Physics (9702) | PET scanning

✨ Comprehensive Study Notes: PET Scanning (9702 Medical Physics) ✨

Welcome to the exciting world of Positron Emission Tomography (PET) scanning! This chapter links together concepts from Nuclear Physics, Quantum Physics, and Energy conservation to explain one of the most powerful diagnostic tools in modern medicine.

Unlike X-rays or CT scans, which mainly show you the body's structure, PET scanning shows you the body's function—how tissues and organs are working metabolically. Let's break down the physics step-by-step!

1. The Tracer and Positron Emission

The entire process starts with a special substance called a tracer.

1.1 What is a Tracer? (Syllabus 24.3.1)

A tracer is a substance that contains radioactive nuclei. This substance is introduced into the patient’s body (usually by injection or inhalation).

• Mechanism: The tracer is chosen because it mimics a naturally occurring substance in the body (like glucose).
• Absorption: Tissues that are highly active (like the brain, or rapidly growing cancer cells) absorb the tracer rapidly because they need more fuel (glucose).
• Function: The nuclei within the tracer then undergo radioactive decay within the targeted tissue.

1.2 The Crucial Decay: $\beta^+$ Emission (Syllabus 24.3.2)

For PET scanning to work, the radioactive nuclei in the tracer must decay via positron emission, also known as beta-plus ($\beta^+$) decay.

• The Particle: A $\beta^+$ particle is a positron.
• Positron Physics: A positron is the antiparticle of an electron. It has the same mass as an electron but carries an opposite charge (+1e).
• Example: A common tracer uses the isotope Fluorine-18 (which decays to Oxygen-18).

2. Annihilation and Energy Release

This is where the real physics magic happens! Once the positron is emitted from the tracer nucleus inside the body, it quickly travels a short distance (a few millimeters) until it encounters an electron from the surrounding tissue.

2.1 The Annihilation Event (Syllabus 24.3.3)

When a particle (the electron, $e^-$) meets its antiparticle (the positron, $\beta^+$), they mutually destroy each other in a process called annihilation.

• Conversion: All of their mass is converted entirely into energy, following Einstein's famous equation, \(E = mc^2\).
• Key Physics Principles: During this conversion, two fundamental physics principles must be conserved:
  1. Mass-Energy Conservation: The total mass-energy remains the same. The mass lost is precisely balanced by the energy of the emitted photons.
  2. Momentum Conservation: The total momentum before the annihilation (which is nearly zero since the particles are moving slowly within the tissue) must equal the total momentum after.

2.2 The Resulting Gamma Rays (Syllabus 24.3.4)

Because momentum must be conserved, the energy released is packaged into two identical high-energy gamma-ray photons.

• The two gamma-ray photons travel outwards in exactly opposite directions (180° separation).
• This opposite direction of travel is crucial for detection and imaging! It allows the scanner to locate precisely where the annihilation occurred.

3. Calculating the Gamma Ray Energy (Syllabus 24.3.5)

We can calculate the exact energy carried by the gamma photons using the principle of mass-energy equivalence.

3.1 Mass Loss and Energy Gain

The mass ($\Delta m$) converted into energy is the total rest mass of the electron ($m_e$) and the positron ($m_{\beta^+}$). Since they have identical masses:

Total Mass Annihilated, \(\Delta m = m_e + m_{\beta^+} = 2m_e\)

The total energy released, \(E_{total}\), is calculated using:

\(E_{total} = (\Delta m) c^2\)

Where \(c\) is the speed of light in a vacuum.

3.2 Energy per Photon

Since the two photons are identical and share the total energy equally:

\(E_{photon} = \frac{E_{total}}{2}\)

Did you know? The rest mass energy of a single electron (or positron) is approximately 0.511 MeV (Mega-electronvolts). Therefore, the total annihilation energy is about 1.02 MeV, and each gamma photon has an energy of 0.511 MeV. This characteristic energy is vital for the detection system.

To Calculate the Energy (The Physics Steps):

1. Find the Mass Defect (\(\Delta m\)): Determine the total mass of the electron and positron in kilograms. (A standard value for \(m_e\) is \(9.11 \times 10^{-31}\) kg).
2. Calculate Total Energy (\(E_{total}\)): Multiply \(\Delta m\) by \(c^2\). (Where \(c = 3.00 \times 10^8\) m/s). This gives \(E_{total}\) in Joules.
3. Calculate Photon Energy (\(E_{photon}\)): Divide \(E_{total}\) by 2.

4. Detection and Image Creation

The final stage involves capturing the energy signals and translating them into a readable map of the patient's internal metabolic activity.

4.1 Gamma Ray Travel and Detection (Syllabus 24.3.6)

The 0.511 MeV gamma-ray photons travel outwards from the annihilation site, passing through the surrounding tissue until they exit the body.

• The patient is placed within a large ring of detectors (often scintillation crystals paired with photomultiplier tubes).
• When a gamma ray hits a detector, it produces a tiny flash of light, which is converted into an electrical signal.

4.2 Coincidence Detection

Since the two gamma photons travel in opposite directions, they hit two detectors on opposite sides of the ring at almost exactly the same time (this is called temporal coincidence).

The PET scanner electronics are programmed to look only for these coincidence events.

• If Detector A and Detector B register hits simultaneously (within a tiny time window, usually nanoseconds), the scanner assumes the annihilation must have occurred somewhere along the line of response (LOR) connecting A and B.

4.3 Creating the Image (Syllabus 24.3.6)

By processing thousands of these coincidence events and recording the exact arrival times of the photons at the detectors, a detailed 3D image can be reconstructed.

• Tracer Concentration: A region of the body that shows a high density of detected LORs indicates a high concentration of the tracer.
• Medical Significance: High tracer concentration means high metabolic activity. This is extremely useful for identifying fast-growing tumors, mapping brain activity, or assessing heart function.
• Image Quality: The final image is essentially a map showing the spatial distribution of the annihilation events.