The Bidomain Model of Cardiac Tissue: From Microscale to Macroscale

  • Craig S. Henriquez
  • Wenjun Ying

Cardiac tissue can be viewed as connected cells (myocytes), organized and tethered through an extracellular matrix to produce a contraction of the heart that is triggered by a highly coordinated spread of electrical activity. The currents underlying the propagation of impulses from cell to cell flow across the cell membrane and through both the intracellular and extracellular spaces in the heart. Over the past 30 years there has been considerable interest in the structures that couple the intracellular spaces of myocytes to one another and their role in arrhythmia.1,2 In cardiac tissue, this coupling takes place though the intercalated discs. The intercalated disc is an interwoven membrane separating adjacent cells and contains both adherens junctions, which anchor the contractile proteins and maintain mechanical strength during contraction, and gap junctions that permit small molecules and ions to pass freely between the cells.3 A gap junction is composed of two hemichannels (connexons), one in each cell, that come together and form a pore, which essentially establishes electrical connectivity.4,5 Under normal conditions, the propagation of action potentials involves both the flux of ions across voltage and ligand gated ion channels and from cell to cell. For the most part, the majority of the gap junctions are found at the ends of the irregularly shaped cardiac cells, although some appear at the lateral faces. The number of gap junctions between cells, in part, determines the strength of connection. It is widely believed that the more gap junctions present, the lower the electrical coupling resistance. These pores act like resistors in parallel in an electrical circuit. The type of proteins (connexins) that form the connexon also helps determine its electrical properties or conductance. Different connexin proteins are found in different regions of the heart.4

The other component of the intracellular resistance is determined by the micro- and nanostructures inside the cell itself. Like most muscle cells, most cardiac cells contain contractile proteins actin and myosin that are anchored by Z-lines. Ventricular mycotyes also possess a highly organized transverse-tubule (T-tubule) system. A T-tubule is a deep invagination of the plasma membrane that allows depolarization of the membrane to quickly penetrate to the interior of the cell. It effectively acts to bring the extracellular environment in proximity to the intracellular space of the cell.6 The presence of the T-tubules, proteins, and other structures will affect or limit ion mobility and flux and hence increase the intracellular resistance of the cell. In some heart cells (atrial cells, conduction system), however, the T-tubule system is less organized or effectively absent, and hence the electrical properties of these cells are expectedly different.6

