Skip to main content
SpringerLink
Log in

Approaches for determining cardiac bidomain conductivity values: progress and challenges

  • Review Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

Modelling the electrical activity of the heart is an important tool for understanding electrical function in various diseases and conduction disorders. Clearly, for model results to be useful, it is necessary to have accurate inputs for the models, in particular the commonly used bidomain model. However, there are only three sets of four experimentally determined conductivity values for cardiac ventricular tissue and these are inconsistent, were measured around 40 years ago, often produce different results in simulations and do not fully represent the three-dimensional anisotropic nature of cardiac tissue. Despite efforts in the intervening years, difficulties associated with making the measurements and also determining the conductivities from the experimental data have not yet been overcome. In this review, we summarise what is known about the conductivity values, as well as progress to date in meeting the challenges associated with both the mathematical modelling and the experimental techniques.

Epicardial potential distributions, arising from a subendocardial ischaemic region, modelled using conductivity data from the indicated studies.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

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

References

  1. Arthur RM, Geselowitz DB (1970) Effect of inhomogeneities on the apparent location and magnitude of a cardiac current dipole source. IEEE Trans Biomed Eng 17:141–146

    CAS  PubMed  Google Scholar 

  2. Austin TM, Trew ML, Pullan AJ (2006) Solving the cardiac bidomain equations for discontinuous conductivities. IEEE Trans Biomed Eng 53(7):1265–1272

    PubMed  Google Scholar 

  3. Barnes JP (2013) Mathematically modeling the electrophysiological effects of ischaemia in the heart. Ph.D. thesis, Griffith University, Brisbane, Australia

  4. Barnes JP, Johnston PR (2012) The effect of ischaemic region shape on epicardial potential distributions in transient models of cardiac tissue. ANZIAM J 53:C110–C126

    Google Scholar 

  5. Barnes JP, Johnston PR (2012) The effect of ischaemic region shape on ST potentials using a half–ellipsoid model of the left ventricle. In: Murray A (ed) Computing in cardiology, vol 39. IEEE Press, IEEE, pp 461–464

  6. Barone A, Fenton F, Veneziani A (2017) Numerical sensitivity analysis of a variational data assimilation procedure for cardiac conductivities. Chaos 27(093):930

    Google Scholar 

  7. Barone A, Gizzi A, Fenton F, Filippi S, Veneziani A (2020) Experimental validation of a variational data assimilation procedure for estimating space-dependent cardiac conductivities. Comput Methods Appl Mech Eng 358(112):615

    Google Scholar 

  8. Barr RC, Plonsey R (2003) Electrode systems for measuring cardiac impedances using optical transmembrane potential sensors and interstitial electrodes — theoretical design. IEEE Trans Biomed Eng 50(8):925–934

    PubMed  Google Scholar 

  9. Bauer S, Edelmann JC, Seemann G, Sachse FB, Dössel O. (2013) Estimating intracellular conductivity tensors from confocal microscopy of rabbit ventricular tissue. Biomedizinische Technik/Biomedical Engineering 58

  10. Boccia E, Luther S, Parlitz U (2017) Modelling far field pacing for terminating spiral waves pinned to ischaemic heterogeneities in cardiac tissue. Philos Trans Royal Soc A 375(2096):20160,289

    Google Scholar 

  11. Caldwell BJ, Trew ML, Sands GB, Hooks DA, LeGrice IJ, Smaill BH (2009) Three distinct directions of intramural activation reveal nonuniform side–to–side electrical coupling of ventricular myocytes. Circ Arrhythm Electropysiol 2:433–440

    Google Scholar 

  12. Clayton RH, Bernus O, Cherry EM, Dierckx H, Fenton FH, Mirabella L, Panfilov AV, Sachse FB, Seemann G, Zhang H (2011) Models of cardiac tissue electrophysiology: progress, challenges and open questions. Prog Biophys Mol Biol 104(1–3):22–48

    CAS  PubMed  Google Scholar 

  13. Clerc L (1976) Directional differences of impulse spread in trabecular muscle from mammalian heart. J Physiol 255:335–346

