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Nuclear radiation can be incredibly dangerous, but it can also be incredibly useful to us. The Shedding Light on Nuclear Radiation series teaches students what nuclear radiation is and how humans have harnessed its awesome power.
Episode 11, Calculating Equivalent and Effective Doses of Radiation teaches students how to calculate equivalent dose and effective dose to assess radiation exposure risks. It covers absorbed dose, the impact of different radiation types, and how organ sensitivity influences overall risk. Step-by-step examples make these calculations easy to follow!
Video coming soon.
The Episode 11 Question Sheet for Students:
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Transcript (More or Less)
Part A: Introduction
Hi everyone. In this lesson, we’re going to look at some examples of how equivalent dose and effective dose are calculated. Applying mathematics usually makes things easier to understand! The potential harm that ionizing radiation can cause us depends on how much radiation we receive, the type of radiation we receive, and which organs are exposed to radiation.
In Episode 9 of this series (which I recommend that you watch first if you haven’t already), we looked at absorbed dose, equivalent dose and effective dose. We saw that Absorbed Dose is a measure of how much energy is absorbed per kilogram of tissue as a result of a person’s exposure to radiation. The unit for absorbed dose is the gray (Gy). We also saw that the equivalent dose a person receives takes into account the type of radiation that the person is exposed to.
Equivalent dose represents the probability of suffering harm as a result of exposure to radiation. Alpha radiation has a greater ionizing ability than other types of radiation so it increases the probability of suffering harm. The unit for equivalent dose is the sievert.
Thirdly, we also saw that the effective dose, which also represents the probability of suffering harm to the body as a result of radiation exposure, also takes into account which tissues of the body are exposed to radiation. Its unit is also the sievert.
Some tissues of the body are more sensitive to radiation than others, so they’re all given a tissue weighting factor. Stomach tissue, for example, is more sensitive to radiation than liver tissue and is given a higher tissue weighting factor.
If, for example, 100 grams of someone’s stomach tissue is exposed to radiation there’s a higher probability of suffering harm from that exposure than if 100 grams of liver tissue was exposed to the exact same amount of radiation.
Equivalent dose and effective dose are calculated values, based on the amount and type of radiation someone is exposed to and on which tissues of the body are exposed.
The effective dose that a person receives is the most widely used measure of the potential for harm to a person’s health from radiation exposure. The harm might include the development of cancer, radiation sickness, or death. Of course, it also includes the harm to (that is the death of) cancerous cells when they’re exposed to ionizing radiation during radiotherapy, which is a good thing.
So let’s explore the mathematics.
We have absorbed dose, equivalent dose, and effective dose.
These figures here are actually called the Radiation Weighting Factors for each type of radiation.
I can put them all into a table.
The radiation weighting factor is given the symbol W subscript R (WR). The W stands for the weighting factor and the R stands for radiation.
To calculate the equivalent dose (in sieverts) from the absorbed dose (in grays) you simply multiply the absorbed dose by the radiation weighting factor.
Now the symbol for absorbed dose is D subscript T (DT). The D stands for dose and the T stands for tissue as in the tissues of the body. The equivalent dose is given the symbol H subscript T (HT). The H stands for Health and the T again stands for tissue. So, the whole equation in symbols looks like this.
The “H” (for health) was chosen as part of the historical development of radiation-protection terminology, to deliberately try to emphasise how someone’s health could be impaired by radiation. It might be better to think of the H as harm to health!
So let’s do an example.
If a radiation leak in a nuclear reactor results in a worker receiving an absorbed dose of 2 grays of alpha radiation, calculate the equivalent dose in sieverts.
Well, we simply multiply the absorbed dose, 2 gray, by the radiation weighting factor, which is 20 for alpha radiation, and we get 40 sieverts.
Now 1 gray (a single gray) is actually a huge dose of radiation, so radiation dose is often measured in milligrays (where 1 gray equals 1000 milligrays) or micrograys (where 1 gray equals 1 million micrograys). The English letter m stands for milli (1 thousandth) while the Greek letter that we call mu, which is the way that Greeks write the letter m, stands for micro (1 millionth).
The same applies for sieverts, millisieverts, and microsieverts.
It’s a bit weird that “milli” sounds like million but means 1 thousandth, not one millionth. Languages develop weirdly sometimes.
Now how do we calculate effective dose from equivalent dose?
Well, we’ll need the table of tissue weighting factors that we first looked at in Episode 9. Different tissues have different susceptibilities to radiation so they have a different tissue weighting factor. The equation will relate the effective dose to the body, which is given the symbol capital E, the equivalent dose to a particular tissue, given the symbol HT, and the tissue weighting factor for each tissue which is given the symbol WT.
So, the effective dose to the body, E, equals the equivalent dose to Tissue 1 times that tissue’s tissue weighting factor plus the equivalent dose to Tissue 2 times that tissue’s tissue weighting factor and so on.
Effective Dose, E = HTissue 1? × WTissue 1 + ? HTissue 2? × WTissue 2 + …
Basically, if only part of the body was exposed to radiation, we multiply the equivalent dose to each type of tissue that is exposed by the tissue weighting factor of that tissue.
We can also write the formula like this: E=?(HT?×WT?).
This might look complicated, but it isn’t really. Let’s do an example.
A woman is exposed to ionizing radiation in a medical procedure and it’s been determined that her colon received an equivalent dose of 20 mSv and her ovaries received an equivalent dose of 15 mSv. What is the effective dose that she received?
Let me re-write the equation and put in the numbers.
The equivalent dose to the colon (which we’ll call Tissue 1 in this example) can be written as Hcolon which is 20 mSv and the tissue weighting factor for the colon is 0.12.
The equivalent dose to the ovaries (Tissue 2), can be written as Hovaries which is 15 mSv and the tissue weighting factor for the ovaries is 0.08.
The equation can be written like this.
Her effective dose is 20 mSv x 0.12 + 15 mSv x 0.08 which equals 2.4 mSv + 1.2 mSv which equals 3.6 mSv.
This is a fairly normal effective dose that someone undergoing a medical procedure that involves being exposed to nuclear radiation might receive.
Here the question uses millisieverts, but other questions might use sieverts or microsieverts. The equation remains the same so just be consistent with the unit.
As often happens with this kind of mathematical stuff, it seems like a lot to take in at first, but once you do some practise questions, you should find that it’s fairly easy.
Now if a radiation source exposes someone’s whole body (that is, all of the person’s tissues) to an equal amount of radiation, then the effective dose is equal to the equivalent dose. This is because the tissue weighting factors all add to one and of course any number multiplied by the number one is the same number. So, if someone’s whole body receives, for example, an equivalent dose of 3,000 microsieverts, then the effective dose is also 3,000 microsieverts.
Remember, calculating the equivalent dose and the effective dose that someone might have been exposed to is a way of estimating the probability of developing cancer or suffering other harm from radiation exposure. It’s kind of a statistical thing. The higher the dose, the higher the chance of developing cancer or suffering other harm, but it’s important to remember that individual outcomes depend on many factors, like for example genetics and overall health, so no-one can ever say for sure what will happen to a specific person.
And so that’s it. We’re all constantly exposed to natural background radiation (and the amount varies a lot depending on where you live), and we’re exposed to more ionizing radiation if we have an X-ray or a CT scan or undergo some kind of radiotherapy. Large doses of radiation can very very harmful, but that very rarely happens.
I hope you’ve learned a lot about nuclear radiation in this series. I’ll see you in the next one.