PET scanning
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What is a radioactive tracer, and how is it used in medical imaging?
A radioactive tracer is a substance containing radioactive nuclei that is introduced into the body and absorbed by the tissue being studied. In medical imaging, it allows the detection and visualisation of specific tissues or processes.
Why is a β+ (positron) emitting tracer used in PET scanning?
PET scanning relies on the annihilation of positrons with electrons. β+ emitting tracers allow positrons to be released within the body, leading to annihilation events and the production of detectable gamma rays.
Describe the process of annihilation in the context of PET scanning.
Annihilation occurs when a positron (emitted by the tracer) interacts with an electron in the tissue. This interaction results in the complete conversion of their mass into energy, producing two gamma-ray photons.
What is produced by the annihilation of a positron and an electron in PET scanning, and in what direction do they travel?
The annihilation produces two gamma-ray photons. These photons travel in approximately opposite directions (180° apart) to conserve momentum.
Explain how the arrival times of gamma-ray photons are used to create an image in PET scanning.
Detectors around the patient register the arrival times of the gamma-ray photons. By identifying coincident detections (photons arriving at opposite detectors simultaneously), the location of the annihilation event can be pinpointed, allowing the construction of an image representing tracer concentration.
How do the laws of conservation of mass-energy and momentum apply in the process of electron-positron annihilation?
The total mass-energy before annihilation (electron + positron) equals the total energy of the photons produced. Momentum is conserved because the photons are emitted in opposite directions with equal momentum magnitudes, resulting in a net momentum of zero (same as initial state).
Calculate the energy of a gamma-ray photon produced during positron-electron annihilation. (Electron/positron mass = 9.11 × 10⁻³¹ kg, c = 3.0 × 10⁸ m/s)
E = mc², where m is the mass of either the electron or positron (9.11 × 10⁻³¹ kg). E = (9.11 × 10⁻³¹ kg) * (3.0 × 10⁸ m/s)² = 8.2 × 10⁻¹⁴ J. The total energy is split equally between the two gamma rays. Alternatively, E = 0.511 MeV.
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