Radiation Exposure - Dose and Dose Rate (the Gray & Sievert)

Published: Dec 13, 2022

    Tags:
  • Gray
  • Sievert
  • Radiation exposure
  • Dose
  • Dose Rate

Source: Ionactive Radiation Protection Resource

The Gray (Gy)

The base unit of radiation exposure is absorbed dose and this is measured in gray (Gy). The Gy is an SI unit (International System of Units). In physics terms, when ionising radiation interacts with a substance, that substance absorbs a dose of radiation of 1Gy at the rate of 1J/kg. The ionising radiation might include alpha / beta particles, x-rays / gamma rays / neutrons or something more exotic (or a combination of more than one).

What surprises many is that an energy absorption of 1J/kg does not sound like much, when you consider, for example, that it takes 4200J to raise 1kg of water by 1C (which is why your kettle will be rated at 3kW or more!). It may surprise further still that a potential lethal dose of ionising radiation to the whole body is somewhere between 3-5 Gy - this is the LD50/60 where 50% of those exposed would die within 60 days without medical intervention. Above about 10Gy whole body dose, the likelihood of death is nearer 100% regardless of medical intervention. What we are describing are deterministic radiation effects which we do not need to get too deep into - suffice to say they are effects with a threshold, below which the effect will not occur. Health effects are clinically observable (e.g. sickness, nausea, reddening of the skin) and the severity will depend on the dose delivered above the threshold and the dose rate of delivery (minutes, hours, days etc).

Note that whilst we have mentioned whole body exposure to a person, the Gy as defined above, can be applied to any material or object. The fact that Gy levels of exposure can lead to significant health effects, for a modest energy input, is because ionising radiation acts on an object at theatomic level - ionising (removal of electrons from an atomic bond causing ion pair production). Not a lot of energy is required to do this, as compared with raising the temperature of water.

Generally the Gy is not used regularly for the purposes of radiation safety - certainly this being the case at high doses / dose rates in the Gy range.

Where might the Gy be used / considered?
  1. Radiotherapy - typical target treatment fraction might be 3Gy, with a total dose of perhaps 40-50 Gy delivered over a number of days or weeks (known as dose fractions). Note these values are NOT whole body doses, they are carefully collimated doses delivered to a tumour whilst minimising doses to healthy surrounding tissue.
  2. Diagnostic imaging - for example measuring skin entrance doses during interventional fluoroscopy. Here units of mGy (0.001 Gy) and Gy.cm2 are often used.
  3. Industrial sterilisation where doses of up to 50kGy may be delivered to an item for the purposes of sterilisation (e.g. hip replacement parts) or for radiation crosslinking (e.g. hardening rubber hoses for the automotive industry).
  4. Environmental studies of ambient natural or man made gamma radiation (generally nGy/h or μGy/h are used). These will be measurements made in air and could undergo conversion to sieverts - see later below for further comment.
  5. Dose assessment following a radiation accident where Gy levels of exposure is suspected or known. This is safety related, but not the type of assessment you want to be involved in routinely since it implies a significant break down in control measures.
The Gy and number multipliers

These have already been used in the above text. A full consideration of this is given in our first resource post for this series - Radiation protection - the number system. Typical examples are:

kGy (103 Gy)

Gy (1 Gy)

mGy (0.001 Gy)

μGy (10-6 Gy)

nGy (10-9 Gy)

The Sievert (Sv)

For many the sievert (Sv) will be more familiar, either due to work in a relevant industry (i.e. radiation related), on product literature, in TV documentaries and so on.

It is important to know that the Sv is a derived quantity and is a modification of dose (or dose rate) in Gy. However, often you will not see 'under the hood' so a radiation monitor may read in μSv/h and a personal dosimetry badge result may be in mSv - however behind the scenes the Gy will have been utilised.

The Sv can be applied to two dose expressions and this might seem confusing at first - they are equivalent dose and effective dose. The order of application is :

Absorbed Dose (Gy) → Equivalent Dose (Sv) → Effective Dose (Sv)

The Sv represents the biological effectiveness of ionising radiation, specifically it's ability to cause changes in the DNA of cells which may lead to cancer or genetic damage. Unlike the Gy which is deterministic (has a threshold), the Sv is a risk term (stochastic) so it is the probability of a health effective which is proportional to radiation exposure, and not the severity. The term LNT (linear no threshold) is often quoted when considering the Sv, as the probability vs dose is expressed as a straight line throughout. There is much more to this, including much controversy from some commentators regarding the validity of LNT. However, for this resource we will stick with what is recognised by most of the radiation protection community such as the ICRP (International Commission on Radiological Protection).

