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You need to give feedback ONLY about my literature review section of a research project that I have done . ONLY ABOUT THIS SECTION. LITERATURE REVIEW Critique the literature review of the pdf “research proposal to critique”. ONLY CRITIQUE THE LITERATURE REVIEW.  no presentation/coherence or other section .ONLY CRITIQUE THE LITERATURE REVIEW SECTION. Read the instruction about how to conduct literature review NO INTRODUCTION,NO CONCLUSION,NO IMAGES, NO STRUCTURE. DONT USE SECTIONS. ONLY WRITE THE CRITIQUE/FEEDBACK ABOUT THE LITERATURE REVIEW!!!! you must use must write around 10 bullet points Bear in mind that by “bullet point” we mean “1 to 3 sentences”.

Physics MSc Project Proposal
Comparative study of Source Localisation Algorithms for Solving the
Electroencephalography Inverse Problem
1 Purpose
1.1 Contextualisation
The human brain contains approximately 1011 neurons capable of communicating with each other through ring
regulated electromagnetic signals [1]. Abnormal transmissions of these signals across the brain, such as a sudden
surge of signals can introduce a seizure. It is estimated that 7 􀀀 10% of the population will experience some form
of seizure throughout their lifetime [2]. Epilepsy, a condition in which a person will have recurrent seizures, is one
of the most common neurological disease aecting 1% of the global population [3]. Due to Epilepsy’s hereditary
nature and prevalence in the population; consistently accurate modelling techniques to localise neural signals and
observe their function is of critical importance in modern medicine.
Evaluating both electrical and magnetic activity within neurons present in the brain are vital to determine disorders.
A neuron uses intracellular and extracellular chemical changes to send and receive signals. These chemical changes
create electric potentials across neurons, which can be modeled as an electric dipole source. Electroencephalogram
(EEG) and Magnetoencephalography (MEG) are the two invasive/non-invasive techniques used to reconstruct
electromagnetic signals of dipole sources representative of the brain activity, in real-time. However, these techniques
have characteristic problems denoted as the Forward and Inverse Problems. The Forward Problem refers to
determining the electric potentials and magnetic elds that result from a primary source. Through using Realistic
models of the head gained from other forms of medical imaging, such as MRI, and applying known real values
of skull-brain resistivity values, the Forward Problem for EEG and MEG can be solved [4]. Its counterpart, the
Inverse Problem is taking the measured quantities and inferring their origin and localising the source [5]. The
solution to the Inverse Problem is more complex. Typically, sources from multiple locations can create a potential
distribution at a detector. This results in the in-ability to localise the source and therefore infer which part of the
brain is producing the signal. To gain a solution to the Inverse Problem there are two common approaches, the
parametric and non-parametric method of which are now both solved computationally. A non-parametric model
uses multiple dipole sources with xed location and orientation distributed in the volume of the brain. Contrasting
to this, a parametric approach assumes dipole locations and orientations are unknown. Due to EEG’s vital role
in the diagnosis of neural conditions, the automation of algorithms to compute the Forward and Inverse Problem
to locate electrical sources is paramount. Currently, there is no standardised method to solve the Inverse Problem
related to EEG. The relative positives and negatives of dierent localisation algorithms promote an opportunity
to adopt the most optimal algorithm for the given properties of the measured source [6]. The proposals aim is to
address these opportunities through the following research title: A Comparative Study of Source Localisation
Algorithms for Solving the Electroencephalography Inverse Problem.
The projects aspiration to complete the comparative study of the Inverse Problem solutions relies on their implementation
of computational algorithms onto head models. Two categories of algorithm will be explored within the
proposal; Tomographic as well as Beamforming. The prior representing a non-parametric approach and the latter
a parametric. Furthermore, the application of the algorithms will occur on both simple Spherical models as well as
Realistic head models. Both models will be created computationally, with the Spherical model consisting of three
homogeneous concentric spheres representing the tissues in the head; the brain, the skull and the scalp respectively.
1
Each tissue will have an attributed signal attenuating parameter. The Realistic model will consist of more nite
divisions of the three dimensional head volume to include further tissues such as grey matter, white matter and
cerebral spinal
uids, which will be arranged not as a simplistic spheres, but arranged to be representative of the
head anatomy. Neural sources will be computationally simulated in both the models at vector locations, both as
a singular source and multiple sources. The comparative study will assess and evaluate the ability of each of the
models, focusing on areas in which certain models succeed and others fail. Special attention will be given to the
uncertainties present due to the head models used.
1.2 Methodology and Objectives
A common parametric approach to the Inverse Problem is a spatial lter referred to as a Beamformer. The spatial
lter incrementally scans through a three dimensional volume returning present signals from each increment. The
signals are returned in a matrix format corresponding to a Cartesian position, from which a dipole location can be
inferred. The proposal will focus on two beamforming lters; A simplistic matched lter as well as a more complex
Linear Constrained Minimum Variance (LCMV).
The selected tomographic approach is that of the Standardised Low-Resolution Electrical Tomography (sLORETA).
A Laplacian operator is used to compare signal intensities between dierent voxels. From the resulting comparisons
yield a three-dimensional intensity map on a head model that contains the highest intensities at a signal location.
Using Dipole Localisation Error (DLE) source location methods can be assessed on their ability to locate the
simulated source. Furthermore, source location signals can be subject to spatial leakage due to external biological
and electrical noise present. The Point Spread Volume (PSV) can be used to estimate the focal point of a source,
when it is in
uenced by the spectral leakage [7]. Direct properties of a dipole neural source such as its distance
from the measurement electrode, its strength as well as orientation in three-dimensional space have a strong involvement
in source localisation. Upon simulating neural sources, these selected parameters will be varied upon
reviewing each source localisation algorithm. Simulation of the sources will occur in both Spherical and Realistic
head models, with the hypothesis that the more realistic data included into a head model, the more accurate a
source localisation will be.
