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Nuclear medicine differs from every other imaging modality in this option by placing the radiation source inside the patient rather than outside. A small, controlled activity of a radioactive tracer is administered (orally, intravenously, or by inhalation); the tracer concentrates in particular tissues according to its biochemistry; and external detectors map the emitted gamma rays or annihilation photons to build an image of function rather than anatomy. The two main imaging techniques — single-photon gamma-camera imaging (sometimes extended to SPECT, single-photon-emission CT) and positron-emission tomography (PET) — together with the closely related field of radionuclide therapy, complete the AQA medical-physics option. This lesson develops the production and detection physics, the dosimetry, and the clinical applications.
Spec mapping: This lesson sits under AQA 7408 section 3.10.6 (Radionuclide imaging and therapy). It covers the principles of the gamma camera (sodium-iodide scintillator activated with thallium, photomultiplier tube array, lead collimator, position-logic electronics, pulse-height analyser); common diagnostic tracers including technetium-99m (⁹⁹ᵐTc) for bone, thyroid and SPECT studies, ¹⁸F-fluorodeoxyglucose (FDG) for oncology PET, and iodine-131 (¹³¹I) for thyroid therapy; the principles of PET imaging (positron emission, electron-positron annihilation into two 511 keV gammas, line-of-response coincidence detection, image reconstruction); physical, biological and effective half-lives with the relation 1/T_eff = 1/T_phys + 1/T_bio; the principles of radionuclide therapy (brachytherapy using sealed sources, systemic radionuclide therapy, external-beam radiotherapy as a brief reference); dose limits and the ALARA principle. (Refer to the official AQA specification document for exact wording.)
Synoptic links:
- Section 3.8 (nuclear physics): the underlying physics of radioactive decay — exponential decay N = N_0 exp(-λt), half-life T_½ = (ln 2)/λ, activity A = λN — is directly extended here to a clinical context. The effective-half-life formula is a small but important generalisation.
- Section 3.10.5 (X-ray imaging): the same scintillator-PMT detection technology underpins many older radiographic imaging chains and the detectors in modern CT systems. The detection physics carries over.
- Section 3.2 (quantum phenomena): the photoelectric absorption in NaI(Tl) and the discrete photon energies of nuclear gammas (140 keV from ⁹⁹ᵐTc; 511 keV from positron annihilation) reinforce the quantum-energy work earlier in the course.
The gamma camera (Anger camera, after its 1957 inventor Hal Anger) is the workhorse of single-photon nuclear medicine. It detects gamma rays emitted by a radiotracer in the patient and builds up a 2-D projection image of the tracer distribution. The key components, from patient outward:
Collimator — a thick lead plate (typically 25-40 mm) drilled with many parallel holes. Only gamma rays travelling closely parallel to the holes reach the detector. The collimator provides the spatial information: a gamma detected at a particular point on the detector came from somewhere along the corresponding parallel ray through the patient. Without the collimator, all directional information would be lost — gammas have no curving paths in tissue analogous to refraction of light.
Scintillator crystal — a large single crystal of thallium-activated sodium iodide, NaI(Tl), typically 9-12 mm thick by 400-500 mm diameter. When a gamma ray photoelectrically absorbs in the crystal, a brief flash of visible (~415 nm) light is produced, with intensity proportional to the gamma energy.
Photomultiplier tube (PMT) array — typically 50-100 PMTs in a hexagonal arrangement, each viewing the back face of the crystal. Each scintillation event distributes its light across nearby PMTs according to a point-spread function determined by crystal geometry.
Position-logic electronics — weighted-sum circuits compute the (x, y) centroid of the PMT response, giving the position of the scintillation event in the crystal to within a few millimetres.
Pulse-height analyser — sums the total PMT signal to give an estimate of the gamma energy. Only events within an "energy window" centred on the expected photopeak (e.g. 140 keV ± 10% for ⁹⁹ᵐTc) are accepted into the image; events outside the window (Compton-scattered, multi-photon pile-up) are rejected.
The image is a 2-D map of accepted-event counts vs (x, y) position, accumulated over a few minutes per view. A typical clinical bone scan acquires whole-body anterior and posterior views over 20-30 minutes.
