OCR A Physics · Module 6: Particles and medical physics
Medical imaging: practice questions with answers
6 exam-style questions on medical imaging. Try each one on paper first, then open the answer to see the full working and the common slips that cost marks.
- Using the right equation2 marks
An X-ray beam passes through 4.0 cm of tissue with linear attenuation coefficient 0.28 cm⁻¹. Calculate the percentage of the intensity transmitted.
I/I₀ = %
Show the answer and working
Answer I/I₀ = 32.6 %
I/I₀ = e^(-μx) = e^(-0.28 × 4.0) = e^(-1.12) = 0.326, which is 32.6%.
- Got 67.4%? This is the percentage absorbed or scattered. The transmitted fraction is e^(-μx) = e^(-1.12) = 32.6%.
- Got 112%? You used μx as the fraction. Use I = I₀e^(-μx): the transmitted fraction is e^(-1.12) = 32.6%.
- Using the right equation2 marks
The linear attenuation coefficient of lead for a beam of gamma rays is 1.4 mm⁻¹. Calculate the half-value thickness of lead, in mm.
x½ = mm
Show the answer and working
Answer x½ = 0.495 mm
I = I₀e^(-μx) with I = I₀/2 gives x½ = ln 2 ÷ μ = 0.693 ÷ 1.4 = 0.495 mm.
- Got 0.714 mm? You used 1/μ, which is the mean free path. The half-value thickness is ln 2 ÷ μ = 0.495 mm.
- Got 0.97 mm? You multiplied instead of dividing. x½ = ln 2 ÷ μ = 0.693 ÷ 1.4 = 0.495 mm.
- Using the right equation3 marks
Soft tissue has density 1060 kg m⁻³ and ultrasound speed 1540 m s⁻¹. Bone has acoustic impedance 7.8 × 10⁶ kg m⁻² s⁻¹. Calculate the percentage of ultrasound intensity reflected at a soft tissue and bone boundary.
Ir/I₀ = %
Show the answer and working
Answer Ir/I₀ = 42.8 %
Z₁ = ρc = 1060 × 1540 = 1.63 × 10⁶ kg m⁻² s⁻¹. Reflected fraction = ((7.8 × 10⁶ - 1.63 × 10⁶) ÷ (7.8 × 10⁶ + 1.63 × 10⁶))² = 0.428, so 42.8%.
- Got 65.4%? You did not square the ratio. Reflected fraction = ((Z₂ - Z₁) ÷ (Z₂ + Z₁))² = (0.654)² giving 42.8%.
- Got 4.38%? You used (Z₁/Z₂)². The reflection equation is ((Z₂ - Z₁) ÷ (Z₂ + Z₁))², giving 42.8%.
- Unit prefixes2 marks
An ultrasound pulse takes 130 μs to travel to a boundary and return as an echo. The speed of ultrasound in tissue is 1540 m s⁻¹. Calculate the depth of the boundary, in cm.
d = cm
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Answer d = 10 cm
Distance there and back = vt = 1540 × 130 × 10⁻⁶ = 0.200 m. Depth = half of this = 10 cm.
- Got 20 cm? You used the total path length. The pulse travels to the boundary and back, so d = vt ÷ 2 = 10 cm.
- Got 0.1 cm? That is the depth in metres. Multiply by 100 to give cm: 10 cm.
- Using the right equation1 mark
In PET scanning, what is detected?
- A Reflected ultrasound pulses from tissue boundaries.
- B Radio waves emitted by protons relaxing in a magnetic field.
- C Two gamma photons emitted in opposite directions from positron-electron annihilation.
Show the answer and working
Answer C: Two gamma photons emitted in opposite directions from positron-electron annihilation.
A positron annihilates with an electron producing two gamma photons in opposite directions, which detectors locate.
- Why not A? That describes ultrasound imaging, not PET.
- Why not B? That describes MRI, not PET.
- Using the right equation1 mark
In MRI, what is the purpose of the gradient magnetic fields?
- A To make the position of the resonating protons identifiable.
- B To produce the radio-frequency pulse.
- C To ionise tissue to produce an image.
Show the answer and working
Answer A: To make the position of the resonating protons identifiable.
The field strength varies with position, so the Larmor frequency of protons depends on position and location can be worked out.
- Why not B? The RF pulse comes from separate radio-frequency coils.
- Why not C? MRI uses non-ionising radio waves and magnetic fields.