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A dimensionless relative attenuation value calibrated so that water is zero and air is approximately $-1000$. It depends on the computed tomography spectrum and material composition. It is not directly a linear attenuation coefficient at the $511\mathrm{keV}$ energy used in positron emission tomography.

Coauthor of research on brain responses to skin warming and cooling. The study connected controlled thermal stimulation with regional signals measured by positron emission tomography in awake humans.^[ref]

Fluorine-18 is a radioactive isotope of fluorine with 9 protons and 9 neutrons. It decays to oxygen-18, mainly by emitting a Positron and also by electron capture. Its approximately 110-minute half-life makes its radioactivity change appreciably over an ordinary laboratory session. It is used in positron emission tomography.^[ref]

The half-life can be measured by following the falling radioactivity, rather than by watching one nucleus wait to decay. A 2010 experiment used ionization chambers, germanium detectors and coincidence counting with fast scintillators, following decay for up to nine half-lives. The combined result was $1.82871(18)\mathrm{h}$. Comparing different detector systems tests whether the inferred decay rate depends on one measurement technique.^[ref]

For a closed sample governed only by radioactive decay, the surviving parent fraction is $N(t)/N(0)=2^{-t/T_{1/2}}$. Taking 110 minutes as an illustrative rounded half-life, 220 minutes leaves one quarter of the original fluorine-18 nuclei. Four half-lives leave $1/16$, not zero. This calculation concerns nuclear survival; movement of a labelled molecule into or out of an observed region is an additional process.

Coauthor of research on brain responses to skin warming and cooling. The study connected controlled thermal stimulation with regional signals measured by positron emission tomography in awake humans.^[ref]

Coauthor of research on brain responses to skin warming and cooling. The study connected controlled thermal stimulation with regional signals measured by positron emission tomography in awake humans.^[ref]

Coauthor of research on brain responses to skin warming and cooling. The study connected controlled thermal stimulation with regional signals measured by positron emission tomography in awake humans.^[ref]

Methods that infer internal biological structure or function from measured signals. Computed tomography, positron emission tomography and single-photon emission computed tomography use different signal-generation and reconstruction physics.

Coauthor of research on brain responses to skin warming and cooling. The study connected controlled thermal stimulation with regional signals measured by positron emission tomography in awake humans.^[ref]

Coauthor of research on brain responses to skin warming and cooling. The study connected controlled thermal stimulation with regional signals measured by positron emission tomography in awake humans.^[ref]

A researcher in quantitative medical imaging whose 2012 study tested computed tomography-based attenuation correction for positron emission tomography of bone. The study compared CT-derived linear attenuation coefficients with measurements made at the 511 keV energy of PET photons. Bone segments provided a controlled test object, while patient data tested the effect on reconstructed tracer uptake. The work shows why an anatomical image cannot simply be reused as an attenuation map without accounting for photon energy and tissue composition.^[ref]

TODO: Biology deferred at the user's request: biological tracer behavior and clinical PET applications.

The generic physics of positron emission tomography uses electron-positron annihilation. A slowly moving electron-positron pair predominantly produces two nearly opposite photons with energy close to $m_e{c}^2=511\mathrm{keV}$ each. A ring of detectors records approximately simultaneous interactions; a coincidence identifies a coincidence line of response along which an annihilation could have occurred. Finite Positron travel before annihilation and nonzero pair momentum limit how directly this line identifies the original emission location.

Many such measurements constrain an emission distribution through a tomography model. Attenuation, scattered coincidences, unrelated random coincidences, finite detector resolution and dead time alter the observed counts and require calibration or modeling. With useful time-of-flight information, the arrival-time difference further localizes position along the line: a timing uncertainty $\delta t$ corresponds to a position scale $c\delta t/2$. The coincidence data therefore provide spatial constraints, rather than each event directly supplying a complete three-dimensional image point.

Single-photon emission computed tomography detects individual gamma rays from a tracer. Mechanically collimated gamma cameras acquire projections from multiple angles for tomography. The collimator discards most emitted photons, creating a strong sensitivity–spatial resolution trade-off.

Positron emission tomography uses a Positron-emitting tracer. The emitted Positron travels a short distance before electron-positron annihilation produces an approximately back-to-back photon pair. Coincident detection in a detector ring defines a line of response, giving electronic collimation and greater detection efficiency; time-of-flight PET further constrains position along that line. The positron range, non-collinearity, detector size, scatter and accidental coincidences limit spatial resolution and quantification. In both hybrids, computed tomography supplies anatomy and an attenuation correction map, with attention to registration and respiratory motion.^[ref]

A CT number is a dimensionless relative attenuation measure, conventionally $H=1000({\mu }_{\mathrm{CT}}-{\mu }_{\mathrm{water},\mathrm{CT}})/{\mu }_{\mathrm{water},\mathrm{CT}}$. The X-ray spectrum used in computed tomography has an effective energy far below $511\mathrm{keV}$ and is polychromatic. Its photoelectric absorption contribution depends strongly on composition, whereas water and soft-tissue attenuation at the positron emission tomography energy is mainly Compton scattering. Thus a CT number is neither a $511\mathrm{keV}$ linear attenuation coefficient nor an energy-independent mass attenuation coefficient.

The usual conversion calibrates a piecewise linear or bilinear relation between CT numbers and $\mu (511\mathrm{keV})$. The air–water branch models predominantly density differences in lung and soft tissue; a separate water–bone branch accounts for the different energy dependence of mineralized tissue. The calibration depends on the computed tomography spectrum. After geometric registration, the resulting linear attenuation coefficient map is forward projected along each coincidence line of response to obtain $\exp (\int {\mu }_{511}ds)$. If a mass coefficient is stored, its conversion to a linear coefficient must also include mass density. Unusual high-atomic-number materials can violate the simple tissue calibration, so the conversion is a physical material model, not a universal arithmetic rescaling.^[ref][ref]

A researcher in positron emission tomography and combined PET/computed tomography instrumentation. His 1998 study demonstrated attenuation correction using registered CT data, comparing methods for converting the CT image to a map appropriate for 511 keV PET photons. Tests with tissue-equivalent objects and human scans linked an imaging calculation to measured performance. The same CT acquisition can therefore supply anatomical localization and information needed to correct the PET signal for photon losses along its path.^[ref]

Coauthor of research on brain responses to skin warming and cooling. The study connected controlled thermal stimulation with regional signals measured by positron emission tomography in awake humans.^[ref]

A photon transfers its energy to a bound electron, ejecting it if energetically allowed. Subsequent atomic relaxation can emit characteristic radiation or additional electrons. Its material and energy dependence differs from Compton scattering, which matters when converting computed tomography attenuation to the higher photon energy of positron emission tomography.

Coauthor of research on brain responses to skin warming and cooling. The study connected controlled thermal stimulation with regional signals measured by positron emission tomography in awake humans.^[ref]