Topological Basis of Flat Electroencephalography’s State Space
DOI:
https://doi.org/10.24203/ajet.v5i2.4756Keywords:
Epilepsy, Flat EEG, Topology, Dynamical Systems.Abstract
Neuroinverse problem are often associated with complex neuronal activity. It involves locating problematic neuron which usually a highly challenging task. While epileptic foci localization is possible with the aid of EEG signals, it relies greatly on the ability to extract hidden information or pattern within EEG signals. Flat EEG being an enhancement of EEG is a way of viewing electroencephalograph on the real plane. In the perspective of dynamical systems, the equivalency of epileptic seizure and Flat EEG is important since the underlying structure of Flat EEG is dynamic. In this paper, a basis for the topological space of Flat EEG is presented. It is expected to facilitate in the constructions of dynamic transformation from epileptic seizure to Flat EEG. It provides a better understanding on Flat EEG itself.
Â
References
Panayiotopoulos, C. P., Atlas of Epilepsies, 1st Edition, Springer-Verlag, London Limited. 2010; Chapter 1, pp: 5.
Jahnecke, C. A. N., Schwarz, L., Sovierzoski, M. A., Azevedo, D. F. M. and Argoud, F. I. M., “C++ Video-EEG Processing System With Sights to the Epileptic Seizure Detectionâ€, World Congress on Medical Physics and Biomedical Engineering, IFMBE Proceedings, 2007; 14(8): 1052-1055.
Wyllie, E., Gupta, A. and Lachhwani, D.K., The treatment of epilepsy: principles & practice, 4th Edition, Lippincott Williams & Wilkins, USA. 2006; pp: 1185.
Sharon, R., David, I.M. and Shlomo, Y., “Anticonvulsant efficiency, behavioral performance and cortisal levels: a comparison of carbamazepine (CBZ) and a fatty acid compound (SR-3)â€, Elsevier, Psychoneuroendocrinology. 2004; 29(2): 113-124.
Stefan, H. and Feuerstein, T. J., “Novel Anticonvulsant Drugsâ€, Elsevier, Pharmacology & Therapeutics. 2007; 113(1): 165-183.
Bennett, T. L., Ciritical issue in Neuropsychology: The Newropsychology of Epilepsy, 2nd Edition, Springer. 1992; pp: 88.
Kiymik, M.K., Guler, I., Dizibuyuk, A. and Akin, M., “Comparison of STFT wavelet transform methods in determining epileptic seizure activity in EEG signals for real-time applicationâ€, Elsevier, Computers in Biology and Medcine. 2005; 35(7): 603-616.
Desco, M., Pascau, J., Pozo, M. A., Santos, A., Reig, S., Gispert, J. and Garcia, B. P., “Multimodality localization of epileptic fociâ€, Physiology and Function from Multidimensional Images, Proceedings of SPIE, Medical Imaging. 2001; 4321(1): pp: 362-370.
Tiihonen, J., Hari, R., Kjola, M., Nousiainen, U. and Vapalahti, M., “Localization of epileptic foci using large-area magnetometer and functional brain anatomyâ€, Wiley, Annals, of Neurology. 2004; 27(3): 283-290.
Evim, A., Canan, A. B., Haluk, B. and Bulent, Y., “Computational analysis of epileptic focus localizationâ€, ACTA Press Anaheim, BioMed’06 Proceedings of the 24th IASTED international conference on Biomedical Engineering. 2006; pp 317-322.
Natasa, M., Malek, D., Ilker, Y. and Prasanna, J., “3-D source Localization of Epileptic Foci Integrating EEG and MRI Dataâ€, Springer-Verlag, Brain Topography. 2003; 16(2): 111-119.
Toni, A., Aopa, N., Matti, S. H., Liro, P. J. Jouko, L., Aki, V. and Mikko, S., “Bayesian analysis of the neuromagnetic inverse problem with lp-norm priorsâ€, Elsevier, Neuroimage. 2005; 26(3): 870-884.
Jan, C. D. M., Fetsje, B., Pawel, G., Cezary, A. S., Maria, I. B. and Heethaar, R. M. A., “Maximum-Likelihood Estimator For Trial-to-Trial Variations in Noisy MEG/EEG Data Setsâ€, IEEE Transactions on Biomedical Engineering. 2004; 51(2): 2123-2128.
Liau, L. Y., “Homeomorfisma Antara S2 Dan E2 MelaluiStrukturPermukaan Riemann Serta Deduksi Teknik Pembuktiannya Bagi Homeomorfisma Pemetaan Topologi Topografi Kabur (FTTM)â€, Master Thesis, UniversitiTeknologi Malaysia, Skudai. 2001.
Tahir, A., Rashdi, S. A., Liau, L. Y., Fauziah, Z. and Wan Eny Zarina, W. A. R., â€Homeomorphisms of Fuzzy Topographic Topological Mapping (FTTM)â€, UTM, Matematika. 2005; 21(1): 35-42.
Fauziah, Z., “Dynamic Profiling Of Electroencephalography Data During Seizure Using Fuzzy Information Spaceâ€, UniversitiTeknologi Malaysia, PhD Thesis, Skudai. 2008.
Eduard, G., Helwig, L. and Raine, W., “Visualization of Dynamical Systems. Elsevier, Future Generation Computer Systemsâ€, 1999; 15(1): 75-86.
Eugene, M. I., “Dynamical System in Neuroscience: The Geometry of Excitability and Burstingâ€, The MIT Press Cambridge, Massachusetts London England. 2007; pp: 8.
Tan, L. K., Tahir, A., Mohd, S. M. and Su. K. N., “Dynamical System of Flat Electroencephalographyâ€, Science Publications, American Journal of Applied Sciences. 2015; 12(7): 495-505.
Tahir, A. and Tan, L. K., “Topological Conjugacy between Seizure and Flat Electroencephalographyâ€, Science Publications, American Journal of Applied Sciences. 2010; 7(3): 1470-1476.
Tahir, A. and Tan, L. K., “Flows of Continuous-Time Dynamical Systems with No Periodic Ordbit as an Equivalence Class under Topological Conjugacy Relationâ€, Science Publications, Journal of Mathematics and Statistics. 2011; 7(3): 207-215.
Faisal, A. M. B. and Tahir, A., “EEG Signals During Epileptic Seizure as a Semigroup of Upper Triangular Matricesâ€, Science Publications, American Journal of Applied Sciences. 2010; 7(4): 540-544.
Tan, L. K. and Tahir, A., “Structural Stability of Flat Electroencephalographyâ€, Marsland Press, Life Science Journal-Acta Zhengzhou University Overseas Edition. 2014; 11(8): 165-170.
Downloads
Published
How to Cite
Issue
Section
License
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.