Page 1 of 11 pages
Technical University of Denmark
Written test, 9 December 2015
Course name: Introduction to medical imaging
Course no. 31540
Aids allowed: None. Pocket calculator is not allowed.
Exam duration: 2 hours.
“Weighting”: All problems weigh equally.
Instruction: See answer sheet.
The right answer is the one which is most correct
Problem 1
Four axial MR brain images are shown below. They are acquired with sequences of repeated 90-degree
excitation pulses with different repetition time TR as indicated under each image (units: milliseconds).
The images are all acquired with an echo time TE=10ms.
Almost all signal is gone in the leftmost image, but some remain in fatty tissues near the skin and skull.
What does that tell you about the relative relaxation time of these fatty tissues compared to the other
imaged brain tissues?
(Ignore the bright spot in the saggital sinus (at bottom, center of the image) caused by signal enhancement due to blood flow. It is irrelevant to the question.)
Answer with one letter on the answer sheet:
A. Fat has a long T1.
B. Fat has a short T1.
C. Fat has a long T2.
D. Fat has a short T2.
E. Do not know.
Page 2 of 11 pages
Problem 2
The figure shows a cross-sectional view of a (single-element) ultrasound planar piston transducer
(blue). Four identical source points on the surface are considered (denoted S1,S2, S3 and S4 in red).
Consider the field point in green: the pressure waveforms in the plots below indicate the pressure due to
each of the four sources as well as the total sum at the field point. Only one of the columns of plots is
correct. Which?
10
5
S4
mm
S3
0
-5
S2
Acoustic axis
S1
-10
0
A
1
5
10
mm
15
B
1
20
C
1
0.5
0.5
0
0
0
0
-0.5
-0.5
-0.5
-0.5
PS1
0.5
-1
0
2
4
6
8
10
+
1
-1
0
2
4
6
8
-1
10
+
1
0.5
0
2
4
6
8
10
+
1
-1
0.5
0
0
0
-0.5
-0.5
-0.5
-0.5
PS2
0.5
0
0
2
4
6
8
10
+
1
-1
0
2
4
6
8
-1
10
+
1
0
2
4
6
8
10
+
1
-1
0.5
0.5
0
0
0
-0.5
-0.5
-0.5
-0.5
-1
-1
-1
PS3
0.5
4
6
8
10
+
1
2
4
6
8
10
+
1
0.5
PS4
0
0
2
4
6
8
10
+
1
0.5
-1
0
0
0
-0.5
-0.5
-0.5
PS1+PS2+PS3+PS4
2
4
6
8
10
||
2
-1
0
2
4
6
8
10
||
2
-1
0
2
4
6
8
10
||
2
-1
1
1
0
0
0
0
-1
-1
-1
-1
0
2
4
6
t (μs)
8
10
-2
0
2
4
6
8
10
t (μs)
Answer with one letter on the answer sheet:
A. The pressure waveforms in A are correct.
B. The pressure waveforms in B are correct.
C. The pressure waveforms in C are correct.
D. The pressure waveforms in D are correct.
E. Do not know.
-2
0
2
4
10
6
8
10
6
8
10
6
8
10
6
8
10
+
0
2
4
+
0
2
4
||
2
1
-2
8
0.5
0
0
6
+
1
0.5
-0.5
-1
4
1
0
2
2
0.5
0.5
0
0
1
0.5
-1
D
1
1
0
2
4
t (μs)
6
8
10
-2
0
2
4
t (μs)
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Problem 3
The figure below (left) shows a planar X-ray image. Two regions of different tissues are outlined. The
figure below (right) shows the content of these two regions. A “hot” color map is used, in order to easily
see the image values in the regions.
0
400
0
700
20
20
350
40
40
600
300
60
60
1
500
80
100
400
120
Vertical (mm)
Vertical (mm)
80
2
300
140
160
250
100
200
120
150
140
160
100
200
180
180
50
100
200
0
50
100
150
Horizontal (mm)
200
200
0
50
100
150
Horizontal (mm)
200
0
If contrast, C, is calculated as the relative difference, what is the absolute contrast (i.e., the sign is ignored)?
