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Probing the hidden secrets of the Brain…
… A physical investigation into the underlying physiology of the brain by Elie Matar
Did you know?
The human brain has, on
average, 100 billion neurons,
and to each neuron there
exists between 10 and 10000
connections to other
neurons. Therefore
theoretically, the minimum
number of activation
patterns possible in the brain
is about 10 raised to the
power of 100 billion – more
than the estimated number
of atoms in the entire
universe!
The problem of ‘unravelling’ what is arguably the most complex system in the
universe – the human brain - has been plaguing scientists for centuries.
However, with the prevalence of new technological advancements and modern
scientific tools, more has become understood of that which is the source of our
cognitive and physical behaviour. Elie Matar reports.
A team of scientists at the University
of Sydney have taken a step back to
focus on an observation made by
Richard Caton in 1875 and since has
become a widely known fact – that the
brain generates electrical activity.
Many
of the approaches to
understanding human brain
function and structure in recent
years
has
involved
the
mathematical modelling of the
complex neural networks or
‘circuits’ that constitute the
major proportion of the brain. It
has been understood that these
are also directly associated with
its organisation and operation.
Such studies have been aided by
the emergence of many new and
viable diagnostic methods that
have allowed different aspects of
brain behaviour to be analysed
and measured. From the
examination of oxygen in the
flow of blood in the brain to the
metabolic processes, terms such
as fMRI (functional Magnetic
Resonance Imaging) and PET
(Positron
Emission
Tomography) have become
commonplace in the realms of
neuroscience. However, it is
renewed exploration of a method
discovered more than a century
ago that has attracted the interest
of Scientific Australian.
Through a device known as an
Electroencephalogram,
(EEG),
a
spectrum of this electrical activity is
resolved and then analysed.
What are EEGs?
Electroencephalograms (EEGs) are
measured scalp potentials as a
result of cortical electrical activity
amassed over scales larger than
single neurons. They are obtained
via the placement of electrodes at
specific points over the surface
area of the scalp. While it has
spatially rough scales of about 2cm,
the time scale is superior to most
other methods, with accuracy to
the scale of milliseconds!
Associations between brain function
and EEG spectra have been used
extensively in diagnostic methods;
however the specific links between
these spectra and the underlying
1.
physiology have not been clearly
understood.
Despite this obstacle, Professor Peter
Robinson and a team of researchers
at the University of Sydney, in
conjunction with the Westmead
Centre
for Brain Dynamics,
developed a continuum model, based
on
experimentally
derived
parameters, that was able to
reproduce the spectra observed from
EEG’s. The success, predominance
and efficacy of the model relied on
its adherence to a strict framework
(below) that aimed to provide
sufficient but detailed mathematical
rationalisation of the most crucial
aspects of the brain in terms of its
electrical activity.
Framework
1. Foundations in real physiology
with the most crucial structures
and their properties taken into
account.
2. Development of a model that
relates global dynamics of EEG
to small scale physiology
3. Description of process in terms
of mathematical steady-state
equations with independently
determined parameters.
4. Reproduce observable EEG
spectra from theory.
A discussion of the model,
according to these criteria, will
follow; along with a sample of
results obtained that demonstrate its
usefulness and application.
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Physiological foundations
The critical physiology of the brain
represented in this model includes
the neuronal populations of the
cortex and the thalamus (see across).
Why these in particular?
It seems quite obvious why the
cerebral cortex should be included.
Not only does it comprise the
greatest volume of the brain, but it is
the structure that lies closest to the
recording electrodes of an EEG.
The reason for the thalamus is no
less obvious, as the primary receiver
of sensory input to the brain,
sensory information from external
stimuli comes through the thalamus
to be then transmitted to other
structures in the brain. In the
process of reading this article, your
vision is transformed into a series of
electrical pulses that travel to the
thalamus and are then sent primarily
to the cerebral cortex where they are
further processed.
This is what leads to the
conceptualization of the key
interactions in the brain as being a
series of circuits or loops between
populations within the thalamus to
the cortex and vice versa.
The thalamus is broken up into two
main divisions, the relay nuclei,
which function to transmit the
signals to the cortex, and the
reticular nucleus, which has an
inhibitory effect on these signals.
The thalamus also receives feedback
from the cortex thus closing what is
called a ‘corticothalamic loop’.
The model treats the populations of
neurons in the brain as a continuum
rather than as individual cells. The
properties of a specific neuron are
averaged over about a tenth of a
millimetre which is a sufficient
approximation, considering an EEG
measures roughly to about 2 cm!
