How Positron Emission Tomography works

This post aims to explain what positron emission tomography (PET) is and how it works.
PET is a unique type of medical imaging that reveals information about the physiology of organs and tissues, unlike CT or MRI machines which only yield images of anatomy. By doing this, PET scans can often detect irregularities such as cancer significantly earlier than other diagnostic tests. The scan works by injecting a radioactive tracer into the patient which is taken up in different parts of the body by varying amounts; the positron decay of the tracer is detected and an image of the body is reconstructed from this data. A specialised radiologist looks at these images and forms a diagnosis.

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Synthesis of radiotracers:
The radiotracers used in a PET scan are synthesised in a cyclotron. The synthesis of radiotracers can be summarised into two stages: firstly a radioactive isotope with a short half-life is created by proton bombardment, and then this radioisotope is chemically incorporated into a biological molecule. The radioactively labelled biological molecule is taken up by the body, and higher concentrations of it show up as hot spots on the scan. The most commonly used radiotracer in PET is fluorodeoxyglucose[1] (FDG), for which this article will mainly be focussed on.

~Diagram showing how a cyclotron works.

The purpose of a cyclotron in PET is to create a β+ (positron) emitting radioisotope that has a short half-life that can be substituted quickly into a molecule such as glucose. A cyclotron achieves this by accelerating protons to bombard a stable target isotope.
A cyclotron works on the principle of using the magnetic force to bend moving charges[2] (protons in our case). It consists of two metal ‘dees’ separated by a gap that has a rapidly reversing electric field across it. When a proton is placed near the centre, it accelerates away from the electric field in the centre. The electric field is then reversed, so the proton turns back on itself and accelerates back towards the centre – this reversing of the electric field repeats itself, and each time the proton gains more kinetic energy[3]. Once the proton has sufficient kinetic energy to enter the nucleus of the target, it is released out of its spiral and bombardment occurs.

Aerial view of the two ‘dees’

For FDG synthesis, the target used is enriched water (H₂¹⁸O). Protons accelerated by the cyclotron knock and replace neutrons from the isotope of oxygen, forming radioactive F-18:

Since the half-life of F-18 is only 110 minutes, it has to be incorporated into glucose to form FDG very quickly. This is done via a complicated chemical process that is usually automated[4]. The end product, FDG is identical to glucose, except that the second OH group has been replaced by the radioactive F-18 made in the cyclotron:

Skeletal formula of FDG (bottom) and glucose (top). The second OH group is replaced by radioactive F-18.
Decay and distribution of FDG:
When FDG taken up into a cell, it is phosphorylated into FDG-phosphate[5], and this molecule cannot be broken down further, so is therefore trapped in the cell. Cancerous cells divide much faster than normal body cells, so their energy needs are much higher. This means that more FDG would be taken up by a cancer cell as compared to a normal cell; resulting in a hot spot on the scan.
Atoms decay when the ratio of protons to neutrons in the nucleus is skewed – a proton enriched nucleus like in F-18 would try to lose its extra proton to become O-18. It does this by positron emission:

Essentially, a proton in the nucleus of F-18 turns into a neutron, releasing a high-speed positron (β⁺) and a neutrino (read up on the weak interaction to find out more). When this decay is complete, the FDG becomes glucose-phosphate, which can be metabolised normally[6].
Annihilation and Detection:
A positron is the anti-matter match to an electron – it has identical properties but an opposite charge. This means that when an electron and a positron meet, they annihilate and their combined mass is completely converted into energy; i.e. high frequency photons. Since momentum is always conserved in collisions, the two photons produced must travel 180 degrees apart in opposite directions.

