Object-Oriented Programming Page 1 of 6 Coursework 1
BEng Biomedical Engineering
Object-Oriented Programming
Coursework 1
Objective
To gain practical experience of C++ coding to solve a simple problem.
Introduction
Magnetic Resonance Imaging is a powerful imaging technique capable of producing images of
internal organs with good soft tissue contrast. It relies on a number of hardware components, as
illustrated in Figure 1: a powerful permanent magnet; magnetic field gradients provided by
dedicated gradient coils (Figure 1, right); and radio-frequency coils to excite the nuclear spins
(typically 1H) and detect the resulting nuclear magnetic resonance signal.
Figure 1: the different hardware components of a typical MRI scanner. Left: a cutaway view showing the
arrangement of the main magnet, gradient coils and RF coil. Right: an example of the design of a gradient
coil, showing the different concentric windings required to impart magnetic field gradients along the x,
y & z axes.
The role of the gradient coils is to impart a linear change in the resonance frequency of the 1H
nuclear spins as a function of position, which allows the position of the signal to be inferred. To
provide full images, these magnetic field gradients need to be rapidly modulated in time, which is
done by driving very large currents through the gradient coils and switching them rapidly on &
off at appropriate times along the appropriate axes.
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Object-Oriented Programming Page 2 of 6 Coursework 1
Eddy-currents in MRI
Because of Faraday’s law of electromagnetic induction, these rapid and intense changes in the
magnetic fields induce voltages, which in turn drive currents in nearby conductive structures.
These eddy currents create magnetic fields that oppose the change in magnetic field that created
them (this is called Lenz’s law).
In MRI, the net result is that the temporal evolution of the magnetic field gradient actually
produced will differ from the waveform provided to the gradient amplifier. This is illustrated in
Figure 2, showing how an ideal 代写5CCYB041 BEng Biomedical Engineeringtrapezoidal input waveform will end up distorted and lagging
behind what was expected, and the resulting impact on images acquired using echo-planar
imaging (a single-shot imaging technique). Eddy currents can affect the images in many different
ways, depending on the type of MRI sequence used and other factors, but they are invariably
problematic. For this reason, a variety of techniques are used to minimise eddy-currents,
including hardware solutions (e.g. actively shielded gradients) and gradient pre-emphasis.
Figure 2: illustration of the effect of eddy-currents. (a) the expected waveform (dotted line) is distorted
due to eddy-currents, resulting in the delayed time evolution of the actual gradients (solid line). (b) The
eddy-currents (solid line) originate from the rapid changes in the magnetic field that occur when there
is a change in the gradient (dotted line). (c) image that would ideally be acquired using echo-planar
imaging (EPI). (d) the image acquired when eddy currents introduce significant delays in the signal
shows clear ‘ghosting’ artefacts.
Gradient pre-emphasis
Gradient pre-emphasis involves modifying the signal time course provided to the gradient
amplifier to compensate for the expected effect of eddy-currents, as illustrated in Figure 3. If the
properties of the eddy-currents are known, it is possible to predict the time course of the actual
gradient for a given input waveform. With pre-emphasis, the input waveform is modified so that
the time course of the actual gradient matches the desired waveform more accurately.
For the purposes of pre-emphasis, eddy-currents are typically modelled as multiple components,
each with a given amplitude and decay rate constant. The parameters of the different eddy current components are measured during routine maintenance as part of the calibration of the
MRI scanner, and stored on the system for use in gradient pre-emphasis.
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Object-Oriented Programming Page 3 of 6 Coursework 1
Figure 3: illustration of gradient pre-emphasis. (a) the desired gradient waveform. (b) the actual gradient
time course obtained differs due to the effects of eddy-currents. (c) with pre-emphasis, a modified
waveform is provided as input to the amplifier, designed in such a way that the actual gradient time
course matches the desired waveform.
Instructions
Your task in this coursework is to write a C++ program to implement a simple gradient pre emphasis strategy. This program should perform the following main steps (these are described in
more detail below):
-
Load the parameters describing the eddy-currents for the system from the file provided.
-
Load the desired time course for the gradient from the file provided.
-
Make a copy the desired time course, which will be the initial input gradient time course.
-
Compute the predicted time course for the input time course by taking the effects of eddy currents into account.
-
Compute the maximum absolute deviation between the desired and predicted time
courses, and display this value on the terminal
-
Display the input and predicted time courses on the terminal.
-
Compute the difference between the desired and predicted time course.
-
Add that difference back to the current input time course.
-
Go back to step 4 and repeat for the desired number of iterations
-
If requested, write the final estimate of the compensated input time course to the file
specified on the command-line
Command-line interface
Your program should accept at least 2 arguments: the configuration file containing the parameters
for the eddy-currents, and the file containing the desired time course. If a third argument is
provided, this should be interpreted as a request to store the estimated compensated time course
to the file specified in that argument.
Your program should also accept a “-n num” command-line option to override the default number
of iterations. If left unspecified, the default number of iterations should be set to 10.