Guide to the Human Brain
The field of neuroscience and Brain
Dynamics is fast emerging in the
scientific world and a working
knowledge
of
the
brain
is
important to keep up with the field.
The aspects of the brain that are
fundamental to this model include
the neuron, the thalamus and the
cortex.
Fig. 3 - A Pyramidal Cell
The neuron (pictured above) is the
most fundamental unit of the brain
and nervous system. These cells
communicate to each other via
connections
from
axons
to
dendrites across a gap called a
synapse.
Impulses
propagate
through these via electrochemical
gradients (action potentials). The
pulses arrive at the dendrites, and
are carried down to the cell body
(soma). They then travel down the
axon hillock to the axonal tree
where they are then imparted to
other neurons. There are different
types of neurons in the brain.
Pyramidal cells are of particular
importance, comprising 90% of the
cerebral cortex and play an
essential part in most neuronal
circuits. There are also inhibitory
cells that inhibit signals by
chemical means, the action of
these are highly localised.
As we can see here, the model was
based on real life physiology that
would account for the theoretical
reproduction of EEG spectra
2.
Fig. 4 – Four lobes of the cerebral cortex
The cortex (pictured above) is the
outermost layer of the brain; it is
the main contributor to the scalp
potentials as it is the closest to the
scalp and the site of termination of
many of the electrical signals that
arrive to the brain. The cortex
receives most of the sensory
information from the thalamus.
With a relative thickness of 2-4 mm,
it is often treated in its unfolded
state as a 2D sheet with a total
length of 1m!
Fig. 5 – Position of thalamus in a medial
cross-section of the brain
The thalamus (above) is the main
gating station for all sensory input
received from the peripheral
nervous system (except smell) and
relays this information to other
parts of the brain, namely the
cortex. It also receives feedback
from the cortex and forms closed
corticothalamic loops. Populations
(nuclei) within the thalamus act to
either relay the signals (excitatory)
or
inhibit
them
(Inhibitory).
In the next sections we will
investigate how the model works to
relate large-scale dynamics (EEG) to
this small-scale physiology.
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Developing the model
So now we deal with the question
of how we break down this
information into a set of
mathematical equations that will
help us extract an EEG from the
basic physiological principles we
just discussed.
The Approach
immeasurably
complex
neurocircuitry in the brain into a viable
and mathematically flexible system
can be a difficult task in the least.
However, these researchers at the
University of Sydney have achieved
such a model that adequately depicts
these circuits in an accessible form.
“...Simplifying the…complex
neurocircuitry in the brain…can
be a difficult task…”
Most modelling theory emanates
from the basic instinct to get from
A to B. Ok, so what is B? Well,
we want a model that gives us the
output of an EEG at the cortical
surface, therefore our endpoint has
to be a power spectrum that is the
sum of all the populations on the
surface of the cortex (remember
this is a continuum model) And
that’s our B!
The elemental features of this
representation include treating the
thalamus as two functioning nuclei the relay nucleus and the reticular
nucleus (refer to previous page).
What about A? As mentioned in
our framework, we want to derive
this model from basics; i.e., from
small-scale physiology. So A has
to be the source of our power
output at a basic structural level.
And what is the primary source of
the impulses in the brain? Casting
our minds to the previous section,
we realize that the thalamus,
which receives almost all the
external input, is an ideal starting
point. So in this model, the
thalamus is our A.
The sum of all the fields over the
cortical loop ultimately affects the
power output. And stepping up the
scale, the sum of all the loops over
the
continuum
of
neuronal
populations over the area covered by
the electrodes determines the final
EEG output spectra.
How do we get from A to B?
Herein lies the ingenuity. In
previous section, we discussed
significance of certain loops in
brain between the cortex in
thalamus.
Simplifying
the
the
the
the
the
Neuro-circuitry:
Any of the complex series of
biological circuits present in the
human brain that are activated
in several patterns cohesively to
perform a given function.
Model Makeover!
Fig. 6 – Schematic interactions between
the thalamus and the cortex
The impulses are defined by the
pulse density field Φ. The inhibitory
and excitatory action of the
respective nuclei in the cortex and
the thalamus are included.
Parameters, Parameters…
And of course no biophysical model
would
be
complete
without
biophysical parameters. Usually, the
more complex a system is, the more
parameters involved. Fortunately in
this model, they have been restricted
sufficiently without sacrifice of
detail to the model. Among these
include the propagation delays,
projection ranges, and damping
rates. Most are independently
measurable
and
have
fixed
anatomical values. These are direct
physiological links in the model.
