Radionuclide imaging and PET

The patient as the source

A tracer is a radioactive nuclide chemically attached to a molecule the body uses, perhaps a glucose analogue or a bone-seeking compound, depending on the question being asked. Injected or swallowed, the molecule goes where the biology sends it, and the nuclide radiates from wherever it accumulates. Detecting that radiation maps function, meaning which tissue is consuming, which is inflamed, and which has stopped working. An X-ray shows what the body looks like. A tracer shows what it is doing.

The nuclide must be chosen with care, on two counts. What reaches the detector has to be photons, since charged particles do not get out. For a gamma camera that means a gamma emitter. An alpha emitter is stopped within a fraction of a millimetre of tissue and a beta-minus emitter within a few millimetres, so almost nothing reaches an external detector; both deposit their energy in the patient and are useless as the directly detected radiation of a conventional external image.

The half-life must suit the job too, long enough to prepare and image, short enough that the patient is not irradiated for weeks. The standard choice is technetium-99m, half-life six hours, a near-pure gamma emitter drawn fresh from a generator as it is needed. Hospitals keep a generator of its parent, molybdenum-99, and elute the technetium as it forms, typically around once a day.

Six hours does not suit every question, and the standard alternative when the biology takes days is indium-111. It decays by electron capture with a half-life of 2.8 days, emitting gamma photons at 171 keV and 245 keV that a gamma camera reads comfortably. Its usual job is labelling a sample of the patient's own white blood cells, which are then returned to the bloodstream and gather wherever there is infection, so a picture taken a day or two later finds an abscess that no shadow image would show. The longer half-life is what makes that possible, and the drawback is that the patient is exposed for longer.

Three half-lives, one that matters

Activity inside a patient falls for two independent reasons, and the specification wants both named and then combined. The physical half-life T_P is the ordinary nuclear one, the time for half the nuclei to decay, and nothing a body does can change it. The biological half-life T_B is the time for the body to clear half the tracer, by the kidneys, the gut or the breath, and it depends entirely on the chemistry the nuclide is riding on rather than on the nuclide itself.

Both drain the same store, and both drain a fixed fraction of what is left per unit time, so the fractional rates simply add. Write each rate as one over its half-life and the result is the effective half-life:

1T_E = 1T_P + 1T_B$\frac{1}{T_E} = \frac{1}{T_P} + \frac{1}{T_B}$1/T_E = 1/T_P + 1/T_B and because rates add, T_E always comes out shorter than either of the two half-lives that made it. That is the number a dose calculation needs, since it describes how long the activity actually stays in the patient, and it is the number a scan has to be timed against.

Catching the gammas

A gamma camera collects the emitted gammas, and its parts come in a fixed order worth learning. First a lead collimator, a block drilled with long parallel channels, which admits only photons travelling nearly straight up them and absorbs the rest. Then a scintillator crystal, usually sodium iodide, which turns each surviving gamma into a flash of light. Behind that sit photomultiplier tubes, which convert the flash to an electrical pulse and amplify it enormously, and position circuits work out from the relative pulse sizes where on the crystal the flash happened. The output is a map of activity, built one photon at a time.

The picture is blunter than a CT slice, and that is acceptable. A tracer answers where the activity is, not what the anatomy looks like. Hospitals routinely overlay the two kinds of scan, taking structure from one and function from the other.

PET: annihilation as a beacon

Positron emission tomography sharpens the idea with antimatter. The tracer, commonly fluorine-18 in a glucose analogue, is a beta-plus emitter, so what it sends out is positrons. That looks like a breach of the rule above, 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.

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. That 511 keV is no accident. It is the electron's rest energy, m₀c² from the antimatter lesson, working a hospital shift.

What the scan then diagnoses follows from the molecule the fluorine-18 is riding on. 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, which is why PET, paired with CT, helps to detect certain cancers, 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, so a PET result is read alongside other evidence rather than as a verdict on its own.

The brain and the heart read the same map differently. Reduced uptake across particular regions of cortex is a marker of dementia, an abnormally active patch can locate where epileptic seizures begin, and heart muscle that still takes up the tracer after a heart attack is muscle worth restoring the blood supply to, while 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 on its own 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

Everything above treats the dose as a cost to be minimised. Turn that around and the same physics becomes treatment, because ionising radiation kills cells, and a tumour can be killed if it can be given far more of it 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 rather than the kilovolts of diagnosis, is rotated around the patient so that it enters through a different path each time while always crossing the tumour. Every path through healthy tissue is used briefly and takes a small share of the dose; the tumour lies on all of them and takes the sum. The energy is chosen high deliberately, because a hard beam is attenuated less on the way in and so deposits proportionately more where it is aimed; a megavoltage beam's dose also builds up over the first centimetre or two rather than peaking at the skin, and collimators shape each beam to the tumour's outline.

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, and the emitters this specification's model names are beta emitters, yttrium-90 or strontium-90 among them; clinical practice also uses other sources under the same geometry. Beta particles are absorbed within a few millimetres of tissue, so the dose is 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 earlier rule about tracers running backwards, 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 that can be cleared. So a permanent seed is chosen with a physical half-life short enough that it has spent itself once the planned dose has been delivered, while a stronger, longer-lived source is put in for a measured number of hours and taken out again.