MATHEMATICAL ANALYSIS OF ELECTROPHYSIOLOGICAL CARDIAC TISSUE MEMBRANE MODELS

  • U. H. Ojimadu
  • A. O. Oluwole
  • A. O. Olasupo
  • M. A. Usman
  • T. J. Odule
  • O. O. Olubanwo
  • O. Oyewole
  • M. A. Ayodele
Keywords: Cardiac electrophysiological models, Restitution curve, Computer simulation, Graphical analysis, Ring length

Abstract

This paper presents some cardiac electrophysiological models. Proper mathematical analysis was done on the proposed models. In the cause of the analysis, several assumptions were made which helped in providing a parallel platform for making qualitative solutions so as to reduce any form of bias. Graphical analysis was adopted in solving the cardiac electrophysiological models using conservation and dispersions equations. The results obtained were derived from computer simulation by observing ring lengths on a valid restitution curve. The restitution curves helps us to subject three different turns of ring lengths and certain observations were made on the behavior of the three ring lengths. An increase in ring length will cause a corresponding increase in blood circulation and vice versa. It was suggested that 2D or 3D computer simulation should be adopted for better performance and yield of the models

References

Adebisi OI, Adejumobi IA, Abiala IO, Omotainse SO. (2012). Mathematical Modelling of Cardiac Electrical Activity Using Bio domain Approach, Journal of Computation and Modelling. 2(3):109-126.

Efimov IR, Nikolski, VP, Salama G. (2004). Optical Imaging of the heart. Circulation Research 286, HZ183 eth 2194.

Hodgkin AI, Huxley AF. (1952). A quantitative description of membrane current and its application to conductor and excitation in nerve. The journal of physiology, 117(4): 500-544.

Fenton FH, Cherry EM. (2008). Models of Cardiac Cell. Scholarpedia, 3(8):1868.

Nash MP, Panfilov AV (2004). Electromechanical model of excitable tissue to study reentrant cardiac arrhythmias. Progress in Biophysics and Molecular Biology, 85(2-3): 501-522

FitzHugh R. (1955). Mathematical model of threshold phenomena in the nerve membrane. The bulletin of mathematical biophysics, 17(4):257-278.

Praveen KC, Neethu PR, Vishnu RN. (2016). Computation Cardiac Electrophysiology, IOSR Journal of Electrical and Electronics Engineering. E-ISSN: 2278-1676, P-ISSN; 2320-3331. 2(3):27-36

Henriquez CS, Papazogou AA. (1996). Using computer models to understand the roles of tissue structure and membrane dynamics.
Arrhythmogenesis. Proceedings of the IEEE 84, 334-354.

Clayton RH., Panfilov AV. (2008). A guide to Modelling Cardiac Electrical Activity in Anatomically Detailed Ventricles. Progress in Biophysics and Molecular Biology 96, 1943

Nash MP, Bradley CP, Sutton PM, Clayton RH, Kallis PH, Paterson MP, Taggart, DJ. (2006). Whole Heart Action Potential Duration Restitution Properties in Cardiac Patients. A combined Clinical and Modelling Study. Experimental Physiology 91 339e354

Niederer SA, Smith NP (2007). An Improved Numerical Method for strong Coupling of Excitation and Contraction Models in the Heart. Progress in Biophysics and Molecular Biology 96, 90e111

Guyton and Hall (1996) Textbook of Medical Physiology, W.B. Saunders Company, Philadephia

Beeler GW and Reuter H. (1977). Reconstruction of the action potential of the ventricular myocardial fibres, Journal of Physiological, 268(1): 177-210.

Boyett MR, Clough A, Dekanski J, Holden AV. (1997). Modelling Cardiac excitation and Excitability in A.V. Panfilov and A.V. Holden, Editors Computational Biology of the heart, ccb1-47, John Wiley and Sons Ltd, Chichester, U.K.

Belhamadia Y (2010) Recent Numerical Methods in Electrophysiology, In D. Campolo (Ed), New Development in Biomedical Engineering, Retrieved September 5, 2011 from Intech Open.

Keener, JP, Sneyd, J (1998) Mathematical Physiology. Springer-Verlag, New York.

Karma A, Levine H, Zou X (1994) Theory of pulse instability in electrophysiological models of excitable tissue, Physica D, 73:113-127.

Chialvo, DR, Gilmour RF and Jalife J (1990) Low dimensional chaos in cardiac tissue. Nature, 343: 653-657

Ito H and L. Glass (1992) Theory of reentrant excitation in a ring of cardiac tissue. Physica D, 56; 84-106.

Kogan, B.Y., W.J. Karplus and M.G. Karpoukhin (1995) The third other action potential for computer simulation of electrical wave propagation in cardiac tissue, in computer simulation in Biomedicine. H. Power and R.T. Hart. Editors, Computational Mechanics Publishers, Boston.
Published
2022-05-11
How to Cite
Ojimadu, U. H., Oluwole, A. O., Olasupo, A. O., Usman, M. A., Odule, T. J., Olubanwo, O. O., Oyewole, O., & Ayodele, M. A. (2022). MATHEMATICAL ANALYSIS OF ELECTROPHYSIOLOGICAL CARDIAC TISSUE MEMBRANE MODELS. FUDMA JOURNAL OF SCIENCES, 6(2), 138 - 143. https://doi.org/10.33003/fjs-2022-0602-931