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Object-Oriented Programming Page 4 of 6 Coursework 1
Loading the input data
You are provided with a text file called parameters.txt file containing the eddy-current
parameters. Each line in this file contains two values: the amplitude and the rate constant for each
eddy-current component.
You are also provided with a text file called gradient.txt file containing the intensity values at
regular sampling intervals for the desired gradient time course.
Computing the predicted gradient time course
The impact of the eddy-currents can be predicted using a simple model. Each eddy-current
component can be modelled independently, and will have an associated current 𝐼𝑛 (with initial
value zero). The instantaneous chance in the gradient, 𝑑𝐺, causes the current to increase in
proportion. At the same time, the resistance in the system causes the current to reduce in
proportion to the magnitude of the current. The predicted gradient is then given as the input
gradient minus the eddy-current contributions, which is the sum of their currents weighted by
their respective amplitude parameter.
This can be written in simplified form as:
𝑑𝐺𝑡 = 𝐺𝑡 − 𝐺𝑡−1
𝐼𝑛,𝑡 = 𝐼𝑛,𝑡−1 + 𝑑𝐺𝑡 − 𝑅𝑛 × 𝐼𝑛,𝑡−1
𝐺𝑡
′ = 𝐺𝑡 − ∑𝐴𝑛 × 𝐼𝑛,𝑡
𝑁
𝑛
where:
• 𝐺𝑡 and 𝐺𝑡
′
are the input and predicted waveforms at time point 𝑡 respectively
• 𝐼𝑛,𝑡
is the value of the current at time point 𝑡 for the nth eddy-current component
• 𝐴𝑛 and 𝑅𝑛 are the amplitude and rate constant parameters for the nth eddy-current
component.
• 𝑁 is the number of eddy-current components listed in the parameter file.
Computing the compensated time course
The compensation to be applied to the waveform can be computed using the following iterative
approach:
Given the desired waveform:
• Initialise the current estimate of the (compensated) input waveform as the desired
waveform
• Repeat for the desired number of iterations:
o Compute the predicted waveform for the current input waveform
o Compute the difference between the desired and predicted waveforms
o Add the computed difference to the current input waveform, to produce the next
estimate of the input waveform
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Object-Oriented Programming Page 5 of 6 Coursework 1
Displaying the waveforms
The various waveforms can be displayed using the terminal_graphics library. Refer to the relevant
course slides and the project README for detailed instructions.
Briefly: download the terminal_graphics.h header and place it in your project folder, alongside
your own code. Make sure to #include that header into your code. Then use the TG::plot()
functionality as illustrated below:
#include "terminal_graphics.h"
...
std::vector desired_gradient, predicted_gradient;
...
TG::plot (width, height)
.add_line (desired_gradient)
.add_line (predicted_gradient, 3);
Writing the final compensated time course
Your program should only store the output if provided with a third argument on the command line. If this is the case, you should write the final compensated time course to the file specified as
the last argument, in the same format as the original desired time course.
Example output
The example below only shows the initial and last iteration of the algorithm:
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Object-Oriented Programming Page 6 of 6 Coursework 1
Reporting Requirements
You should submit a C++ project that meets as many of the requirements as possible. You do not
need to submit any written report but do try to use variable/function naming, comments and
indentation to make your program as easy to understand as possible. Also try to make your
program as resilient to runtime errors as possible.
Submission will be via the KEATS system. The submission point will only allow you to upload a
single file so you should combine all files into a single ZIP file. Please only include your .cpp and
.h files (please run “oop_build clean” first to remove any executables or object files).
The hand-in date is 25 Feb 2025, 4 pm. Late submissions (within 24 hours of this deadline) will
be accepted but will be capped at the module pass mark (i.e. 40%).
If your program does not meet all requirements, then please submit what you have written by the
deadline.
Assessment
Your coursework will be marked on a number of factors:
• Does the program work? Does it meet all requirements? Has it been tested extensively?
(60%)
• Program design and appropriate use of C++ language features, e.g. control structures,
functions, data types, etc. (30%)
• Use of comments, indentation and variable/function names to make code easy to
understand (10%)
The overall mark for this coursework will make up 10% of your total mark for this module.
This is an individual assignment. You are not permitted to work together with any other
student. Note that general discussions about design decisions and/or coding strategies are
permitted, and such discussions can be a useful learning experience for you. But you should not,
under any circumstances, share details of designs or code.
Code generated using AI assistants, etc. is also not permitted. While these tools may
(potentially) be useful in your learning to help clarify certain concepts, this is only true if they are
used very cautiously and sparingly. Over-reliance on these tools to give you ready answers will
inhibit your learning by preventing you from working things out for yourself. This will result in
failure in the final exam where you will have no access to these tools (note that the final exam
accounts for 60% of the overall marks on this module). We therefore strongly discourage the use
of any form of AI assistants – in our opinion (and that of many others), these are detrimental to
your performance on the course.
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