Fukushima in Japan has become newsworthy again recently. Many residents have been allowed back to their homes. In January 2019, Scientific American reported that radiation:
“in some places continues to measure at least 5 millisieverts (mSv) a year beyond natural background radiation, five times the added level Japan had recommended for the general public prior to the incident.”
Which all seems very understandable. And then I thought: “what do we even mean by a radiation dose? What’s a millisievert, really?” And that opened a whole can of worms. As I don’t want to deal with this worm-can by myself, I am about to share it with you…
What we learned at school
There are some quantities in radioactivity that are reasonably familiar to many. Half-life is perhaps the most familiar one. It is the time taken for half the radioactive nuclei in a sample to ‘decay’ (transform), and also time for the activity of the sample to fall by half. The activity of a source is the number of nuclear transformations per unit time, measured in s-1 and given the special name becquerel (Bq), so that 1 Bq is one nuclear transformation per second. And 16-18 year old physicists in the UK (and presumably elsewehere) learn that decay constant is the probability per unit time that a given nucleus will decay.
If you want to know more about that stuff, try this post here… Otherwise, continue!
Moving on
As we saw in the quote from Scientific American, the general public seem comfortable thinking about the idea of a “dose” of radiation, and that a dose might be quantified (in millisieverts, for example).
But the idea of a dose is quite complicated, and it’s what this post is about. We’ll lead up to it step by step. We have a fair amount of ground to cover, and new concepts and quantities to meet.
The radiation field
The radiation field is a concept, rather than a quantity to be measured. The diagram shows a schematic of the radiation field arising from the emissions of 16 simultaneously decaying nuclei (the radiation field will change over time, unlike my diagram). I can’t explain it in words any more clearly than the diagram, so I won’t try…
Radiometric and dosimetric quantities
Now we can introduce fluence, which is a property of the radiation field. The fluence at a point is the number of particles incident on a sphere of infinitesimal cross-sectional area. A sphere is chosen to make the fluence independent of the direction of the radiation – a sphere has the same cross-section from every direction. And the sphere is of infinitesimal size to make fluence a point quantity – it has a value at each point in the radiation field.
Now, the quantities we have seen so far (activity, fluence…) are properties of the radioactivity itself. Such quantities are called radiometric quantities…
…And then there are quantities called dosimetric quantities that we haven’t met yet. Dosimetric quantities measure the effects of the radiation on matter in the radiation field.
One dosimetric quantity that is important for our purposes is absorbed dose (there are others such as kerma). Absorbed dose is the amount of energy deposited by radiation per unit mass of a medium at a point. The unit of absorbed dose is therefore the joule per kilogram (J kg-1), which is given the special name gray (Gy), to distinguish it from other quantities that are measured in J kg-1.
Notice that (to return to the premise of this post for a moment), despite the word ‘dose’ in the name, the unit of absorbed dose is the gray, not the sievert. We’re coming to that…
The radiometric and dosimetric quantities mentioned so far are all physical quantities, by which we mean that they are directly measurable. For example, you can measure dosimetric quantities by calorimetric methods (measure how much the radiation warms something up, and infer the amount of energy from that).
But although dosimetric quantities tell you about the effect of radiation in general, they don’t necessarily tell you about the effect on human beings in particular…
Protection quantities
The International Commission on Radiological Protection (ICRP) has defined a set of protection quantities, to estimate the health effects of radiation. They are needed because radiation can have different biological effects, depending on its type and energy, and the type and timescale of the biological exposure.
In addition, absorbed dose is a point quantity. That’s not so useful when worrying about radiation exposure to the human body – it would be better to assess dose across a whole tissue/organ/body.
So here are the protection quantities…
Equivalent dose takes into account the fact that some types of radiation are more harmful to living tissue than others. It does that by multiplying absorbed dose by a weighting factor. For example, gamma rays have a weighting factor of 1, and alpha particles’ weighting factor is 20.
Equivalent dose provides an estimate of ‘chance’ health effects such as cancer, rather than ‘guaranteed’ effects such as burns and tissue damage at higher doses.