The approach to the question is linear, it is aimed in the study to compare the results between multiple source
localisation algorithms. The models will be applied and assessed on both simplistic and Realistic head models.
A pre-built tomographic algorithm, sLORETA, and a Realistic head model will be granted to the author from
the project supervisor: Dr. Beltrachini. The project will be performed in MATLAB and in conjunction with
Cardi University Brain Research Imaging Centre (CUBRIC). CUBRIC have provided access to their supercomputer/
cluster network which will be used to submit computational scripts to execute.
Below is a summarised list of the key objectives that will take place throughout the duration of the project.
1.2.1 Summarised Objectives
1. Creation of the Beamforming Inverse Problem solutions in the form of a Linearly Constrained Minimum-
Variance (LCMV) and Matched Filter in MATLAB.
2. Understand/familiarise with the sLORETA algorithm in MATLAB and validate its mathematics studied in
the preliminary literature review.
3. Optimise and apply the Beamforming and Tomographic approaches to a simplistic Spherical head model
with a simulated singular and multiple electrical dipole(s).
4. Optimise and apply the Beamforming and Tomographic approaches to a Realistic head Model with a simulated
singular and multiple electrical dipole(s).
5. Vary the strength of a simulated dipole signal in both head models, to investigate and assess the source
localisation algorithms ability to work with weaker sources.
6. Create variations within the head models to assess the uncertainties from within them.
7. Simulate noise to increase the SNR within the head models, to investigate and assess the source localisation
algorithms ability to work in realistic conditions.
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1.3 Importance
With the prevalence of neural disorders within society and the detrimental eects that they possess, the development
and potential improvements in EEG is imperative. The comparative study has the potential to impact the
study and localisation of neural sources as it could provide improvements upon existing techniques. Diagnosis and
treatment of neural disorders is heavily reliant on the accuracy of source localisation within an EEG examination.
When examining a patient with an EEG, there are many external factors that contribute to countering a source
localisation, such as; source location, source orientation, patient movement, biological noise as well as electrical
noise [8]. Although dierent localisation techniques are implemented into EEG examinations, as aforementioned,
there is no standardised approach. The importance of completing a comparative study is to categorise areas in
which certain approaches prevail, to eventually apply the techniques to EEG examinations to increase their source
localisation accuracy.
2 Literature Review
Monitoring and evaluating electrical activity from within the brain was rst approached and developed by Berger
in the mid 1920’s [9]. Since then, advances in technology have aided the analysis of signals from an EEG. However,
the core principal behind Berger’s design has remained unchanged. The simplicity of its design, expanded in
Section 2.3, and ability to couple with other imaging techniques have enhanced its performance in giving accurate
diagnosis and contributed to its longevity at the forefront of medicine.
2.1 Neurons and Electricity
As aforementioned, the brain encompasses 1010 neurons, of which dier from typical cells due to their ability to
diversify as they grow to dierent shapes and sizes. A neuron cell consists of three sections; the Soma which
represents the cell body and houses the cells nucleus, the Dendrites which receive signals from other neurons in
the form of neurotransmitters, and one Axon which branches from an Axon Hillock. Dendrites can grow up to
a few hundred micrometres [10]. The axon can grow to lengths of 1m in the brain and branches into several
axon terminals. Neurons communicate with each other through neurochemical transmitters at a synapse. Here,
the axon terminal of one presynaptic neuron is connected via a microscopic gap, a synapse cleft 20 􀀀 40nm, to a
dendrite of a postsynaptic neuron [11]. A single neuron has near 7,000 synaptic connections to others [12].
Figure 1: Two connected neurons lled with a
uorescent dye to increase their contrast, viewed from a
microscope. The red arrows depict the direction of the signal transmission [13].
The intra and extracellular movement of Sodium (Na+), Chloride (Cl), and Potassium (K+) ions across an
electrochemical gradient over the neurons, induces a current
ow inside and outside of the neurons. At rest
the neuron has a voltage 􀀀70mV with respect to the extracellular surroundings, before being raised to 30mV
when a neuron sends a signal. Attributing Maxwell’s equations, the movement of electric charge generates an
electromagnetic eld. Action potentials are not suitable signals to be detected and used in EEG due to their
properties; the axons of neurons are arranged randomly, leading to many action potentials cancelling each other
out and they are short lived, lasting for 0.5 to 2ms. As a neurotransmitter leaves the presynaptic neuron and
3
binds to the postsynaptic neuron, the inward
ow of Sodium into the membrane of the postsynaptic neuron’s
membrane causes the membrane to become positively charged and the extracellular space around the neuron
becomes negatively charged. As ions leave this neuron, the outward
ow of the positive ions leaves the extracellular
space positively charged. This creates an electrical dipole between dierent parts of the neuron. Individually, the
neurons dipole is undetectable through an EEG. However, as many neurons exists in a small volume and are
stimulated simultaneously, the sum of individual dipoles form to create a larger detectable dipole.
2.2 The Electroencephalogram’s role in neurology
EEGs role in monitoring brain activity is not a singularity in the eld. Functional imaging techniques such as
functional magnetic resonance imaging (fMRI), positron emission tomography (PET) and MEG oer diering
modalities to extract information. However, each technique varies in terms of its spatial and temporal resolutions.
The diversity of techniques is a positive within medicine allowing for the selection of a certain technique to suit
the needs of a diagnosis.