Answer with one letter on the answer sheet:
A. ⏐C⏐ = 0.007.
B. ⏐C⏐ = 0.07.
C. ⏐C⏐ = 0.7.
D. ⏐C⏐ = 7.
E. Do not know.
Problem 4
Consider the following MATLAB code, where Data is a SIS structure with a 3D image of the phantom
in such a way, that the first two dimensions of Data.Images hold images that are perpendicular to the
long-axis of the phantom (i.e., the images are orientated the same way as the slices, during slicing of the
phantom).
Tops = sis_zoom( Data, [20.4 -inf -inf], [21.1 inf inf], 'mmm');
TopsR = sis_reorder( Tops, [3 2 1 ] );
Top = sis_collapse( TopsR, 3, 'mean');
sis_view( Top);
When executed in MATLAB (assuming the correct toolboxes are available), what will happen?
Answer with one letter on the answer sheet:
A. The code will never work.
B. The code will produce an image that is equal to the mean of the three images closest to the center
of the phantom.
C. The code will produce an image showing the top surface of the phantom with the fiducial markers
etc.
D. The code will produce an image that is nearly the same as a planar X-ray image of the phantom.
E. Do not know.
Page 4 of 11 pages
Problem 5
The figure below shows a cross-sectional view of a simplified version of the phantom used in the
course imaged by a planar X-ray system in (a) and different versions of the associated X-ray image in
(b). However, only one of the images in (b) is correct. Which?
The phantom contains four holes (Danish: huller) in the top and four pins (Danish: tapper) at the bottom. These are used for stacking (Danish: stable) the phantoms. Both the drawing (a) and the images (b)
are sketches and not drawn completely to scale and fading is approximate. Only the circles are changed
in the different answers. The drawing in (a) is kept in colors to reduce the risk of confusion with the images in (b). The red line underneath the film represents the corresponding distance on the images.
X-ray tube
Detector or film
Focus point
(source of
X-ray)
A:
B:
C:
D:
Phantom
= air
= agar
= acrylic
(a)
Answer with one letter on the answer sheet:
A. The sketch in A is most correct.
B. The sketch in B is most correct.
C. The sketch in C is most correct.
D. The sketch in D is most correct.
E. Do not know.
(b)
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Problem 6
Below are four examples of text that could appear in a report about medical imaging. Only one is not
in conflict with standard scientific notation used throughout this course. Which?
Answer with one letter on the answer sheet:
A. Consider a given material. The linear attenuation coefficient, μ, is 22 m-1. The (physical) density,
ρ, is provided in units of kg/m3 in the appendix.
B. Consider a given material. The linear attenuation coefficient, μ, is 22. The (physical) density, ρ,
is provided in units of kg/m3 in the appendix.
C. Consider a given material. The linear attenuation coefficient, μ, is 22. The (physical) density, ρ,
is provided in units of kg/m3 in the appendix.
D. Consider a given material. The linear attenuation coefficient, μ, is 22 m-1. The (physical) density,
ρ, is provided in units of kg/m3 in the appendix.
E. Do not know.
Problem 7
In diagnostic ultrasound, interference (both constructive and destructive) takes place:
Answer with one letter on the answer sheet:
A. Only among echoes from closely spaced changes in specific acoustic impedance (this is what creates the speckle pattern).
B. Only when the individual waves from all the sources on the transducer surface interact (this is
what creates (the shape of) the transmitted beam).
C. In both cases described in A and B.
D. Never.
E. Do not know.
Problem 8
Which one of the following statements, attempting to describe a planar X-ray system, is correct?
Answer with one letter on the answer sheet:
A. The system produces images of the shadow of electron density. The images provide little soft tissue contrast.
B. The system produces images of the shadow of electron density. The images provide large contrast
between various soft tissue components.
C. The system produces images of the shadow of proton density. The images provide little soft tissue
contrast.
D. The system produces images of the shadow of proton density. The images provide large contrast
between various soft tissue components.
E. Do not know.
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Problem 9
This problem concerns MRI. Define the following ranges in the electromagnetic spectrum:
Lower end: Below 1 MHz
Middle part: 1 MHz to 900 MHz
Upper end: Above 900 MHz
With this defined, the interaction of the RF-pulse and the tissue is between ...
