A2 Physics;Research Report - Use and Function of Positron Emission Tomography

The Use and Function of Positron Emission Tomography Scanners

Introduction

Positron emission tomography (PET) is a technique that is revolutionizing research into the activity of the brain. A patient inhales carbon monoxide containing some carbon-11 isotopes or some other biologically active molecules which emit positrons. Carbon monoxide attaches to haemoglobin molecules in red blood cells with a greater affinity than oxygen, to form carboxyhaemoglobin almost irreversibly.

Using the example of carbon-11, when areas of the brain are active the blood flow to them increases, so the concentration of carbon-11 in that part of the brain increases. The 11C isotope of carbon is artificial and decays by β+ (positron) emission. Within about 1mm of its emission point a positron will annihilate with an electron to produce two gamma-ray photons. As the positrons are not moving that quickly when they annihilate with an electron the two photons emerge virtually back-to-back, which conserves momentum. The patient is surrounded by a ring of scintillation counters with detect the emerging gamma-ray photons (scintillation counters are photomultiplier tubes, each with its own sodium iodide crystals). A computer processes this information to reconstruct, very accurately, the point inside the patient from which the photons originated. The result is a map of the blood flow in the brain. If the patient is asked to carry o some activity such as reading, the PET scanner can detect the change in blood flow as parts of the brain become active. One disadvantage of the technique is that it cannot record the activity of parts of the brain that are constantly active – only changes in blood flow can be detected.

Basic Nuclear Physics

Atomic Structure and Radioactivity

Matter is composed of atoms. An atom consists of a nucleus containing protons and neutrons, collectively called nucleons, and electrons existing as orbitals around the nucleus. The electrons, within this state, move without loss of energy. The number of protons and neutrons in a nucleus are represented by Z and N respectively. The sum of the number of neutrons and protons is the mass number denoted by A. A unique combination of a given number of protons and neutrons in a nucleus leads to an atom called the nuclide. A nuclide X is represented by .

The properties of discussed subatomic particles are listed below:

(a.m.u. refers to atomic mass units; a scale upon which one carbon-12 atom has a mass of exactly 12 atomic mass units. 5s.f. is short for 5 significant figures)

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The properties of discussed subatomic particles are listed below:

(a.m.u. refers to atomic mass units; a scale upon which one carbon-12 atom has a mass of exactly 12 atomic mass units. 5s.f. is short for 5 significant figures)

The electrons exist as different energy shells designated as K-shell, L-shell, M-shell etc., with the K-shell being the innermost shell. In the most stable configuration, the electrons occupy the innermost orbits, where they are most tightly bound by the attraction of the relatively heavy nucleus. Electrons can be moved to higher orbits, but this requires the input of energy to move the electron from the tightly bound orbits to higher orbits. If sufficient energy is delivered to the electron, the atom can be ‘ionized’, that is the electron is completely removed from the atom.

Each shell further consists of subshells:

Thus the K-shell can contain up to 2 electrons; once this shell is filled, the L-shell begins to fill and the maximum number of electrons it can contain is 8. This process of filling by the Aufbau principle, results in this process continuing so that the M-shell contains a maximum of 18 electrons, the N-shell contains a maximum of 32 electrons and so on.

The definition of ‘radiation’ is basically energy in transit. If the energy of the radiation is sufficient to remove an electron from an atom, the radiation is said to be ionizing. Ionizing radiation, i.e. radiation providing sufficient energy to ionize atoms, comes in two main forms. The first form is particulate radiation. This radiation consists of atomic or subatomic particles that carry energy in the form of kinetic energy such as the emission of alpha particles or electrons. The second form is electromagnetic radiation in which energy is carried by electromagnetic waves such as in X-rays or Gamma-rays.

Not all combinations of neutrons and protons produce stable nuclides. Some nuclides are stable, while others are unstable. The unstable nuclides are termed the radionuclides, most of which are artificially produced in the cyclotron or reactor, with a few naturally occurring. These unstable nuclides emit energy in the form of particles and/or electromagnetic radiation, i.e. these nuclides emit ionizing radiation, to transform themselves into a more stable configuration of neutrons and protons. This transformation is the process known as ‘radioactive decay’.

