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Modeling the cardiac tissue electrode interface using fractional calculus. (English) Zbl 1229.92018
Summary: The tissue electrode interface is common to all forms of biopotential recording (e.g., ECG, EMG, EEG) and functional electrical stimulation (e.g., pacemaker, cochlear implant, deep brain stimulation). Conventional lumped element circuit models of electrodes can be extended by generalization of the order of differentiation through modification of the defining current-voltage relationships. Such fractional order models provide an improved description of observed bioelectrode behaviour, but recent experimental studies of cardiac tissue suggest that additional mathematical tools may be needed to describe this complex system.

MSC:
92C30 Physiology (general)
78A70 Biological applications of optics and electromagnetic theory
26A33 Fractional derivatives and integrals
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[1] Bottelberghs, P.H., 1978, ”Low-frequency measurements on solid electrolytes and their interpretations,” in Solid Electrolytes: General Principles, Characterization, Materials, Applications, P. Hagenmuller and W. Van Gool, eds. Academic Press, New York, pp. 145-172.
[2] Cymes, G.D., Nature 438 pp 975– (2005) · doi:10.1038/nature04293
[3] Dissado, L.A., Nature 279 pp 685– (1979) · doi:10.1038/279685a0
[4] Dymond, A.M., IEEE Transactions on Biomedical Engineering 23 pp 274– (1976) · doi:10.1109/TBME.1976.324585
[5] Forde, M. and Ridgely, P., 2000, ”Implantable cardiac pacemakers,” in The Biomedical Engineering Handbook, J. D. Bronzino ed. CRC Press, Boca Raton, FL, pp. 1-12.
[6] Geddes, L.A., Electrodes and the Measurement of Bioelectric Events (1972)
[7] Grahame, D.C., Journal of Electrochemical Society 99 pp 370C– (1952) · doi:10.1149/1.2779638
[8] Greatbatch, W., Annals of the New York Academy of Science 148 pp 235– (1968) · doi:10.1111/j.1749-6632.1968.tb20352.x
[9] Grimnes, S., Bioimpedance and Bioelectricity Basics (2000)
[10] Gulrajani, R.M., Bioelectricity and Biomagnetism (1998)
[11] DOI: 10.1142/3779 · doi:10.1142/3779
[12] Jonscher, A.K., Dielectric Relaxation in Solids (1983)
[13] Latimar, D.C., IEEE Transactions on Biomedical Engineering 45 pp 1449– (1998) · doi:10.1109/10.730438
[14] Magin, R.L., Critical Reviews in Biomedical Engineering 32 (1) pp 1– (2004) · doi:10.1615/CritRevBiomedEng.v32.10
[15] Magin, R.L., Critical Reviews in Biomedical Engineering 32 (2) pp 105– (2004) · doi:10.1615/CritRevBiomedEng.v32.i2.10
[16] Magin, R.L., Critical Reviews in Biomedical Engineering 32 (3) pp 195– (2004) · doi:10.1615/CritRevBiomedEng.v32.i34.10
[17] Nyikos, L., Electrochimica Acta 30 pp 1533– (1985) · doi:10.1016/0013-4686(85)80016-5
[18] Ovadia, M. and Brink, P.R., 2000, ”Channels, ischemia and stunning: Cellular electrophysiology and intercellular communication,” in Myocardial Viability: A Clinical and Scientific Treatise, V. Dilsizian , ed. Futura, Mt. Kisco, NY , pp. 115-179.
[19] Ovadia, M., Electroanalysis 10 pp 262– (1998) · doi:10.1002/(SICI)1521-4109(199804)10:4<262::AID-ELAN262>3.0.CO;2-W
[20] Ovadia, M., Chemical Physics Letters 390 pp 445– (2004) · doi:10.1016/j.cplett.2004.04.046
[21] Ovadia, M., Chemical Physics Letters 424 pp 285– (2006) · doi:10.1016/j.cplett.2006.04.054
[22] Ovadia, M., Chemical Physics Letters 419 pp 277– (2006) · doi:10.1016/j.cplett.2005.11.053
[23] Plonsey, R., Bioelectric Phenomena (1969)
[24] Reilly, J.P., Applied Bioelectricity: From Electrical Stimulation to Electropathology (1998) · doi:10.1007/978-1-4612-1664-3
[25] Schwan, H.P., 1957, ”Electrical properties of tissue and cell suspensions,” in Advances in Biological and Medical Physics, Academic Press, New York, pp. 147-209.
[26] Schwan, H.P., Annals of the New York Academy of Science 148 pp 191– (1968) · doi:10.1111/j.1749-6632.1968.tb20349.x
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