2.2.1 fMRI
fMRI is regarded as the most common imaging technique to recording neural activity, due to its ability to be
performed on a clinical 1:5T MRI magnet. fMRI focuses on hemodynamic changes within the brain, of which
are used to indirectly infer brain activity. Active areas of the brain require more oxygenated blood causing blood

ow toward these areas, creating images of blood-oxygenated dependent contrast (BOLD) between activated and
inactivated areas. However, fMRI is attributed to having spatial and temporal resolutions. The spatial resolution
of a 1:5T fMRI is situated at 1mm3; a typical 1mm3 can contain upwards of 60; 000 neurons[14][15]. Furthermore,
the temporal resolution is hindered by hemodynamic response time, as it takes several seconds for blood
ow to
change, giving fMRI temporal resolution of around 3s. The poor temporal frequency results in poor accuracy in
determining the exact time an area of brain becomes active. The image succumbs to temporal smoothing in which
the image is representative of the average activity over a time period and not a nite time point.
2.2.2 MEG
MEG is a functional imaging technique that measures the external magnetic elds generated from neuronal activity
in the brain. As neurons electrically communicate, the electric currents sent induce a magnetic eld. The electric
voltages are in the order of 10’s of millivolt magnitudes, however, the magnetic elds induced are of femtoTeslas.
To override the minimalism of magnetic signal, J.E. Zimmerman implemented the superconducting quantum
interference device (SQUID). A SQUID uses liquid helium to lower the magnets temperature to 􀀀269C, allowing
the magnet to have a low impedance and amplify neural magnetic elds to detectable ranges [16]. The magnetic
elds induced from neural signals are not distorted by the tissues located in the head: the scalp, skull and brain.
Moreover, electrical elds are distorted by these mediums. Because of this, MEG provides an increase in spatial
resolution over EEG. This being 2 􀀀 3mm [17].
2.2.3 PET
Positron Emission Tomography (PET), like fMRI, is both a functional and structural form of imaging. Injected
radioisotopes are present in the brain and decay emitting a positron, which annihilates through colliding with
an electron to release to gamma photons. These gamma photons are detected 180 degrees from each other by a
scintillator detector creating a line of response. The line of response uses the timings between the two photons
being detected to infer a location of annihilation. From this, computational algorithms are used to reconstructed
spatial distributions of the radio-tracer to represent a functional process. PET has a weak spatial resolution of
5-10mm, with even poorer temporal resolution, ranging from 10s to 60s [18]. The modality is of key importance in
studying the brains neurophysiology and neurochemistry, with glucose metabolism within the brain being a main
staple in PET imaging [19].
4
Technique Temporal resolution Spatial resolution
fMRI 3s 1mm3
MEG 1ms 2 􀀀 3mm3
PET 10 􀀀 60s 5 􀀀 10mm3
EEG 1ms 10mm3
Table 1: Comparison of Temporal and Spatial resolutions for fMRI, MEG, PET and EEG functional imaging
techniques.
2.3 In-depth Electroencephalogram
To obtain the electrical signals, electrodes are placed either through non-invasive measures by being attached to
the scalp or by invasive measures with surgically arranged intracranial electrodes. The information gained from
an EEG is the electrical activity dierences between two electrodes. A typical electrode pattern, is the 10-20
system. This technique allows electrode placement to be standardised for all patients. The term 10-20 refers to the
proportional distance between the ears and nose in which the electrodes are placed. This method provided a clear
coverage of the brain. Reference electrodes of known voltages are present, connected to electrodes at the scalp.
The electrodes measure a de
ected signal from the dipole in the brain and from the de
ection in signal compared
to the reference electrodes, a measurement can be taken.
Electrode Lobe
F Frontal
T Temporal
C Central*
P Parietal
O Occipital
Figure 2: A 2-dimensional top-down view of the 10-20 electrode placement used to help standardise EEG
measurements. The electrodes are labeled with respect to which lobe they are measuring [20].
No central lobe exists, C is stated as the central point of the head. In addition, A1 and A2 are signal ampliers.
The even and odd numbers represent the right hemisphere and left hemisphere respectively with z representative
of being placed on the heads mid-line. The solution of the Inverse Problem relies on a solution to the Forward
Problem. To solve the Forward Problem simulation of neural signals in a head model are required [21].
A simulated dipole source has several attributing parameters that will aect the ability of a source localisation.
The distance of the source is from the surface electrode, referred to as a source depth, has a strong in
uence on
the localisation error. Sources present near the surface are located with smaller error than those located deeper in
the head as a result of the SNR being greater at the deeper locations. Menninghaus et al. [22] concluded that in a
Spherical model of sources positioned at (1􀀀3)cm from the surface had an attributed error of (2􀀀4)cm. A further
parameter of a source is its orientation. Sources can either be situated tangentially or radially to the surface.
Due to the composition of the brain, radial sources are more prevalent in the surface of the brain. Therefore,
radial sources dominate the sources detected by an electrode, although tangential sources are still detectable [23].
Furthermore, a nal parameter of source strength can be a limiting factor. Evidently, weak signals are subject to
higher localisation as they will be attenuated by biological tissue. In addition, a source of considerable strength
will dominate the electrode detection and increase the localisation error of other sources present.
5
2.3.1 Head Modelling
Models of the human head are characterised with two approaches: a simplistic Spherical head model as well as
a more complex Realistic model. The two models are used to aid mathematical formulae to model current
ow
within the brain. Their critical importance derives from the in
uence of a brains tissue distorting the electric
dipoles ability to be detected. These tissues are accounted for in modelling and the inclusion provides increased
source localisation accuracy [24].
