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PET scanning and radiotherapy

In PET, positrons from a beta-plus tracer annihilate with electrons, giving two 511 keV photons that travel in opposite directions. Detecting both photons together places the annihilation on the line between two detectors. Radiotherapy uses ionising radiation on purpose to treat a tumour, with megavoltage X-ray beams from many angles or with a beta-emitting implant.

Year 13AQA 3.10.6.1, 3.10.6.4, 3.10.6.5, 3.10.6.6CIE 24.3.2, 24.3.3, 24.3.4, 24.3.5, 24.3.6OCR A 6.5.2(a), 6.5.2(d), 6.5.2(e)

Radionuclide imaging and PET, part 2 of 2. Part 1 is Radionuclide imaging and the gamma camera.

Builds on Radionuclide imaging and the gamma camera and Antimatter and photons.

IN THIS TOPIC

  • Explain PET: annihilation into two 511 keV photons, and coincidence detection locating the source.
  • Say what PET scanning is used to diagnose, and why it is paired with a CT scanner.
  • Explain how high-energy X-ray beams and beta-emitting implants deliver a dose to a tumour and spare the tissue around it.

COMMON MISCONCEPTION

Misconception:

A PET scanner works by sending radiation into the body.

PET sends no radiation in: a positron-emitting tracer inside the body is the source, and the scanner detects the back-to-back 511 keV photons produced when positrons annihilate with electrons.

PET: annihilation as a beacon

Positron emission tomography uses the same tracer principle, but with antimatter. The tracer is still a radionuclide attached to a molecule the body uses, and the image is still a map of where the body took it. What changes is the radiation that is detected. The tracer, commonly fluorine-18 in a glucose analogue, is a beta-plus emitter, so it emits positrons.

That looks like a breach of the rule that only photons get out of the patient, and it is not. Each positron travels only a millimetre or so before it meets an electron, so the positron itself never leaves the patient. The pair annihilates, both particles vanish, and their rest energy leaves as two gamma photons of 511 keV each, flying in opposite directions to conserve momentum. Those photons are what the scanner detects, and they escape as readily as any other gamma.

A ring of detector segments with an annihilation point inside it and two amber 511 keV photon arrows leaving in exactly opposite directions to strike opposite segments: a coincidence that places the source on the line between them.
FIG. 1Annihilation inside the detector ring: the two 511 keV photons leave back to back, strike opposite detectors at nearly the same moment, and the source must lie on the line joining them. Many such lines cross at the tracer.

The scanner is a ring of detectors watching for coincidences, meaning two 511 keV photons arriving at opposite sides at effectively the same instant. Each coincidence pins the annihilation to the straight line between the two detectors, and hundreds of thousands of such lines intersect at the places the tracer gathered. The 511 keV is the electron's rest energy m0c2.

What the scan diagnoses depends on the molecule the fluorine-18 is attached to. In a glucose analogue it goes wherever the body is burning sugar, so the image is a map of metabolic rate. Many tumours consume glucose faster than the tissue around them and show as bright spots. That is why PET, paired with CT, helps to detect certain cancers. It also helps to stage them, by picking up secondary tumours anywhere in the body, and to check afterwards whether treatment has quietened them.

The uptake is not specific to cancer, though. Infection and inflammation burn sugar too and also light up, and not every tumour takes up the tracer strongly. A PET result is one piece of evidence among several.

The same map is read differently for the brain and for the heart. Reduced uptake across particular regions of cortex is a marker of dementia, and an abnormally active patch can locate where epileptic seizures begin. In the heart, muscle that still takes up the tracer after a heart attack is worth restoring the blood supply to. Muscle taking up none has died.

Every one of those diagnoses rests on the same property. PET measures function, and it is poor at anatomy, so a bright spot does not say which organ it is in. Scanners are therefore built as PET rings wrapped around a CT scanner, and the two images are laid on top of each other: one says what is happening and the other says where.

When the dose is the point

Diagnostic imaging treats the dose as a cost to be minimised. In treatment the same physics is used the other way, because ionising radiation damages cells: a tumour can be destroyed if it receives a much larger absorbed dose than the tissue around it. Radiotherapy rests on that comparison, and there are two ways of achieving it.

The first is to aim from outside. A beam of high-energy X-rays, megavolts and not the kilovolts used in diagnosis, is rotated around the patient so that it enters through a different path each time while always crossing the tumour. Each path through healthy tissue is used briefly and receives a small share of the dose, while the tumour lies on every path and receives the total.

The energy is chosen high on purpose. A hard beam is attenuated less on the way in, so it deposits proportionately more where it is aimed. A megavoltage beam's dose also builds up over the first centimetre or two, so it does not peak at the skin. Collimators shape each beam to the tumour's outline.

Relative dose against depth in tissue for a kilovoltage diagnostic beam and a 6 MV therapy beam, each normalised to its own maximum: the kilovoltage beam peaks at the skin and is nearly gone by 10 cm, while the megavoltage beam builds up to its maximum 1.5 cm in and still delivers two thirds of it at the depth of the tumour
Describe the drawing

Two curves of relative dose against depth in tissue, each normalised to its own maximum. The kilovoltage diagnostic beam is at its strongest right at the skin and falls away steadily, so by the 10 cm depth of the tumour it is down to about a sixth. The 6 MV therapy beam instead builds up over the first centimetre and a half, reaches its maximum there rather than at the surface, and is still delivering about two thirds of that maximum at the tumour, several times what the softer beam has left. A hard beam is attenuated less on the way in and its dose builds up past the skin, which is why radiotherapy is done in megavolts. The build-up here is a model of the shape, written as one minus an exponential times an exponential, rather than a measured depth-dose table.

