The University of Melbourne
Department of Biomedical Engineering
Semester 1 2017, Exam BMEN90021 Medical Imaging
Reading time – 15 min Writing time – 3 hours This paper has 6 pages.
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Authorised materials –
The following items are authorised – Calculators – Casio FX82 calculators only
Instructions to invigilators
Students require –
• script books X
• graph paper
Paper can go to library Yes X No
Instructions to students
This Examination is worth 60% of your assessment for this subject.
You should attempt ALL twelve (12) questions.
All answers are to be written in the exam booklets provided.
There are a total of 100 marks available in this Examination.
Questions are NOT of equal value and marks are shown in parentheses.
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Question 2 (10 marks)
BMEN90021 Medical Imaging
Question 1 (10 marks)
Consider the following 5×5 diagonal image, I1, that has intensity values equal to one on the diagonal (white) and zero (black) elsewhere:
(a) Find a symmetric 3×3 filter, f, such that in the resultant image, I2 = f * I1, the pixel values are swapped. That is, white pixels in I1 become black pixels in I2, and black pixels in I1 become white pixels in I2. Your answer needs only to be valid on the central 3×3 block of pixels in I2. (8 marks)
(b) Is the filter, f, unique? Justify your answer. (2 marks)
The following matrix, 𝐴𝐴, is a 2-dimensional linear transformation matrix: 0 −1 0
𝐴𝐴 = �2 0 001
(a) Sketch that image that results when 𝐴𝐴 is applied to the square object shown on the
axes below. (5 marks)
(b) For each one of the following statements, state whether or not it describes the linear transformation given by 𝐴𝐴. Briefly justify each answer. (5 marks)
(i) Shear followed by translation (ii) Translation followed by shear (iii) Rotation followed by scaling (iv) Scaling followed by rotation (v) Scaling
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BMEN90021 Medical Imaging
Question 3 (5 marks)
Consider a 2-dimensional imaging system characterised by the following point spread function (PSF).
(a) Will the imaging system yield greater spatial resolution in the vertical or horizontal orientation? Briefly justify your answer. (2 marks)
(b) Sketch the magnitude spectrum of the modulation transfer function (MTF) of the system. (3 marks)
Question 4 (5 marks)
(a) What is a “K-edge” in X-ray imaging and what effect is it associated with? Why
is this effect useful in X-ray imaging? (3 marks)
(b) Name one X-ray contrast agent and describe briefly how it is used in X-ray
imaging. (2 marks) Question 5 (10 marks)
Consider the following field-of-view containing four circular objects, to be imaged using CT.
Sketch the sinogram that would be obtained from parallel beam CT imaging of these four objects. Ensure you label the sinogram axes. Assume the convention with respect to the projection angles: 0° is a projection from the top (X-ray sources) to the bottom of the image (detectors), and the angle increases anti-clockwise (counter-clockwise).
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BMEN90021 Medical Imaging
Question 6 (5 marks)
(a) In a proton-density weighted MRI scan, the image intensities reflect differences in the density of protons in tissue, rather than T1 or T2 differences. Should the echo time, TE, and repetition time, TR, be short or long to achieve proton-density weighting? Justify your answer. (2 marks)
(b) Explain “slice selection”, that is, how a 2-dimensional slab of tissue is excited in MRI. (3 marks)
Question 7 (10 marks)
Each of the following statements about Magnetic Resonance Imaging is false. For each statement, explain why it is false, and correct the statement to make it true.
(a) “The RF coils produce static magnetic fields that vary linearly in space.” (2 marks)
(b) “The repetition time, TR, is typically shorter in T2-weighted imaging than T1- weighted imaging.” (2 marks)
(c) “The k-space variables, kx(t) and ky(t), are temporal frequencies because they are functions of time.” (2 marks)
(d) “Echo Planar Imaging is used in functional MRI to acquire high resolution images in less time than standard Gradient Echo imaging.” (2 marks)
(e) “T2* decay is faster than T2 decay because T2* decay includes the recovery of the bulk magnetisation in the z-direction.” (2 marks)
Question 8 (10 marks)
Two lines of k-space, shown as solid vertical gray lines in the following diagram, are to be acquired using 2-dimensional Spin-Echo MRI. The first line is from point A to point B. The second line, from point C to point D, is acquired with a separate RF pulse. Assume that the system starts at the centre of k-space.
Sketch the sequence diagram, showing RF pulses and x- and y- gradients. Indicate on your sequence diagram the points that correspond to A-D, and indicate periods when the receiver is on.
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BMEN90021 Medical Imaging
Question 9 (5 marks)
An ultrasound transducer, operating at 3 MHz, receives a signal from a boundary 5 cm deep in tissue. The tissue between the transducer and boundary has an attenuation of 2.5 dB cm-1 MHz-1. The received signal is 80 dB less intense than the transmitted signal. What percentage of the transmitted signal is reflected by the boundary?
Question 10 (10 marks)
An ultrasound scanner operating in B-mode has a central frequency of 5 MHz and a pulse repetition frequency of 5 kHz. Each pulse consists of two cycles of the transmitted wave. The image depth is 15cm and 60 scan lines are acquired per image. Assume the speed of sound in tissue to be 1500 m/s.
(a) Explain the practical difference between a ‘central’ frequency and a ‘pulse repetition’ frequency in ultrasound. (2 marks)
(b) How long does it take for one line to be acquired, from the time the pulse is sent out, to the time its reception is completed? (5 marks)
(c) How many images per second can be acquired? (3 marks)
Question 11 (10 marks)
A pulsed wave Doppler ultrasound system operates at 5 MHz, with a pulse repetition frequency (PRF) of 3 kHz. Assume the speed of sound in tissue to be c = 1500 m/s.
(a) What is the purpose of a ‘range gate’, and how does it work? (2 marks)
(b) Calculate the time between pulses, TPRF. (1 mark)
The Doppler shift is given by
where va is the speed of the object.
(c) What is the Doppler shift caused by blood moving at 30 cm/s away from the
transducer? (2 marks)
(d) Find a higher velocity moving away from the transducer that will be indistinguishable from the blood moving 30 cm/s away from the transducer. (5 marks)
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BMEN90021 Medical Imaging
Question 12 (10 marks)
In a SPECT system, Compton scattering of a γ-ray with incident energy Einc (keV) by a deflection angle θ° produces a γ-ray with energy
where EPET is 511 keV.
(a) Why does the normalising constant EPET = 511 keV appear in this expression,
rather than a constant of ESPECT = 140 keV? (1 mark)
(b) Give one advantage and one disadvantage of having a wide acceptance window in
a SPECT system. (2 marks)
(c) What piece of equipment is used to record γ-rays in SPECT imaging? (1 mark)
(d) Describe the process used to reconstruct a SPECT image from γ-ray detections. (2 marks)
Consider a clinical PET detector ring consisting of 360 evenly spaced detectors,
{D1, D2, …, D360}, where detector D1 is at the top of the ring. Four γ-rays are detected within 2ns of eachother, one at each of detectors D45, D135, D225 and D315.
(e) Using diagrams, indicate where the two events that gave rise to these four detections may have originated. (3 marks)
(f) If the two events were emitted from radioactive decay at a small tumour, where is the tumour most probably located? (1 mark)
END OF EXAM QUESTIONS
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