The Spherical Head Model
A Spherical model involves reducing a head shape to a simplistic sphere, constructed of 3 homogeneous layered
shells representing the brain, skull and scalp. They are integral within clinical and research, being routinely used.
As mentioned in[25], the validity between the 3 layered Spherical model was assessed against a human brain
suspended in an electrolytic tank as well as from an invasive study from the brain of a spider monkey. With each
layer comes a change in the conductive properties, which in turn aects an electrodes ability to detect a neural
signal. Extensive research has been performed in evaluating the properties of biological material. It is concluded
that conductive properties of the skull cannot identied as a singular value, but instead a range of values. Geddes
and Baker have established a range for the skull of (0:006 􀀀 0:015)Sm􀀀1[26]. For the simplistic geometry of a
Spherical model, the solutions to the Forward Problem becomes an analytical solution.
Tissue Geddes et al. (1967)[25] Gutierrez et al. (2004)[27] Lai et al. (2005)[28] Ramon et al. (2006)[24]
Brain (0:12 􀀀 0:48) 0:31 0:33 0:14
Skull (0:006 􀀀 0:015) 0:012 0:013 0:006
Scalp 0:43 0:75 0:33 0:44
Table 2: Comparison of conductance levels for the Brain, Skull and Scalp obtained from literature.
The Realistic Head Model
To gain numerical solutions to the Forward Problem Realistic head models are used over their simplistic counterparts.
More accurate representations of the head can be obtained through various imaging techniques such as MRI
or compute tomography (CT). The boundary element method (BEM) uses a triangulated mesh to describe the
interface layers of head tissues, with the assumption that each dierent tissue type is isotropic and homogeneous
[29]. A matrix is used to describe the electric potentials at dierent vector locations on the surface. Simulated
sources and sensor locations can be implemented upon BEM meshes and applied to both Realistic and Spherical
models, although is situated far better to Spherical [30].
The nite element method (FEM), unlike BEM, is more commonly used within Realistic models as it is more
suited to complex shapes. FEM segments an acquired image of the brain, into mesh composed of three-dimensional
tetrahedra. This allows for dierent tetrahedra to represent dierent tissues in the brain. For FEM, this means
that dierent tissues can be an-isotropic allowing for the electric current to vary in dierent compartments of the
brain [31]. Although computationally demanding, the FEM approach shows an exceptional increase in accuracy
when locating sources that are present in the brain in areas of varying tissue [21][32].
Comparative reviews of head models demonstrate that complexity of a head model strongly in
uences the source
localisation accuracy. Models containing more realistic tissue data perform better at source localisation than more
simplied models [24][33].
2.4 The Forward Problem
To relate neural sources to EEG measurements mathematical models are used. Firstly, the Forward Problem is
approached by computing electric potentials recorded through electrodes present at the scalp. To solve the problem
the model uses a combination of the source distribution from the brain, a Realistic model of the head as well as a
conductivity map depicting the attenuation that certain tissues may cause to the signal [34]. As expanded on in
2.1, ions diuse through a neuron’s membrane creating an electrochemical potential over the membrane. Maxwell’s
equations state that as a current of electric charge moves, an electromagnetic current is induced.
The Forward Problem relates to the discovery of a potential generated by a dipole located from within the brain.
The dipole detected at a surface electrode, active at a location rq, will have associated Spherical coordinates
6
represented as = (; ) as well as a magnitude q = jjqjj. From this the scalp electric eld can be started as m(r),
with the solution of the Forward Problem for a dipole with amplitude and orientation being a(r; rdip; ). Linear
superposition allows for the summation of each individual dipole within a location, rqi as they are simultaneously
active. The summation is also dependent on the orientation of dipole. Synchronised dipole signals situated opposite
to each other, will invalidate each other, resulting in no signal detection.
m(r) =
X
i
a(r; rqi;i)qi (1)
Figure 3: (Left) Diagram of a 3 layered Spherical head model with labelled electric dipole coordinates [35].
(Right) Simulated EEG signals measured at 27 dierent electrodes [36].
For N electrode sensors and P dipoles, the following matrix is obtained:
m =
2
64
m(r1
…
m(rN)
3
75
=
2
64
a(r1; rq1;1) : : : a(r1; rqP ;P )
…
. . .
…
a(rN; rq1;1) : : : a(rN; rqP ;P )
3
75
2
64
q1
…
qP
3
75
= A(rqi;i)ST (2)
The term of m relates a matrix of measurements with matrix S relating the source amplitudes. The term A relates
a singular dipole current
ow to an array of electrode measurements for that dipole. The model above assumes
that dipole orientation is unknown, however, the property of pyramidal neurons being aligned perpendicular to the
scalp allows for the orientation being assumed [37]. Implementing this assumption leads to only the magnitude of
a dipole being variable. Furthermore, the model is extendable to include a time component for the time-evolution
for each dipole. For each source, P, time samples, T, can be used to form the spatio-temporal model [37].
M =
2
64 m
(
r1; 1) :
:
:
m
(
r1; T
)
…
. . .
…
m(rs; 1) : : : m(rs; T)
3
75
= A(ri;i)
2
64
ST
1
…
ST
P
3
75
(3)
Attributed to the measurements at the surface electrodes will be additional noise. This is added to M, through
the matrix n, resulting in the nal format of:
M = A(rqi;i)ST + n (4)
From the equation, the solving the Inverse Problem to nd the source localisation relies computing the most
optimal set for (rqi;i) and the attributing value of time series, S, for a given electrode measurement at the scalp.
7
2.5 The Inverse Problem
Various techniques have been established in order to solve the Inverse Problem related to EEG source localisation.