3.
Fig. 7 – The simplified representation of
the Corticothalamic loop
Both figures stress the primary
structures of the brain – the cortex
and the thalamus as well as the
corticothalamic loop that connects
them. The Subscript ‘e’ denotes
excitatory action and ‘i’ inhibitory.
Φ represents the average of the
field potential of each population.
The loop begins with the external
impulse Φn feeding into the relay
nuclei (s). The signal is then relayed
to the cortex (e) via Φs. This signal is
then processed in the cortex with
regulatory action Φi accounted for
by
inclusion
of
inhibitory
populations within the cortex itself.
The corticothalamic circuit is
completed by cortical feedback
Φe to the thalamus.
An EEG
measures Φe at the cortical surface.
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Oct 04
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The Physics of the model
Fundamentally, the physics is
based on these corticothalamic
loops being the driving force
behind the EEG spectra. This
article will now only discuss the
theory at a superficial level and
leave it to the reader’s own
curiosity to indulge in the
rigorous details of the proofs.
(See Further Reading)
2. Pulse Generation
The action potentials generated at the
axon hillock are averaged over a
population of neurons. The properties
of the population are statistically
analysed and, along with deviation
between different populations, are
taken into account in a formula
describing the firing rate.
A theoretical perspective
3. Propagation
The main aspects of theory:
The propagation of the pulses
throughout the neural matrix are
analysed using the mathematical
concept of propagators, (outlined
below). Linear propagation is
assumed as an approximation in this
model and describes the transfer of
the impulses across the axonal tree
and the dendrites of the receiving
neuron. The expression for the
propagators takes into consideration
the arborisation (tree-like branching)
of these respective structures.
1. Soma potential, synaptic
and dendritic dynamics
2. Pulse generation at the
axon
3. Propagation of the pulses
within and between
neuron populations
4. Parameters involved
5. Relation to
corticothalamic loops
1. Soma potential and
synaptodendritic dynamics
In accordance with the continuum
model, the mean soma potential is
calculated for a particular
population of neurons. This was
done by making a linear
summation over all the potential
contributions arriving at the soma
from the dendrites of the cell.
The dynamics are in terms of
spatiotemporal coordinates. The
spatial coordinates are derived
from a primary topographic
mapping between the thalamus
and cortex, treating the cortex as a
2D sheet in its unfolded state.
The corresponding responses of
the subpotentials in a cell due to
the synaptodendritic dynamics are
approximated by a differential
equation. (One of many!) Thus,
the power output observed in an
EEG of the brain begins at the
scale of subpotentials.
The theory then goes on to show the
way a signal travels is approximately
the same as a damped wave! So a
second order differential equation (an
equation that governs wave motion)
is substituted. This is in terms of
projection ranges and damping rates.
A simplified and rearranged equation
for
propagator
Γab
(denoting
Propagators:
Propagators
are
essentially
functions that allow you to
determine where a particular
subject (such as an impulse) will be
given its spatial coordinates at an
earlier time. Here is the expression
for the propagator Γab(0) after
simplification in terms of angular
frequency ‘’ and the wave vector
‘k’ . Note: q2r2 is a function of 
4.
propagation between population ‘b’ to
‘a’ is shown in terms of the wavenumber ‘k’, the damping coefficient
γab, and projection ranges rab.
4. Parameters
The
equations
describing
the
propagation of the pulses throughout
the brain rely on roughly 40
physiologically dependent parameters.
In this article, we detail the
investigation of one such parameter rab denoting the projection range
(explained later). Other parameters
include the already mentioned
damping and synaptodendritic rates,
but also propagation delays, gains and
projection velocities.
The Transfer function:
The equation below is called the
‘transfer function’ and is the ratio of
the averaged impulses Φe at the
cortex to the input Φn at the
thalamus.
The magnitude of this expression
squared yields the power spectra
relating to that observed by an EEG
in terms of  and k.
5. Corticothalamic loops
All parameters above are given for
each set of populations – intracortical,
intrathalamic and corticorthalamic shown on the schematic diagram on
the previous page. All these terms
appear in the final treatment of the
mathematics exemplified in the
transfer function evaluated and
manipulated to obtain the power
spectrum at the cortex, as we will see
next.
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EEG spectra – General Results
Now comes some reward for all
that ‘brain strain’ - the muchanticipated results! But before you
switch your brain waves into
alpha (a stable resting mode), a
tiny bit more theory is required to
understand the added twist
included in this section.
