Abstract
The following text is a review of mathematical models and computer simulation projects aimed at reproducing cardiac arrhythmogenic processes, operation of artificial pacemakers, and electrophysiological mechanisms related to high energy defibrillation. The aim of the text is to present key achievements in this area of basic electrophysiological research and to demonstrate future possibilities of cardiac computer models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
van der Pol B, van der Mark J. The heartbeat considered as a relaxation oscillation, and an electrical model of the heart. Philos Mag 1928;6:763–775.
van der Pol B. On “relaxation-oscillations”. Philos Mag 1926;2:978–992.
Bethe A. Die biologischen Rhythmus — Phaenomene als selbstaendige bzw. erzwungene Kippvorgange betrachtet. Pfluegers Arch Physiol 1940;244:1–42.
Roberge FA, Bhereur P, Nadeau RA. A cardiac pacemaker model. Med Biol Eng 1971;9:3–12.
Bhereur P, Roberge FA, Nadeau RA. A simulation unit for cardiac arrhythmias. Med Biol Eng 1971;9:13–21.
Hursta WN, Wells RT, Steinhaus BM. Real-time PC-based heart simulator. Abstracts of the AAMI Meeting, 1991; in press (abstr).
Mines GR. On dynamic equilibrium in the heart. J Physiol 1913;46:349–383.
Mines GR. On circulation excitations on heart muscles and their possible relation to tachycardia and fibrillation. Trans R Soc Can 1914;4:43–53.
Garrey WE. Nature of fibrillary contraction in the heart. Am J Physiol 1914;33:397–414.
Mayer AG. Rhythmical pulsation in scyphomedusae. Papers Torgugas Lab Carnegie Inst Wash 1908;1:115–131.
Arshavskii YI, Berkinblit MB, Kovalev SA, et al. Periodic transformation of rhythm in a nerve fiber with gradually changing properties. Biofizika 1964;9:365–371.
Ostwald W. Periodische Erscheinungen bei der Aufloesung des chrom in Saeuren. Zeit Phys Chem 1900;35:33–76, 204–256.
Smith EE, Guyton AC. An iron heart model for study of cardiac impulse transmission. Physiologist 1961;4:112 (abstract).
Nagumo J, Suzuki R, Sato S. Electrochemical Active Network. In: Notes of Professional Group on Nonlinear Theory of IECE, February 26, 1963; (in Japanese; cited in [14]).
Winfree AT. The Geometry of Biological Time. 1980; New York: Springer.
Farley BG, Clark WA. Activity in networks of neuron-like elements. In: Information theory, 4th London Symposium, (ed.) Cherry C. 1961; London: Butterworth’s.
Moe GK, Rheinboldt WC, Abildskov JA. A computer model of atrial fibrillation. Am Heart J 1964;67:200–220.
Balakhovskii IS. Several modes of excitation movement in ideal excitable tissue. Biophysics 1965;10:1175–1179.
Krinskii VI. Spread of excitation in an inhomogeneous medium. Biofizika 1966;11:676–683.
Gulko FB, Petrov AA. Mechanism of formation of closed pathways conduction in excitable media. Biofizika 1972;17:261–270.
Shcherbunov AI, Kukushkin NI, Saxon ME. Reverberator in a system of interrelated fibers described by the Noble equation. Biofizika 1973;18:519–525.
Allesie MA, Bonke FIM, Schopman FJG. Circus movement in rabbit atrial muscle as a mechanism of tachycardia. Circ Res 1973;33:54–62.
Allesie MA, Bonke FIM, Schopman FJG. Circus movement in rabbit atrial muscle as a mechanism of tachycardia. II. The role of non-uniform recovery of excitability of the occurrence of unidirectional block, as studied with multiple electrodes. Circ Res 1976;39:168–177.
Allesi MA, Bonke FIM, Schopman FJG. Circus movement in rabbit atrial muscle as a mechanism of tachycardia. III. The “leading circle” concept: a new model of circus movement in cardiac tissue without the involvement of an anatomical obstacle. Circ Res 1977; 41:9–18.
Moe GK. On the multiple wavelet hypothesis of atrial fibrillation. Arch Int pharmacodyn 1962;140:183–188.
Winfree AT. When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias. 1987; Princeton: Princeton University Press.
Winfree AT. Electrical instability in cardiac muscle: phase singularities and rotors. J Theor Biol 1989;138:353–405.
Swenne CA. Computer simulation of compound reentry. In: Computers in Cardiology New York: IEEE 1987;445–448.