The techniques are typically categorised into parametric and non-parametric methodologies. The parametric
approach estimates dipole parameters of a prior determined number of dipoles. Algorithms search for the most
optimal dipole orientation and position from within a model. Its complexity can be varied, ranging from a singular
dipole in a Spherical head model to multiple models in a Realistic head model. Non-parametric is based from the
dipole orientation and magnitude of xed distribution of dipoles from within the brain [38].
2.5.1 The Parametric Beamforming Approach
The principle of a beamforming lter, W, is to repress every dipole signal apart from one that is equal to a selected
Forward solution.The following approach is detailed by S. Baillet [37]. The brain is divided into a three-dimensional
grid. A beamformer consists of a spatial lter applied to each section of the brain to return the most probable
location of a dipole. If the selected dipole is of unknown orientation, the spatial lter is segmented into three
Cartesian coordinates x;y;z. To locate source q(t) located in the head model, the data from each electrode
at time t, m1(t);m2(t) : : :mN(t) from the Forward model is obtained. Applying a linear transformation to the
data will reconstruct source activity. The product of the signal at time t, m(t) with a 3 N spatial lter matrix,
WT gives the output of a beamformer, y(t) as a vector. The approach operates by scanning various locations for
a dierent weight of spatial lter at each location and recording y(t).
y(t) = WTm(t) (5)
m(t) = A(r)s(r; t) (6)
y(t) = WTA(r)s(r; t) (7)
Where A(r) is the Forward model represented as a 3 N matrix A(r) = [a(r;x); a(r;y); a(r;z)]. Equation 7
reveals to nd a dipole signal at y(t), it requires the product of the spatial lter, source vector at a given time,
s(r; t), Forward model solution of that point, A(r). An idealistic spatial lter would return signals from a singular
dipole whilst suppressing neural signals from other dipoles in the brain. However, there remains spectral leakage
between the other dipoles and the observed dipole. An advantage to the approach is that source quantity is
not determined prior to applying the lter. As each section of the brain is individually ltered, they method is
minimally in
uenced by background noise. Any uniform noise from individual signals present in multiple other
signals can be compared and minimised. A detriment to the beam form approach originates in its ability to focus
on a singular location. If the combination of other dipoles in the brain is similar to the solution to the Forward
Problem, the beamformer can falsely reconstruct this combination as a singular source [38].
2.5.2 Simplistic Matched Filter
The most simplistic approach to solving the Inverse Problem is a matched lter. To obtain a matched lter, the
columns of matrix A(r) is normalised and transposed. A spatial lter for a certain location, s is shown in Equation
8 below.
WT
s =
A(r)Ts
jjA(r)sjjF
(8)
Although simplistic, the lter will return a guaranteed signal when a singular source is active. The absolute
maximum of this returned signal will be characteristic of the signal. However, due to the nature of the matched
lter only functioning for a single source, it is usually disregarded. This is due to, realistic conditions typically
require the localisation of multiple source [39].
8
2.5.3 Linear Constrained Minimum Variance (LCMV)
LCMV lters are used broadly implemented spatial lters using data obtained from the time domain [40]. As
the brain is segmented into a three-dimensional grid, the LCMV lter, WLCMV is applied to each voxel in the
brain-grid and suppresses signals from the other voxels.
WLCMV = A(rq)TC􀀀1
m (9)
Cm, is a covariance matrix from the data used to minimise the readings from any location not representative of rqi.
LCMV covariance matrix works by the time domain. This works under the assumption that rqi is the only active
dipole at the time of measurement. In the absence of a signal, a LCMV beamformer will still produce an output
from noise, becoming detrimental to the approach [37]. To account for the non-uniform noise present in a head
model, the LCMV is normalised. The approach taken in [41], normalises the data’s spatial spectrum with respect
to an estimated noise spectrum in a process referred to as the \neural activity index”. Cn, is the covariance matrix
relating to a noise only measurement.
var(rq) =
tr[A(rq)TC􀀀1
m A(rq)T ]
tr[A(rq)TC􀀀1
n A(rq)T ]
(10)
Through varying the location rq through all voxels, an estimate of neural activity. These can be spatially represented
onto three-dimensional Realistic head models of a subject.
2.5.4 Multiple signal Classication (MUSIC)
The MUSIC method approaches the separation of two interacting sources into two separate sub-spaces. In a
subspace, is the electric potential related to the dipole source [42]. Generally, the vector space/ Head model is split
into two sub-spaces; signal and noise-only. Here, the noise-only is orthogonal to the signal. The Musics algorithm
is based upon locating the dominant sub-spaces located within a head model. Simply, the algorithm scans over
all possible source locations, estimating whether a source at a given location is consistent with the measure EEG
data. This scan includes the possibility that several dipole sources may be active and not independent of each
other [42].
J(r; ) =
jjP?
s a(r; )jj22
jja(r; )jj22
(11)
Here, a(r; ) is the true source locations r = rqi and orientations i where i = 1; 2:::N . P?
s is representative of the
orthogonal projector onto the subspace. Moreover, it has been shown that the approach struggles to locate multiple
signals In noiseless data, dipole sources that are located within close proximity will still be localised separately.
However when noise is present, the algorithm will fail to dierentiate between two strong sources located in close
proximity [37].
2.5.5 Low-Resolution Electrical Tomography (LORETA)
LORETA forms the basis of tomographic approaches to solving the Inverse Problem. It has been developed in
through exact low-resolution tomography (eLORETA) and standardised low-resolution tomography. (sLORETA).
