# Basic Physics of Nuclear Medicine/Production of Radioisotopes

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Most of the radioisotopes found in nature have relatively long half
lives. They also belong to elements which are not handled well by the
human body. As a result medical applications generally require the use
of radioisotopes which are produced artificially.

We have looked at the subject of radioactivity in earlier chapters of
this wikibook and have then progressed to cover the interaction of
radiation with matter, radiation detectors and imaging systems. We
return to sources of radioactivity in this chapter in order to learn
about methods which are used to make radioisotopes.

The type of radioisotope of value to nuclear medicine imaging should
have characteristics which keep the radiation dose to the patient as low
as possible. For this reason they generally have a short half life and
emit only gamma-rays - that is no alpha-particle or beta-particle
emissions. From an energy point of view the gamma-ray energy should not
be so low that the radiation gets completely absorbed before emerging
from the patient\'s body and not too high that it is difficult to
detect. For this reason most of the radioisotopes used emit gamma-rays
of medium energy, that is between about 100 and 200 keV. Finally since
the radioisotope needs to be incorporated into some form of
radiopharmaceutical it should also be capable of being produced in a
form which is amenable to chemical, pharmaceutical and sterile
processing.

The production methods we will consider are nuclear fission, nuclear
bombardment and the radioisotope generator.

## Nuclear Fission

We were introduced to spontaneous fission in chapter
2
where we saw that a heavy nucleus can break into a number of fragments.
This disintegration process can be induced to occur when certain heavy
nuclei absorb neutrons. Following absorption of a neutron such nuclei
break into smaller fragments with atomic numbers between about 30 and
65. Some of these new nuclei are of value to nuclear medicine and can be
separated from other fission fragments using chemical processes.

The fission process is controlled inside a device called a nuclear
reactor. One such reactor exists in
Australia at Lucas Heights in New South Wales and
many others exist throughout the world.

## Nuclear Bombardment

In this method of radioisotope production charged particles are
accelerated up to very high energies and caused to collide into a target
material. Examples of such charged particles are protons, alpha
particles and deuterons. New nuclei can be formed when these particles
collide with nuclei in the target material. Some of these nuclei are of
value to nuclear medicine.

An example of this method is the production of ^22^Na where a target of
^24^Mg is bombarded with deuterons, that is:
`{{nowrap|{{chem|24|Mg}} + {{chem|2|H}} → {{chem|22|Na}} + {{chem|4|He}}.}}`{=mediawiki}

A deuteron you will remember from chapter
1 is the second most common
isotope of hydrogen, that is ^2^H. When it collides with a ^24^Mg
nucleus a ^22^Na nucleus plus an alpha particle is produced. The target
is exposed to the deuterons for a period of time and is subsequently
processed chemically in order to separate out the ^22^Na nuclei.

The type of device commonly used for this method of radioisotope
production is called a cyclotron. It consists
of an ion gun for producing the charged particles, electrodes for
accelerating them to high energies and a magnet for steering them
towards the target material. All arranged in a circular structure.

## Radioisotope Generator

![](NM11_2.gif "NM11_2.gif"){width="140"}

This method is widely used to
produce certain short-lived radioisotopes in a hospital or clinic. It
involves obtaining a relatively long-lived radioisotope which decays
into the short-lived isotope of interest.

A good example is ^99m^Tc which as we have noted before is the most
widely used radioisotope in nuclear medicine today. This isotope has a
half-life of six hours which is rather short if we wish to have it
delivered directly from a nuclear facility. Instead the nuclear facility
supplies the isotope ^99^Mo which decays into ^99m^Tc with a half life
of about 2.75 days. The ^99^Mo is called the **parent** isotope and
^99m^Tc is called the **daughter** isotope.

So the nuclear facility produces the parent isotope which decays
relatively slowly into the daughter isotope and the daughter is
separated chemically from the parent at the hospital/clinic. The
chemical separation device is called, in this example, a **^99m^Tc
Generator**:

It consists of a ceramic column with ^99^Mo
adsorbed onto its top surface. A solution
called an **eluent** is passed through the column, reacts chemically
with any ^99m^Tc and emerges in a chemical form which is suitable for
combining with a pharmaceutical to produce a radiopharmaceutical. The
arrangement shown in the figure on the right is called a **Positive
Pressure** system where the eluent is forced through the ceramic column
by a pressure, slightly above atmospheric pressure, in the eluent vial.

The ceramic column and collection vials need to be surrounded by lead
shielding for radiation protection purposes. In addition all components
are produced and need to be maintained in a sterile condition since the
collected solution will be administered to patients.