Just remember that sievert is all about risk.

In order to derive the risk term (effective dose) we need to use two modifiers.

1) Radiation Weighting Factor (RWF) - this modifies the Gy by considering the radiobiological effectiveness of a given type of ionising radiation to cause damage to the DNA of cells. Examples:

Beta, Gamma, X-ray → RWF = 1

Alpha Particles → RWF = 20

It is a simple multiplication of the Gy by this factor and the result is Equivalent Dose (Sv).

2) Tissue Weight Factor (TWF) - this modifies the Equivalent Dose further by considering the relative susceptibility of individual body tissues to yield a radiation induced cancer. Examples:

  • Lung → 0.12
  • Liver → 0.04
  • Brain → 0.01
  • Others → (Google them!)
  • Remainder→ 0.12

We have not listed every TWF - but you get the basic idea. An important point, often not highlighted sufficiently, is that all the TWF together add up to 1, and "1" therefore represents a uniform radiation exposure (whole body exposure).

Note that both RWF / TWF are technically dimensionless, the unit names are changed by convention as required.

To see how this works consider the following examples.

Example 1 - simple whole body exposure to a broad beam of x-rays

The body is being exposed to a uniform dose rate of 1mGy/h x-rays. What is the whole body effective dose after 1 hour?

Equivalent Dose (mSv) = 1Gy/h x RWFx-ray (1) = 1mSv/h

Effective whole body dose = 1mSv/h x TWFbody (1) = 1mSv/h

So for one hour we have 1mSv effective whole body dose.

So far so good, and at this stage you may wonder what the whole point of this is! Read on, check out example 2.

Example 2 - lung exposure to radon gas (alpha emitter)

It is known that the lung of a person has been exposed to 0.42 mGy of radon gas (an alpha emitter). What is the whole body effective dose?

You might at once wonder how you can you obtain a whole body dose from radon exposure to the lungs? You cannot (physically!), but by using the above method we can express the risk of that exposure as a whole body effective dose.

Equivalent Dose (Sv) = 0.42mGy x RWFAlpha (20) = 8.4mSv

Effective Whole Body Dose (Sv) = 8.4mSv x TWFLung (0.12) = 1.008 mSv (so very near 1mSv)

What do you notice? The whole body effective doses are the same for the x-ray exposure over the whole body, and the radon exposure to the lung !

Why is this? Both results of 1mSv represent the overall risk of radiation induced cancer. This allows us to compare risks from whole body exposures, with exposures to specific parts of the body - using a common unit of effective whole body dose. Obviously we have chosen specific starting doses in mGy in order to end up with the same effective dose (mSv) - this was deliberate to help explain this concept.

Finally, what is the actual risk of the radiation exposure based on LNT and ICRP?

Broadly speaking it is 5% / Sv (there are subtle differences for different age groups but not enough to materially change our discussion). This is excess risk, i.e. risk of radiation induced cancer over and above expected cases of fatal cancer in a population from all other causes.

This means the the 1mSv calculated for the x-ray exposure and the radon lung exposure have an excess cancer risk of 1:20,000 (remember LNT means linear). In the UK compare that with the life time risk of developing and dying of cancer which is about 1:4.

For more information on UK occupational dose limits please see this Ionactive resource : IRR17 (12) - Dose limitation

And this is (basically) how the sievert works.

Where might the Sv be used / considered?

Generally the Sv may be considered in one of three broad categories.

