Quadratic Sample Entropy of the Electroencephalogram in Alzheimer’s Disease

Transcription

Quadratic Sample Entropy of the Electroencephalogram in Alzheimer’s Disease
Quadratic Sample Entropy of the
Electroencephalogram in Alzheimer’s Disease
A Corin Group Prize, IMechE Presentation
Samantha Simons
Contents
1. Remit of the project
2. Introduction into Alzheimer’s Disease and the techniques used
in this project
3. Overview of the techniques used and their results
4. Discussion of results
5. Identification of further work
6. Conclusions
7. Questions
Project Scope
• The aim is to analyse the electrical activity of the brain –
recorded in the electroencephalogram (EEG) –using non-linear
techniques to investigate the changes caused by Alzheimer’s
Disease (AD)
• Why non-linear analysis? Non-linearity in the brain is introduced
even at the cellular level → Non-linear analysis can help in the
characterisation of the electrical activity of the brain
Hypotheses:
1. The repetition of patterns in the signals of AD patients will be
significantly different to that of control subjects
2. The EEG of AD patients will be more regular/repetitive than that
of control subjects due to a reduced neurone network and
increased plaques interfering with neurotransmissions
Alzheimer’s Disease
• AD is the biggest cause of Dementia in the western world
• It is caused by degeneration of the nerve cells of the brain but
the cause of this is still unknown
• Diagnosis is currently made through a review of medical history
and tests on mental and physical abilities
Image courtesy of the Alzheimer’s Disease Education and
Referral Centre, National Institute of Aging
The EEG and the Subject Group
• An EEG is a recording of the electrical
activity of the brain caused by the
synchronised firing of neurones
• The EEG was recorded using the
international 10-20 electrode placement
system in a resting but awake state with
eyes closed
• 22 subjects, 11 AD patients with moderate
dementia and 11 age matched controls
• 5 second artefact free epochs were
selected
• These were then filtered using a bandpass filter between 0.5 and 40Hz to
further reduce interference
The 10-20 electrode placement
Image courtesy of MIT Cog Net
Entropy in Biological Systems
• Initial non-linear analysis techniques came from chaos theory
but the assumptions in the models were not conducive for use
with biological signals
• Entropy is a measure of repeatability within a time series, more
positive entropy signifies a less regular time series
• Entropy techniques developed specifically to cope with
biological signals have since been developed:
• Approximate entropy: useful, but lacks relative consistency
• Sample entropy: improvement, but dependent on
parameters
• New entropy analysis methods have been designed to try and
overcome these limitations
Quadratic Sample Entropy (QSE)-Theory
• QSE gives a numerical value for how well vectors match along
a given numerical series (i.e. an EEG epoch)
• m = length of the vector created from the time series
• r = tolerance for matching of the vector
• p = conditional probability that a set of subsequent points will
match for the same m and r
QSE = -ln(p/2r) = -ln(p) + ln(2r) = SampEn + ln(2r)
• Based on the Heavyside function
• Data were normalised and then the QSE was calculated for
each epoch for each separate electrode
• m was two integers between 1 and 2 and r four values
equidistant between 0.1 and 0.25
Quadratic Sample Entropy (QSE)-Results
• Statistical analysis
• Student’s t-test with p<0.01
• Receiver operating characteristic
(ROC) curves with accuracy
defined as the highest combined
sensitivity and specificity
• Entropy for AD patients was lower
than control subjects for all
electrodes with statistically
significant differences at the back of
the brain
• Most statistically significant
differences were seen when m=1
• Maximum accuracy was 81.8%
P<0.01
P<0.05
Statistically significantly different electrodes for AD
patients and control subjects for m=1, r=0.1
Fuzzy Entropy-Theory
• Fuzzy Entropy was calculated for each epoch for each separate
electrode
• Fuzzy Entropy gives a numerical value for how well vectors
match along a given numerical series
• m = length of the matching template
• r = tolerance for matching
Fuzzy Entropy = lnΦm – lnΦm+1
• Based on a fuzzy function
• n = power of the exponential
Fuzzyfunction = exp((-(dijm)n)/r)
Fuzzy Entropy-Results
• Entropy for AD patients was lower
than control subjects for all
electrodes with statistically
significant differences at the back
of the brain
• The most accurate results were
obtained with n=1 with more
statistically significant results when
m=2 in this instance.