The unit of equivalent dose is the joule per kilogram (J kg-1), but to differentiate it from absorbed dose, the J kg-1 in this case is given the special name ‘sievert’ (Sv). (So here’s the first time we’ve met that sievert thing. Note that the size of normal doses over normal timescales means that they are usually reported in millisieverts.)
Effective dose incorporates the different effects of different radiation types too, but it goes further. It also takes into account the different vulnerability of organs within the body. For example, bone marrow has a tissue weighting factor of 0.12, whereas that for skin is 0.01.
Effective dose is also measured in sieverts, and is found by multiplying an equivalent dose by the tissue weighting factor. It is used to evaluate the ‘chance’ health risk to the whole body. So for example, the average annual UK effective radiation dose is 2.7 mSv. To put that in context, a chest X-ray gives you an effective dose of about 0.014 mSv and eating 100 g of brazil nuts results in a dose of 0.01 mSv. More examples are brilliantly given in this infographic from informationisbeautiful.net.
So where’s this can of worms?
But that’s not that hard to understand (apart from the fact we have met three quantities with the word ‘dose’ in the name, and might get them mixed up). What’s the problem? Well…
The protection quantities (you know, those things measured in sieverts) are inherently unmeasurable.
They are calculated from physical quantities such as absorbed dose using conversion factors. Someone has to work out those conversion factors! They are generated through computer models using experiments on ‘anthropomorphic phantoms’. (Yes, that’s a real term! – models that simulate the shape, size and structure of a human body.)
We can’t just leave it there though, or we’d never know how many millisieverts anything is! We need quantities that can be measured and that give estimates of the protection quantities. Luckily, they exist – they are called operational quantities.
Before we meet them, we need to extend our concept of the radiation field.
The ‘expanded and aligned field’ and the ‘ICRU sphere’
Operational quantities are based on doses at a point in phantoms of simple shapes (rather than anthropomorphic ones). One simple phantom is the ‘ICRU sphere’, although I have read that it is being phased out from new definitions. It is a sphere of 30 cm diameter that models human tissue by being composed of C, H, O and N in defined proportions, and having the density of water.
There is a potential problem, in that operational quantities are defined as point functions but they are related to protection quantities that are deliberately not point functions (we want to know the dose to the whole body). So operational quantities refer to the hypothetical ‘expanded and aligned field’:
- An expanded field is the uniform radiation field that agrees with the actual field at the specified point. (It doesn’t really look like the one in the diagram below, because I’ve chosen just nine points for display purposes, but I hope you get the idea)
- An expanded and aligned field is the uniform and unidirectional field that has the same fluence distribution as the expanded field. It is introduced so that the operational quantities do not depend on directional properties of the field.
Operational quantities
Here are three operational quantities, which are all measured in sieverts. They are designed to provide conservative estimates of the protection quantities, and are determined from the physical quantities by measurements on simple phantoms:
Ambient dose equivalent at a point is the dose equivalent that would be produced by the corresponding expanded and aligned field, in the ICRU sphere at a given depth on the radius opposing the direction of the aligned field.
Directional dose equivalent is similar, but the field is only expanded, not aligned. It’s of use in the assessment of dose to the skin or eye lens, where the direction of the radiation matters.
These two quantities are relevant where doses are estimated from monitoring an area for radioactivity. If monitoring a person, personal dose equivalent is relevant, measured with a detector worn at the surface of the body and covered with an appropriate thickness of tissue-equivalent material.
Outro
Any rigour in this post comes from the annals of the International Commission on Radiation Units and Measurements, and International Commission on Radiological Protection. Any mistakes are due to me misunderstanding them. I’m not an expert in this, and I’m sure I haven’t taught you how to measure anything in radiation physics.
But when we read that some members of the Japanese population are still receiving [an effective dose of] 5 mSv per year more than the upper recommended limit, I hope I’ve shown how involved, complicated and detailed a statement that is. For example, when personal dosemeters, like those worn by radiation workers, are calibrated, all these types of quantity are at play in the calibration, to give a single estimate of whatever is meant by ‘dose’.