A nuclear image is a map of where a radioactive tracer has gone in the body. The patient is injected with a molecule that carries a radioactive atom, the molecule accumulates wherever the body uses it, and a detector outside the body counts the photons the atom emits: a ring of detectors around the patient in PET, a flat camera that moves around the patient in SPECT. Radiography and CT show structure, but many diseases begin without a visible change in structure. A lymph node full of tumor cells can look like any other lymph node on CT and still be the brightest thing in the body on PET because it burns glucose faster than everything around it. The brain in early Alzheimer's disease looks intact on MRI while its glucose use has already fallen. Heart muscle that is dying in an infarction has the same size and shape as healthy muscle but no blood flow. Compared with the radiographs of 2.2 X-ray radiography and the CT of 2.4 CT — Computed tomography, PET and SPECT images are blurrier and noisier and do not inherently show anatomical features other than the ones involved in tracer uptake. For this reason they are almost always read superimposed on a CT acquired in the same session.
Left: whole-body FDG PET as a rotating maximum-intensity projection; brain, heart, kidneys and bladder take up the tracer normally, the spot in the chest is a tumor. Middle: FDG PET-CT of a breast cancer; PET projection and PET slice above, CT slice and PET in color over CT below, which is how it is read. Right: bone scans, normal on the left, prostate cancer spread to bone on the right, every dark spot a metastasis. Wikimedia Commons: Jens Maus (public domain), Hg6996 (CC BY-SA 3.0), CC BY 3.0, CC BY-SA 4.0.
The idea behind nuclear imaging is the tracer principle. Attach a detectable label to a molecule the body uses, give the patient a tiny amount of it, and follow where it goes. In nuclear imaging the label is a radioactive isotope (radionuclide), and the molecule is chosen for the biological process it takes part in. Together the carrier molecule and label form a radiotracer (or radiopharmaceutical).
Radiotracer. A radioactive label, fluorine-18, is attached to a carrier molecule the body uses, here glucose; the pair is the tracer FDG. A few nanomoles are injected into a vein, spread with the blood within a minute, and collect where the carrier is used most, here a tumor that burns glucose. The radioactive label decays and sends out radiation, most of it from where the tracer has collected.
The type of carrier molecule determines where the tracer accumulates: a sugar goes where sugar is burned, a phosphonate goes where bone is being built. The isotope decides the photon energy and how fast the activity decays, its half-life. Typically only a few nanomoles of radiotracer is given, about a million times less than a dose of a drug. The body handles the tracer exactly as it handles the natural molecule. The radiation dose is a few mSv for a typical examination, comparable to CT. Most tracers are injected into an arm vein and spread with the blood within a minute; a few are inhaled (lung ventilation) or swallowed (iodine for the thyroid).
The table below lists common tracers. The naming convention is that the isotope comes first and the molecule it labels follows. The superscript is the mass number of the isotope, the number of protons and neutrons in the nucleus: ¹⁸F is the fluorine isotope with 9 protons and 9 neutrons, while ordinary fluorine, ¹⁹F, has one neutron more.
| Tracer | Modality | What it follows | Typical use | Half-life | Photon energy |
|---|---|---|---|---|---|
| ¹⁸F-FDG | PET | Glucose consumption | Cancer staging and follow-up, dementia, inflammation | 110 min | 511 keV |
| ⁶⁸Ga- or ¹⁸F-PSMA | PET | A membrane protein on prostate cancer cells | Prostate cancer staging and recurrence | 68 min (⁶⁸Ga), 110 min (¹⁸F) | 511 keV |
| ¹⁸F-florbetapir, flutemetamol | PET | Amyloid plaques | Alzheimer's disease | 110 min | 511 keV |
| ⁹⁹ᵐTc-MDP or HDP | SPECT, planar | Bone turnover | Bone metastases, fractures | 6.0 h | 140 keV |
| ⁹⁹ᵐTc-sestamibi, tetrofosmin | SPECT | Blood flow in heart muscle | Coronary artery disease | 6.0 h | 140 keV |
| ¹²³I, ¹³¹I | SPECT, planar | Iodine uptake | Thyroid disease and cancer | 13 h (¹²³I), 8.0 d (¹³¹I) | 159 keV (¹²³I), 364 keV (¹³¹I) |
PET (positron emission tomography) uses tracers that emit positrons. Within about a millimeter the positron meets an electron; both annihilate, and two photons leave in opposite directions. The scanner counts a decay when two detectors on opposite sides fire at the same moment. Timing the two arrivals also places the decay along the line to within a few centimeters (time-of-flight PET). The most common examination is PET with FDG, a radioactive sugar. It is used to stage cancer, that is, to find where in the body it has spread, which decides the treatment, and to look for recurrence after treatment.
Left: the PET-CT scanner. The CT ring at the front spins around the patient; behind it the PET ring, a full circle of detector blocks is stationary. Right: The PET ring, one slice. Fluorine-18 decay sends a positron about a millimeter into the tissue, where it meets an electron; both vanish and two 511 keV photons fly apart. Two detector blocks fire at the same moment, determining a line between them where the decay occurred.
Consider the animation above. The scanner records one radioactive decay per line (two strikes on the detector). Each line is parameterized by its direction $\theta$ and its distance $t$ from the center. The count of radioactive decays detected on a given line is given by $p(t,\theta)$. This is a radial projection, as we saw in 2.4 CT — Computed tomography, and the counts form a sinogram.
If every photon pair reached the detector, $p(t,\theta)$ would be the activity concentration $a(x,y)$ summed along the line, up to a constant for scan time and detector sensitivity: a projection of $a$, as a CT projection is a projection of $\mu$. Not every pair is counted: a photon that is absorbed or scattered in the body is lost. In 2.4, the fraction of X-rays that crosses the body along a line $L$ is $e^{-\int_L \mu\,ds}$. The same fraction applies to a photon pair: the two photons fly in opposite directions along $L$, one to each end, so between them they cross the whole of $L$ inside the body, wherever on it the decay happened. The count on a line is therefore the line sum of $a$, reduced by a factor that depends on the length and properties of the line but not on where along it the decays were:
$$ p(t,\theta)=e^{-\int_{L}\mu\,ds}\int_{L} a(x,y)\,ds\tag{2.5.1} $$
where $L$ is the line $x\cos\theta+y\sin\theta=t$ and $\mu$ is the attenuation coefficient of 2.4 CT — Computed tomography at 511 keV, the energy of every annihilation photon whatever the tracer. The first factor is known: the scanner has just taken a CT of the same patient, which gives $\mu$ at every point once the HU are converted to attenuation at 511 keV, so the factor can be computed for every line. Dividing each measured count by it undoes the attenuation:
$$ \frac{p(t,\theta)}{e^{-\int_{L}\mu\,ds}}=\int_{L} a(x,y)\,ds\tag{2.5.2} $$
The left side is the count the scanner would have recorded if the body absorbed nothing. Over all lines it is a sinogram of $a$, the same kind of data CT gives for its attenuation coefficient. We can apply the Fourier slice theorem and filtered back-projection of 2.4 CT — Computed tomography unchanged. The main difference is what each entry of the sinogram means: in CT it is how much the beam was weakened along the line, here it is how many radioactive decays were counted on the line.