  1. Public exposure. This might be from naturally occurring exposures (such as radon gas or K-40 in foods), or from artificial derived exposures such as doses from radioactive discharges to the environment. In the UK an example might be that the average person is exposed to 3000μSv of background radiation per year (with radon gas being the biggest contributor).
  2. Occupational Exposure. This is exposure to individuals who work with ionising radiation as part of their employment. The average UK occupational exposure is < 1mSv effective whole body dose per year. Higher occupational categories will include long haul airline cabin view and pilots on about 3mSv/year (cosmic radiation), and perhaps cyclotron engineers (who support medical PET radionuclide production) who may be on 5mSv or more a year. The legal limit in the UK is 20mSv whole body effective dose (other equivalent dose limits apply to extremities, skin, and eyes). It may surprise you that nuclear industry workers do not get a mention (they do now) - average effective whole body exposures across the nuclear industry are substantially < 1mSv/year.
  3. Medical exposures. Medical exposures are on average much higher than public or occupational exposures. This is justified because the benefit gained from ionising radiation used in diagnosis or treatment will outweigh the risk (i.e. the medical procedure might be life saving). For example, a typical x-ray at the dentist may yield up 30μSv for a panoramic examination (note this is expressed as effective whole body dose, even though the x-ray is delivered to the head). A whole body CT scan may yield a whole body effective dose of 20mSv or more. When discussing the Gy earlier we mention that a full radiotherapy treatment might be 50Gy (on target). The Gy is the correct unit since radiotherapy relies on controlled deterministic effects. However, whole body effective dose cannot be avoided due to scattered radiation and leakage from the radiotherapy unit. This might amount to perhaps 200-400 mSv whole body dose for a full treatment. Whilst this might sound a lot when compared to occupational exposure, you need to recall that radiotherapy is life saving so the risk of future radiation induced cancer (from the treatment) needs to be offset against the 'do nothing' approach which may lead to early end of life.

Note: From time to time you may, incorrectly, see the Sv is used thus- 'they had a whole body dose of 20Sv and died'. This type of statement has appeared in TV documentaries. At that level of "dose" they should be talking in Gray (Gy), cancer risk is a diversion where deterministic effects dominate.

The Sv and number multipliers

The proceeding section will make this section rather short and obvious. Typical multipliers will be as follows:

Sv - 1 (rarely used / measured in occupational radiation protection)

mSv - 0.001 of a Sv

μSv - 0.001 of a mSv

nSv - 0.001 of a μSv (rarely used, might find this in environmental dose rate assessments).

Very unlikely to see kSv or MSv, if you do then these should be expressed in Gy as explained earlier. A possible exception is where the term person-Sv is used (or Man-Sv). This is not widely used and is related to collective dose. Collective dose is where you add up many small μSv level doses to persons in a large population which yields a large collective dose (e.g. if the population was > 1 million). Some have used this approach to calculate likely detriment to a population such that you can express this as numbers of excess radiation induced cancers. Many consider this to be a major simplification and most radiation safety legislation today is based on protection of the individual rather than sharing risk amongst a large population.

Dose and dose rate

This should be simple - and it is! However, we see many errors, miscalculations and poor record keeping regarding this subject, so it is worth a few words to state the obvious!

  • μSv is a Dose.
  • μSv/h is a Dose Rate.

In the UK (for example) you have to be careful with the legal definition. Reg (2) of IRR17 (see Ionactive IRR17 radiation protection guide) defines dose rate as 'dose rate of ionising radiation averaged over 1 minute'. In most cases, practically speaking this means the dose rate that you read from your radiation monitor. However, consider a dose 'rate' of 60μSv/h for two seconds followed by 0.05 μSv/h (background) for the other 58 seconds of the minute. That is an average of about 2μSv/h (as defined by IRR17). It is beyond the scope of this resource to discuss this result in more detail, but suffice to say there are interesting applications in radiotherapy where this definition comes in very useful. Note also that even where you might specify an instantaneous dose rate (IDR), the definition still applies - so instantaneous can still be averaged over a minute (if there is an advantage in doing so).

The Rad and the Rem

We finish this resource by just touching on the Non-SI units (which of course came before the Gray and the Sievert). These units are still regularly used in the USA but even here official technical papers are heading towards SI units.

The conversion is simple.

  • 1Gy = 100 Rad
  • 1Sv = 100 Rem

Despite being simple, there is still some head scratching involved in swapping between units. Ionactive is involved in several joint projects involving US clients and so conversions have to be carefully checked! Examples are as follows.

  • 10μSv/h = 1 mRem/h
  • 1μRem = 0.01μSv
  • 1Rad = 0.01Gy

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