Week 7: Nuclear Imaging

Nuclear imaging: basic idea

Give the patient a RADIOTRACER → decay happens INSIDE the patient → γ-photons leave the body → detector OUTSIDE builds an image of where the activity is

Why can only γ radiation be used for imaging?

α and β particles are stopped inside the body. Only γ photons escape the patient and can be measured outside

Radiotracer = ?

A molecule that follows a physiological process (metabolism, receptor, enzyme, transporter) + a radioactive nucleus attached to it

Nuclear imaging vs radiology (CT/MRI)

CT/MRI = ANATOMY (morphology). Nuclear imaging = FUNCTION/physiology, extremely sensitive (10⁻⁹–10⁻¹² mol, resolution ~1 mm) but poor anatomical information

Radiotracer distribution depends on (3 things)

1) Chemical properties of the tracer 2) Tissue perfusion 3) Target protein expression in the tissue

Ideal γ-energy for a radiotracer

Between 70 keV and 1 MeV. >70 keV = penetrant enough to leave the patient. <1 MeV = still detected efficiently (higher energy flies straight through the detector)

Why must the emission spectrum be "clean"?

No interfering radiation, and a low absorbed dose for the patient (ideal: only a γ-photon in the detectable range, nothing else)

Radiotracer half-life rules

Physical T½ > 1 h and effective T½ < 2–3 days

Why must the half-life be neither too short nor too long?

Too short: tracer must be made, transported, distributed and imaged before it decays away. Too long: patient stays radioactive longer → higher radiation dose

Atomic shells: names + max electrons

K (n=1), L (n=2), M (n=3). Max electrons per shell = 2n²

Electron binding energy

Energy needed to completely remove an electron from its shell. K_B > L_B > M_B (inner electrons are held tightest)

Why is it called "ionising" radiation?

It has enough energy to eject an electron from an atom (= ionise it)

Inner-shell vacancy: what happens?

An outer electron fills it within <10⁻¹⁵ s and the energy is released as a characteristic X-ray (E = K_B − L_B for L→K) OR an Auger electron

Nuclear notation: Z, N, A

Z = protons (defines the element), N = neutrons, A = Z + N (mass number)

Isotopes / isobars / isotones

Same Z / same A / same N. Mnemonic: the order is Z-A-N

Why do nuclei need neutrons?

Protons repel each other (Coulomb). The short-range nuclear force attracts close nucleons; neutrons add attraction without repulsion → the "glue" that keeps the nucleus stable

Mass defect + binding energy of a nucleus

Nuclide mass < sum of its separate protons + neutrons. Missing mass = binding energy (E = mc²) = minimal energy needed to split the nucleus into single nucleons

Radioactive decay: definition

Spontaneous process where an unstable nucleus (parent) transforms into a more stable one (daughter), often emitting ionising radiation. Ground state = lowest energy state of the nucleons

Line of stability

Stable nuclei cluster around it on the Z-vs-N chart. During decay a radionuclide moves TOWARD this line

The 3 main nuclear radiations

α = ⁴He nucleus. β = electron (β⁻) or positron (β⁺). γ = photon

Chart colours: which decay where?

Neutron-rich side (blue) → β⁻. Proton-rich side (pink) → β⁺ / EC. Heaviest nuclei (yellow) → α (and spontaneous fission)

α-decay equation

^A_Z P → ^A-4_Z−2D + ⁴₂He (P = parent, D = daughter nucleus)

Why do heavy nuclei emit α?

