[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Computer modelling of the sinoatrial node

  • Special Issue
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

An Erratum to this article was published on 07 June 2007

Abstract

Over the past decades patch-clamp experiments have provided us with detailed information on the different types of ion channels that are present in the cardiac cell membrane. Sophisticated cardiac cell models based on these data can help us understand how the different types of ion channels act together to produce the cardiac action potential. In the field of biological pacemaker engineering, such models provide important instruments for the assessment of the functional implications of changes in density of specific ion channels aimed at producing stable pacemaker activity. In this review, an overview is given of the progress made in cardiac cell modelling, with particular emphasis on the development of sinoatrial (SA) nodal cell models. Also, attention is given to the increasing number of publicly available tools for non-experts in computer modelling to run cardiac cell models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  1. As set out in detail by Garny et al. [26], the model equations listed in the paper by Zhang et al. [93] do not match the simulation results presented in the same paper. The action potentials and current traces shown in Fig. 6 have been obtained with the correct equations, which are listed by Garny et al. as the ‘0D capable’ version of the models [26].

  2. There is a discrepancy between the percentages shown in Fig. 7 and those reported by Zhang et al. [95]. The most striking one is in the percentage obtained with the Dokos et al. model: 27.5% in Fig. 7 versus 0.8% in the study by Zhang et al. [95]. The latter discrepancy seems to be related to an error in current amplitudes in the study by Zhang et al. [95], e.g. in the sodium background current, which has a peak amplitude >100 nA in their implementation of the Dokos et al. model (their Fig. 3B), whereas the correct value is <40 pA (Fig. 5 of Ref. [16]).

References

  1. Beeler GW, Reuter H (1977) Reconstruction of the action potential of ventricular myocardial fibres. J Physiol 268:177–210

    Google Scholar 

  2. Bernus O, Wilders R, Zemlin CW, Verschelde H, Panfilov AV (2002) A computationally efficient electrophysiological model of human ventricular cells. Am J Physiol Heart Circ Physiol 282:H2296–H2308. DOI 10.1152/ajpheart.00731.2001

    Google Scholar 

  3. Bondarenko VE, Szigeti GP, Bett GC, Kim SJ, Rasmusson RL (2004) Computer model of action potential of mouse ventricular myocytes. Am J Physiol Heart Circ Physiol 287:H1378–H1403. DOI 10.1152/ajpheart.00185.2003

    Google Scholar 

  4. Boyett MR, Honjo H, Kodama I (2000) The sinoatrial node, a heterogeneous pacemaker structure. Cardiovasc Res 47:658–687. DOI 10.1016/S0008-6363(00)00135-8

    Google Scholar 

  5. Boyett MR, Zhang H, Garny A, Holden AV (2001) Control of the pacemaker activity of the sinoatrial node by intracellular Ca2+. Experiments and modeling. Philos Trans R Soc Lond A Math Phys Eng Sci 359:1091–1110. DOI 10.1098/rsta.2001.0818

    Google Scholar 

  6. Bristow DG, Clark JW (1982) A mathematical model of primary pacemaking cell in SA node of the heart. Am J Physiol 243:H207–H218

    Google Scholar 

  7. Cabo C, Boyden PA (2003) Electrical remodeling of the epicardial border zone in the canine infarcted heart: a computational analysis. Am J Physiol Heart Circ Physiol 284:H372–H384. DOI 10.1152/ajpheart.00512.2002

    Google Scholar 

  8. Courtemanche M, Ramirez RJ, Nattel S (1998) Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model. Am J Physiol 275:H301–H321

    Google Scholar 

  9. de Boer TP, van Veen TAB, Houtman MJC, Jansen JA, van Amersfoorth SCM, Doevendans PA, Vos MA, van der Heyden MAG (2006) Inhibition of cardiomyocyte automaticity by electrotonic application of inward rectifier current from Kir2.1 expressing cells. Med Biol Eng Comput 44:537–542. DOI 10.1007/s11517-006-0059-8

    Google Scholar 

  10. Demir SS (2006) Interactive cell modeling web-resource, iCell, as a simulation-based teaching and learning tool to supplement electrophysiology education. Ann Biomed Eng 34:1077–1087. DOI 10.1007/s10439-006-9138-0

    Google Scholar 

  11. Demir SS, Clark JW, Murphey CR, Giles WR (1994) A mathematical model of a rabbit sinoatrial node cell. Am J Physiol 266:C832–C852

    Google Scholar 

  12. Demir SS, Clark JW, Giles WR (1999) Parasympathetic modulation of sinoatrial node pacemaker activity in rabbit heart: a unifying model. Am J Physiol 276:H2221–H2244

    Google Scholar 

  13. Denyer JC (1989) Isolation and electrophysiological characteristics of rabbit sino-atrial node cells. Ph.D. thesis, University of Oxford

  14. DiFrancesco D, Noble D (1985) A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philos Trans R Soc Lond B Biol Sci 307:353–398

    Article  Google Scholar 

  15. DiFrancesco D, Noble D (1989) Current If and its contribution to cardiac pacemaking. In: Jacklet JW (ed) Neuronal and cellular oscillators. Marcel Dekker, New York, pp 31–57. ISBN 0-8247-8030-2

  16. Dokos S, Celler B, Lovell N (1996) Ion currents underlying sinoatrial node pacemaker activity: a new single cell mathematical model. J Theor Biol 181:245–272. DOI 10.1006/jtbi.1996.0129

    Google Scholar 

  17. Dokos S, Celler BG, Lovell NH (1996) Vagal control of sinoatrial rhythm: a mathematical model. J Theor Biol 182:21–44. DOI 10.1006/jtbi.1996.0141

    Google Scholar 

  18. Drouhard JP, Roberge FA (1987) Revised formulation of the Hodgkin–Huxley representation of the sodium current in cardiac cells. Comput Biomed Res 20:333–350. DOI 10.1016/0010-4809(87)90048-6

    Google Scholar 

  19. Earm YE, Noble D (1990) A model of the single atrial cell: relation between calcium current and calcium release. Proc R Soc Lond B Biol Sci 240:83–96

    Google Scholar 

  20. Endresen LP, Hall K, Høye JS, Myrheim J (2000) A theory for the membrane potential of living cells. Eur Biophys J 29:90–103. DOI 10.1007/s002490050254

    Google Scholar 

  21. Fenton F, Karma A (1998) Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: filament instability and fibrillation. Chaos 8:20–47. DOI 10.1063/1.166311

    Google Scholar 

  22. Fenton FH, Cherry EM, Hastings HM, Evans SJ (2002) Real-time computer simulations of excitable media: JAVA as a scientific language and as a wrapper for C and FORTRAN programs. Biosystems 64:73–96. DOI 10.1016/S0303-2647(01)00177-0

    Google Scholar 

  23. FitzHugh R (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1:445–466

    Google Scholar 

  24. Fox JJ, McHarg JL, Gilmour RF Jr (2002) Ionic mechanism of electrical alternans. Am J Physiol Heart Circ Physiol 282:H516–H530. DOI 10.1152/ajpheart.00612.2001

    Google Scholar 

  25. Garny A, Noble PJ, Kohl P, Noble D (2002) Comparative study of rabbit sino-atrial node cell models. Chaos Solitons Fractals 13:1623–1630. DOI 10.1016/S0960-0779(01)00171-0

    Google Scholar 

  26. Garny A, Kohl P, Hunter PJ, Boyett MR, Noble D (2003) One-dimensional rabbit sinoatrial node models: benefits and limitations. J Cardiovasc Electrophysiol 14:S121–S132. DOI 10.1046/j.1540.8167.90301.x

    Google Scholar 

  27. Garny A, Kohl P, Noble D (2003) Cellular open resource (COR): a public CellML based environment for modelling biological function. Int J Bifurcat Chaos 13:3579–3590. DOI 10.1142/S021812740300882X

    Google Scholar 

  28. Greenstein JL, Winslow RL (2002) An integrative model of the cardiac ventricular myocyte incorporating local control of Ca2+ release. Biophys J 83:2918–2945

    Google Scholar 

  29. Guevara MR, Lewis TJ (1995) A minimal single-channel model for the regularity of beating in the sinoatrial node. Chaos 5:174–183. DOI 10.1063/1.166065