Smith JM, Cohen RJ. Simple finite-element model accounts for wide range of cardiac dysrhythmias. Proc Natl Acad Sci USA 1984;81:233–237.
Ritzenberg AL, Smith JM, Grumbach MP, et al. Precursor to fibrillation in cardiac computer model. In: Computers in Cardiology (ed.) Ripley KL. New York: IEEE 1984; pp. 171–174.
Holley L, Uther J. A computer model of ventricular electrical activity and its application to ventricular arrhythmias. Austral Phys Eng Sci Med 1985;8:88–93.
Thakor NV, Eisenman LN. Three-dimensional computer model of the heart: fibrillation induced by extrastimulation. Comput Biomed Res 1989;22:532–545.
Fishier M, Thakor N. Tachyarrhythmia threshold of ischemic heart in 3-dimensional computer model. In: Proceedings of the Annual International Conference of the IEEE Engineering in Medicine in Biology Society (eds.) Kim Y, Spelman FA. New York: IEEE 1989;94–95.
Province R, Fishier M, Thakor N. Defibrillation threshold simulations on three-dimensional computer heart model. In: Proceedings of the Twelfth Annual International Conference on the IEEE Engineering in Medicine and Biology Society, (eds.) Pedersen PC, Onaral B. New York: IEEE 1990;638–639.
Malik M, Camm AJ. Computer model of cardiac repolarization processes and of the recovery sequence. Comput Biomed Res 1989;22:160–180.
van Capelle FJL, Durrer D. Computer simulation of arrhythmias in a network of coupled excitable elements. Circ Res 1980;47:454–466.
Janse MJ, van Capelle FJL. Electrotonic interactions across an inexcitable region as a cause of ectopic activity in acute myocardial ischemia. A study in intact porcine and canine hearts and computer models. Circ Res 1982;50:527–537.
Beeler GW, Reuter H. Reconstruction of the action potential of ventricular myocardial fibres. J Physiol 1977;268:177–210.
Barr RC, Plonsey R. Propagation of excitation in idealized anisotropic two-dimensional tissue. Biophys J 1984;45:1191–1202.
Roberge FA, Vinet A, Victori B. Reconstruction of propagated electrical activity with a two-dimensional model of anisotropic heart muscle. Circ Res 1986;58:461–475.
Kadish A, Shinnar M, Moore EN, et al. Interaction of fiber orientation and direction of impulse propagation with anatomic barriers in anisotropic canine myocardium. Circulation 1988;78:1478–1494.
Lesh DL, Pring M, Spear JF. Cellular uncoupling can unmask dispersion of action potential duration in ventricular myocardium. A computer modeling study. Circ Res 1989; 65:1426–1440.
Kogan BY, Karplus WJ, Pang AT. Simulation of nonlinear distributed parameter systems on the connection machine. Simulation 1990;55:271–281.
Kogan BY, Karplus WJ, Billett BS, et al. The simplified FitzHugh-Nagumo model with slow recovery properties and 2-D wave propagation. UCLA Technical Report CSD-900016, Los Angeles 1990.
Kogan BY, Karagueuzian HS, Karplus WJ, et al. Unidirectional conduction block caused by variations in pathway geometry: A new mechanism for reentry. J Am Coll Cardiol 1991;17:386A (abstr).
Jack JJB, Noble D, Tsien RW. Electric Current Flow in Excitable Cells. Oxford: Clarendon Press 1975.
Spach MS, Miller WT III, Geselowitz DB, et al. The discontinuous nature of propagation in normal canine muscle. Evidence for recurrent discontinuities of intracellular resistance that affect the membrane currents. Circ Res 1981;48:39–54.
Spach MS, Kootsey JM, Sloan JD. Active modulation of electrical coupling between cardiac cells of the dog. A mechanism for transient and steady state variations in conduction velocity. Circ Res 1982;51:347–362.
Rudy Y, Quan W. A model study of the effects of the discrete cellular structure on electrical propagation in cardiac tissue. Circ Res 1987;61:815–823.
Rudy Y, Quan W. The role of cellular discontinuities in reentry of cardiac excitation. In: Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society (eds.) Harris G, Walker C. New York: IEEE 1988;946–947.
Quan W, Rudy Y. Unidirectional block and reentry of cardiac excitation. A model study. Circ Res 1990;66:367–382.