• Maximum accuracy was 86.4%
• As n got larger the results had less
statistically significant differences
between the two groups
P<0.01
P<0.05
Statistically significantly different electrodes for AD
patients and control subjects for n=1, m=2, r=0.1
Multi-Scale Entropy (MSE)-Theory
• MSE allows for closer examination of the time series by
interrogating different time scales within the data series
• Two step process
• Coarsegraining of the time series
Scale 2
X1 X2 X3 X4 X5 X6 …... Xi Xi+1
Y1
Scale 3
Y2
Y3
…...
Yj =(Xi + Xi+1)/2
X1 X2 X3 X4 X5 X6 …... Xi Xi+1Xi+2
Y1
Y2
…...
Yj =(Xi + Xi+1 + Xi+2)/2
Figure modified from Costa, Goldberger and Peng, (2002)
• Sample Entropy Calculation for each coarsegrained
sequence
Multi-Scale Entropy with QSE-Results
• Preliminary results
• AD patients have a
significantly different
entropy profile for
sequentially
coarsegrained data
than control patients
• Entropy in the AD
patient is lower than
that of the control
until grain 10 or 11
• Large differences in
the entropy are
found around grain 6
Results for AD patient (dashed line) and control
patient (solid line) for m=2 r=0.25
Discussion
• First time QSE, Fuzzy Entropy and MSEQSE have been used in
EEG analysis in AD
• Statistically significant differences can be seen in all methodologies
at the back of the brain at electrodes O1, O2, P3 and P4
• QSE gives a more reliable entropy estimation than Sample Entropy,
although statistically similar results were found in this study
• Fuzzy Entropy is 9% more accurate than Approximate and Sample
Entropies (published in Clinical Neurophysiology and Medical and
Biological Engineering and Computing)
• Fuzzy Entropy shows statistically significant differences at more
electrodes than Sample Entropy, notably electrode T6
• Small group size
• Are the changes noted unique to AD?
Further Work
• Different approaches:
• Combine MSE with Fuzzy Entropy
• Introduce Multivariate techniques
• Further work with the methodologies already described
• Leave-one-out cross validation in the statistical analysis
• Compare subject-based classification with epoch-based
classification
• The short-term objective would be to publish the preliminary
results of this project
• The long-term objective would be to obtain an EEG entropy
threshold for AD diagnosis in a clinical setting
Conclutions
• All current results support the hypotheses given at the
beginning of the presentation → AD is characterised by a
significant decrease of the entropy of the EEG
• Further work must be completed in order to fully asses the
techniques available and the statistical significance of those
results
• The small sample size will limit this work to a pilot study.
Further subjects and more wide ranging disabilities would have
to be tested to carry out a large scale, clinically relevant, study
Acknowledgements
• Dr Daniel Abasolo for his continued support as my project
supervisor
• Dr Javier Escudero for his kind recommendations of Matlab
methodologies
• Prof Mike Hughes for making me aware of this project prize
• Jack Stone in reviewing the Matlab code
References
•
Healthcareinformation.org, Diagnosing Alzheimer’s Disease. Available at: www.healthcare-information.org/diseases/alzheimers/diagnosis.html (Accessed 20/feb/2012)
•
MIT Cog Net, The Brain Sciences Connection. Available at:
http://cognet.mit.edu/library/erefs/hackenlively/images/fig0015.16_p03_c015.jpg
(Accessed: 14/feb/2012)
•
Stam, C.J. (2005) Nonlinear dynamical analysis of EEG and MEG: Review of an emerging
field. Clinical neurophysiology, 116, pp. 2266-2301
•
Pincus, S.M. (1991) Approximate entropy as a measure of system complexity. Proc. Natl.
Acad. Sci., 88, pp. 2297-2301
•
Richman, J.S., Moorman, J.R. (2000) Physiological time-series analysis using approximate
entropy and sample entropy. Am J Physiol Heart Circ Physiol, 278, pp. H2039-H2049
•
Lake, D.E. (2011) Improved entropy rate estimation in physiological data. 33rd Annual
Conference of the IEEE EMBS, Boston, Massachusetts, USA, August 30-September 3
2011, pp. 1463-1466
•
Cheng, W., Wang, Z., Xie, H., Yu, W. (2007) Characterisation of surface EMG signal based
on fuzzy entropy. IEEE Transactions on Neural Systems and Rehabilitation Engineering,
15(2), pp. 266-272
•
Costa, M., Goldberger, A.L., Peng, C.-K. (2005) Multiscale entropy analysis of biological
signals. Physical review E, 71, 021906
Thank you for listening
Any Questions?
ROC Plots
x
y/11
x/11
ROC Plots
threshold
sensitivity
specificity
accuracy
area under
curve
-0.1286
0.7273
0.9091
0.8182
0.8347