Answer with one letter on the answer sheet:
A. the electron shell(s) of the atoms and RF-pulses at the “Lower end” in the electromagnetic spectrum.
B. the electron shell(s) of the atoms and RF-pulses at the “higher end” in the electromagnetic spectrum.
C. the nucleus of the atoms and RF-pulses at the “middle part” in the electromagnetic spectrum.
D. the nucleus of the atoms and RF-pulses at the “Higher end” in the electromagnetic spectrum.
E. Do not know.
Problem 10
In a PET system scanning a human, the following happens at a point in time: An annihilation process
takes place, and two photons are emitted in opposite directions. One has to travel 30 cm towards the detector, while the other has to travel 60 cm in the opposite direction towards another detector. The speed
of light in the medium and the surrounding air is assumed to be 3×108 m/s. If this event should be detected, what is the smallest possible minimum width of the window of the coincidence detector?
Answer with one letter on the answer sheet:
A. 0.1 ns wide.
B. 1 ns wide.
C. 2 ns wide.
D. 10 ns wide.
E. Do not know.
Problem 11
Which type(s) of radiation can penetrate human tissue, be measured and therefore used for whole body
imaging?
Answer with one letter on the answer sheet:
A. alfa radiation.
B. alfa and beta radiation.
C. alfa, beta and gamma radiation.
D. gamma radiation.
E. Do not know.
Page 7 of 11 pages
Problem 12
This question concerns Magnetic Resonance. Which equations below correctly describe the return of
the magnetization to equilibrium (Mxy = 0, Mz = M0) after a single 180 degree inversion pulse? (Mxy and
Mz are the transversal and longitudinal magnetizations, respectively. The variable t is time after inversion).
Answer with one letter on the answer sheet:
A. |Mxy(t)| = 0 and Mz(t) = M0(1 - exp(-t/T1)).
B. |Mxy(t)| = 0 and Mz(t) = M0(1 - 2 exp(-t/T1)).
C. |Mxy(t)| = M0exp(-t/T2) and Mz(t) = M0(1 - exp(-t/T1)).
D. |Mxy(t)| = M0exp(-t/T2) and Mz(t) = M0(1 - 2 exp(-t/T1)).
E. Do not know.
Problem 13
The ultrasound image in the figure below is recorded with a linear array transducer with about 100 elements. It has a vertical white band (all image values within the white band is equal to the highest possible value that can be shown). What is the most likely reason for this white band?
Answer with one letter on the answer sheet:
A. There is a collection of air bubbles just underneath the transducer where the white band is present.
B. For those scan lines that are completely white, there is a malfunctioning in the transducer crystals
and/or in the electronic circuits that receives the echoes for these crystals.
C. A metal object is located inside the tissue where the white band is located.
D. At the location of the white band, the tissue contains muscle fibers oriented perpendicular to the
beam.
E. Do not know.
Page 8 of 11 pages
Problem 14
Below is a plot of the normalized pressure, pn, of a plane wave (within a small spatial window). What
is the frequency of this wave, if the sound speed c = 1500 m/s?
Answer with one letter on the answer sheet:
A. 1 MHz.
B. 5 MHz.
C. 10 MHz.
D. 20 MHz.
E. Do not know.
Problem 15
The mass attenuation coefficient, μ/ρ, of lead is 5.5 cm2/g at 100 keV. The density of lead is 11.35 g/
cm3. What is the intensity, I, of a narrow 100 keV beam after penetrating a slab (Danish: en skive) of
lead of thickness 50 μm? The intensity of the incoming radiation is I0.
Answer with one letter on the answer sheet:
A. I ≅ I0exp(-0.003).
B. I ≅ I0exp(-0.3).
C. I ≅ I0exp(0.003).
D. I ≅ I0exp(0.3).
E. Do not know.
Page 9 of 11 pages
Problem 16
In a conventional X-ray system, a collimator (raster or grid) between patient and detector normally...