    CAS  PubMed  PubMed Central  Google Scholar 

  14. Colli Franzone P, Guerri L (1993) Spreading of excitation in 3–D models of the anisotropic cardiac tissue I: validation of the eikonal model. Math Biosci 113:145–209

    Google Scholar 

  15. Colli Franzone P, Guerri L, Taccardi B (1993) Spread of excitation in a myocardial volume: Simulation studies in a model of anisotropic ventricular muscle activated by point stimulation. J Cardiovasc Electrophysiol 4(2):144–160

    Google Scholar 

  16. Colli Franzone P, Guerri L, Taccardi B (2004) Modeling ventricular excitation: axial and orthotropic anisotropy effects on wavefronts and potentials. Math Biosci 188(1–2):191–205

    PubMed  Google Scholar 

  17. Colli Franzone P, Pavarino LF, Scacchi S (2007) Dynamical effects of myocardial ischemia in anisotropic cardiac models in three dimensions. Math Models Methods Appl Sci 17(12):1965–2008

    Google Scholar 

  18. Coltart DJ, Meldrum SJ (1970) A comparison of the transmembrane action potential of the human and canine myocardium. Cardiology 55:340–350

    Google Scholar 

  19. Costa CM, Hoetzl E, Rocha BM, Prassl AJ, Plank G (2013) Automatic parametrization strategy for cardiac electrophysiology simulations. In: Computing in cardiology, vol 40, pp 373–376

  20. Coudiere Y, Davidovic A, Poignard C (2014) The modified bidomain model with periodic diffusive inclusions. In: Murray A (ed) Computing in cardiology, vol 41, pp 1033–1036

  21. Edwards AG, Louch WE (2017) Species-dependent mechanisms of cardiac arrythmia: a cellular focus. Clin Med Insights Cardiol 11:1179546816686,061

    Google Scholar 

  22. Foster KR, Schwan HP (1989) Dielectic properties of tissue and biological materials: a critical review. Crit Rev Biomed Eng 17(1):25–104

    CAS  PubMed  Google Scholar 

  23. Gielen FL, Wallinga-de Jonge W, Boon KL (1984) Electrical conductivity of skeletal muscle tissue: experimental results from different muscles in vivo. Med Biol Eng Comput 22:569–577

    CAS  PubMed  Google Scholar 

  24. Gokhale TA, Medvescek E, Henriquez CS (2017) Modeling dynamics in diseased cardiac tissue: impact of model choice. Chaos 27:093,909

    Google Scholar 

  25. Graham LS, Kilpatrick D (2010) Estimation of the Bidomain conductivity parameters of cardiac tissue from extracellular potential distributions initiated by point stimulation. Ann Biomed Eng 38(12):3630–3648

    PubMed  Google Scholar 

  26. Greiner J, Sankarankutty AC, Seemann G, Seidel T, Sachse FB (2018) Confocal microscopy-based estimaton of parameters for computational modeling of electrical conduction in the normal and infarcted heart. Front Physiol 9(239):1–15

    Google Scholar 

  27. Gulrajani RM (1998) Bioelectricity and biomagnetism. (John) Wiley and Sons, New York

    Google Scholar 

  28. Hand P, Griffith B, Peskin C (2009) Deriving macroscopic myocardial conductivities by homogenization of microscopic models. Bull Math Biol 71(7):1707–1726

    PubMed  Google Scholar 

  29. Henriquez CS (2014) A brief history of tissue models for cardiac electrophysiology. IEEE Trans Biomed Eng 61(5):1457–1465

    PubMed  Google Scholar 

  30. Hooks D (2007) Myocardial segment-specific model generation for simulating the electrical action of the heart. BioMed Eng OnLine 6(1):21–21

    PubMed  PubMed Central  Google Scholar 

  31. Hooks DA, Tomlinson KA, Marsden SG, LeGrice IJ, Smaill BH, Pullan AJ, Hunter PJ (2002) Cardiac microstructure: Implications for electrical propagation and defibrillation in the heart. Circ Res 91(4):331–338

