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