Abstract
Electroencephalograph is one of the useful and favored instruments in diagnosing various brain disorders especially in epilepsy due to its non-invasive characteristic and ability in providing wealthy information about brain functions. While epileptic foci localization is possible with the aid of EEG signals, it relies greatly on the ability to ex-tract hidden information or pattern within electroencephalography signals. Flat electroencephalography being an enhancement of electroencephalography carries affluent information about seizure process. In the perspective of topological dynamical systems, epileptic seizure and Flat EEG are two equivalent object, hence, findings attained from Flat EEG can be implied on epileptic seizure. In other words, Flat EEG serves as a great alternative platform to study epileptic seizure. Although there exists various researches on Flat EEG utilizing various mathematical models, topological study on its states connectivity has yet to exist. Since both events of epileptic seizure and Flat EEG are continuous processes, topological studies on its states connectivity can provides great in-sight into seizure process. In this paper, structures of the events will be modelled and explored topologically. In addition, the extracted topological properties will also be interpreted physically. Based on the theorems derived, Flat EEG is found to be well-behaved from topological viewpoint.
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References
Panayiotopoulos, C.P.: Atlas of Epilepsies. Springer, London (1992)
Jahnecke, C.A.N., Schwarz, L., Sovierzoski, M.A., Azevedo, D.F.M., Argoud, F.I.M.: C++ Video-EEG processing system with sights to the epileptic seizure detection. In: World Congress on Medical Physics and Biomedical Engineering. IFMBE Proceedings, pp 1052–1055 (2007)
Sanei, S., Chambers, J.: EEG Signals Processing. Wiley, England (2007)
Popp, A.J., Deshaies, E.M.: A Guide to the Primary Care of Neurological Disorders. American Associations of Neurosurgeons, Thieme (2007)
Yudofsky, S.C., Hales, R.E.: The American Psychiatric Publishing Textbook of Neuropsychiatry and Behavioral Neurosciences. American Psychiatric Publishing, USA (2008)
Gilhus, N.E., Barnes, M.R., Brainin, M.: European Handbook of Neurological Management. Wiley, England (2011)
Miller, J.W., Cole, A.J.: Is it necessary to define the ictal onset zone with EEG prior to performing respective epilepsy surgery? Elsevier Epilepsy Behav. 20(2), 178–181 (2011)
Desco, M., Pascau, J., Pozo, M.A., Santos, A., Reig, S., Gispert, J., Garcia, B.P.: Multimodality localization of epileptic foci. In: Proceedings of SPIE, Medical Imaging Physiology and Function from Multidimensional Images, pp 362–370 (2001)
Tiihonen, J., Hari, R., Kjola, M., Nousiainen, U., Vapalahti, M.: Localization of epileptic foci using large-area magnetometer and functional brain anatomy. Ann. Neurol. 27(3), 283–290 (2004)
Evim, A., Canan, A.B., Haluk, B., Bulent, Y.: Computational analysis of epileptic focus localization. In: ACTA Press Anaheim, BioMed 2006 Proceedings of the 24th IASTED International Conference on Biomedical Engineering, pp 317–322 (2006)
Natasa, M., Malek, D., Ilker, Y., Prasanna, J.: 3-d source localization of epileptic foci integrating EEG and MRI data. Brain Topogr. 16(2), 111–119 (2003)
Toni, A., Aopa, N., Matti, S.H., Liro, P.J., Jouko, L., Aki, V., Mikko, S.: Bayesian analysis of the neuromagnetic inverse problem with lp-norm priors. Neuroimage 26(3), 870–884 (2005)
Jan, C.D.M., Fetsje, B., Pawel, G., Cezary, A.S., Maria, I.B., Heethaar, R.M.: A maximum-likelihood estimator for trial-to-trial variations in noisy MEG/EEG data sets. IEEE Trans. Biomed. Eng. 51(2), 2123–2138 (2004)
Fauziah, Z.: Dynamic profiling of electroencephalography data during seizure using fuzzy information space. Ph.D. Thesis, Universiti Teknologi Malaysia (2008)
Faisal, A.M.B., Tahir, A.: EEG signals during epileptic seizure as a semigroup of upper triangular matrices. Am. J. Appl. Sci. 7(4), 540–544 (2010)
Tan, L.K., Tahir, A.: Structural stability of flat electroencephalography. Life Sci. J. 11(8), 165–170 (2014)
Tahir, A., Tan, L.K.: Topological Conjugacy between seizure and flat electroencephalography. Sci. Publ. Am. J. Appl. Sci. 7(3), 1470–1476 (2010)
Munkres, J.R.: Topology. Pearson Prentice Halls, USA (2000)
Asano, E., Otto, M., Aashit, S., Csaba, J., Diane, C.C., Jean, G., Harry, T.C.: Qualitative visualization of ictal subdural EEG changes in children with neocortical focal seizures. Clin. Neurophysiol. 115(12), 2718–2727 (2004)
Davis, S.W.: Topology. McGraw-Hill, Singapore (2005)
Acknowledgement
The authors would like to thank their family members and friends, for their continuous support and assistance. The authors would also like to express his appreciation to Universiti Teknologi Malaysia. This research is supported by the university GUP Tier 1 grant Vot No. 15H42.
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Ken, T.L. et al. (2019). Topological Properties of Flat Electroencephalography. In: Kor, LK., Ahmad, AR., Idrus, Z., Mansor, K. (eds) Proceedings of the Third International Conference on Computing, Mathematics and Statistics (iCMS2017). Springer, Singapore. https://doi.org/10.1007/978-981-13-7279-7_25
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DOI: https://doi.org/10.1007/978-981-13-7279-7_25
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