Some general results
Fig. 7 (left) – Spectra obtained
from an adult subject (solid)
against model predictions (dotted)
Fig. 8 (bottom left) – The isolated
model predictions for power
spectrum in terms of the
frequency
Over the next couple of pages, we
will see some general results
proving the validity of the model
and outlining generic features of
the spectra for the untrained eye.
Then we will follow an
exploration conducted on the
effect of the projection range
parameter (rab) in the model.
Fig. 9 (below) – The power
spectrum in terms of the wave
number
The general results
Two-dimensional
integration
resolves the power spectra as a
function of ‘’ or ‘k’, which is
used in this section to analyse the
results. All parameters and
observed readings have been
obtained from an adult in relaxed,
eyes closed state.
All graphs presented in this article
have been calculated and plotted
using IDL (Interactive Data
Language).
Before we continue, we shall first
confirm the validity of the model
using Figure 7. In this figure, the
input signal Φn is approximated
by white noise across all
frequencies. As we can see, there
is a strong correlation between the
theoretical predictions and the
observed data. Most of the results
to follow will be reproduced in
terms of frequency-dependent
power spectra to allow for a more
straightforward interpretation. The
spectrum in terms of the wave
number in Fig. 9 is only included
for the interest of completeness
The general features of the curves in
normal steady state mode such as that
shown in Figures 7 and 8 include
alpha and beta peaks, which are
simply
resonance
phenomena
occurring within the 8-12 Hz and 13+
Hz range respectively. There is a
predominant alpha peak at about
10 Hz and is a dominant feature in
these corticothalamic loops. It has
come to be realized that the stronger
these loops, the greater the resonance
at 10 Hz by which they have thus
come to be defined by.
It can also be noted that there is a
dominance of the spectra at low
frequencies with a leveling effect
occurring in the range of 0.1-4 Hz.
This is due to an effect known as
‘low pass filtering’, which occurs at
the synaptodendritic scale, allowing
only the lowest frequencies to
dominate in the power spectra. Also
as a result, there is a sharp decline in
5.
the power spectrum after a cut-off
frequency occurring at about 15 Hz.
While this model accounts for all the
features of an EEG, there remains
some uncertainty shrouding the exact
physiological basis of some of the
features, and in particular, their
dependence on the individual factors
in the transfer function.
Terminology:
White Noise: A random signal with
equal power across all frequencies.
Alpha Range: Frequency band in
the range 8-12 Hz
Beta Range: Frequency band in the
range 13 Hz and above
Resonance: The prominence of a
particular frequency or band in
response to a stimulus.
Cut-off frequency: A frequency that
marks the transition of a signal or
spectra towards zero.
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EEG spectra – An exploration of the projection range parameter
Scientific curiosity coupled with
man’s thirst for knowledge has
always been a driving force that
leads scientists to explore, analyse
and draw meaning out of any
phenomenon with as much depth as
possible.
In trying not to break such a
fundamental law, we include some
details of a project that gives greater
insight into the structure of the brain
and its corresponding observed
electrical phenomena. The essence
of the project relies on varying the
projection ranges in the model and
interpreting the EEG output. But
first - a little bit more on projection
ranges.
The Results
(a)
(b)
(c)
(d)
What are projection ranges?
The parameter rab refers to the
projection range from population b
to a. It is defined as the spatial range
over which the signal is transmitted.
In other words it is a measure of the
dispersion of the signal throughout
the brain.
Fig. 11 a) Varying relay-cortex
b) Varying cortex-thalamus
c) Varying intrathalamic ranges
d) Varying intracortical excitatory
e) Varying intracortical inhibitory
(e)
A decrease in the range would
correspond to an increase in the
specificity of the signal. Conversely,
an increase in the range would lead
to a decrease of the specificity. The
diagram below summarises this in
terms of the corticothalamic
interactions.
The solid lines in the graphs
indicate the original value of
parameters for a normal steady
state of a typical adult and the
others
are
the
result
of
changing one or more values of
ranges res, rse, rre, rsr rrs, ree and rei
Projection Ranges
Fig. 10 - Difference between specific and diffuse projection ranges for signals – ‘es’
(blue) and ‘se’ (red). Left has small projection range while the right a large range.
6.
The results above look similar at
first glance, but on further
inspection, one sees that there are
subtle but noticeable differences
owing to changing different
parameters in different populations
with either inhibitory or excitatory
roles. By brief mathematical
analysis, we can guess what the
trends should appear like and then
look at them in further detail.