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Severs NJ, Coppen SR, Dupont E, Yeh HI, Ko YS, Matsushita T. Gap junction alterations in human cardiac disease. Cardiovasc Res 2004;62:368–377PubMedCrossRefGoogle Scholar
  2. 2.
    Saffitz JE, Davis LM, Darrow BJ, Kanter HL, Laing JG, Beyer EC. The molecular-basis of anisotropy — role of gap-junctions. J Cardiovasc Electrophysiol 1995;6:498–510PubMedCrossRefGoogle Scholar
  3. 3.
    Severs NJ. Microscopy of the gap junction – a historical-perspective. Microsc Res Tech 1995;31:338–346PubMedCrossRefGoogle Scholar
  4. 4.
    Evans WH, Martin PE. Gap junctions: structure and function (review). Mol Membr Biol 2002;19:121–136PubMedCrossRefGoogle Scholar
  5. 5.
    Saffitz JE, Hoyt RH, Luke RA, Kanter HL, Beyer EC. Cardiac myocyte interconnections at gap-junctions — role in normal and abnormal electrical-conduction. Trends Cardiovasc Med 1992;2:56–60CrossRefGoogle Scholar
  6. 6.
    Brette F, Orchard C. T-tubule function in mammalian cardiac myocytes. Circ Res 2003;92:1182–1192PubMedCrossRefGoogle Scholar
  7. 7.
    Frank JS, Langer GA. Myocardial interstitium — its Structure and its role in ionic exchange. J Cell Biol 1974;60:586–601PubMedCrossRefGoogle Scholar
  8. 8.
    Baudino TA, Carver W, Giles W, Borg TK. Cardiac fibroblasts: friend or foe? Am J Physiol Heart Circ Physiol 2006;291:H1015–H1026PubMedCrossRefGoogle Scholar
  9. 9.
    Kleber AG, Rudy Y. Basic mechanisms of cardiac impulse propagation and associated arrhythmias. Physiol Rev 2004;84:431–488PubMedCrossRefGoogle Scholar
  10. 10.
    Kleber AG. Conduction of the impulse in the ischemic myocardium — implications for malignant ventricular arrhythmias. Experientia 1987;43:1056–1061PubMedCrossRefGoogle Scholar
  11. 11.
    Fleischhauer J, Lehmann L, Kleber AG. Electrical resistances of interstitial and microvascular space as determinants of the extracellular electrical-field and velocity of propagation in ventricular myocardium. Circulation 1995;92:587–594PubMedGoogle Scholar
  12. 12.
    Henriquez CS, Papazoglou AA. Using computer models to understand the roles of tissue structure and membrane dynamics in arrhythmogenesis. Proc IEEE 1996;84:334–354CrossRefGoogle Scholar
  13. 13.
    Pullan AJ, Cheng LK, Buist ML. Mathematically Modelling the Electrical Activity of the Heart: From Cell to Body Surface and Back Again. Hackensack, NJ: World Scientific;2005Google Scholar
  14. 14.
    Neu JC, Krassowska W. Homogenization of syncytial tissues. Crit Rev Biomed Eng 1993;21:137–199PubMedGoogle Scholar
  15. 15.
    Pennacchio M, Savare G, Franzone PC. Multiscale modeling for the bioelectric activity of the heart. Siam J Math Anal 2006;37:1333–1370CrossRefGoogle Scholar
  16. 16.
    Keener JP, Sneyd J. Mathematical Physiology, corrected 2nd edn. New York: Springer;2001Google Scholar
  17. 17.
    Hornung U. Homogenization and Porous Media. New York: Springer; 1997Google Scholar
  18. 18.
    Miller WT, Geselowitz DB. Simulation studies of electrocardiogram. 1. Normal heart.Circ Res 1978;43:301–315PubMedGoogle Scholar
  19. 19.
    Henriquez CS. Simulating the electrical behavior of cardiac tissue using the bidomain model. Crit Rev Biomed Eng 1993;21:1–77PubMedGoogle Scholar
  20. 20.
    Plonsey R, Barr RC. A critique of impedance measurements in cardiac tissue. Ann Biomed Eng 1986;14:307–322PubMedCrossRefGoogle Scholar
  21. 21.
    Jongsma HJ, Wilders R. Gap junctions in cardiovascular disease. Circ Res 2000;86:1193–1197PubMedGoogle Scholar
  22. 22.
    Weingart R, Maurer P. Action-potential transfer in cell pairs isolated from adult-rat and guinea-pig ventricles. Circ Res 1988;63:72–80PubMedGoogle Scholar
  23. 23.
    Shaw RM, Rudy Y. Ionic mechanisms of propagation in cardiac tissue — roles of the sodium and L-type calcium currents during reduced excitability and decreased gap junction coupling. Circ Res 1997;81:727–741PubMedGoogle Scholar
  24. 24.
    Legrice IJ, Smaill BH, Chai LZ, Edgar SG, Gavin JB, Hunter PJ. Laminar structure of the heart — ventricular myocyte arrangement and connective-tissue architecture in the dog. Am J Physiol Heart Circ Physiol 1995;38:H571–H582Google Scholar
  25. 25.
    Streeter DD Jr, Spotnitz HM, Patel DP, Ross J Jr, Sonnenblick EH. Fiber orientation in the canine left ventricle during diastole and systole. Circ Res 1969;24:339–347PubMedGoogle Scholar