    CAS  PubMed  Google Scholar 

  32. Hooks DA, Trew ML, Caldwell BJ, Sands GB, LeGrice IJ, Smaill BH (2007) Laminar arrangement of ventricular myocytes influences electrical behavior of the heart. Circ Res 101(10):e103–112–e103–112

    CAS  PubMed  Google Scholar 

  33. Hopenfeld B, Stinstra JG, MacLeod RS (2004) Mechanism for ST depression associated with contiguous subendocardial ischaemia. J Cardiovasc Electrophysiol 15:1200–1206

    PubMed  Google Scholar 

  34. Hopenfeld B, Stinstra JG, MacLeod RS (2005) The effect of conductivity on ST-segment epicardial potentials arising from subendocardial ischemia. Ann Biomed Eng 33(6):751–763

    PubMed  Google Scholar 

  35. Huang Q, Eason JC, Claydon FJ (1999) Membrane polarization induced in the myocardium by defibrillation fields: an idealized 3-d finite element bidomain/monodomain torso model. IEEE Trans Biomed Eng 46(1):26–34

    CAS  PubMed  Google Scholar 

  36. Janse MJ, Opthof T, Kléber AG (1998) Animal models of cardiac arrhythmias. Cardiovasc Res 39:165–177

    CAS  PubMed  Google Scholar 

  37. Johnston BM (2013) Design of a multi–electrode array to measure cardiac conductivities. ANZIAM J 54:C271–C290

    Google Scholar 

  38. Johnston BM (2013) Using a sensitivity study to facilitate the design of a multi–electrode array to measure six cardiac conductivity values. Math Biosci 244:40–46

    PubMed  Google Scholar 

  39. Johnston BM (2016) Six conductivity values to use in the bidomain model of cardiac tissue. IEEE Trans Biomed Eng 63(7):1525–1531

    PubMed  Google Scholar 

  40. Johnston BM, Barnes JP (2014) Exploiting GPUs to investigate an inversion method that retrieves cardiac conductivities from potential measurements. ANZIAM J 55:C17–C31

    Google Scholar 

  41. Johnston BM, Barnes JP, Johnston PR, Murray A (2016) The effect of conductivity values on activation times and defibrillation thresholds. In: Computing in cardiology, vol 43, pp 161–164

  42. Johnston BM, Coveney S, Chang ETY, Johnston PR, Clayton RH (2018) Quantifying the effect of uncertainty in input parameters in a simplified bidomain model of partial thickness ischaemia. Med Biol Eng Comput 56:761–780

    PubMed  Google Scholar 

  43. Johnston BM, Johnston PR (2013) A multi-electrode array and inversion technique for retrieving six conductivities from heart potential measurements. Med Biol Eng Comput 51(12):1295–1303

    PubMed  Google Scholar 

  44. Johnston BM, Johnston PR (2013) The sensitivity of the passive bidomain equation to variations in six conductivity values. In: Boccaccini A (ed) Proceedings of the IASTED international conference biomedical engineering (BioMed 2013). IASTED, ACTA Press, Calgary, pp 538–545

  45. Johnston BM, Johnston PR (2014) How accurately can cardiac conductivity values be determined from heart potential measurements?. In: Murray A (ed) Computing in cardiology, vol 41. IEEE, pp 533–536

  46. Johnston BM, Johnston PR (2015) Determining six cardiac conductivities from realistically large datasets. Math Biosci 266:15–22

    PubMed  Google Scholar 

  47. Johnston BM, Johnston PR (2018) Determining the most significant input parameters in models of subendocardial ischaemia and their effect on ST segment epicardial potential distributions. Comput Biol Med 95:75–89

    PubMed  Google Scholar 

  48. Johnston BM, Johnston PR (2018) Sensitivity analysis of ST-segment epicardial potentials arising from changes in ischaemic region conductivities in early and late stage ischaemia. Comput Biol Med 102:288–299

    PubMed  Google Scholar 

  49. Johnston BM, Johnston PR (2019) Differences between models of partial thickness ischaemia and subendocardial ischaemia in terms of sensitivity analyses of ST-segment epcicardial potential distributions. Math Biosci 318:108,273