Malik M, Camm AJ. Discrete model of myocardial electrotonic interactions. In: Proceedings of the Twelfth Annual International Conference on the IEEE Engineering in Medicine and Biology Society (eds.) Pedersen PC, Onaral B. New York: IEEE 1990;610–611.
Malik M, Camm AJ. Computer simulation of myocardial fibrillation using a one-dimensional model of excitation and recovery processes. Cardiovasc Res 1989;23:132–144.
Malik M, Camm AJ. Computer simulation of electrotonic interactions during excitation and repolarization of myocardial tissue. Med Biol Eng Comput 1991; in press.
Millane RP, Bones PJ, Ikram H, et al. A computer model of cardiac conduction. Austral Phys Eng Sci Med 1980;3:205–209.
Heethaar RM, van der Gon DJJ, Meijler FL. Mathematical model of AV conduction in the rat heart. Cardiovasc Res 1973;7:14–18.
Ross DL, Dassen WR, Vanagt EJ, et al. Cycle length alternation in circus movement tachycardia using an atrioventricular accessory pathway. A study of the role of the atrioventricular node using a computer model of tachycardia. Circulation 1982; 65:862–868.
Dorveaux L, Heddle W, Jones M, et al. Examination of an exponential model of conduction through the human atrioventricular node. PACE 1985;8:646–655.
Malik M, Cochrane T, Davies DW, et al. Clinically relevant computer model of cardiac rhythm and pacemaker/heart interaction. Med Biol Eng Comput 1987;25:504–512.
Dassen WRM. A mathematical Model to Study Reentrant Cardiac Arrhythmias. Thesis, University of Limburg, Maastricht 1983.
Hagen CT, Dassen WRM, Bump TE, et al. Arrhythmia simulation by computer modeling of cardiac conduction. In: Computers in Cardiology (ed.) Ripley KL. New York: IEEE 1983; 217–220.
Malik M, Camm AJ. Compensating conduction times as a mechanism of alternating reentry tachycardia: computer modelling experiments. J Electrocardial 1989; 22:73–80.
Schamroth L, Sareli P. Compensating conduction times as a mechanism for alternation during reciprocating tachycardia. J Electrocardiol 1986;19:291–294.
Malik M, Davies DW, Cochrane T, et al. A one dimensional model of atrioventricular nodal conduction. Int J Bio-Med Comput 1987;21:13–32.
Malik M, Cochrane T, Camm AJ. Computer simulation of the cardiac conduction system. Comput Biomed Res 1983;16:454–468.
Wei D, Yamada G, Musha T, et al. Computer simulation of supraventricular tachycardia with the Wolff-Parkinson-White syndrome using three-dimensional heart models. J Electrocardiol 1990;23:261–273.
Goldberger AL, West BJ. Fractals in phsyiology and medicine. Yale J Biol Med 1987;60:421–435.
Barnsley MF, Massopust P, Strickland H, et al. Fractal modeling of biological structures. Ann New York Acad Sci 1987;504:179–194.
Caplan DT, Cohen RJ. Fibrillation vs. random noise: a comparison using dimensionality calculation. In: Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society (eds.) Kim Y, Spelman FA. New York: IEEE 1989;92–93.
Holden AV, Lab MJ. Chaotic behavior in excitable systems. Ann New York Acad Sci 1990;591:303–315.
Chialvo DR, Michaels D, Jalife J. Supernormal excitability as a mechanism of chaotic dynamics of activation in cardiac Purkinje fibers. Circ Res 1990;66:525–545.
Chialvo DR, Gilmour RF Jr, Jalife J. Low dimensional chaos in cardiac tissue. Nature 1990;343:653–657.
Vinet A, Chialvo DR, Jalife J. Irregular dynamics of excitation in biologic and mathematical models of cardiac cells. Ann New York Acad Sci 1990;601:281–298.
Doian AM, Horacek BM, Rautaharju PM. Evaluation of cardiac defibrillation using a computer model of the thorax. Med Instrument 1978;12:53–54.
Kothiyal KP, Shanakar B, Fogelson LJ, et al. Three-dimensional computer model of electric fields in internal defibrillation. Proc IEEE 1988;76:720–730.
Fahy JB, Kim Y, Ananthaswamy A. Optimal electrode configuration for external cardiac pacing and defibrillation: an inhomogeneous study. IEEE Trans Biomed Eng 1987;BME-34:743–748.
Barnett DW, Fahy JB, Wu H-J, et al. Finite element model applications in defibrillation and external cardiac pacing. In: Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society (eds.) Harris G, Walker C. New York: IEEE 1988;200–201.