Answer with one letter on the answer sheet:
A. amplifies the ionizing radiation.
B. reduces the amount of scattered radiation to the detector.
C. removes direct radiation from the X-ray tube to the detector.
D. limits the X-ray beam to only hit the object under investigation.
E. Do not know.
Problem 17
In diagnostic ultrasound imaging, what is A-mode, B-mode and M-mode?
Answer with one letter on the answer sheet:
A. A-mode: Amplitude mode. B-Mode: Brightness mode. M-mode: Motion mode.
B. A-mode: Amplitude mode. B-Mode: Bulk mode. M-mode: Manual mode.
C. A-mode: Attenuation mode. B-Mode: Bulk mode. M-mode: Manual mode.
D. A-mode: Attenuation mode. B-Mode: Brightness mode. M-mode: Motion mode.
E. Do not know.
Problem 18
In a scintillation crystal in a SPECT or PET system, an incoming gamma photon with energy of 140
keV is converted to 5000 photons of approximately 10 eV each.What is the energy loss in this conversion?
Answer with one letter on the answer sheet:
A. 32%.
B. 64%.
C. 100%.
D. There is no loss in the crystal.
E. Do not know.
Page 10 of 11 pages
Problem 19
Consider a photon of energy 200 keV. What is the frequency and wavelength? Planck's number, h =
6.62×10-34 Js = 4.13×10-15 eVs. The speed of light is 3×108 m/s.
Answer with one letter on the answer sheet:
A. ν = 2.80×10-19 Hz and λ = 6.2 mm.
B. ν = 4.80×10-19 Hz and λ = 6.2 pm.
C. ν = 2.40×1019 Hz and λ = 6.2 μm.
D. ν = 4.80×1019 Hz and λ = 6.2 pm.
E. Do not know.
Problem 20
In an X-ray tube, what is the kinetic energy of electrons just before they hit the anode, in case the voltage difference over the electrodes is 200kV? The mass of one electron is me.
Answer with one letter on the answer sheet:
A. 200keV/me.
B. 100 keV.
C. 200 keV.
D. 511 keV.
E. Do not know.
Problem 21
What is the frame rate (in units of hertz) in an ultrasound scanner, when the maximal depth the scanner
records from is Dmax, the number of scan lines in the image is Nl and the speed of sound is assumed to
be c?
Answer with one letter on the answer sheet:
A. fr = Nl × c/(2Dmax).
B. fr = Nl × c/Dmax.
C. fr = 1 / (Nl × Dmax/c).
D. fr = 1 / (Nl × 2Dmax/c).
E. Do not know.
Page 11 of 11 pages
Problem 22
In diagnostic ultrasound, when the emitted pulse travels through soft tissue (fat, muscle, liver, pancreas,
but not air, bone, etc), the average attenuation is, as a rule of thumb, 1 dB/(cmMHz). For a given frequency, say, 10 MHz, this amounts to 10 dB/cm. This attenuation is sought compensated by a function,
gTGC(t), called Time-Gain-Compensation (TGC). The received envelope detected signal is multiplied
by this function to yield an attenuation compensated envelope signal. What form should this function
have? b is a constant. t is the time in the received signal.
Answer with one letter on the answer sheet:
A. gTGC(t) = b×t.
B. gTGC(t) = log(b×t).
C. gTGC(t) = 20×log(b×t).
D. gTGC(t) = exp(b×t).
E. Do not know.
Problem 23
Identify the false statement among the following statements concerning weaknesses of MRI.
Answer with one letter on the answer sheet:
A. Not all objects can safely be brought near an MR scanner.
B. MR images can be difficult to interpret since they typically reflect several tissue parameters at
once.
C. Only hydrogen nuclei can be detected with MRI.
D. Solid substances (for example bone) are not visible on normal MR images.
E. Do not know.
Problem 24
Consider a MR sequence acquired with a very long repetition time, TR, of 20 seconds, and a short echo
time TE of 4 ms. Select the correct continuation of the following sentence: For most tissues, the resulting
proton density weighted (PD-weighted) image will be proportional to...
Answer with one letter on the answer sheet:
A. the water content since most hydrogen giving signal, is in water.
B. the true proton density, meaning the concentration of protons.
C. the protein content.
D. the T1 relaxation times of the tissues.
E. Do not know.