Image credit: astronomy.swin.edu.au

The positron emitted from the decay of FDG usually meets and annihilates an electron within a very short distance (usually much smaller than 1mm)[7]; this distance has little effect on the accuracy of the scan.
In a PET machine, the photons emitted by the positron-electron are sensed by multiple rings of detectors that surround the object being scanned. These detectors are comprised of two parts; a scintillator crystal optically coupled to a photomultiplier tube (PMT)[8].
As a high energy photon from annihilation passes through the scintillator, it interacts with an electron in one of the atoms of the crystal, energising it according to the photoelectric effect. This excited electron (known as a photo-electron) moves through the scintillator, exciting many other electrons in the process and causing them to ‘jump’ energy levels. When these electrons return to their ground state, they re-emit the absorbed energy as even more photons. The photons produced by the scintillator are then converted into an electrical signal by the PMT, which is processed by a computer in order to form an image.[9]

Image credit: ILC-Sefuri

Image Reconstruction:
The annihilation of a positron and electron result in two photons being emitted at the same time and energy at 180 degrees apart. In effect, this does not always happen due to scattering and attenuation of photons as well as the time lag inherent in most scintillator detectors. Therefore parameters for time difference and energy of two photons detected are decided – if a pair of photons meet these criteria, it is assumed that they came from the same annihilation (termed as a ‘coincidence’)[10]. A line of response (LOR) is drawn between where the two photons are detected; somewhere along this line an annihilation occurred (assuming it is a true coincidence).

Diagram showing LOR and coincidences. Credit: depts.washington.edu

One method for forming an image from this data is to back-project from where signals were detected in order to determine a space in which higher concentrations of annihilation reactions would have occurred:

Each shaded line represents a LOR between two detectors. (Image Credit: depts.washington.edu)

Points where more LOR’s intersect are shown up as hot spots on the scan where higher concentrations of the tracer are (cancerous and rapidly dividing cells when using FDG).[11]
However, the image formed by doing this is two-dimensional, to form a 3D image many of these cross-section images are taken and stacked onto each other.
In reality, this method of image reconstruction is not so simple – complicated computer programs are employed in order to mitigate the inaccuracies caused by scattering, absorption of photons, and other sources of error. Despite this, the back-projection method often produces noisy images. Better ways of reconstructing images are constantly being developed; some involve measuring the difference in time-of-flight between coincident photons in order to extrapolate their origin, others relying on iterative reconstruction techniques. [12]
Since PET images do not provide as much anatomical detail as other imaging techniques, they are often used in conjunction with a CT scan. These images are superimposed onto each other to give more precise information and therefore a more accurate diagnosis.

Image showing a PET scan, a CT scan, and a PET/CT scan from left to right. The orange and green areas represent high concentrations of tracer. Credit: SEELA, UCLA

Conclusion:
PET’s major drawbacks are its expense and poor resolution compared to CT or mri scan. The requirement of an on-site cyclotron to produce radioisotopes and facilities to incorporate them into biological molecules mean that PET is incredibly expensive. The poor resolution of PET also means that irregularities less than 1mm are not usually detected; although this disadvantage is lessened by the development of PET/CT.
PET’s greatest strength lies in its versatility. There are many different tracers that can be used in order to measure a range of activity such as blood flow, oxygen usage, tissue pH, and cell metabolism. For example, a radioactive oxygen tracer is used to measure blood flow in the brain, allowing for various neurological diseases such as Alzheimer’s, Parkinson’s, and epilepsy to be investigated. This information about physiology of the body often enables a diagnosis to be formulated much earlier than with other medical scans. In addition, it allows for physicians to assess the effectiveness of certain treatments such as chemotherapy. However, the largest application of PET is in detecting and differentiating malignant from benign cell growths, meaning early detection and therefore higher chances of survival in cancer patients.
[1] cancerquest.org
[2] hyperphysics.phy-astr.gsu.edu
[3] webphysics.davidson.edu
[4] Radionuclides: Guidance on Facility Design and Production of [¹⁸F]Fluorodeoxyglucose (FDG) – International Atomic Energy Agency
[5] med.harvard.edu
[6] med.harvard.edu
[7] Michael E. Phelps (2006). PET: physics, instrumentation, and scanners
[8] med-ed.virginia.edu
[9] Introduction to PET Physics, Section 5 – Ramsey Badawi – depts.washington.edu
[10] med-ed.virginia.edu
[11] owlnet.rice.edu
[12] Tomographic Image Reconstruction. An Introduction. – Milan Zvolský (Lecture)