# Basic Physics of Nuclear Medicine/Units of Radiation Measurement

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## Introduction

This is the fourth chapter of a wikibook entitled Basic Physics of
Nuclear Medicine.

After that rather long and detailed chapter we have just finished we
will now proceed at a more leisurely pace for a short treatment of some
of the more common units of measurement used in this field.

Before we do so however it is useful to consider the typical radiation
environment. By doing so we will gain an appreciation of the various
quantities that can be measured before considering the units which are
used to express such measurements. So, we will first of all consider a
typical radiation situation and then go on to consider the various units
of measurement.

## A Typical Radiation Situation

A typical radiation set-up is shown in the figure below. Firstly there
is a **source** of radiation, secondly a radiation **beam** and thirdly
some **material** which absorbs the radiation. So the quantities which
can be measured are associated with the source, the radiation beam and
the absorber.

```{=html}
<div class="center">
```
![](NM5_1.gif "NM5_1.gif")

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This type of environment could be one where the radiation from the
source is used to irradiate a patient (that is the absorber) for
diagnostic purposes where we would place a device behind the patient for
producing an image or for therapeutic purposes where the radiation is
intended to cause damage to a specific region of a patient. It is also a
situation where we as an absorber may be working with a source of
radiation.

## The Radiation Source

When the radiation source is a radioactive one the quantity that is
typically measured is the radioactivity of the source. We saw in the
previous chapter that the units used to express radioactivity are the
**becquerel** (SI unit) and the **curie** (traditional unit).

## The Radiation Beam

The characteristic of a radiation beam that is typically measured is
called the **Radiation Exposure**. This quantity expresses how much
ionisation the beam causes in the air through which it travels.

We will see in the following
chapter
that one of the major things that happens when radiation encounters
matter is that ions are formed -- air being the form
of matter it encounters in this case. So the radiation exposure produced
by a radiation beam is expressed in terms of the amount of ionisation
which occurs in air.

A straight-forward way of measuring such ionisation is to determine the
amount of electric charge which is produced. You will remember from your
high school physics that the SI unit of electric charge is the
**coulomb**.

The SI unit of radiation exposure is the **coulomb per kilogram** -- and
is given the symbol C kg^-1^. It is defined as the quantity of X- or
gamma-rays such that the associated electrons emitted per kilogram of
air at standard temperature and pressure (STP) produce ions carrying 1
coulomb of electric charge.

The traditional unit of radiation exposure is the **roentgen**, named in
honour of Wilhelm Roentgen (who
discovered X-rays) and is given the symbol R. The
roentgen is defined as the quantity of X- or
gamma-rays such that the associated electrons emitted per kilogram of
air at STP produce ions carrying 2.58 x 10^-4^ coulombs of electric
charge.

So 1 R is a small exposure relative to 1 C kg^-1^ -- in fact it is 3,876
times smaller.

Note that this unit is confined to radiation beams consisting of X-rays
or gamma-rays.

Often it is not simply the exposure that is of interest but the exposure
rate, that is the exposure per unit time. The units which tend to be
used in this case are the C kg^-1^ s^-1^ and the R hr^-1^.

## The Absorber

Energy is deposited in the absorber when radiation interacts with it. It
is usually quite a small amount of energy but energy nonetheless. The
quantity that is measured is called the **Absorbed Dose** and it is of
relevance to all types of radiation be they X- or gamma-rays, alpha- or
beta-particles.

The SI unit of absorbed dose is called the **gray**, named after a
famous radiobiologist, LH Gray, and is
given the symbol Gy. The gray "wikilink") is defined as
the absorption of 1 joule of radiation energy per kilogram of material.
So when 1 joule of radiation energy is absorbed by a kilogram of the
absorber material we say that the absorbed dose is 1 Gy.

The traditional unit of absorbed dose is called the **rad**, which
supposedly stands for Radiation Absorbed
Dose "wikilink"). It is defined as the absorption of
10^-2^ joules of radiation energy per kilogram of material.

As you can figure out 1 Gy is equal to 100 rad.

There are other quantities derived from the gray and the rad which
express the biological effects of such absorbed radiation energy when
the absorber is living matter -- human tissue for example. These
quantities include the Equivalent Dose,
`<span style="color:red;">`{=html}H`</span>`{=html}, and the Effective
Dose,
`<span style="color:red;">`{=html}E`</span>`{=html}. The Equivalent Dose
is based on estimates of the ionization capability of the different
types of radiation which are called **Radiation Weighting Factors**,
`<span style="color:red;">`{=html}w~R~`</span>`{=html}, such that

```{=html}
<div class="center">
```
`<span style="color:red;">`{=html}`<big>`{=html}H = w~R~
D`</big>`{=html}`</span>`{=html}

```{=html}
</div>
```
where `<span style="color:red;">`{=html}D`</span>`{=html} is the
absorbed dose. The Effective Dose includes
`<span style="color:red;">`{=html}w~R~`</span>`{=html} as well as
estimates of the sensitivity of different tissues called **Tissue
Weighting Factors**,
`<span style="color:red;">`{=html}w~T~`</span>`{=html}, such that

```{=html}
<div class="center">
```
`<span style="color:red;">`{=html}`<big>`{=html}E = Σ w~T~
H`</big>`{=html}`</span>`{=html}

```{=html}
</div>
```
where the summation,
`<span style="color:red;">`{=html}Σ`</span>`{=html}, is over all the
tissue types involved. Both the Equivalent Dose and the Effective Dose
are measured in derived SI units called sieverts
(Sv).