    Google Scholar 

  50. Johnston BM, Johnston PR, Kilpatrick D (2006) Analysis of electrode configurations for measuring cardiac tissue conductivities and fibre rotation. Ann Biomed Eng 34(6):986–996

    PubMed  Google Scholar 

  51. Johnston BM, Johnston PR, Kilpatrick D (2006) A new approach to the determinination of cardiac potential distributions: application to the analysis of electrode configurations. Math Biosci 202(2):288–309

    PubMed  Google Scholar 

  52. Johnston BM, Narayan A, Johnston PR (2020) A comparison of methods for examining the effect of uncertainty in the conductivities in a model of partial thickness ischaemia. In: Pickett C (ed) Computing in cardiology, vol 46, pp 1–4

  53. Johnston PR (2005) The effect of simplifying assumptions in the bidomain model of cardiac tissue: application to ST-segment shifts during partial ischaemia. Math Biosci 198(1):97–118

    PubMed  Google Scholar 

  54. Johnston PR (2010) A finite volume method solution for the bidomain equations and their application to modelling cardiac ischaemia. Comput Methods Biomech Biomed Eng 13(2):157–170

    Google Scholar 

  55. Johnston PR (2011) Cardiac conductivity values — a challenge for experimentalists? Noninvasive Functional Source Imaging of the Brain and Heart & 2011 8th International Conference on Bioelectromagnetism (NFSI & ICBEM), 39–43

  56. Johnston PR (2011) A non-dimensional formulation of the passive bidomain equation. J Electrocardiol 44(2):184–188

    PubMed  Google Scholar 

  57. Johnston PR (2011) A sensitivity study of conductivity values in the passive bidomain equation. Math Biosci 232(2):142–150

    PubMed  Google Scholar 

  58. Johnston PR, Kilpatrick D (2003) The effect of conductivity values on ST segment shift in subendocardial ischaemia. IEEE Trans Biomed Eng 50(2):150–158

    PubMed  Google Scholar 

  59. Johnston PR, Kilpatrick D, Li CY (2001) The importance of anisotropy in modelling ST segment shift in subendocardial ischaemia. IEEE Trans Biomed Eng 48(12):1366–1376

    CAS  PubMed  Google Scholar 

  60. Keller DUJ, Webster FM, Seemann G, Dössel O. (2010) Ranking the influence of tissue conductivities on forward-calculated ECGs. IEEE Trans Biomedial Eng 57(7):1568–1576

    Google Scholar 

  61. Kleber AG, Riegger CB (1987) Electrical constants of arterially perfused rabbit papillary muscle. J Physiol 385:307–324

    CAS  PubMed  PubMed Central  Google Scholar 

  62. Krassowska W, Neu JC (1992) Theoretical versus experimental estimates of the effective conductivities of cardiac muscle. In: Computers in cardiology 1992, IEEE, pp 703–706

  63. Kwon H, Guasch M, Nagy JA, Rutkove SB, Sanchez B (2019) New electrical impedance methods for the in situ measurement of the complex permittivity of anisotropic skeletal muscle using multipolar needles. Sci Rept 9:3145

    CAS  Google Scholar 

  64. Kwon H, Nagy JA, Taylor R, Rutkove SB, Sanchez B (2017) New electrical impedance methods for the in situ measurement of the complex permittivity of anisotropic biological tissues. Phys Med Biol 62:8616–8633

    CAS  PubMed  Google Scholar 

  65. Le Guyader P, Savard P, Trelles F (1995) Measurement of myocardial conductivities with an eight–electrode technique in the frequency domain. 17th IEEE-EMBS, 71–72

  66. Le Guyader P, Savard P, Trelles F (1997) Measurement of myocardial conductivities with a four–electrode technique in the frequency domain. In: Proceedings of 19th international conference, IEEE/EMBS, pp 2448–2449

  67. Le Guyader P, Trelles F, Savard P (2001) Extracellular measurement of anisotropic bidomain myocardial conductivities. I. theoretical analysis. Ann Biomed Eng 29:862–877

