Department of Biomedical Engineering
BMEN90021 Medical Imaging
End of Semester 1 2018
Reading Time: 15 minutes – no writing or annotating allowed anywhere Writing time: 180 minutes
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• The examination paper IS TO REMAIN in the examination room.
• Students are to be provided with one script book.
• Provide extra script books on request.
Instructions to Students
• Total marks for this paper is 100.
• Ensure your student number is written on all script books and answer sheets during
writing time. No annotating is allowed in reading time or after the end of writing time.
• Attempt all 10 questions, which are each worth 10 marks.
• Answer all questions on the right-hand lined pages of the script book.
• Start the answer to each question on a new page in the script book and write the question
number in the top right hand corner.
• The left-hand unlined pages of script books are for draft working and notes and will not be
• Write legibly, preferably in blue or black pen.
• Show all working for each problem.
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Paper to be lodged with Baillieu Library
Page 1 of 6
BMEN90021 Medical Imaging
Question 1 (10 marks)
The 11×11 pixel image shown below, I, consists of black and white pixels with intensities of zero and one, respectively.
(a) Sketch the magnitude of the 2-d Fourier Transform of I, showing the locations of the five dominant peaks (spikes). (5 marks)
(b) What are the spatial frequencies of these peaks? (5 marks)
Question 2 (10 marks)
(a) When downsampling an image, why is it better to apply a low-pass filter prior to decimating the image (removing rows and columns from the image matrix)?
(b) Is the 2-d linear transformation of an object unique, or is there more than one linear transformation that can result in exactly the same transformation result? Give an example to support your answer, using a square object centred at the origin as shown in the figure below. (4 marks)
(c) Consider a single slice of a 2-d MRI scan that is 2 mm thick. The field-of-view that contains the object is 20 cm x 20 cm, and the k-space matrix size is 200 x 200. What is the image matrix size? What is the volume of each voxel?
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Question 3 (10 marks)
BMEN90021 Medical Imaging
When interacting with biological tissue, X-rays can undergo photoelectric absorption, Compton scattering and/or coherent scattering.
(a) What does it mean for radiation to be ‘ionizing’? Which, if any, of the above three effects are non-ionizing processes? (4 marks)
(b) Which of the above three effects contributes the most to contrast in an X-ray image? (1 mark)
(c) Which of the above three effects dominates at high X-ray energies? (1 mark)
(d) How does a collimator help reduce scatter? Include a sketch in your solution.
(e) The bars in a collimator are doubled in height. List one advantage and one
disadvantage of this new collimator. (2 marks)
Question 4 (10 marks)
Consider the following sinogram from a parallel beam CT acquisition. The horizontal axis is distance and the vertical axis is the angle of the sources and detectors, starting at 0° at the top row of the sinogram.
(a) What is the maximum angle in the sinogram? Justify your answer. (1 mark)
(b) Sketch the arrangement of object or objects that would give rise to this sinogram.
(c) Sketch the shape of a Ram-Lak filter, labelling your axes. (2 marks)
(d) What modification is made practically to the Ram-Lak filter, and why? (2 marks)
(e) Is the Ram-Lak filter applied using addition, multiplication or convolution? Is it applied to data in the image domain? If no, what domain is the data in when the Ram-Lak filter is applied? (2 marks)
Page 3 of 6
EPI images is 128 × 128. The ac for one image is 100 ms and ev
Gxx ReScigenivael r
BMEN90021 Medical Imaging
Chapter 4: Magnetic resonance imaging
Question 5 (10 marks)
(a) “A gradient, Gz, turned on during slice selection, rotates the bulk magnetisation
that as little signal decays as possible before it is detected.” (2 marks)
Each of the following statements about Magnetic Resonance Imaging is false. For each Modulus of raw data
statement, explain why it is false, and suggest a correction to make the sentence true.
around the z-axis.” (2 marks)
(b) “The echo tim1.0e, TE, is typically as short as possible in T2-weighted imaging, so
(c) “In T1-weighted imaging, the RF coils detect the changing bulk magnetisation in
the z-direction, as it r1e0c0overs to equilibrium.” (2 marks) 50 Readout
oxyhemoglobin is paramagnetic.” (2 marks) 0.05
(e) “The k-space variables, kx(t) and ky(t), are temporal frequencie0s.” (2 marks)
Question 6
Figure 4.21 Multiple echoes per excitation cause blurring. Assume that the image to be reconstructed is a Dirac imp (10 marks) ⃗
direction, dephasing clearly affects the measurements in the phase-encoding direction. Without T2∗ (or T2, depending
Phase-encoding 50
(d) “BOLD fMRI is sensitive to localised changes in oxyhemoglobin, as
(a) Sketch the trajectory of the three lines in k-space. Label your diagram, and
amplitude equal to 1. (a) Modulus of the measured data in the k-space. Although the raw data are more or less constan
modulus of the raw data would have been constant. (b) One column of the modulus of the reconstructed image, whic Consider the following sequence diagram depicting the acquisition of three lines of 2-
Dirac impulse has been blurred.
dimensional k-space using Echo Planar Imaging.