Developed in [43], LORETA approaches the inverse solution through combining the dipole measurements A(rq),
with a three-dimensional Laplacian operator. The Laplacian operator compares the current density at one voxel to
its adjacent voxels and returns a \smoothness” in voxel signal representative of a dipole. The inverse solutions are
represented as a \blur-localised” three-dimensional image of dipoles in which conserve the location of maximum
activity [42]. Furthermore, although LORETA introduced a new approach to solving the Inverse Problem, it came
with complications. The notable obstacle came with its in ability to locate sources located deep within the brain
tissue [44]. Developed methods of eLORETA and sLORETA aim to improve upon this.
sLORETA, diers from LORETA through assuming a standardisation of dipole current density. This results
in both the noise from EEG measurements and biological variance of signal is considered [45]. eLORETA, also
assumes a standardisation of current density achieves a zero-error source localisation when operating in a zero-noise
environment. However, is non-zero with noise conditions, with validation obtained from real EEG recordings [46].
9
W = [A(rq)T (A(rq)C􀀀1A(rq)T + H)+L]
1
2 (12)
The (e,s)LORETA methods low resolution \smoothness” is a limiting factor when considering dipoles sources that
are located within the near-by regions. These signals will overlap when represented as distribution. A key benet
of the (e,s)LORETA approach comes from the aforementioned problem that source depth in
uences the source
location error. The normalisation of the signal, A, allows for sources close to the surface as well as deeper ones
the same opportunity to be located [35].
2.6 Source Localisation Evaluation
2.6.1 Dipole Localisation Error (DLE)
Simulating a dipole source allows for its location to be known, and to be tested against a localisation algorithms
prediction. The localisation error is computed as the Euclidean distance between the predicted and simulated
vector positions of the source [47]. Errors can be returned as vectors or as grid references for either singular or
multiple simulated sources. As reliant on Euclidean space, DLE is subject to the resolution of a head model used.
With lowered resolution, the error obtained has potential to be low. In the review [48], the LORETA approach
was applied to a 3-layered Spherical head model of 818 voxels with a single simulated dipole. The returned DLE
was recorded at 1 voxel. The sLORETA applied to a 3-layered Spherical mode of 6340 voxels was found to give a
localisation error of zero voxels [35].
2.6.2 Point Spread Volume (PSV)
When locating a source, an ideal spatial lter will return a response at the signal location and zero elsewhere.
However, in reality there is limited spatial selectivity as a product of the presence of noise. This causes lter
leakage between neighbouring locations, returning an estimated signal over a small volume and not the precised
source location. This distribution around the focal point is referred to as the focality and is dependent on the
sources, strength, orientation and distance from sensor. The PSV is a measure of this focality, being dened as
the total volume occupied by the source activity above a variable threshold value [46].
3 Research Plan
The project will run a duration of 12 weeks starting on the 15/06/20 and concluding on 28/08/20. The plan for
this 12 week period is split into 5 dierent Phases, with key milestones expected to be reached at the end of each
Phase. The key milestones have been selected based upon their importance to the project’s function.
3.1 Project Phases
3.1.1 Phase 1
Phase 1 will begin two weeks prior to the start date on 01/06/20. These prior weeks will be dedicated to preliminary
work on the project. Preliminary work includes:
1. Refresher course in MATLAB. The author has not programmed in MATLAB for over 12 months, therefore
attention to re-familiarising with the syntax of MATLAB is of high importance to ensure the successful launch
of the project. The author has access to self-made scripts developed in MATLAB in which will act as the
refresher material. Furthermore, supplementary relevant MATLAB material can be found from EEGLAB.
EEGLAB oers an interactive tool for analysing EEG signals [46]. Using the tool to refresh the author in
MATLAB will help hone their MATLAB experience in the correct eld of study.
2. A Refresh of the Theory. As the timeline of the project sits post of the authors examination season, there
will be a signicant gap between the submission of this proposal and the projects commencement. A refresh
on the theory described in the document will also aid the launch of the project.
10
3. Review and feedback implementation. The Literature review present in the proposal has the potential to
act as the Literature review for the nal MSc Dissertation for module PXT999 at Cardi University School
of Physics and Astronomy. Prior to the projects beginning, feedback upon the proposal will be distributed
from Dr Richard Lewis (MSc Coordinator). This feedback is to be digested and relevant improvements to
be implemented to ensure the Literature review is of its highest quality.
3.1.2 Phase 2
Phase 2, beginning on the 15/06/2020, signals the ocial start of the project. Upon prior agreement with the
project supervisor: Dr. Beltrachini, the starting date will also involve the distribution of the sLORETA algorithm
and Realistic head model. Phase 2 will conclude on 04/07/20 and consist of the following:
1. Creating Spherical Models. The creation of a 3-layered Spherical model consisting a brain, skull and scalp
layers will begin the project. Each layer of the Spherical models will be homogeneous in conductivity value.
It is aimed to create three dierent models of dierent conductivity values, to be used throughout the course
of the project to assess each source localisation algorithm.
2. Creation of the Matched Filter. The time post creation of the Spherical model will be spent on implementing
a simple matched lter.
3. Understanding the distributed code. Although the author is expected to be familiarised with MATLAB by
15/06/20 as well as the theory behind solving the Inverse Problem with sLORETA, connecting the former
and the latter together is expected to not be an instantaneous achievement. Therefore, a dedicated period
stemming from 22/06/20 to 29/06/20 will be used to review this.
4. Plan B. Phase 2 will conclude with the completed development of the Spherical Head Model, LCMV and
Matched Filter. The success in the development assessed and reviewed. If the created models are not
functioning as expected, a Plan B will be approached. As explained in Section 3.2, Plan B oers a branching
point to explore EEGLAB.