FIG. 2The two beams compared down the same depth of tissue, each drawn relative to its own maximum. The kilovoltage beam is strongest at the skin and has little left by 10 cm; the megavoltage beam builds up to its maximum a centimetre and a half in and is still worth two thirds of it at the tumour, several times the softer beam. The build-up is modelled; the figure is drawn to show the ordering at depth.
Radiotherapy's two geometries: external megavoltage beams that overlap only at the rotation centre where the tumour sits, and an implanted beta seed whose whole dose lands within a few millimetres
Describe the drawing

Two treatments side by side. On the left, a patient cross-section with one megavoltage beam drawn at three rotation positions spread evenly round the body, each a lightly shaded band from an external source right through the patient: the bands overlap only at the small tumour at the rotation centre, where the shading is darkest, so each entry path through healthy tissue is used briefly while the tumour collects every pass. On the right, a close-up of tissue with a beta-emitting seed implanted at the centre of a tumour: the dose halo hugs the seed within a few millimetres and the healthy tissue is unshaded beyond, with a one-centimetre scale bar, and an inset graph of dose against distance on the same scale falls to exactly nothing before the one-centimetre mark.

FIG. 3Two ways to give the tumour more dose than anything else. On the left, a megavoltage X-ray beam rotates about the patient: each entry path through healthy tissue is used briefly, while the tumour sits at the centre of every sweep and collects the sum. On the right, a beta-emitting seed sits in the tumour itself, and its few-millimetre range in tissue means the dose falls to almost nothing a centimetre away.

The second is to put the source inside. A radioactive implant is a sealed source, a seed or a small rod, placed in the tumour or against it. The emitters the specification names are beta emitters, yttrium-90 or strontium-90 among them, though clinical practice also uses other sources placed the same way. Beta particles are absorbed within a few millimetres of tissue. The dose is therefore enormous where the seed sits and negligible a centimetre away, and the healthy tissue beyond that range is untouched however long the source is left.

That is the tracer rule applied in reverse, and it is worth saying so in an answer. A beta-minus emitter is unsuited to gamma-camera imaging precisely because its radiation cannot escape the body, and it is well suited to an implant for precisely the same reason. Unsealed sources exploit chemistry instead of geometry, iodine-131 being swallowed and concentrated by the thyroid itself, and there the tissue to be destroyed does the aiming.

Two numbers then shape the treatment. The activity of the source sets the scale of the dose rate, though the dose delivered also depends on the radiation's energy and on how the surrounding tissue absorbs it, and the half-life fixes how quickly that rate falls.

For a sealed implant the half-life that matters is the physical one, because the body cannot excrete a sealed source. The effective half-life belongs to unsealed tracers, which the body can clear. A permanent seed is therefore chosen with a physical half-life short enough that it has spent itself once the planned dose is delivered. A stronger, longer-lived source is instead put in for a measured number of hours and taken out again.

ASSESSMENT FOCUS

  • Keep the two instruments apart when the emission type is asked for. A gamma camera needs a gamma emitter. PET needs a positron emitter, and the radiation that gets out is the pair of annihilation photons, not the positron. Writing "never use a beta emitter" contradicts the whole of PET.
  • Give the PET chain in order, in five steps. Positron emitted, annihilates with an electron, two 511 keV photons in opposite directions, detected in coincidence, source located on the line between the two detectors.
  • Opposite directions is a momentum statement, so say so. The pair is nearly at rest when it annihilates, so the two photons must carry equal and opposite momentum. The 511 keV itself comes from the electron rest mass through E = mc2, and you can quote it without deriving it unless asked.
  • Therapy answers turn on range. A beta-emitting implant delivers its energy within a few millimetres of the seed, so the tumour is destroyed and tissue a centimetre away is spared, while an external beam achieves the same comparison by crossing the tumour from many directions. Saying that a beta emitter is unsuited to gamma-camera imaging for the very reason it suits an implant is the observation that completes the answer.
  • Diagnosis questions want the biology of the tracer, not the physics again. Fluorine-18 in a glucose analogue maps how fast tissue burns sugar, so many tumours light up, which helps find and stage a cancer; reduced uptake in the cortex marks dementia, and heart muscle that still takes up the tracer after a heart attack is still alive. Finish by saying PET is paired with CT because function alone does not say where.

CHECK YOURSELF

Explain why the two photons produced in PET annihilation travel in opposite directions, and why both must be detected for the event to be useful.

Show a hint

Start from the momentum of the electron-positron pair just before annihilation.

Show the answer

The pair is very nearly at rest, with total momentum close to zero. Momentum is conserved, so the two photons must leave with equal and opposite momenta, which means back to back.

One photon alone gives only a direction from one detector. Two in coincidence define the whole line through the annihilation point, and it is the intersection of many such lines that locates the tracer.

Annihilation gives two 511 keV photons back to back, and coincidence detection turns each pair into a line. The lines cross where the tracer is.

PET maps function and CT maps structure, which is why the scanner is built as both and the two images are overlaid.

A beta-minus emitter cannot reach a gamma camera because its range is millimetres, and an implant treats for that reason.

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  • Explain PET: annihilation into two 511 keV photons, and coincidence detection locating the source.
  • Say what PET scanning is used to diagnose, and why it is paired with a CT scanner.
  • Explain how high-energy X-ray beams and beta-emitting implants deliver a dose to a tumour and spare the tissue around it.

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