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

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Introduction

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.

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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.

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Conclusion

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.

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