Positron Imaging Centre

The Physics of PET and PEPT

The basis of PET and PEPT is the detection of the photons emitted when a positron, produced by the beta decay of an unstable nucleus, annihilates with an electron. This annihilation occurs when the positron is essentially at rest, and conservation of energy and momentum then require that two 511keV (=mec2) photons are emitted back-to-back (180° apart). Simultaneously detecting both photons defines a line, and the annihilation is assumed to have occurred somewhere along this line. In PEPT detection of a few such events is sufficient to locate the position of the single tracer particle, whereas in PET it is necessary to detect a large number of events from which the spatial distribution of the tracer can be inferred.

Positron energy distribution

Positrons are emitted in the beta decay of nuclei which contain too many protons for their mass. One proton is converted into a neutron, and a positron and a neutrino are emitted. Because of the three body nature of the decay, the emitted positrons have a range of kinetic energies. The energy distributions are shown below for the four radio nuclides most commonly used in PET.

In a condensed medium (e.g. a solid or liquid), the emitted positron slows down to thermal energies in a few ps, travelling up to 1mm (less in a very dense medium). After a period in thermal equilibrium the positron will annihilate with an electron usually into two 511keV photons. The average lifetime for this is 100-500ps dependent on the material characteristics. Alternatively, in a molecular medium, the bound state of an electron and positron (positronium), may be formed during the slowing down process, in which case one would expect the decay to produce either two or three photons depending on the angular momentum of the bound state. However, the two gamma lifetime for the singlet parapositronium is 125ps while the triplet orthopositronium has a three gamma lifetime of 142ns, so that in practice most orthopositronium states convert to parapositronium and decay by two photon emission.

The kinetic energy of the annihilating electron positron pair (in practice that of the electron as the positron has slowed to thermal energies) leads to an acollinearity of the emitted photons in the laboratory frame of <1°.

The resolution achievable by any PET imaging system is ultimately limited by the finite range of the positron prior to annihilation and the effect of the slight acollinearity of the two photons. If a pair of detectors separated by 50cm is used to detect the photons then the uncertainty in location arising from this acollinearity is around 1mm, comparable to the range of the emitted positrons. In practice, detector systems never achieve this level of precision. For PET, the best resolution achievable is around 8mm with the original Birmingham camera or 5mm with the Forte. However in PEPT a stationary tracer can be located arbitrarily well by using sufficient events.

PET and PEPT rely on the coincident detection of photons in two detectors. Pulses are considered to be coincident if they occur in two detectors within a specified resolving time τ of each other. Because of this finite resolving time there is the possibility of two independent pulses occurring by chance so as to produce a random coincidence. The rate of random coincidences is given by Randoms = 2τ R1 R2, where R1 and R2 are the singles count rates in the individual detectors. Thus the randoms rate is proportional to the square of the activity, and this may limit the activity which may usefully by imaged. For a point source mounted centrally between two identical detectors it is easy to show that

Randoms  =   
ε2
  (Reals)2
where ε is the efficiency of each detector for detecting 511keV photons. Thus as the real coincidence count rate increases, the proportion of randoms increases and eventually becomes unacceptable, and this is particularly serious when the efficiency of the detectors is low.

In principle it is possible to detect just the random coincidences by introducing a delay into one arm of the coincidence circuit, and these can then be subtracted from the full data. In many commercial PET systems randoms measurement is done in parallel with the normal data logging, but on the Birmingham cameras one has to alternate between logging all data and just randoms. Although in principle this enables an exact correction to be made for the presence of randoms, in practice because of limited statistics the quality of the data deteriorates dramatically once the number of randoms exceeds the number of real coincidences.

The resolving time τ was 12.5ns for the original Birmingham camera, but is 7.5ns for the Forte. This, coupled with the increase in efficiency from 7% to 23%, explains why the current system can operate at a count rate at least 20 times higher than the older one.

Two other types of unwanted event may interfere with the data. Firstly, photons may be scattered prior to detection and hence arrive at the wrong point. Also, some positron emitting radionuclides (e.g. 22Na, 124I) emit gamma-rays in association with the beta decay, giving the possibility of detecting associated gamma-ray coincidences in which a gamma-ray is detcted in coincidence with an annihilation photon (or another gamma-ray). Some PET systems employ collimating septa which block photons incident at large angles in an attempt to discriminate against unwanted coincidences, but the Birmingham cameras have a completely open geometry. The original camera has no energy resolution and suffers seriously from background due to these types of event, whereas the Forte's energy resolution is able to discriminate against most associated gamma-rays, and against 511keV photons scattered by more than 30°.

Reconstruction