Answer all SIX questions from Section A,
ONE question from Section B and ONE question from Section C.
The numbers in square brackets indicate the provisional allocation of maximum
marks per sub-section of a question.
The gyromagnetic ratio for Hydrogen nuclei, ” = 42.6 × 2 × 10, rad.s-1
.T-1
= 26.752 × 10/ rad.s-1
.T-1
Speed of light = 3 × 103 m.s-1 unless otherwise stated.
Planck’s constant, = 6.626 × 10567 J.s
SECTION A
Answer ALL SIX questions
1. The centres of two small, spherical volumes of water are separated by 3.5 cm and are
imaged using a magnetic-field gradient of 16 mT.m-1 applied parallel to the direction of their
separation. What is their separation in frequency
[3]
If one of the volumes was experiencing a non-uniformity in the main magnetic field
corresponding to a frequency shift of 8 kHz, what would be the error in its position
[3]
2.
a) In a gradient-echo 2DFT sequence, with a field of view of 204.8 mm, what gradients are
required to form an image with an in-plane spatial resolution of 0.8 mm if the phase
encoding gradient is applied for 4 ms and the spin-echo signal is sampled for 7 ms
[6]
b) If the imaging sequence in a) was a multi-slice sequence with a matrix size of 256 x 256
and a TR = 53 ms, how many slices could be imaged in a total scan time of 4 minutes
and 31.36 seconds Assume that the slices are imaged sequentially without inter-leaving.
[2]
3. A signal is sampled using 128 data points for a total sample time of 2 ms.
What is the frequency resolution of the spectrum
[2]
What is the total bandwidth of the final spectrum
[2]
At what frequency should the filter cut-off be set
[2]
PLEASE TURN OVER
MPHY0019 / 2019 2
4. Pulse oximeters are the most common form of medical optical device. Explain how pulse
oximeters are able to use light to provide an estimate of the oxygen saturation of arterial
blood.
[4]
5.
a) Explain the concept of coherence as it pertains to light.
[2]
b) Describe the fundamental principles of:
i. time domain optical coherence tomography [3]
ii. frequency domain optical coherence tomography. [3]
6. A collimated beam of light is incident on a cuvette of thickness d (in cm) containing a
non-scattering, absorbing solution with a specific absorption coefficient a (in cm-1 Molar-1
),
and a concentration C (in Molar). The incident light intensity is I0 and the transmitted
intensity is I.
a) Write down an expression for the transmitted intensity (I) in terms of I0, a, C, and d.
[1]
b) What are the definitions of absorbance, A, and transmittance, T.
[2]
c) What is meant by the term ‘absorption mean free path’ Write down an expression for
the absorption mean free path using the terms defined above.
[2]
d) If
A = 0.7 and d = 0.5 cm, what is the absorption mean free path of this solution
[3]
CONTINUED
MPHY0019 / 2019 3
SECTION B
Answer ONE QUESTION from this section
7.
a) Using both k-space and a pulse sequence diagram, briefly describe the operation of the
spin-echo 2DFT imaging method.
[8]
b) Explain the reasons and processes for demodulation and phase-sensitive detection of the
radio-frequency (RF) MR signal.
[10]
c) Describe how Gd-DTPA causes increased tissue contrast in clinical MRI.
[5]
Ignoring the effects of T2-relaxation, if the presence of this contrast agent reduces the
T1 value of tumour tissue from 900 ms to 360 ms, what would be the percentage change
in the magnitude of the tumour signal in an inversion recovery spin-echo sequence with
TIR = 500 ms
[3]
d) A blood vessel contains blood flowing perpendicular to (i.e. through) the plane of an MR
image with a slice thickness of 1.5 mm. At which blood flow velocity would the blood
in the vessel appear fully bright in a gradient-echo sequence with TR = 31 ms
[2]
e) Above which blood flow velocity will the signal in the vessel in (d) completely disappear
when imaged with a spin-echo sequence with TE = 15 ms and a slice thickness of 2 mm
[2]
PLEASE TURN OVER
MPHY0019 / 2019 4
8.
a) Using both a pulse sequence and a k-space diagram, briefly describe the operation of the
spin-echo Echo-Planar Imaging (SE-EPI) sequence.
[8]
b) A tissue has T2 = 74 ms and T2* = 33 ms. Calculate the ratio of the tissue signal intensity
in a spin-echo EPI acquisition compared to a gradient-echo EPI acquisition acquired with
an identical echo time TE = 40 ms, assuming all other experimental parameters and
conditions are the same.
[4]
c) Briefly explain the origin of BOLD contrast in MRI and describe how it is used to study
the brain.
[6]
d) Describe the origin of the chemical shift artefact in MRI.
[4]
If the difference in chemical shift between water and fat resonances is 3.5 parts per
million and the body is imaged with a MR sequence with a total spin-echo sampling
time of 4 ms, what will be the spatial shift in image pixels between the fat and water
images in a 3 Tesla magnet
[4]
e) If an imaging slice is to be selected using a field gradient of 12 mTm-1
, what would you
change, and by how much, to image another slice positioned a further 4 cm along the
slice selection direction
[2]
f) How can the slice thickness be increased
[2]
CONTINUED
MPHY0019 / 2019 5
SECTION C
Answer ONE QUESTION from this section
9. In the transport theory of light propagation, the radiance f, is a function of position (r),
direction ( ) and time (t). The radiance satisfies the Radiative Transfer Equation (RTE),
which can be written in the following form:
1