Figure4.22 (a)SchematicrepresentationoftheT∗-weightedblippedGEEPIsequence.Aseriesofgradient-echoesa clearly indicate the order and directions in wh2ich the lines are acquired. Indicate
sampled. (b) Corresponding trajectory in k-space. Each “blip” in the phase-encoding direction selects a new row in the on the diagram where echoes form, if there are any. (7 marks)
(b) If the RF pulse was a 45° pulse, rather than a 90° pulse, how would the acquired
echoes, for example, the acquisition time TA is or GE sequence, and the absen
image change? (1 mark)
explains the time gain. All ech
(c) What does “Receiver on” mean? How is a signal generated in the RF receive
TA = 4 coils? (2 marks)
= 160 seconds < 3 minutes. (4.70)
in one excitation (Figures 4.22 a
• Echo planar imaging (EPI) This is the fastest 2D imaging sequence currently available. It is a SE
Signal 0.4
of the T ∗ dephasing, however, 2
the number of echoes that can b
noise level. A typical size of the
BMEN90021 Medical Imaging
Question 7 (10 marks)
For each of the following questions, justify your answer.
(a) Is the transducer’s central frequency lower than the pulse repetition frequency in
Doppler ultrasound? (2 marks)
(b) An ultrasound transducer, operating at 6 MHz, receives a signal from a boundary 2 cm deep in tissue. The tissue between the transducer and boundary has an attenuation of 2.4 dB cm-1 MHz-1. The received signal is one million times less intense than the transmitted signal. Is the boundary a perfectly reflecting boundary? (4 marks)
(c) Is it possible to distinguish the boundaries of a 1 mm wide blood vessel using a 5 MHz ultrasound that transmits pulses that are 3 wavelengths long? Assume the speed of sound is 1500m/s. What is the axial resolution of this system?
Question 8 (10 marks)
In pulsed wave Doppler ultrasound, the Doppler shift is given by
fD =−2va fT, c
Assume that the speed of sound is 1500 m/s, that the transducer central frequency is 3 MHz, and that an object is moving directly toward the transducer (at 0 degrees to the transducer axis) at a speed of 25 cm/s.
(a) Calculate the Doppler shift. (2 marks)
(b) Calculate the Pulse Repetition Time such that the object moving toward the transducer at 25 cm/s is indistinguishable from an object moving away from the transducer at 75 cm/s. (5 marks)
(c) Is the Doppler shift constant as the object approaches the transducer? Explain your answer. (1 mark)
(d) If the object changes direction so that it now moves in a plane perpendicular to the transducer axis, how does the Doppler shift change? (2 marks)
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BMEN90021 Medical Imaging
Question 9 (10 marks)
Consider a patient being given a PET scan in a hospital. It is known that before injecting the patient, the radiotracer loses 39.4% of its count-rate in 20 minutes. The PET scan begins 30 minutes after injection, as it is known to take 30 minutes for the radiotracer to accumulate sufficiently in the organ of interest. The biological half-life is estimated to be 70 minutes, and the scan is one hour long.
(a) What is the effective half-life of the radiotracer, TE? (4 marks)
(b) Let N(0) be the count rate of the radiotracer at the time of injection. After the one
hour scan, what proportion of N(0) remains in the patient? (5 marks)
(c) What would be the effect of beginning the scan immediately after injection of the
radiotracer, rather than 30 minutes after injection? (1 mark)
Question 10 (10 marks)
(a) What is the primary difference between an X-ray and a gamma ray? (1 mark)
(b) Does an X-ray travel faster than a gamma ray? Explain your answer. (1 mark)
(c) Does an X-ray have a shorter wavelength than a gamma ray? Explain your answer. (1mark)
(d) What piece of equipment is used to record g-rays in SPECT imaging? (1 mark)
(e) A gamma ray used in PET has a wavelength of 2.4 x 10-12 m and energy of 8.19 x 10-14 Joules. What is the equivalent wavelength and energy of a SPECT gamma ray? Justify your answers. (4 marks)
(f) Both SPECT and CT images can be reconstructed using Filtered Back-Projection. What is the primary difference between SPECT projection data and CT projection data? (1 mark)
(g) Why is SPECT said to be a more ‘specific’ imaging technique than CT? (1 mark)
END OF EXAM QUESTIONS
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