Sodium iodide has high effective Z (53 for iodine), so it absorbs gammas at diagnostic energies (140 keV from ⁹⁹ᵐTc) by photoelectric absorption with high efficiency. Thallium doping introduces luminescent centres that radiate visible light at 415 nm — close to the peak sensitivity of bialkali photomultiplier cathodes. The crystal is relatively cheap to grow in large diameters. Modern alternatives (BGO, LSO, LYSO) are used in PET (where higher Z and faster decay matter more) but NaI(Tl) remains standard for gamma cameras.
A radiotracer combines a useful radionuclide with a biochemical carrier that targets a specific physiological process.
| Tracer | Radionuclide | Carrier | Emission | T_½ (physical) | Application |
|---|---|---|---|---|---|
| ⁹⁹ᵐTc-MDP | ⁹⁹ᵐTc | methylene diphosphonate | 140 keV γ | ~6 hr | Bone scan |
| ⁹⁹ᵐTc-pertechnetate | ⁹⁹ᵐTc | TcO_4⁻ ion | 140 keV γ | ~6 hr | Thyroid imaging |
| ⁹⁹ᵐTc-MAG3 / DMSA | ⁹⁹ᵐTc | renal tracers | 140 keV γ | ~6 hr | Renal imaging |
| ¹⁸F-FDG | ¹⁸F | fluorodeoxyglucose | β⁺ → 2 × 511 keV γ | ~110 min | PET — oncology, neurology |
| ¹³¹I-iodide | ¹³¹I | NaI | 364 keV γ + β⁻ | ~8 days | Thyroid therapy |
| ⁶⁷Ga-citrate | ⁶⁷Ga | citrate | 93, 184, 296 keV γ | ~3.3 days | Infection / lymphoma imaging (legacy) |
Technetium-99m has dominated single-photon imaging for fifty years for the same reasons every textbook recites: 140 keV gamma (low patient dose; excellent gamma-camera detection efficiency); 6 hr half-life (long enough for transport and imaging; short enough to clear quickly after the study); pure gamma emission (no beta dose to patient); and ready availability from a ⁹⁹Mo/⁹⁹ᵐTc generator producing fresh activity in any nuclear-medicine department.
The activity of a radiotracer in the body falls because of two independent processes: physical radioactive decay (rate constant λ_phys) and biological clearance through metabolism and excretion (rate constant λ_bio). The combined rate constant is
λ_eff = λ_phys + λ_bio
and the effective half-life is therefore
1 / T_eff = 1 / T_phys + 1 / T_bio
The effective half-life is always shorter than either component. It is the relevant time constant for dosimetry, because it governs how long the tracer actually deposits dose in the patient.
A patient is administered ⁹⁹ᵐTc-MAG3 for renal imaging. The physical half-life of ⁹⁹ᵐTc is 6.0 hr; the biological half-life of MAG3 from a normally functioning kidney is 25 min. Calculate the effective half-life.
Convert both to consistent units. T_phys = 360 min; T_bio = 25 min.
1/T_eff = 1/360 + 1/25 = 0.00278 + 0.0400 = 0.0428 min⁻¹.
T_eff = 1/0.0428 = 23.4 min.
The effective half-life is dominated by the much faster biological clearance — making MAG3 an exceptionally low-dose tracer.
PET uses radionuclides that decay by positron (β⁺) emission: ¹⁸F, ¹¹C, ¹³N, ¹⁵O and a handful of less-common emitters. The positron travels at most a few millimetres in tissue before annihilating with an electron, producing two 511 keV gamma photons emitted at almost exactly 180° apart. Conservation of energy and momentum forces the back-to-back geometry; the small deviation from 180° (a few mrad) arises from residual positron-electron momentum at the moment of annihilation.
A PET scanner is a ring of fast-scintillator detectors surrounding the patient. When two opposite detectors register 511 keV events within a coincidence window of a few nanoseconds, the system records a line of response (LOR) — the chord joining the two detectors, along which the annihilation must have occurred. Reconstruction algorithms (analytic filtered back-projection, or modern iterative algorithms such as OSEM) combine millions of LORs to produce a 3-D map of tracer distribution.
PET advantages over single-photon imaging:
Disadvantages:
The dominant clinical PET tracer is ¹⁸F-fluorodeoxyglucose (FDG), a glucose analogue. Tumour cells (and active inflammation, and the brain in normal circumstances) have elevated glucose uptake; FDG concentrates and the trapped fluorine-18 emits positrons. PET-CT (combined PET and CT in a single scanner) is now the standard machine for oncological staging, restaging, and therapy-response monitoring.