²⁰⁸Pb is the heaviest stable nuclide. Nuclear force is short-range, so in a huge nucleus nucleons on opposite sides don't "feel" each other → it sheds a very stable ⁴He (A−4, Z−2)

β⁻ decay: when + what happens

Neutron excess: n → p + e⁻ + anti-neutrino. Z+1, A unchanged. ^A_ZP → ^A_Z+1D + β⁻ + ν̄

Positron Emission → β⁺ decay: when + what happens

Proton excess: p → n + e⁺ + neutrino. Z−1, A unchanged. ᴬZ P → ^A_Z−1D + β⁺ + ν

Quick rule: β⁻ vs β⁺

Too many NEUTRONS → β⁻ (Z goes UP). Too many PROTONS → β⁺ or EC (Z goes DOWN). A never changes

Why is a neutrino emitted in β decay?

Without it energy and momentum would not be conserved; the (almost massless) neutrino carries the missing energy

Positron

Antimatter partner of the electron (same mass, positive charge). Not stable: it quickly annihilates with an electron

Electron capture (EC)

Proton excess: nucleus captures an orbital (K-shell) electron: p + e⁻ → n + ν. Z−1, A unchanged. Competes with β⁺

γ emission

Not a primary decay. Follows α/β decay when the daughter is left excited: ^A_Z P* → ^A_Z P + γ.

Example: ⁹⁹ᵐTc (T½ 6 h) → ~140 keV γ

Activity: definition + formula

Disintegrations per second, unit Bq. A(t) = |dN/dt| = λN(t) = A(0)e^(−λt)

Why is decay exponential?

Each nucleus decays independently with constant probability (Poisson process): −dN = λN d_t → N(t) = N(0)e^−λt

Half-life formulas

T½ = ln2 / λ. A(t) = A(0)·(½)^(t/T½).

Activity left: 100% → 50% → 25% → 12.5% per half-life

Does a radioactive nucleus "age"?

No. Decay is a stochastic one-shot process: until it decays, its decay probability stays constant

3 ways to produce radionuclides

Nuclear reactor (e.g. Pallas, Petten), radionuclide generator, cyclotron

Radionuclide generator

Long-lived parent keeps producing a short-lived daughter (⁹⁹Mo → ⁹⁹ᵐTc). The daughter is eluted ("washed off") with saline from the column

Scintillator

Material that emits UV/visible-light photons when an excited electron returns to its ground state

How does a scintillator work?

Absorbed radiation lifts electrons from valence band → conduction band (across the forbidden gap). When they fall back they emit scintillation photons. Light output ∝ absorbed energy

Photomultiplier tube (PMT)

Scintillation light hits the photocathode → electrons are accelerated through stages of rising voltage (100→500 V), multiplying each time → electrical pulse. Pulse height ∝ absorbed energy

Gamma camera: how is position found?

Many PMTs sit on one large scintillator; PMT closest to the interaction sees the most light; the computer calculates where the γ was absorbed from all PMT outputs

Why does a gamma camera need a collimator?

The crystal can't tell which direction a photon came from, and γ cannot be focused with a lens. A lead collimator with parallel holes lets only perpendicular photons through

Cost of collimation

~99.99% of photons are absorbed by the collimator → very low sensitivity

What does a planar scintigraphy image show?

A 2D projection: each pixel = SUM of all activity along the perpendicular line through the body (depth information is lost)

Spatial resolution: definition + rule

Ability to separate two high-contrast objects = FWHM of the point spread function. Objects must be MORE than 1 FWHM apart (d > FWHM) to be distinguished

Intrinsic resolution

Resolution of the detector without collimator. Limited by statistical fluctuation of light across the PMTs + scattering in the crystal. Typically 3–4 mm

Collimator resolution

Depends on collimator design and source-to-collimator distance. Further away → more holes see the source → blurrier. So keep the patient as close to the collimator as possible

System resolution (planar)

Intrinsic + collimator resolution combined (they add in quadrature; the collimator dominates). Typically 10–14 mm at organ depths of 5–10 cm

SPECT: principle

Single Photon Emission Computed Tomography: rotate gamma camera(s) around the patient → many 2D projections → reconstruct the 3D activity distribution

Simple backprojection

Smear each projection back along its line and sum them. A point source comes out blurred; the blur PSF ∝ 1/r