    Google Scholar 

  30. Guo J, Ono K, Noma A (1995) A sustained inward current activated at the diastolic potential range in rabbit sino-atrial node cells. J Physiol 483:1–13

    Google Scholar 

  31. Hedley WJ, Nelson MR, Bullivant DP, Nielsen PF (2001) A short introduction to CellML. Philos Trans R Soc Lond A Math Phys Eng Sci 359:1073–1089. DOI 10.1098/rsta.2001.0817

    Google Scholar 

  32. Henriquez CS (1993) Simulating the electrical behavior of cardiac tissue using the bidomain model. Crit Rev Biomed Eng 21:1–77

    Google Scholar 

  33. Hilgemann DW, Noble D (1987) Excitation–contraction coupling and extracellular calcium transients in rabbit atrium: reconstruction of the basic cellular mechanisms. Proc R Soc Lond B Biol Sci 230:163–205

    Google Scholar 

  34. Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500–544

    Google Scholar 

  35. Hund TJ, Rudy Y (2004) Rate dependence and regulation of action potential and calcium transient in a canine cardiac ventricular cell model. Circulation 110:3168–3174. DOI 10.1161/01.CIR.0000147231.69595.D3

    Google Scholar 

  36. Irisawa H, Noma A (1982) Pacemaker mechanisms of rabbit sinoatrial node cells. In: Bouman LN, Jongsma HJ (eds) Cardiac rate and rhythm: physiological, morphological, and developmental aspects. Martinus Nijhoff, London, pp 35–51. ISBN 90-247-2626-3

  37. Irisawa H, Brown HF, Giles W (1993) Cardiac pacemaking in the sinoatrial node. Physiol Rev 73:197–227

    Google Scholar 

  38. Iyer V, Mazhari R, Winslow RL (2004) A computational model of the human left-ventricular epicardial myocyte. Biophys J 87:1507–1525. DOI 10.1529/biophysj.104.043299

    Google Scholar 

  39. Jafri S, Rice JR, Winslow RL (1998) Cardiac Ca2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys J 74:1149–1168

    Google Scholar 

  40. Joyner RW, Wilders R, Wagner MB (2006) Propagation of pacemaker activity. Med Biol Eng Comput. DOI 10.1007/s11517-006-0102-9 (in press)

  41. Kneller J, Ramirez RJ, Chartier D, Courtemanche M, Nattel S (2002) Time-dependent transients in an ionically based mathematical model of the canine atrial action potential. Am J Physiol Heart Circ Physiol 282:H1437–H1451. DOI 10.1152/ajpheart.00489.2001

    Google Scholar 

  42. Krogh-Madsen T, Schaffer P, Skriver AD, Taylor LK, Pelzmann B, Koidl B, Guevara MR (2005) An ionic model for rhythmic activity in small clusters of embryonic chick ventricular cells. Am J Physiol Heart Circ Physiol 289:H398–H413. DOI 10.1152/ajpheart.00683.2004

    Google Scholar 

  43. Kurata Y, Hisatome I, Imanishi S, Shibamoto T (2002) Dynamical description of sinoatrial node pacemaking: improved mathematical model for primary pacemaker cell. Am J Physiol Heart Circ Physiol 283:H2074–H2101. DOI 10.1152/ajpheart.00900.2001

    Google Scholar 

  44. Kurata Y, Hisatome I, Imanishi S, Shibamoto T (2003) Roles of L-type Ca2+ and delayed-rectifier K+ currents in sinoatrial node pacemaking: insights from stability and bifurcation analyses of a mathematical model. Am J Physiol Heart Circ Physiol 285:H2804–H2819. DOI 10.1152/ajpheart.01050.2002

    Google Scholar 

  45. Kurata Y, Hisatome I, Matsuda H, Shibamoto T (2005) Dynamical mechanisms of pacemaker generation in IK1-downregulated human ventricular myocytes: insights from bifurcation analyses of a mathematical model. Biophys J 89:2865–2887. DOI 10.1529/biophysj.105.060830