Show that the gamma photons produced when a slow positron annihilates with an electron each have energy 511 keV. Take the electron rest mass m_e = 9.11 × 10⁻³¹ kg.
The positron and electron have the same rest mass. When they annihilate at rest, total rest energy 2 m_e c² is shared equally between two photons emitted back-to-back (momentum conservation: zero net momentum before, zero net momentum after).
Photon energy = m_e c² = (9.11 × 10⁻³¹) × (3.00 × 10⁸)² = 8.20 × 10⁻¹⁴ J.
Converting: 8.20 × 10⁻¹⁴ / (1.60 × 10⁻¹⁹) = 5.12 × 10⁵ eV ≈ 511 keV. ✓
graph TD
A["Patient with<br/>⁹⁹ᵐTc tracer"] --> B["Lead collimator<br/>parallel holes"]
B --> C["NaI(Tl) crystal<br/>scintillation event"]
C --> D["PMT array<br/>50-100 tubes"]
D --> E["Position-logic<br/>x, y centroid"]
D --> F["Pulse-height<br/>analyser"]
F -->|in 140 keV window| G["Accept event"]
F -->|outside window| H["Reject event<br/>(scattered)"]
E --> G
G --> I["Image: counts<br/>vs (x, y)"]
style C fill:#3498db,color:#fff
style G fill:#27ae60,color:#fff
style H fill:#e74c3c,color:#fff
Where imaging delivers a small dose (a few mSv) deliberately limited to allow diagnosis, radionuclide therapy delivers a large dose deliberately targeted to destroy tissue. Three modes:
A small sealed source (encapsulated radionuclide) is placed in or adjacent to the tumour:
The advantage is the inverse-square-law fall-off of dose with distance from the source: the tumour receives a large dose while surrounding healthy tissue is spared.
A radiopharmaceutical with biological targeting is administered, and concentrates in the tumour or affected tissue. Classical examples:
External-beam radiotherapy delivers MV-energy photons (or, in proton therapy, protons or heavier ions) to the tumour from outside the patient. It is the dominant radiotherapy modality numerically, but it is not "radionuclide therapy" per se — modern linear accelerators produce photons rather than gammas from a radionuclide source. (Historical cobalt-60 teletherapy machines were genuine radionuclide-based external-beam therapy, but they are now rare in the developed world.)
Nuclear-medicine dose is limited and audited under national and international standards (ICRP recommendations, UK IRR17 and IR(ME)R 17 regulations). Typical effective doses:
| Procedure | Effective dose (mSv) |
|---|---|
| ⁹⁹ᵐTc bone scan | ~3-4 |
| ⁹⁹ᵐTc renal scan | ~1 |
| ¹⁸F-FDG PET-CT (oncology) | ~10-14 |
| ¹³¹I diagnostic thyroid (small activity) | varies |
| ¹³¹I thyroid therapy (ablation dose) | dose to thyroid only — therapeutic intent |
The ALARA principle governs every nuclear-medicine procedure: dose to the patient As Low As Reasonably Achievable consistent with achieving the diagnostic or therapeutic goal. Pregnancy is a particular consideration; lactation requires advice on temporary cessation of breastfeeding for some tracers.
Occupational dose limits (UK): 20 mSv per year for radiation workers (ICRP recommendation; UK statutory limit similar). Members of the public: 1 mSv per year. Nuclear-medicine technologists and PET-imaging staff typically receive 1-3 mSv per year occupational dose with modern shielding.
Specimen question modelled on the AQA A-Level Physics paper format (Paper 3 Option B).
(a) Describe the function of each of the following components of a gamma camera: (i) the lead collimator, (ii) the NaI(Tl) crystal, (iii) the photomultiplier-tube array, and (iv) the pulse-height analyser. (6 marks)
(b) Technetium-99m has a physical half-life of 6.0 hr. A patient administered a ⁹⁹ᵐTc-labelled bone-scan agent has an effective half-life for the tracer in the body of 3.0 hr. Calculate the biological half-life. (3 marks)
(c) Explain why the two gamma photons emitted following positron annihilation each have an energy of 511 keV, and why they are emitted at approximately 180° to each other. (4 marks)
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