I've had maybe 5 or 6 CT scans over the course of my life, and I'm only 27.
What risk do those CTs present to someone like me?
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Every procedure has to be weighed for potential costs and benefits. Cancer is a risk already present and might shorten a life, CT scans on the other hand are done to prolong a life.
The exact risks (costs) for CT scans is unknown, especially the exact risks for you, since we only have statistical data to estimate that.
Prior data forms the basis for this statistical risk assessment. For example: Radiation exposure from CT scans in childhood and subsequent risk of leukaemia and brain tumours: a retrospective cohort study:
Although CT scans are very useful clinically, potential cancer risks exist from associated ionising radiation, in particular for children who are more radiosensitive than adults. We aimed to assess the excess risk of leukaemia and brain tumours after CT scans in a cohort of children and young adults. […] Use of CT scans in children to deliver cumulative doses of about 50 mGy might almost triple the risk of leukaemia and doses of about 60 mGy might triple the risk of brain cancer. Because these cancers are relatively rare, the cumulative absolute risks are small: in the 10 years after the first scan for patients younger than 10 years, one excess case of leukaemia and one excess case of brain tumour per 10 000 head CT scans is estimated to occur. Nevertheless, although clinical benefits should outweigh the small absolute risks, radiation doses from CT scans ought to be kept as low as possible and alternative procedures, which do not involve ionising radiation, should be considered if appropriate. (emphasis added)
The technology and methods are constantly improved upon. Unnecessary scans should be avoided though. Whole-Body PET/CT Scanning: Estimation of Radiation Dose and Cancer Risk:
Whole-body PET/CT scanning is accompanied by substantial radiation dose and cancer risk. Thus, examinations should be clinically justified, and measures should be taken to reduce the dose.
But that does not mean you should deny any further scans. But make sure your doctors know about prior scans. Especially when changing doctors. Sometimes old scans are unknown to exist but just as useful.
To visualise that you can not avoid all radiation and to put the doses you receive from scans in perspective, this looks very useful:
Do not take this chart as a reliable guide or definitive advice. But do a mathematical comparison of two figures: "Chest CT scan" and "Maximum yearly dose permitted for US radiation workers." (The equivalent of 7 of these scans in one year would still be considered "OK" under these workplace regulations.)
In more practical terms this might translate into something like "How Much Do CT Scans Increase the Risk of Cancer?":
For a more detailed breakdown consult information like "Computed Tomography (CT) Scans and Cancer" from the National Cancer Institute: