Introduction and Terminology.

Radiation is all around you. There is the cosmic background radiation that fills the universe pretty uniformly. It is felt to be the “leftover” energy from the Big Bang. Whether you adhere to the idea of Big Bang or not, as far as I can tell, there is no alternative explanation for the cosmic radiation if the Big Bang did not occur. The radiation received by humans is the cosmic radiation plus other sources of radiation around humans. Did you know that humans give off a small amount of radiation?
To measure radiation we give it a unit of measurement. For small doses of radiation we use sieverts and for even smaller doses we use millisieverts named after Rolf Maximillian Sievert, a Swedish physicist.
There are other radiation measurement units such as Gray and Rads. These are inter convertible by using simple equations. An online converter can be found here.
Effective dose is a common term used in Medical terminology. The issue is that different tissues have different radiosensitivity and it may differ from person to person, type of X-ray, type of tissue imaged, sex etc. Effective dose is the measure of radiation averaged over the whole body.

[time for a break, my backyard Redbud Avondale]

Early human studies of Medical radiation induced cancer risks.

In 2001 one of the earliest studies was published on the subject. It concluded the following:

The best available risk estimates suggest that pediatric CT will result in significantly increased lifetime radiation risk over adult CT, both because of the increased dose per milliampere-second, and the increased lifetime risk per unit dose.

A second series of reports looked at radiation risk of atomic bomb survivors from Japan. Despite differences between atomic bomb radiation and Medical radiation, it did not stop some to extrapolate these results to Medical imaging. Perhaps flawed in comparison, it still brought more awareness. The study reported the following:

(a) although it is becoming clearer that the excess relative risk for those exposed as children has declined over the follow-up, the excess absolute risk has increased rapidly with time; and (b) although the excess relative risk at a given age depends substantially on sex and age at exposure, the age-specific excess absolute risk depends little on these factors.

There are other studies that have estimated the risks. These risks are small. In a study by Pearce, it is estimated it estimated that one head CT in the first 10 years of life will cause one additional case of leukemia and one additional case of brain tumor per 10000 people.
The risk is real but small.

The usefulness of CT scans.

CT scans are here to stay. They provide information valuable enough to save many lives and detect and diagnose many tumors and other life threatening illnesses. A study on relative risk and benefits to get exact data on lives saved vs cancers caused is nearly impractical.
The trick really is to use them wisely. For example with the new recommendations of low dose CT scans for lung cancer screening in smokers, the radiation dose is extremely reduced.The procedure saves lives.
There is Literature being published of overuse of CT scans in Emergency Departments. In a 2015 report is is reported.

more than four out of five head CT scans performed in 2013 didn’t meet specialty society recommendations for appropriate use.

The balance between overuse and underuse is precarious and we are far from achieving perfection. From a physician perspective, the risk of missing an immediate life saving diagnosis often outweighs the small longer term risk of CT radiation. A greater willingness to reduce overuse of CT may be found if cultural expectations and subsequent legal consequences are based on merits of science taking into account the current limitations of science.

How much Radiation do we actually get from CT scans?

Keep in mind that an average human gets approximately 3 millisieverts of radiation from naturally occurring radiation yearly.
On a background of this information the following estimates of are available for the effective radiation dose for some common radiography procedures.

CHEST.

X-RAY gives you 0.1 millisieverts.
CT chest gives you 7 millisieverts.
Low dose screening Chest CT gives you 1.5 millisieverts.

ABDOMEN AND PELVIS.

CT Abdomen and Pelvis gives you 10 millisieverts.

CARDIAC / CORONARY

CORONARY CT Angiography gives you 12 millisieverts.

It is good to know that common procedures such as bone density ( DEXA) and Mammography only give 0.001 and 0.4 millisieverts respectively.
The reference for this section can be found here. The reference also lists other exposure radiation data for those interested.

Bottom line.

CT is extremely useful in its application. It is a life saving diagnostic procedure. Is is overused? Perhaps the answer is yes. Are other modalities in Medicine overused? Yes they are. Patients are advised to question the need twice and discuss it with their physicians. On the other hand for physicians to use CT scans more judiciously, society guidelines and recommendations are not going to be enough. A cultural change at many levels will be needed.