Let us pause here for a bit to ponder on the use of the term *dose*. It
usually has a medical connotation in that we can say that someone had a
dose of the \'flu, or that the doctor prescribed a certain dose of a
drug. What has it to do with the deposition of energy by a beam of
radiation in an absorber? It could have something to do with the initial
applications of radiation in the early part of the 20^th^ century when
it was used to treat numerous diseases. As a result we can speculate
that the term has stayed in the vernacular of the field. It would be
much easier to use a term like absorbed radiation energy since we are
talking about the deposition of energy in an absorber. But this might
make the subject just a little too simple!

## Specific Gamma Ray Constant

A final quantity is worth mentioning with regard to radiation units.
This is the Specific Gamma-Ray Constant for a radioisotope. This
quantity is an amalgam of the quantities we have already covered and
expresses the exposure rate produced by the gamma-rays emitted from a
radioisotope.

It is quite a useful quantity from a practical viewpoint when we are
dealing with a radioactive source which emits gamma-rays. Supposing you
are using a gamma-emitting radioactive source (for example ^99m^Tc or
^137^Cs) and you will be standing at a certain distance from this source
while you are working. You most likely will be interested in the
exposure rate produced by the source from a radiation safety point of
view. This is where the Specific Gamma-Ray Constant comes in.

It is defined as the exposure rate per unit activity at a certain
distance from a source. The SI unit is therefore the

```{=html}
<div class="center">
```
`<span style="color:red;">`{=html}`<big>`{=html}C kg^-1^ s^-1^ Bq^-1^ at
1 m `</big>`{=html}`</span>`{=html},

```{=html}
</div>
```
and the traditional unit is the

```{=html}
<div class="center">
```
`<span style="color:red;">`{=html}`<big>`{=html}R hr^-1^ mCi^-1^ at 1 cm
`</big>`{=html}`</span>`{=html} .

```{=html}
</div>
```
These units of measurement are quite cumbersome and a bit of a mouthful.
It might have been better if they were named after some famous scientist
so that we could call the SI unit 1 **smith** and the traditional unit 1
**jones** for example. But again things are not that simple!

## The Inverse Square Law

Before we finish this chapter we are going to consider what happens as
we move our absorber away from the radiation source. In other words we
are going to think about the influence of distance on the intensity of
the radiation beam. You will find that a useful result emerges from this
that has a very important impact on radiation safety.

The radiation produced in a radioactive source is emitted in all
directions. We can consider that spheres of equal radiation intensity
exist around the source with the number of photons/particles spreading
out as we move away from the source.

Consider an area on the surface of one of these spheres and assume that
there are a certain number of photons/particles passing though it. If we
now consider a sphere at a greater distance from the source the same
number of photons/particles will now be spread out over a bigger area.
Following this line of thought it is easy to appreciate that the
radiation intensity, I will decrease with the square of the distance, r
from the source, i.e.

```{=html}
<div class="center">
```
$I \propto \frac{1}{r^2}$

```{=html}
</div>
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This effect is known as the Inverse Square
Law. As a result if we double the
distance from a source, we reduce the intensity by a factor of two
squared, that is 4. If we triple the distance the intensity is reduced
by a factor of 9, that is three squared, and so on.

This is a very useful piece of information if you are working with a
source of radiation and are interested in minimising the dose of
radiation you will receive.

## External links

-   Radiation and
    Risk -- covers
    the effect of radiation, how risks are determined, comparison of
    radiation with other risks and radiation doses.
-   Radiation Effects
    Overview -- results
    of studies of victims of nuclear bombs including early effects on
    survivors, effects on the in utero exposed, and late effects on the
    survivors -- from the Radiation Effects Research Foundation, a
    cooperative Japan-United States Research Organization.
-   The Radiation and Health Physics Home
    Page -- all you ever wanted to know
    about radiation but were afraid to ask\....with hundreds of WWW
    links -- from the Student Chapter of the Health Physics Society,
    University of Michigan containing sections on general information,
    regulatory Information, professional organizations and societies,
    radiation specialties, health physics research and education.
-   What You Need to Know about
    Radiation
    -- to protect yourself to protect your family to make reasonable
    social and political choices -- covers sources of radiation and
    radiation protection -- by Lauriston S. Taylor.