Sepulveda NG, Echt DS, Wikswo JP Jr. Finite element models used for the analysis of cardiac defibrillation. In: Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society (eds.) Harris G, Walker C. New York: IEEE 1988;198–199.
Sepulveda NG, Wikswo JP Jr, Echt DS. Finite element analysis of cardiac difibri1lation current distributions. IEEE Trans Biomed Eng 1990; BME-37:354–365.
Plonsey R, Barr RC. Inclusion of junction elements in a linear cardiac model through secondary sources: application to difibrillation. Med Biol Eng Comput 1986;24:137–144.
Krassowska W, Pilkington TC, Ideker RE. Potential distribution in three-dimensional periodic myocardium — Part I: Solution with two-scale asymptotic analysis. IEEE Trans Biomed Eng 1990; BME-37:252–266.
Krassowska W, Frazier DW, Pilkington TC, et al. Potential distribution in three-dimensional periodic myocardium — Part II: Application to extracellular stimulation. IEEE Trans Biomed Eng 1990; BME-37:267–284.
Steinhaus BM. Estimation cardiac transmembrane activation and recovery times from unipolar and bipolar extracellular electrograms: A Simulation study. Circ Res 1989;64:449–462.
Dube B, LeBlanc AR. Contribution a la modelisation du systeme de conduction cardiaque. University of Montreal Technical Report IGB-86-11-01, Montreal 1986.
Ahlfeldt H, Tanaka H, Nygards M-E, et al. Computer simulation of cardiac pacing. PACE 1988;11:174–184.
Malik M, Nathan A, Camm AJ. Computer simulation of dual chamber pacemaker algorithms using a realistic heart model. PACE 1985;8:579–588.
Dassen W, Brugada P, den Dulk K, et al. A mathematical model to study pacemaker related tachyarrhythmias. In: Computers in Cardiology (ed.) Ripley KL. New York: IEEE 1983;407–410.
Dassen WRM, den Dulk K, Gorgels APM, et al. Evaluation of pacemaker performance using computer simulation. PACE 1985;8:795–805.
Malik M. Present status of computer models of heart-pacemaker interaction. Cardiovasc World Report 1989;2:4–10.
Fukushima M, Inoue M, Fukunami M, et al. Computer-assisted education system for arrhythmia (CAESAR). Comput Biomed Res 1984;17:376–388.
Byrd CB, Byrd CL. A computerized system for modeling pacemaker rhythm. J Electrocardiol 1987;20:Suppl. October:28–33.
Dassen WRM, van der Steld A, van Braam W, et al. PACTOT: A reprogrammable software pacing system. PACE 1985;8:574–578.
Malik M, Davies DW, Camm AJ. Limiting factors in the use of DDD pacemakers to prevent junctional reentry: computer modeling experiments. Clin Prog Pacing Electrophys 1986;4:137–146.
Malik M, Davies DW, Camm AJ. Computer modeling of DDD pacemakers for use in prophylaxis of junctional re-entry trachycardia. PACE 1987;10:839–852.
Malik M, Davies DW, Camm AJ. Modification of DDD pacing mode to prevent junctional reentry tachycardia: Computer modelling experiments. PACE 1988;11:1465–1478.
Malik M, Camm AJ. The pacemaker inverse problem — computer diagnosis of paced electrocardiograms. Comput Biomed Res 1988;21:289–306.
Malik M, Camm AJ. Diagnosis of paced electrocardiograms by inverse modeling of pacemaker actions. PACE 1988;11:2093–2100.
Stevenson WG, Nademanee K, Weiss JN, et al. Programmed electrical stimulation at potential ventricular reentry circuit sites. Comparison of observations in humans with predictions from computer simulations. Circulation 1989;80:793–806.
Shumaker JM, Clark JW, Giles WR, et al. A model of the muscarinic receptor-induced changes in K+-current and action potentials in the bullfrog atrial cell. Biophys J 1990;57:567–576.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media New York
About this chapter
Cite this chapter
Malik, M. (1993). Computer Modelling of Cardiac Arrhythmias. In: Ostadal, B., Dhalla, N.S. (eds) Heart Function in Health and Disease. Developments in Cardiovascular Medicine, vol 140. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3090-9_12
Download citation
DOI: https://doi.org/10.1007/978-1-4615-3090-9_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6350-7
Online ISBN: 978-1-4615-3090-9
eBook Packages: Springer Book Archive