Ten original structured questions in the style of Paper 4, covering the whole of Medical physics: ultrasound and acoustic impedance, X-ray production and attenuation, CT, and PET scanning. The last questions compare the methods and link the tracer back to radioactive decay. Each is tagged with its lessons; attempt them all, then reveal the worked solutions.
Soft tissue has density 1060 kg m⁻³ and the speed of sound in it is 1540 m s⁻¹.
(a) State what is meant by the specific acoustic impedance of a medium. [1]
(b) Calculate the acoustic impedance of soft tissue. [2]
(c) Explain how a piezoelectric transducer both generates and detects ultrasound. [3]
(d) State why ultrasound, rather than audible sound, is used for imaging. [1]
At a boundary, the intensity reflection coefficient is Iᵣ/I₀ = (Z₁ − Z₂)²/(Z₁ + Z₂)². Impedances (×10⁶ kg m⁻² s⁻¹): fat 1.38, muscle 1.70, air 0.0004.
(a) Calculate the fraction of intensity reflected at a fat-muscle boundary. [2]
(b) Calculate the fraction reflected at a tissue (Z = 1.63)-air boundary. [2]
(c) Use your answers to explain why a coupling gel is used. [2]
(d) State why little of the ultrasound is reflected at a fat-muscle boundary. [2]
In an A-scan, an echo from a boundary returns 40 µs after the pulse is sent. The speed of sound in the tissue is 1540 m s⁻¹.
(a) Calculate the depth of the boundary below the probe. [3]
(b) Explain why the factor of one half appears in your calculation. [2]
(c) State what the size of an echo indicates. [1]
In an X-ray tube, electrons are accelerated through a p.d. of 80 kV before striking the target.
(a) Calculate the maximum kinetic energy of an electron, in joules. [2]
(b) Hence state the maximum energy of an X-ray photon produced. [1]
(c) Calculate the minimum wavelength of the X-rays. [3]
(d) State what happens to most of the electrons' energy at the target. [2]
An X-ray beam passes through soft tissue of linear attenuation coefficient 0.20 cm⁻¹.
(a) Calculate the fraction of the beam transmitted through 10 cm of tissue. [2]
(b) Calculate the half-value thickness of the tissue. [2]
(c) Bone has a much larger attenuation coefficient. State and explain what this does to the image. [2]
(d) State one advantage and one disadvantage of a CT scan over a single X-ray image. [2]
A CT scanner builds an image from many X-ray exposures.
(a) Outline how a CT scan produces a three-dimensional image. [3]
(b) State why image contrast for soft tissue is better in CT than in a single X-ray. [2]
(c) State why the radiation dose is a concern. [1]
In PET, a positron from the tracer annihilates with an electron.
(a) Show that the energy of each gamma photon produced is about 0.51 MeV. [3]
(b) State the directions in which the two photons travel, and why. [2]
(c) Explain how detecting the pair locates a line of response. [2]
(d) State what a PET scan shows that a CT scan does not. [1]
Describe how a PET scan is carried out and how the image is formed.
(a) State the type of tracer used and how it reaches the region of interest. [2]
(b) Describe what happens to the emitted positrons. [2]
(c) Explain how many lines of response build up an image. [2]
(d) State why the tracer must have a short half-life. [1]
A common PET tracer is fluorine-18, which has a half-life of 110 minutes. (ln2 = 0.693)
(a) Calculate the decay constant of fluorine-18, in min⁻¹. [2]
(b) A sample is prepared with activity 8.0 × 10⁸ Bq. State its activity after 220 minutes. [2]
(c) Calculate the activity after 60 minutes. [3]
(d) State why the short half-life is both useful and inconvenient. [1]
A clinic must choose an imaging method for three cases.
(a) State which of the three techniques use ionising radiation, and which does not. [2]
(b) Suggest the best method to monitor a developing fetus, with a reason. [2]
(c) Suggest the best method to check for a bone fracture, with a reason. [2]
(d) Suggest the best method to find an area of unusually high metabolic activity, with a reason. [3]
Mark this once you have attempted all ten questions and checked your working against the solutions. Revealing the solutions alone does not count.