Finally an Isotope
Calibrator
is needed when a ^99m^Tc Generator is used to determine the
radioactivity for preparation of patient doses and to check whether any
^99^Mo is present in the collected solution.\

## Operation of a 99m-Tc Generator

Suppose we have a sample of ^99^Mo and suppose that at time $t=0$ there
are $N_0$ nuclei in our sample and nothing else. The number $N(t)$ of
^99^Mo nuclei decreases with time according to radioactive decay law as
discussed in Chapter
3:\
\

```{=html}
<div class="center">
```
$N(t)=N_\mathrm{0}e^{-\lambda_\mathrm{Mo}t}$

```{=html}
</div>
```
\
where $\lambda_\mathrm{Mo}$ is the decay constant for ^99^Mo.\
\
Thus the number of ^99^Mo nuclei that decay during a small time interval
$dt$ is given by\
\

```{=html}
<div class="center">
```
$\mathrm{d}N(t)=-\lambda_\mathrm{Mo} N_\mathrm{0} e^{-\lambda_\mathrm{Mo}t}\mathrm{d}t$

```{=html}
</div>
```
\
Since ^99^Mo decays into ^99m^Tc, the same number of ^99m^Tc nuclei are
formed during the time period $dt$. At a time $t'$, only a fraction
$\mathrm{d}n(t')$ of these nuclei will still be around since the ^99m^Tc
is also decaying. The time for ^99m^Tc to decay is given by $t'-t$.
Plugging this into radioactive the decay law we arrive at:\
\

```{=html}
<div class="center">
```
$\mathrm{d}n(t')=-\mathrm{d}N(t)e^{-\lambda_\mathrm{Tc}\left(t'-t\right)}=\lambda_\mathrm{Mo} N_\mathrm{0}e^{-\lambda_\mathrm{Mo}t}e^{-\lambda_\mathrm{Tc}\left(t'-t\right)}\mathrm{d}t$

```{=html}
</div>
```
\
Now we sum up the little contributions $\mathrm{d}n(t')$. In other words
we integrate over $t$ in order to find the number $n(t')$, that is the
number of all ^99m^Tc nuclei present at the time $t'$:\
\

```{=html}
<div class="center">
```
$n(t')=\int_0^{t'}-\mathrm{d}N(t')e^{-\lambda_\mathrm{Tc}\left(t'-t\right)}=\lambda_\mathrm{Mo}N_\mathrm{0}e^{-\lambda_\mathrm{Tc}t'} \int_0^{t'}e^{\left( \lambda_\mathrm{Tc}-\lambda_\mathrm{Mo}\right)t} \mathrm{d}t$

```{=html}
</div>
```
\
Finally solving this integral we find:

```{=html}
<div class="center">
```
$\begin{matrix}
\Rightarrow n(t')&=& \frac{\lambda_\mathrm{Mo}}{\lambda_\mathrm{Tc}-\lambda_\mathrm{Mo}}N_\mathrm{0} e^{-\lambda_\mathrm{Tc}t'}\left(e^{\left( \lambda_\mathrm{Tc}-\lambda_\mathrm{Mo}\right)t'} -1\right) \\
\end{matrix}$

```{=html}
</div>
```
The figure below illustrates the outcome of this calculation. The
horizontal axis represents time (in days), while the vertical one
represents the number of nuclei present (in arbitrary units). The green
curve illustrates the exponential decay of a sample of pure ^99m^Tc. The
red curve shows the number of ^99m^Tc nuclei present in a ^99m^Tc
generator that is never eluted. Finally, the blue curve shows the
situation for a ^99m^Tc generator that is eluted every 12 hours.

!Comparison of the physical decay of ^99m^Tc with its activity arising
from ^99^Mo decay in a radioisotope generator with and without elution
at 12 hour
intervals.

Photographs taken in a nuclear medicine hot lab are shown below:

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  !Pb shielding surrounding the laminar flow cabinet, where radiopharmaceuticals are prepared.{width="180"}   !Another view of the Pb shielding surrounding a laminar flow cabinet.{width="180"}
                                                                                                                                                                                                                                                    
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## External links

-   Concerns over Molybdenum
    Supplies
    -- news from 2008 compiled by the British Nuclear Medicine Society.
-   Cyclotron Java
    Applet -- a
    Java-based interactive demonstration of the operation of a cyclotron
    from GFu-Kwun Hwang, Dept. of Physics, National Taiwan Normal
    University, Virtual Physics Laboratory.
-   Nuclear Power Plant
    Demonstration -- a
    Java-based interactive demonstration of controlling a nuclear
    reactor. Also contains nuclear power Information links.
-   ANSTO -- information about Australia\'s
    nuclear organization.
-   Medical
    Valley --
    contains information on what nuclear medicine is, production of
    nuclear pharmaceuticals, molybdenum and technetium -- from The
    Netherlands Energy Research Foundation Petten.