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EEG spectra – An exploration of the projection range – (Cont’d)
In the mathematical model, most
of the range terms exist in the
denominator of the transfer
function. Therefore by mere
inspection we can roughly assume
that by increasing the ranges the
spectral power density will
decrease.
Some of the more specific features
of the results can also be inferred
by realising that increasing the
specificity of the impulse further
emphasises the corticothalamic
loops in the model. The stronger
and more defined that these loops
become, the more the features that
are dependent on the loop - such as
the peaks - are accentuated.
Fig. 11 (a) represents the spectra
when range res - from the thalamus
to the cortex - is increased from
0.3 mm (solid line), to 0.5 m. We
can note the obvious shift
downward in the power spectrum,
confirming our hypothesis. In fact,
increasing the ranges of all the
excitatory populations such as in
Fig. 11 (b), and (d), display that
property of a decreasing power
output.
An interesting note can be made
when observing the degree to
which the output spectra decline.
The shift up or down in the spectra
refers to its normalization. In (a)
which denotes variations in the
relay to cortical ranges, there is a
10-fold decline in the output
spectra. Meanwhile there is only a
barely noticeable (25%) decline in
the cortex to the thalamus
spectrum. This means that the
cortical feedback loops play a
much less important role in the
normalization, and thus the
magnitude, of the output power
spectrum at the cortical surface.
In harmony with this decline in
power spectra, there is also a
noticeable smearing effect on the
features of the curve. The alpha and
beta peaks become much less
prominent in all cases (a), (b) and
(d). So it can be added that while the
cortical feedback loops do not
strongly affect the normalization,
they have a significant effect on the
fine resonance features of the
graphs. In the case of all of the
figures, the smearing effect on the
output can be attributed to a
smearing effect occurring at a
physiological scale, whereby the
connections in the corticothalamic
loops are ‘smeared’ or spread out
and deviate from the loops.
Consequently, decreased weighting
on the loops by increasing range
results in the loss of power emitted
at the resonant frequency by these
loops - recalling the dependency
relationship of these peaks with
respect to the corticothalamic loop.
Parallels may also be drawn between
the
intrathalamic
and
the
intracortical spectra in Fig 11. (c),
(e). For (c) the ranges rsr and rrs were
increased together. While for the
intracortical diagram, only the
inhibitory ranges rei were increased.
But here, the power spectrum
increases with increasing range!
While this may appear to contradict
our earlier argument, remember that
the action of these populations or
connections is inhibitory. And so by
increasing the diffuseness of the
connections we are decreasing their
action on the corticothalamic
circuits, which is analogous to
increasing the excitatory impulses.
Thus the loops become less
inhibited, more defined and lead to a
greater power output at the cortical
surface.
7.
The last main thing to note in the
diagrams is the variance in the low
pass filtering effects. Essentially, by
looking at the graphs that have main
effects on EEG – (a) and (d) we can
see the cut off frequency, before the
spectrum begins to decline, decreases
so that the effect of low pass filtering
is stronger. How might this correspond
to what is actually happening
according to the physiology? As we
know, increasing the projection ranges
increases the dispersal of the signals.
On a physiological level, this
corresponds to the spreading out of a
signal across the axons and their
reception across different lengths of
the dendrites. This changes the
temporal profile of the signals when
they reach the soma and are then
relayed. This is what causes the
observed low pass filtering in the first
place, remembering that the dispersal
of the signal happens anyway but not
to the same extent.
We shall leave the discussion at that,
but the ‘take-home lesson’ is evident
in the scope of skills employed and the
results obtained by analysing only a
small part of the model as a whole.
Like a fractal image of the brain, the
closer we look, the more we find out.
Simple circuits: A useful analogy
It may help to think of the corticothalamic loop as a simple, ideal
electrical circuit.
A light bulb connected in series to a
fixed power source (input stimulus)
can be the EEG output. The circuit
represents a corticothalamic loop.
Increasing the projection ranges is
analogous to sequentially adding
resistors to the circuit in parallel. The
current is divided and decreases in
the main loop, thus the power
running through that section of the
circuit will also decrease along with
the intensity of the light.
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Implications – What can we do with this?
At this point, the implications of
this work should have become
self-evident. Just by exploring a
single parameter, we have been
able to infer what happens in the
brain at a real physical scale.
There are numerous implications
of this model with respect to
further research as well as in the
pragmatic sense of practical
application.
The model’s explanation of the
basis for EEG spectra will allow
us
to
‘probe’
underlying
physiological
parameters
from
observed output spectra of subjects.