    Google Scholar 

  46. Lei M, Brown HF (1996) Two components of the delayed rectifier potassium current, IK, in rabbit sino-atrial node cells. Exp Physiol 81:725–741

    Google Scholar 

  47. Lei M, Honjo H, Kodama I, Boyett MR (2000) Characterisation of the transient outward K+ current in rabbit sinoatrial node cells. Cardiovasc Res 46:433–441. DOI 10.1016/S0008-6363(00)00036-5

    Google Scholar 

  48. Lindblad DS, Murphey CR, Clark JW, Giles WR (1996) A model of the action potential and underlying membrane currents in a rabbit atrial cell. Am J Physiol 271:H1666–H1691

    Google Scholar 

  49. Lloyd CM, Halstead MD, Nielsen PF (2004) CellML: its future, present and past. Prog Biophys Mol Biol 85:433–450. DOI 10.1016/j.pbiomolbio.2004.01.004

    Google Scholar 

  50. Lovell NH, Cloherty SL, Celler BG, Dokos S (2004) A gradient model of cardiac pacemaker myocytes. Prog Biophys Mol Biol 85:301–323. DOI 10.1016/j.pbiomolbio.2003.12.001

    Google Scholar 

  51. Luo C-H, Rudy Y (1991) A model of the ventricular cardiac action potential: depolarization, repolarization and their interaction. Circ Res 68:1501–1526

    Google Scholar 

  52. Luo C-H, Rudy Y (1994) A dynamic model of the cardiac ventricular action potential, I: simulations of ionic currents and concentration changes. Circ Res 74:1071–1096

    Google Scholar 

  53. Maltsev VA, Vinogradova TM, Bogdanov KY, Lakatta EG, Stern MD (2004) Diastolic calcium release controls the beating rate of rabbit sinoatrial node cells: numerical modeling of the coupling process. Biophys J 86:2596–2605

    Google Scholar 

  54. Mangoni ME, Traboulsie A, Leoni AL, Couette B, Marger L, Le Quang K, Kupfer E, Cohen-Solal A, Vilar J, Shin HS, Escande D, Charpentier F, Nargeot J, Lory P (2006) Bradycardia and slowing of the atrioventricular conduction in mice lacking CaV3.1/α1G T-type calcium channels. Circ Res 98:1422–1430. DOI 10.1161/01.RES.0000225862.14314.49

    Google Scholar 

  55. Matsuoka S, Sarai N, Kuratomi S, Ono K, Noma A (2003) Role of individual ionic current systems in ventricular cells hypothesized by a model study. Jpn J Physiol 53:105–123. DOI 10.2170/jjphysiol.53.105

    Google Scholar 

  56. Mazhari R, Greenstein JL, Winslow RL, Marban E, Nuss HB (2001) Molecular interactions between two long-QT syndrome gene products, HERG and KCNE2, rationalized by in vitro and in silico analysis. Circ Res 89:33–38. DOI 10.1161/hh1301.093633

    Google Scholar 

  57. McAllister RE, Noble D, Tsien RW (1975) Reconstruction of the electrical activity of cardiac Purkinje fibres. J Physiol 251:1–59

    Google Scholar 

  58. Mitsuiye T, Shinagawa Y, Noma A (2000) Sustained inward current during pacemaker depolarization in mammalian sinoatrial node cells. Circ Res 87:88–91

    Google Scholar 

  59. Noble D (1960) Cardiac action and pacemaker potentials based on the Hodgkin–Huxley equations. Nature 188:495–497

    Article  Google Scholar 

  60. Noble D (1962) A modification of the Hodgkin–Huxley equations applicable to Purkinje fibre action and pace-maker potentials. J Physiol 160:317–352

    Google Scholar 

  61. Noble D, Noble SJ (1984) A model of sino-atrial node electrical activity based on a modification of the DiFrancesco–Noble (1984) equations. Proc R Soc Lond B Biol Sci 222:295–304

    Article  Google Scholar 

  62. Noble D, DiFrancesco D, Denyer JC (1989) Ionic mechanisms in normal and abnormal cardiac pacemaker activity. In: Jacklet JW (ed) Neuronal and cellular oscillators. Marcel Dekker, New York, pp 59–85. ISBN 0-8247-8030-2

