They DO do radiation scans. One that is done fairly commonly on older men or those with other risk factors is called myocardial perfusion imaging. Also known as a cardiac stress test.
They use a generator (casually called a “cow”) that has a core of molydenum-99, a radioactive isotope, that decays at a known rate into metastable Technetium-99 (Tc-99m). Tc-99m is non-toxic, has a low activity (is not super radioactive), and a nice short half life of about 6 hours. So it will die down to below background level fairly rapidly (rather than stickinga round inside you exposing you to radiation). This makes it ideal for use in a lot of nuclear medecine scans. You periodically ‘milk’ the generator to get the Tc-99m, then combine that with various other compounds to create different types of imaging agents for different scans.
For myocardial perfusion imaging they will mix it with a drug called Cardiolite (or some other generic or equivalent), which is designed specifically to bind to only heart muscle tissue. So the idea is you take the patient, give them this injection, then put them in front of a gamma camera (that can detect the radiation the Tc-99m emits) and put them under some amount of cardiovascular stress (typically running on a treadmill, though for some patients they may sue an adrenaline dose to mimic the same response). Anywhere in the heart that is getting good blood supply will glow in the gamma camera (because the cardiolite-bonded Tc-99m will end up sticking there). Anywhere that is NOT getting good blood supply will be noticeable from the lack of gamma emission.
they have similar scans for all sorts of physiological processes (white blood cell labelling with indium for finding infections, kidney scans, gallbladder scans, etc etc). The cool thing about nuclear medicine is that unlike most other forms of medical imaging, it doesn;t just show anatomy, it shows physiology and metabolism. You can directly image not just the physical structure of the body, but also its actual biological and metabolic functioning.
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