It also follows that we can work
backwards so that we start from an
EEG reading and from that, infer the
values of different states and
projection ranges. This paves the
way for EEGs being used as
diagnostic
tools
for
finding
abnormalities in patients, tracing
specific features of EEGs to their
physiological source. In fact, the
model is currently being used to
analyze the spectra of people
suffering from epilepsy, tumors and
attention deficit hyperactivity disorder
(ADHD) as well as gauging the effects
of the presently available treatments.
(See Further Reading)
Stepping up to a more general scale,
the model may even shed light on why
certain structures of the brain are
organized the way they are - taking us
one step closer to the ultimate goal of
a complete understanding of the
human brain.
Future work - Where do we go from here?
research into the effects of other
parameters, for example the,
propagation delays or projection
velocities would increase its
precision.
Fig 12 – Electron micrograph of a neural
network
The model in its entirety leaves a
lot of facets to be explored, an
example being the case study of
the effect of the projection range
variation within the model. Further
The inclusion of other subcortical
structures such as the basal ganglia
or the brain stem would improve the
accuracy of the model by further
accounting for the subtle but
complex contributions of these
structures
outside
the
corticothalamic loops. The inclusion
of modulating dynamics in and
between these extra structures with
the extra feedback loops would serve
as a definite enhancement to the
model.
On the same idea of physiological
truthfulness, extra populations in the
thalamus may be included greater as
there are really 12 nuclei in the
thalamus.
These are simply some of the
possible future investigations that
will yield greater resolution of the
EEG spectra in terms of specific
coordinates.
Conclusion
The human brain, while aweinspiring, was and still remains an
enormous source of frustration as
an obstacle to all who thirst to
understand the inner workings of
the mind. However through the
growing wealth of scientific
knowledge demonstrated by this
article, the ever expanding frontier
of technological advancement, and
through the persistence and innovation
of dedicated scientists such as those at
the University of Sydney - we are
slowly, but surely…unravelling the
secrets of the human brain. ■
An
Updat
VERY SCIENTIFIC AUSTRALIAN
Oct 04
e ofIssue 1
the
Acknowledgements
Huma
8.
n
I thank my Supervisor, Prof. Peter Robinson for his tutelage throughout this TSP project. The time and patience
Brain
spent on us (especially the times when we were eating away at your schedule!) was greatly appreciated.
The field of
Thanks also to Peter Robens for his collaborative effort on this project.
neuroscien
ce and
Brain
Dynamics
is
Further
Reading
fast
emerging
in the Robinson PA, (2004). Propagator theory of brain dynamics. Physical Review E, 72: 011904
scientific
world Robinson
and
PA, (2003). Brain Waves. The Physicist, Vol 40, No. 5. pp 132-137
a working
knowledge
Robinson PA (2003). Interpretation of scaling properties of electroencephalographic fluctuations via
of the brain
spectral analysis and underlying physiology. Physical Review E, 67: 032902.
is important
to keep up!
The Robinson PA, Rennie, CJ, Rowe, DL (2003). Estimation of multiscale neurophysiologic parameters by
electroencephalographic
means. Human Brain Mapping, 23: 53-72.
aspects
of
the brain
that are
Robinson PA, Rennie CJ, Rowe DL (2003). Neurophysical modelling of brain dynamics.
fundament
Neuropsychopharmacology, 28: S74-S79.
al to this
model
Robinson PA, Rennie CJ, Wright JJ, Bahramali H, Gordon E, Rowe DL (2001). Prediction of
include the
electroencephalographic spectra from neurophysiology. Physical Review E, 63: 021903.
neuron, the
thalamus
Rowe DL, Robinson PA, Gordon E. (2004). Stimulant drug action in attention deficit hyperactivity
and the
cortexdisorder
all of (ADHD): inference of neurophysiological mechanisms via quantitative modelling. Clinical
whichNeurphysiology,
are
2004: 1-12.
discussed
below.O’Connor SC, Robinson PA (2005) Analysis of electroencephalographic activity associated with thalamic
tumors. Journal of Theoretical Biology, 233 (2005) 271 - 286
The neuron
is the most
Wright JJ, Rennie
fundament
al unitand
of global scales.
the brain
and
nervous
system,
these cells
communic
ate to
each other
via
connection
s from
axons to
dendrites
across a
gap called
a synapse.
Impulses
propagate
CJ, Robinson PA (2003). Simulated electrocortical activity at microscopic, mesoscopic
Neuropsychopharmacology, 28: S80-S93.
9.