Medial Physical (Copy)

A2 Level Physics – Section 24: Medical Physics (Detailed Notes)

24.1 Production and Use of Ultrasound

1. Piezoelectric Effect

• A piezoelectric crystal changes shape when a potential difference is applied across it.
• It also produces a voltage (e.m.f.) when its shape is mechanically deformed.
• This property allows piezoelectric crystals to act as both transmitters and receivers of ultrasound.

2. Ultrasound Transducers

• Ultrasound generation: applying an alternating voltage to the piezoelectric crystal causes it to vibrate and emit ultrasonic waves.
• Detection: incoming ultrasound waves deform the crystal, generating a voltage signal.
• Typically used in pulse-echo systems for imaging.

3. Reflection of Ultrasound at Tissue Boundaries

• When ultrasound pulses encounter a boundary between two media (e.g. muscle and bone), part of the wave is reflected, and part is transmitted.
• The reflected signals (echoes) provide information about internal structures, including depth and type of tissue.

4. Specific Acoustic Impedance (Z)

• Defined as:
  Z = ρ·c
  • ρ = density of the medium (kg/m³)
  • c = speed of sound in the medium (m/s)
  • Z = acoustic impedance (kg·m⁻²·s⁻¹)
• Large mismatch in Z between media → strong reflection

5. Intensity Reflection Coefficient (IR / I₀)

• IR / I₀ = ((Z₁ – Z₂)²) / ((Z₁ + Z₂)²)
  • IR = reflected intensity
  • I₀ = incident intensity
  • Z₁, Z₂ = acoustic impedances of the two media
• Used to calculate how much ultrasound is reflected vs transmitted

6. Attenuation of Ultrasound

• As ultrasound travels through tissue, intensity decreases due to absorption and scattering:
  I = I₀·e^(–μx)
  • I = intensity after distance x
  • μ = attenuation coefficient (m⁻¹)
  • x = distance traveled (m)

24.2 Production and Use of X-Rays

1. X-Ray Production

• Produced when high-speed electrons strike a metal target (e.g. tungsten).
• Electrons are accelerated by a high voltage (V), gaining kinetic energy:
  E = eV
• Minimum wavelength (λ_min) of emitted X-rays:
  λ_min = hc / eV
  • h = Planck’s constant
  • c = speed of light
  • e = elementary charge
  • V = accelerating voltage

2. X-Ray Imaging and Contrast

• Contrast: difference in X-ray absorption between tissues.
  • Bone absorbs more (appears white)
  • Soft tissue absorbs less (appears darker)
• Use of contrast media (e.g. iodine, barium) improves visibility of soft tissue

3. Attenuation of X-Rays

• Follows the same exponential law:
  I = I₀·e^(–μx)
  • I = transmitted intensity
  • μ = attenuation coefficient
  • x = thickness of material

4. CT (Computed Tomography) Scanning

• Produces 3D images by:
  1. Taking multiple X-ray images from different angles in one section → 2D slice
  2. Repeating this for multiple slices along the body
  3. Combining all slices computationally to produce a 3D image

24.3 PET (Positron Emission Tomography) Scanning

1. Tracers

• A tracer is a biologically active substance containing a radioactive isotope.
• It is injected into the body and absorbed by specific tissues.

2. β⁺ Emission

• PET uses isotopes that undergo positron emission (β⁺ decay).

3. Annihilation

• A positron emitted by the tracer annihilates with an electron in tissue.
• This process conserves momentum and energy.

4. Gamma Ray Production

• Each annihilation event produces two gamma-ray photons, each with energy:
  E = mc² = (9.11 × 10⁻³¹ kg)(3.00 × 10⁸ m/s)² = 8.19 × 10⁻¹⁴ J ≈ 0.511 MeV
• Photons are emitted in opposite directions (180° apart).

5. Detection and Imaging

• Gamma rays exit the body and are detected by scintillation detectors placed in a ring.
• Coincidence detection: when two opposite detectors detect gamma rays simultaneously → event location is recorded
• Repeated detections are processed to create a 3D image showing tracer concentration in tissue