Thus, radionuclides are unstable due to an unsuitable composition of neutrons and protons, or excess energy, and therefore decay by radiation such as the emission of α particles, particles (electrons) or particles (positrons). (These examples are types of particulate radiation.)

α decay: This decay occurs in heavy nuclei such as 235U, 239Pu, etc. which need to lose mass to become stable. For example,

Alpha particles are essentially nuclei of helium atoms consisting of 2 protons and 2 neutrons. The α-particles are emitted with discrete energy and have a very short range in matter, e.g., about 0.03mm in human tissues.

decay: decay occurs in radionuclides that are neutron rich. In the process, a neutron in the nucleus is converted to a proton along with the emission of an electron (a particle) and an anti-neutrino, . The proton is retained within the nucleus and the electron and anti-neutrino are emitted with kinetic energy.

e.g EQ1

The energy difference between the two nuclides (i.e. between and in the above example) is called the decay energy or transition energy, which is shared between the () particle and the antineutrino . Therefore, particles are emitted with a spectrum of energies with the transition energy as the maximum kinetic energy, and with an average kinetic energy equal to one-third of the maximum energy.

Positron Physics

A positron, mentioned earlier, is an anti-electron or in other words, a positively charged electron. It is the anti-matter partner of an electron and all particles mentioned thus far have an antimatter version. Every particle has the same mass as its anti-matter partner, but some of its properties are opposite (such as electrical charge). Thus, without going into the complexities of what antimatter actually is, the positron can be thought of as an electron with a positive charge. Positrons are produced by nuclei that are unstable and have an excess of protons.

Positron () decay: When a radionuclide is proton rich, it decays by the emission of a positron () along with a neutrino (). When an atom undergoes radioactive decay by positron emission, a proton in the nucleus is transformed into a neutron and a positron.

The positron is then ejected from the nucleus with the neutrino carrying off a variable amount of excess energy. Examples of positron emission include:

EQ2

EQ3

Annihilation

If any matter particle and an anti-matter particle of the same type come into contact, then they spontaneously convert into energy; this process is known as annihilation. The positron is extremely unstable outside the nucleus and combines with a nearby electron to form the positronium ion. This ion is also unstable and annihilates by the conversion of its mass into pure energy (as predicted). This process is governed by Einstein’s mass-energy principle, which states that a particle of mass M can be converted into energy E by the equation E = mc2, where c is the speed of light. Since the mass of the positronium ion is known (the mass of an electron and a positron, both having the same mass), we are able to calculate the amount of energy that will be obtained:

EQ4

This energy exists as a pair of gamma ray photons. The annihilation for an electron and a positron can thus be represented as following:

EQ5

Thus the energy obtained, 1022keV, will be shared equally by both gamma ray photons, i.e. each photon will subsequently have an energy of (1022keV/2 =)ASK 511keV. The photons are simultaneously produced and emitted in opposite directions i.e. at 180° to each other.

In any particle annihilation, conservation laws restrict what can happen; only changes in which all conserved quantities remain the same can occur. Therefore the following are conserved:

Charge
Momentum (linear and angular)
Energy (including the result energy Erest = mc2)

Therefore annihilation will only occur if conservation of these happen.

Energy is conserved as follows:

EQ6

Momentum is conserved as follows:

EQ7

If the photons were not emitted in opposite directions, the total linear momentum after the collision would not equal zero and momentum would therefore not be conserved. Thus, the photons are emitted at 180° to each other for the conservation of (linear) momentum.

Charge is conserved as follows:

EQ8

The annihilation process takes place extremely rapidly (within 2 nanoseconds) following the emission of the positron from the nucleus, in general occurring no more than 1mm to 2mm from the atom that emitted the positron. The basic physics on which PET imaging is based is the detection of these two simultaneous opposing gamma ray photons generated by every decay event.