  63. Noble D, Noble SJ, Bett GC, Earm YE, Ho WK, So IK (1991) The role of sodium–calcium exchange during the cardiac action potential. Ann NY Acad Sci 639:334–353

    Article  Google Scholar 

  64. Noble D, Denyer JC, Brown HF, DiFrancesco D (1992) Reciprocal role of the inward currents i b,Na and i f in controlling and stabilizing pacemaker frequency of rabbit sino-atrial node cells. Proc R Soc Lond B Biol Sci 250:199–207

    Article  Google Scholar 

  65. Noble D, Varghese A, Kohl P, Noble P (1998) Improved guinea-pig ventricular cell model incorporating a diadic space, iKr and iKs, and length- and tension-dependent processes. Can J Cardiol 14:123–134

    Google Scholar 

  66. Nordin C (1993) Computer model of membrane current and intracellular Ca2+ flux in the isolated guinea pig ventricular myocyte. Am J Physiol 265:H2117–H2136

    Google Scholar 

  67. Nygren A, Fiset C, Firek L, Clark JW, Lindblad DS, Clark RB, Giles WR (1998) Mathematical model of an adult human atrial cell: the role of K+ currents in repolarization. Circ Res 82:63–81

    Google Scholar 

  68. Pandit SV, Clark RB, Giles WR, Demir SS (2001) A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes. Biophys J 81:3029–3051

    Google Scholar 

  69. Potse M, Dubé B, Richer J, Vinet A, Gulrajani RM (2006) A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart. IEEE Trans Biomed Eng (in press). DOI 10.1109/TBME.2006.880875 (in press)

  70. Priebe L, Beuckelmann DJ (1998) Simulation study of cellular electric properties in heart failure. Circ Res 82:1206–1223

    Google Scholar 

  71. Puglisi JL, Bers DM (2001) LabHEART: an interactive computer model of rabbit ventricular myocyte ion channels and Ca transport. Am J Physiol Cell Physiol 281:C2049–C2060

    Google Scholar 

  72. Ramirez RJ, Nattel S, Courtemanche M (2000) Mathematical analysis of canine atrial action potentials: rate, regional factors, and electrical remodeling. Am J Physiol Heart Circ Physiol 279:H1767–H1785

    Google Scholar 

  73. Reiner VS, Antzelevitch C (1985) Phase resetting and annihilation in a mathematical model of sinus node. Am J Physiol 249:H1143–H1153

    Google Scholar 

  74. Rosen MR, Brink PR, Cohen IS, Robinson RB (2006) Biological pacemakers based on If. Med Biol Eng Comput. DOI 10.1007/s11517-006-0060-2 (in press)

  75. Sarai N, Matsuoka S, Kuratomi S, Ono K, Noma A (2003) Role of individual ionic current systems in the SA node hypothesized by a model study. Jpn J Physiol 53:125–134. DOI 10.2170/jjphysiol.53.125

    Google Scholar 

  76. Sarai N, Matsuoka S, Noma A (2006) SimBio: a Java package for the development of detailed cell models. Prog Biophys Mol Biol 90:360–377. DOI 10.1016/j.pbiomolbio.2005.05.008

    Google Scholar 

  77. Shannon TR, Wang F, Puglisi J, Weber C, Bers DM (2004) A mathematical treatment of integrated Ca dynamics within the ventricular myocyte. Biophys J 87:3351–3371. DOI 10.1529/biophysj.104.047449

    Google Scholar 

  78. Shinagawa Y, Satoh H, Noma A (2000) The sustained inward current and inward rectifier K+ current in pacemaker cells dissociated from rat sinoatrial node. J Physiol 523:593–605

    Article  Google Scholar 

  79. Silva J, Rudy Y (2003) Mechanism of pacemaking in IK1-downregulated myocytes. Circ Res 92:261–263. DOI 10.1161/01.RES.0000057996.20414.C6

    Google Scholar 

  80. ten Tusscher KHWJ, Panfilov AV (2006) Alternans and spiral breakup in a human ventricular tissue model. Am J Physiol Heart Circ Physiol 291:H1088–H1100. DOI 10.1152/ajpheart.00109.2006

