shows their structure. Many scanners combine the two.