Fuzzy information graph of epileptic seizures
DOI:
https://doi.org/10.11113/mjfas.v10n1.69Keywords:
Electroencephalography, Epilepsy, Shannon entropy, Fuzzy graphAbstract
The mathematical modelling of EEG signals provides valuable data to neurologists, and is heavily utilized in the diagnosis and treatment of epilepsy. The erratic nature of these signals, coupled with their lack of a consistent visible trend results in a high degree of difficulty in forming a statistical model to describe seizures. Working with Delia-normalized signals, the authors compute the associated Shannon entropies for three sets of data, and show via construction that the information flow during an epileptic seizure can be viewed as a type-2 fuzzy graph.References
WHO, Epilepsy factsheet, 2009.
H. Gastaut, Epilepsia, vol. 11, no. 1, pp.102–112, 1970.
T. Ahmad, R. A. Fairuz, F. Zakaria, and H. Isa,Proceedings of the 7th WSEAS InternationalConference on Signal Processing, Robotics and Automation, pp. 270–273, World Scientific and Engineering Academy and Society _WSEAS_,Stevens Point,Wis, USA, 2008.
F. Zakaria, Universiti Teknologi Malaysia, 2008.
E. Niedermeyer and F. H. L. Silva, Medicine Series, Lippincott Williams &Wilkins, 2005.
A. Babloyantz and A. Destexhe, Proceedings of the National Academy of Sciences, 83(10) (1986) 3513.
C. J. Stam, Clinical Neurophysiology, 116(10) (2005) 2266.
L. D. Iasemidis, S. J. Chris, H. P. Zaveri, and W. J. Williams, Brain Topography, 2(3)(1990) 187.
G. W. Frank, T. Lookman, M. A. H. Nerenberg, C. Essex, J. Lemieux, and W. Blume, Physica D, 46(3)(1990) 427.
J. Theiler, Physics Letters A, 196(5-6) (1995) 335.
N. Schiff, J. Victor, A. Canel, and D. Labar, Biological Cybernetics, 72(6) (1995) 519.
R. Friedrich and C. Uhl, Physica D, 98(1) (1996) 171.
J. L. Hernndez, P. A. Valds, and P. Vila, NeuroReport, 7(13) (1996) 2246.
M. Le van Quyen, J. Martinerie, C. Adam, and F. J. Varela, Physical Review E, 56(3) (1997) 3401.
M. Feucht, U. Mller, H.Witte et al., Cerebral Cortex, 8(6) (1998) 524.
T. E. Peters, N. C. Bhavaraju, M. G. Frei, and I. Osorio, Journal of Clinical Neurophysiology, 18(6) (2001) 545.
C. E. Elger and K. Lehnertz, European Journal of Neuroscience, 10(2) (1998) 786.
J. Martinerie, C. Adam, M. Le van Quyen et al., Nature Medicine, 4 (1998) 1173.
H. R. Moser, B. Weber, H. G. Wieser, and P. F. Meier, Physica D, 130(3-4) (1999) 291.
Y. C. Lai, M. A. F. Harrison, M. G. Frei, and I. Osorio, Physical Review Letters, 91(6) (2003) Article ID 068102.
I. Osorio, M. A. Harrison, Y. C. Lai, andM. G. Frei, Journal of Clinical Neurophysiology, 18(3) (2001) 269.
M. A. F. Harrison, I. Osorio, M. G. Frei, S. Asuri, and Y. C. Lai, Chaos, 15(3) (2005) Article ID 33106.
S. Kalitzin, J. Parra, D. N. Velis, and F. H. Lopes da Silva, IEEE Transactions on Biomedical Engineering, 49(11) (2002) 1279.
W. van Drongelen, S. Nayak, D. M. Frim et al., Pediatric Neurology, 29(3) (2003) 207.
F. Mormann, R. G. Andrzejak, C. E. Elger, and K. Lehnertz, Brain, 130(2) (2007) 314.
P. McSharry, T. He, L. Smith, and L. Tarassenko, Medical and Biological Engineering and Computing, 40(4) (2002) 447.
D. Kugiumtzis and P. G. Larsson, Chaos in Brain?: Proceedings of theWorkshop, K. Lehnertz and C. E. Elger, Eds., pp. 329–332, World Scientific, 1999.
K. K. Jerger, T. I. Netoff, J. T. Francis et al., Journal of Clinical Neurophysiology, 18 (2001) 259.
S. Baillet and L. Garnero, IEEE Transactions on Biomedical Engineering, 44(5) (1997) 374.
J. R. StevensElectroencephalography and Clinical Neurophysiology, 12(2) (1960) 431.
O. Faust, R. U. Acharya, A. R. Allen, and C. M. LinIng´enierie et Recherche Biom´edicale, 29(1) (2008) 44.
N. Sivasankari and K. Thanushkodi, International Journal of Soft Computing Applications, 1(2) (2009) 1.
T. Ahmad, R. S. Ahmad, F. Zakaria, and L. L. Yun, in Proceedings of the BIOMED 2000, pp. 119–121, University of Malaya, September 2000.
T. Ahmad, R. S. Ahmad, W. E. Z. W. Abdul Rahman, L. L. Yun, and F. Zakaria, Journal of Interdisciplinary Mathematics, 11 (2008) 381.
A. Idris, T. Ahmad, and N. Maanin Proceedings of the International Conference on Applied Mathematics and Informatics, pp. 94–99, 2010.
Tahir Ahmad and Vinod Ramachandran, Journal of Applied Mathematics, (2012) Article ID 926358. doi:10.1155/2012/926358
Thomas M. Cover, Joy A. Thomas, John Wiley & Sons, 2006.
Tahir, A., Sabariah, B., Arshad, Khairil, Journal of Mathematical Chemistry 47(4) (2010) 1263.