5. Plan C. A secondary branching point of the Project is shown in Plan C. In the event of a failure to implement a
Matched Filter or a LCMV algorithm, one could be switched for the implementation of the MUSIC algorithm.
The Project would continue as expected, using MUSIC to complete a comparative study.
3.1.3 Phase 3
Phase 3 signals the start of data acquisition. In its simplicity, from the period of 13/07/20 to 27/07/20, it is aimed
to simulate neural sources in both head models and locate them with each of the three algorithms.
1. Spherical and Realistic model. Data acquisition will begin with simulating a singular neural source in the
Spherical model. This will then be used to as the base to assess the three algorithms. It is expected to
perform this section locally on the authors computer. On the other hand, implementing the algorithms with
the Realistic model will require the intervention of CUBRIC’s supercomputer. This is a result of the Realistic
model being a larger data set. Methods to reduce the size of the Realistic model have been researched and
due to CUBRIC’s availability, may be implemented. This is discussed in Section 3.2 below.
3.1.4 Phase 4
Phase 4 is dedicated to manipulation of the stimulated sources as well as creating variations within the head models.
Up to this point, it is expected to achieve accurate and successful source localisation from each implemented
algorithm on each head model. This Phase oers the most variations in whats to be achieved. But, it is reliant on
the success of the previous Phases 1-3.
1. Variations of Dipole. As mentioned previous, dipoles have specic parameters that are characteristic in
the success of a source localisation algorithm. It is aimed to simulate these dipoles of varied, Strengths,
Orientations and Depths to explore their eects on source localisation.
11
2. Variations of Head models. Variations in conductivity levels, as well as sizing of tissue distributions within
the Head models will in
uence source localisation. It is aimed to explore these variations in great depths for
both Spherical and Realistic models. As the Realistic models contain more data, it is expected that great
attention will be given to varying its parameters. It must be noted that any implemented variations in the
model will align with realistic anatomy as testing source localisation with models that are unrealistic is not
an accurate representation of an algorithms source localisation ability.
3.1.5 Phase 5
Phase 5 of the project is dedicated to the construction of the nal dissertation document. Applying applicable
experience from completing an Undergraduate Dissertation, to ensure the document is completed in a timely
manner, Phase 5 begins on 10/07/20.
1. Methodology and Results. To secure clarity within the results and methodology, the completion of each Phase
is met with a write up. These are indicated in Tasks 6.1-6.4. The completion of the write up will aid a timely
draft to be submitted to the supervisor 2 weeks prior to submission.
2. Mentor Meetings. The rst of two Mentor meetings with Dr.Roche will take place in the week 06/07/20 –
10/07/20. It is expected for this meeting that the author will have relevant work to show their progression.
It is planned, that by 06/07/20, Phase 1 will have been completed and the Dissertations Literature Review
to be adequately changed to incorporate the feedback given. In addition, the second meeting will occur in
the week 10/08/20 – 14/08/20. Upon this meeting, it is planned to be in the latter stages of Phase 4 and
preparing to switch full attention to writing the Dissertation.
3. Supervisor Meetings. Along with the pre-dened Mentor meetings, weekly supervisor meetings have been
conrmed. These meetings are currently subject to an available time-slot. In these supervisor meetings, the
author will obtain a chance to ask any questions relating to the completion of the Project.
3.2 Project Contingencies
As the pre-built sLORETA method and head models are provided from Dr. Beltrachini, the project has a strong
foundation. Moreover, the main contingency stems from the construction of the two Beamforming approaches.
Relevant literature [37][41], gives mathematical explanations to LCMV and explaining Matched Filtering. However,
the inability to implement these techniques would be detrimental to the comparative study. To ensure the
acquisition of Beamforming technique, the EEGLAB developed by Swartz Centre for Computational Neuroscience
(SCCN) package for MATLAB oer pre-built Beamforming algorithms [49]. The decision upon deciding when to
make use of EEGLAB’s pre-constructed beamforming algorithms will be made by week 4 of the 12 week project,
this is denoted in the Gantt chart as “Plan B”. “Plan C” oers a further safety net incase implementation of the
LCMV or Matched Filter becomes in achievable. The MUSIC algorithm will be explored, with example scripts
being found as inspiration [50].
A further contingency stems from the inability to perform adequate computational simulations locally due the
memory requirements it possesses. As aforementioned, the project will be able to utilise CUBRIC’s high performance
cluster to execute to simulate inverse solutions on Realistic head models. Having already been provided
access to the cluster during completion of module PXT3315 at Cardi University School of Physics and Astronomy,
using the service will be a formality. The cluster will provide the required computational power to execute scripts
using the data-heavy Realistic models and a selected algorithm. The reliance on the cluster is currently seen as
an essential requirement for the ability to obtain a prosperous review on the inverse solution techniques.As with
the nature of MATLAB, the Realistic model is a three-dimensional representation of a head volume built up of
individual voxels. Re-scaling the data set to decrease its size, will result in a decrease in the resolution of each
voxel. For example, take an original data set A of size 600 600 600 to reduce its size by a factor of 3 to make
it data set B of size 200 200 200. The scale reduction of 3 means that information that was once displayed in
3 voxels is now displayed in 1. The loss in resolution may potentially diminish the accuracy of source localisation
for each algorithm.