    Google Scholar 

  81. ten Tusscher KHWJ, Noble D, Noble PJ, Panfilov AV (2004) A model for human ventricular tissue. Am J Physiol Heart Circ Physiol 286:H1573–H1589. DOI 10.1152/ajpheart.00794.2003

    Google Scholar 

  82. ten Tusscher KHWJ, Bernus O, Hren R, Panfilov AV (2006) Comparison of electrophysiological models for human ventricular cells and tissues. Prog Biophys Mol Biol 90:326–345. DOI 10.1016/j.pbiomolbio.2005.05.015

    Google Scholar 

  83. van Capelle FJL, Durrer D (1980) Computer simulation of arrhythmias in a network of coupled excitable elements. Circ Res 47:454–466

    Google Scholar 

  84. van der Pol B, van der Mark J (1928) The heartbeat considered as a relaxation oscillation and an electrical model of the heart. Philos Mag 6:763–775

    Google Scholar 

  85. Verkerk AO, van Ginneken ACG (2001) Considerations in studying the transient outward K+ current in cells exhibiting the hyperpolarization-activated current. Cardiovasc Res 52:517–520. DOI 10.1016/S0008-6363(01)00482-5

    Google Scholar 

  86. Viswanathan PC, Coles JA Jr, Sharma V, Sigg DC (2006) Recreating an artificial biological pacemaker: insights from a theoretical model. Heart Rhythm 3:824–831. DOI 10.1016/j.hrthm.2006.03.012

    Google Scholar 

  87. Wilders R (2006) Dynamic clamp: a powerful tool in cardiac electrophysiology. J Physiol 576:349–359. DOI 10.1113/jphysiol.2006.115840

    Google Scholar 

  88. Wilders R, Jongsma HJ (1993) Beating irregularity of single pacemaker cells isolated from the rabbit sinoatrial node. Biophys J 65:2601–2613

    Article  Google Scholar 

  89. Wilders R, Jongsma HJ, van Ginneken ACG (1991) Pacemaker activity of the rabbit sinoatrial node: a comparison of mathematical models. Biophys J 60:1202–1216

    Google Scholar 

  90. Winslow RL, Rice J, Jafri S, Marbán E, O’Rourke B (1999) Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, II: model studies. Circ Res 84:571–586

    Google Scholar 

  91. Yanagihara K, Noma A, Irisawa H (1980) Reconstruction of sino-atrial node pacemaker potential based on the voltage clamp experiments. Jpn J Physiol 30:841–857

    Google Scholar 

  92. Zaniboni M, Pollard AE, Yang L, Spitzer KW (2000) Beat-to-beat repolarization variability in ventricular myocytes and its suppression by electrical coupling. Am J Physiol Heart Circ Physiol 278:H677–H687

    Google Scholar 

  93. Zhang H, Holden AV, Kodama I, Honjo H, Lei M, Varghese T, Boyett MR (2000) Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node. Am J Physiol Heart Circ Physiol 279:H397–H421

    Google Scholar 

  94. Zhang H, Holden AV, Noble D, Boyett MR (2002) Analysis of the chronotropic effect of acetylcholine on sinoatrial node cells. J Cardiovasc Electrophysiol 13:465–474. DOI 10.1046/j.1540-8167.2002.00465.x

    Google Scholar 

  95. Zhang H, Holden AV, Boyett MR (2002) Sustained inward current and pacemaker activity of mammalian sinoatrial node. J Cardiovasc Electrophysiol 13:809–812. DOI 10.1046/j.1540-8167.2002.00809.x

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physiology, Academic Medical Center, University of Amsterdam, Meibergdreef 15, 1105 AZ, Amsterdam, The Netherlands

    Ronald Wilders

Authors
  1. Ronald Wilders
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ronald Wilders.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s11517-006-0147-9

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wilders, R. Computer modelling of the sinoatrial node. Med Bio Eng Comput 45, 189–207 (2007). https://doi.org/10.1007/s11517-006-0127-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-006-0127-0

Keywords

Search

Navigation