  26. 26.
    Hsu EW, Henriquez CS. Myocardial fiber orientation mapping using reduced encoding diffusion tensor imaging. J Cardiovasc Mag Reson 2001;3:339–347CrossRefGoogle Scholar
  27. 27.
    Scollan DF, Holmes A, Winslow R, Forder J. Histological validation of myocardialmicrostructure obtained from diffusion tensor magnetic resonance imaging. Am J Physiol Heart Circ Physiol 1998;44:H2308–H2318Google Scholar
  28. 28.
    Gupta M, Rollins AM, Izatt JA, Efimov IR. Imaging of the atrioventricular node using optical coherence tomography. J Cardiovasc Electrophysiol 2002;13:95PubMedCrossRefGoogle Scholar
  29. 29.
    LeGrice I, Sands G, Hooks D, Gerneke D, Smaill B. Microscopic imaging of extended tissue volumes. Clin Exp Pharmacol Physiol 2004;31:902–905PubMedCrossRefGoogle Scholar
  30. 30.
    Franzone PC, Guerri L, Pennacchio M, Taccardi B. Spread of excitation in 3-D models of the anisotropic cardiac tissue. III. Effects of ventricular geometry and fiber structure on the potential distribution. Math Biosci 1998;151:51–98CrossRefGoogle Scholar
  31. 31.
    Taccardi B, Macchi E, Lux RL, Ershler PR, Spaggiari S, Baruffi S, Vyhmeister Y. Effect of myocardial fiber direction on epicardial potentials. Circulation 1994;90:3076–3090PubMedGoogle Scholar
  32. 32.
    Franzone PC, Guerri L, Pennacchio M, Taccardi B. Anisotropic mechanisms for mul-tiphasic unipolar electrograms: simulation studies and experimental recordings. Ann Biomed Eng 2000;28:1326–1342PubMedCrossRefGoogle Scholar
  33. 33.
    Roth BJ, Lin SF, Wikswo JP. Unipolar stimulation of cardiac tissue. J Electrocardiol 1998;31:6–12PubMedCrossRefGoogle Scholar
  34. 34.
    Trayanova NA, Roth BJ, Malden LJ. The Response of a spherical heart to a uniform electric-field — a bidomain analysis of cardiac stimulation. IEEE Trans Biomed Eng 1993;40:899–908PubMedCrossRefGoogle Scholar
  35. 35.
    Miller WT, Geselowitz DB. Simulation studies of electrocardiogram. 2. Ischemia and infarction. Circ Res 1978;43:315–323PubMedGoogle Scholar
  36. 36.
    Sepulveda NG, Roth BJ, Wikswo JP Jr. Current injection into a two-dimensional anisotropic bidomain. Biophys J 1989;55:987–999PubMedGoogle Scholar
  37. 37.
    Wikswo JP, Lin SF, Abbas RA. Virtual electrodes in cardiac tissue: a common mechanism for anodal and cathodal stimulation. Biophys J 1995;69:2195–2210PubMedCrossRefGoogle Scholar
  38. 38.
    Colli Franzone P, Guerri L, Taccardi B. Potential distributions generated by point stimulation in a myocardial volume: simulation studies in a model of anisotropic ventricular muscle. J Cardiovasc Electrophysiol 1993;4:438–458PubMedCrossRefGoogle Scholar
  39. 39.
    Muzikant AL, Hsu EW, Wolf PD, Henriquez CS. Region specific modeling of cardiac muscle: comparison of simulated and experimental potentials. Ann Biomed Eng 2002;30:867–883PubMedCrossRefGoogle Scholar
  40. 40.
    Spach MS, Barr RC. Effects of cardiac microstructure on propagating electrical waveforms. Circ Res 2000;86:E23–E28PubMedGoogle Scholar
  41. 41.
    Spach MS, Heidlage JF, Dolber PC, Barr RC. Extracellular discontinuities in cardiac muscle: evidence for capillary effects on the action potential foot. Circ Res 1998;83:1144–1164PubMedGoogle Scholar
  42. 42.
    Hooks DA, Tomlinson KA, Marsden SG, LeGrice IJ, Smaill BH, Pullan AJ, Hunter PJ.Cardiac microstructure — implications for electrical, propagation and defibrillation in the heart. Circ Res 2002;91:331–338PubMedCrossRefGoogle Scholar
  43. 43.
    Hou TY, Wu XH. A multiscale finite element method for elliptic problems in composite materials and porous media. J Comput Phys 1997;134:169–189CrossRefGoogle Scholar
  44. 44.
    Beard DA, Bassingthwaighte JB, Greene AS. Computational modeling of physiological systems. Physiol Genomics 2005;23:1–3PubMedCrossRefGoogle Scholar
  45. 45.
    Trew ML, Caldwell BJ, Sands GB, Hooks DA, Tai DCS, Austin TM, LeGrice IJ, Pullan AJ, Smaill BH. Cardiac electrophysiology and tissue structure: bridging the scale gap with a joint measurement and modelling paradigm. Exp Physiol 2006;91:355–370PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  • Craig S. Henriquez
    • 1
  • Wenjun Ying
    • 2
  1. 1.Duke UniversityDurhamUSA
  2. 2.Department of Biomedical EngineeringDuke UniversityDurhamUSA

Personalised recommendations