# 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 22Na where a target of 24Mg is bombarded with deuterons, that is: 24Mg + 2H22Na + 4He.

A deuteron you will remember from chapter 1 is the second most common isotope of hydrogen, that is 2H. When it collides with a 24Mg nucleus a 22Na 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 22Na 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.

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 99mTc 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 99Mo which decays into 99mTc with a half life of about 2.75 days. The 99Mo is called the parent isotope and 99mTc 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 99mTc Generator:

It consists of a ceramic column with 99Mo adsorbed onto its top surface. A solution called an eluent is passed through the column, reacts chemically with any 99mTc 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 99mTc Generator is used to determine the radioactivity for preparation of patient doses and to check whether any 99Mo is present in the collected solution.

## Operation of a 99m-Tc Generator

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

${\displaystyle N(t)=N_{\mathrm {0} }e^{-\lambda _{\mathrm {Mo} }t}}$

where ${\displaystyle \lambda _{\mathrm {Mo} }}$ is the decay constant for 99Mo.

Thus the number of 99Mo nuclei that decay during a small time interval ${\displaystyle dt}$ is given by

${\displaystyle \mathrm {d} N(t)=-\lambda _{\mathrm {Mo} }N_{\mathrm {0} }e^{-\lambda _{\mathrm {Mo} }t}\mathrm {d} t}$

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

${\displaystyle \mathrm {d} n(t')=-\mathrm {d} N(t)e^{-\lambda _{\mathrm {Tc} }\left(t'-t\right)}=\lambda _{\mathrm {Mo} }N_{\mathrm {0} }e^{-\lambda _{\mathrm {Mo} }t}e^{-\lambda _{\mathrm {Tc} }\left(t'-t\right)}\mathrm {d} t}$

Now we sum up the little contributions ${\displaystyle \mathrm {d} n(t')}$. In other words we integrate over ${\displaystyle t}$ in order to find the number ${\displaystyle n(t')}$, that is the number of all 99mTc nuclei present at the time ${\displaystyle t'}$:

${\displaystyle n(t')=\int _{0}^{t'}-\mathrm {d} N(t')e^{-\lambda _{\mathrm {Tc} }\left(t'-t\right)}=\lambda _{\mathrm {Mo} }N_{\mathrm {0} }e^{-\lambda _{\mathrm {Tc} }t'}\int _{0}^{t'}e^{\left(\lambda _{\mathrm {Tc} }-\lambda _{\mathrm {Mo} }\right)t}\mathrm {d} t}$

Finally solving this integral we find:

${\displaystyle {\begin{matrix}\Rightarrow n(t')&=&{\frac {\lambda _{\mathrm {Mo} }}{\lambda _{\mathrm {Tc} }-\lambda _{\mathrm {Mo} }}}N_{\mathrm {0} }e^{-\lambda _{\mathrm {Tc} }t'}\left(e^{\left(\lambda _{\mathrm {Tc} }-\lambda _{\mathrm {Mo} }\right)t'}-1\right)\\\end{matrix}}}$

The figure below illustrates the outcome of this calculation. The horizontal axis represents time (in days), while the vertical one represents the number of nulcei present (in arbitrary units). The green curve illustrates the exponential decay of a sample of pure 99mTc. The red curve shows the number of 99mTc nuclei present in a 99mTc generator that is never eluted. Finally, the blue curve shows the situation for a 99mTc generator that is eluted every 12 hours.

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

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

 Pb shielding surrounding the laminar flow cabinet, where radiopharmaceuticals are prepared. Another view of the Pb shielding surrounding a laminar flow cabinet.