12
Phase Task Week
-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
1 1.1 Implement Proposal Feedback
1,2 MATLAB Refresh
1.3 Theory Refresh
2 2.1 Construct Spherical Models
2.2 Construct Simple Matched Filter
2.3 Construct LCMV Beamformer Plan B/C
2.4 Digest distributed sLORETA algorithm
3 3.1 Apply algorithms to the Spherical
Model with a single simulated source
3.2 Apply algorithms to the Realistic Model
with a single simulated source
3.3 Repeat 3.1 and 3.2 for multiple simulated
dipoles
4 4.1 Vary Dipole: Strength and Depth, for
the both head models
4.2 Vary conductivity levels within Realistic
Models: assess DLE and PSV for both
single and multiple sources
5 5.1 Write up methodology sections for 2.1-
2.4
5.2 Write up results for sections 3.1-3.3
5.3 Write up results for sections 4.1-4.4
5.4 Produce draft for for Supervisor
5.5 Implement Supervisor feedback
5.6 Submission of Dissertation
5.7 Supervisor Meetings
Table 3: A Gantt chart depicting the projects life cycle of the 12 week period. The project is divided into 5
distinct Phases, of which are displayed in dierent colours: Phase 1,Phase 2, Phase 3, Phase 4 and Phase 5.
Floats have been implemented into Phase 3 and Phase 4 to highlight possible variations to the original time plan.
Furthermore, two potential deviations in the project time is labelled as Plan B/C. This is discussed in Section 3.2
above.
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15

¿HOW TO CONDUCT LITERATURE REVIEW CRITIQUE?
INSTRUCTIONS FOR THE ASSIGNMENT.
What sort of questions should I be asking when conducting a critique of a literature review?
When critiquing a literature review, you are assessing the review’s context, motivation, novelty and how well it reassures you, the reader. In other words, a literature review should:
– Contextualise the research within the wider literature.
– Motivate why the research is significant.
– Distinguish the research from other work.
– Reassure the reader that the author is competent.
In order to conduct a critique, you should be asking (and then answering) the kinds of questions that are suggested below. Comments have been included with each question as a guide. Note that these questions are not exhaustive and further questions should present themselves as you work from this starting point. It also goes without saying that you should read the paper in its entirety, skim read all the references, and explore the wider literature. A good starting point would be to take the paper’s keywords and search Google Scholar with those. A critique is a critical evaluation and therefore you will be making an argument. A critique is not a report or a derivation in the sense that there will be one correct answer or format. As with all academic arguments, you will need to back them up with references, quotations and other supporting material. Note that the document whose literature review you are critiquing is itself a document that you will need to include as a reference in your bibliography if you include the work in your own writing. Determining whether a literature review contextualises the research within the wider literature
What is the gist of the literature review’s contextualisation? This is a description of what the author has done in a very condensed, brief form – essentially a summary of their literature review.
Has the literature review presented a predictable (orthodox) contextualisation? Is this appropriate? In other words, the literature review will likely emphasise certain topics to the exclusion of others – from your wider reading and consideration of the interests of the target journal, can you determine whether this was appropriate?
Given the previous point, can you “add in” the extra context into which this paper would fit? By extending the existing literature review to include a wider scope, you are demonstrating that you have read around and understand the “global” (in the mathematical sense) context. Typically, papers have to be concise and hence cannot contain every last link between the work and the literature. By answering this question you will probably be able to comment further on the above two points.
What was the impact factor of the journal at the time in which the paper was published? Do you think that the journal was an appropriate place to publish this work? These are two separate by intimately linked questions – do you think the importance of the results align with the impact factor / turnaround time of the target journal? Determining whether a literature review motivates why the research is significant
Given the content of the entire paper, are the explicitly stated motivations appropriate? Note that although you are looking primarily at the literature review, the entire paper is part of its wider context, and hence will provide extra information regarding the motivation for the research.
Is the motivation logically sound and internally consistent? Most probably it will be, but can you see any areas which the motivation might have glossed over or aggressively reduced? This might be appropriate if the paper is a letter or short communication. If this is the case, can you expand on the motivation to make it clearer?
Does the work fit in with the aims and objectives of the author’s group at the time? This may be difficult to determine for groups outside Cardiff, but bear in mind that many papers are published to raise the profile of the group (“here we are!”), rather than being “major results”. The paper may therefore not be part of a group’s explicitly-stated research strategy but rather perhaps a “spin-off” paper which was published for its impact alone. Alternatively, the paper might be seminal.
Determining whether a literature review distinguishes the research from other work
Is the work completely novel or is it a derivative work? This might not be easy to determine from the literature review alone. By reading the wider literature you should be able to make this distinction with a bit more precision and hence comment on whether the authors have themselves appropriately motivated their work in this sense.
If the work is completely novel or speculative, does the author adequately characterise the impact this work would have? By reading the wider literature this should be straightforward to determine. If it is a derivative work, can you comment on how the author’s contextualisation and motivation support the author’s declaration of novelty? If the work is derivative, have the authors made sufficiently clear the element of their work which qualifies the publication of the whole as novel?
Are there any similar techniques /concepts / results not mentioned in the literature review which would cast a different light on the declared novelty of the work presented? Did the author miss anything? Would it have been reasonable to expect the author to know about these publications? For example, an author writing in the US in 1960 could not be reasonably be expected to know about classified Soviet research that may only have made it into the public domain following the collapse of the USSR.
Determining whether a literature review reassures the reader that the author is competent
Given all the above, are you reassured that the author is competent? Note that by “competent” we would generally mean it in the general sense, but here you can take the more restricted view of whether the author has generated their literature review competently.
If you had been acting as a reviewer for this paper, could you comment on any changes you might have wanted to see made to the text? You should refer to the target journal’s submission criteria in order to answer this. Possible changes should suggest themselves if you have thoroughly answered the questions under “context”, “motivation” and “novelty”.