Filtered backprojection (FBP)

Filter the projections before backprojecting to cancel the 1/r blur. Works well only with low-noise data, but SPECT counts are low → noisy results

Iterative reconstruction (the loop)

Image estimate → forward projection (calculated projections) → compare with measured projections → update estimate → repeat. Image gets better each iteration; high computation time

SPECT vs planar: pros

3D activity distribution (no superimposed activity), better contrast, attenuation correction possible (with CT)

SPECT vs planar: cons

Many projections → long acquisition (30–60 min), restricted field of view (one bed position), no dynamic scanning

PET: how are the photons created?

β⁺ decay → positron slows down → annihilates with an electron → TWO 511 keV photons emitted back-to-back (~180°, momentum conservation)

Coincidence detection + LOR

Ring of detectors. Two photons detected within the coincidence window (6–12 ns) → the annihilation lies on the line between those detectors = line of response (LOR)

Electronic collimation

The coincidence defines the LOR, so no lead collimator is needed → much higher sensitivity, and no detector rotation is needed

How do LORs become an image?

Group LORs into projections at many angles (like CT), then reconstruct 3D with similar techniques as SPECT

PET detector: parts + requirements

Scintillator crystals (LSO = lutetium oxyorthosilicate) + photodetectors (APDs/SiPMs now replace PMTs). Needs: high stopping power at 511 keV, good energy resolution (reject scatter), fast timing, small crystals

Time of flight (TOF) PET

Photon arrival-time difference (picoseconds) shows where on the LOR the annihilation happened (within a few cm) → less noise, better image

PET vs SPECT: where PET wins

Sensitivity ~100× higher, spatial resolution ~2× better, better absolute quantification (easier corrections), allows dynamic studies

PET vs SPECT: where SPECT wins

More radiopharmaceuticals commercially available, less penetrant γ-photons (less shielding needed), much cheaper (equipment AND tracers)

FDG: what is it?

Fluorodeoxyglucose = glucose analog with the 2' OH group replaced by ¹⁸F. The most used PET radiotracer

How does FDG get trapped?

Taken up like glucose (brain, myocardium, cancer cells), then hexokinase phosphorylates it to FDG-6-PO₄, which can't be metabolised further → accumulates and stays in the cell

FDG clinical uses

Oncology (detection, staging, treatment response), cardiology (myocardial viability), neurology (Alzheimer, Parkinson). Research: brown fat (BAT) glucose metabolism

SUV formula

SUV = C_T,PET / (A_inj / m): tissue activity concentration ÷ injected activity per body mass. Clinical routine, semi-quantitative (one parameter)

Shortcomings of the SUV

Depends on uptake time, whole-body distribution volume, and FDG availability from the blood. Discrepancies vs true glucose consumption (Km) can lead to wrong conclusions about disease progress

FDG two-tissue compartment model

C_A (blood) →K₁→ C_F (free) →k₃→ C_B (trapped). k₂ = back to blood, k₄ = 0 (FDG-6-PO₄ doesn't leave). Metabolic rate Kᵢ = K₁·k₃ / (k₂ + k₃)

What do you need to calculate Kᵢ?

A DYNAMIC scan: blood (input) time-activity curve + tissue (output) time-activity curve → fit the rate constants

Static vs dynamic PET scan

Static: short, whole body, easy, semi-quantitative, one parameter (SUV). Dynamic: long, only 1 bed position, elaborate, fully quantitative, many parameters (K₁, k₂, k₃, Kᵢ)

Why hybrid imaging?

Nuclear imaging = function, poor anatomy → combine PET with anatomical CT or MRI for complementary information

PET/CT: two types of CT

Low-dose CT: localisation + attenuation & scatter correction. Diagnostic CT: high dose, with contrast

PET/MRI advantages

Superior soft-tissue contrast vs CT, one-stop-shop for PET + MRI, lower radiation burden than PET/CT