    PubMed  Google Scholar 

  68. LeGrice IJ, Hunter PJ, Smail BH (1997) Laminar structure of the heart: a mathematical model. Am J Physiol 272:H2466–H2476

    CAS  PubMed  Google Scholar 

  69. LeGrice IJ, Smaill BH, Chai LZ, Edgar SG, Gavin JB, Hunter PJ (1995) Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. Am J Physiol 269:H571–H582

    CAS  PubMed  Google Scholar 

  70. Li Q (2005) Transmyocardial ST potential distributions in ischaemic heart disease. Ph.D. thesis, University of Tasmania

  71. Lombaert H, Peyrat J, Croisille P, Rapacchi S, Fanton L, Cheriet F, Clarysse P, Magnin I, Delingette H, Ayache N (2012) Human atlas of the cardiac fiber architecture: study on a healthy population. IEEE Trans Med Imaging 31(7):1436–1447

    PubMed  Google Scholar 

  72. MacLachlan MC, Sundnes J, Lines GT (2005) Simulation of ST segment changes during subendocardial ischemia using a realistic 3-D cardiac geometry. IEEE Trans Biomed Eng 52(5):799–807

    PubMed  Google Scholar 

  73. van Oosterom A, de Boer RW, Dam RTV (1979) Intramural resistivity of cardiac tissue. Med & Biol Eng & Comput 17:337–343

    Google Scholar 

  74. Plonsey R, Barr RC (1982) The four-electrode resistivity technique as applied to cardiac muscle. IEEE Trans Biomed Eng 29(7):541–546

    CAS  PubMed  Google Scholar 

  75. Plourde E, Savard P, Le Guyader P (2000) Electrical alignment of a cardiac impedance probe. In: Computers in cardiology, vol 27, IEEE, IEEE Press, pp 773-775

  76. Pollard AE, Barr RC (2006) Cardiac micro–impedance measurement in two–dimensional models using multisite interstitial stimulation. Am J Physiol-Heart Circ Physiol 290(5):H1976–H1987

    CAS  PubMed  Google Scholar 

  77. Pollard AE, Barr RC (2010) A biophysical model for cardiac microimpedance measurements. Am J Physiol-Heart Circ Physiol 298:H1699–H1709

    CAS  PubMed  PubMed Central  Google Scholar 

  78. Pollard AE, Barr RC (2013) A new approach for resolution of complex tissue impedance spectra in hearts. IEEE Trans Biomed Eng 60(9):2494–2503

    PubMed  PubMed Central  Google Scholar 

  79. Pollard AE, Barr RC (2014) A structural framework for interpretation of four-electrode microimpedance spectra in cardiac tissue. In: Conference proceedings of IEEE engineering in medicine and biology society, pp 6467–6470

  80. Pollard AE, Ellis CD, Smith WM (2008) Linear electrode arrays for stimulation and recording within cardiac tissue space constants. IEEE Trans Biomed Eng 55(4):1408–1414

    PubMed  Google Scholar 

  81. Pollard AE, Hooke N, Henriquez CS (1992) Cardiac propagation simulation. Crit Rev Biomed Eng 20:171–210

    CAS  PubMed  Google Scholar 

  82. Pollard AE, Smith WM, Barr RC (2004) Feasibility of cardiac microimpedance measurement using multisite interstitial stimulation. Am J Physiol Circ Physiol 287:H2402–H2411

    CAS  Google Scholar 

  83. Pormann JB (1999) A simulation system for the bidomain equations. Ph.D thesis, Duke University, Durham NC

  84. Potse M, Coronel R, Falcao S, LeBlanc AR, Vinet A (2007) The effect of lesion size and tissue remodeling on ST deviation in partial-thickness ischemia. Heart Rhythm 4(2):200–206

    PubMed  Google Scholar 

  85. Potse M, LeBlanc AR, Cardinal R, Vinet A (2006) ST elevation or depression in subendocardial ischemia?. In: 28Th IEEE EMBS annual international conference, pp 3899–3902

  86. Roberts DE, Hersh LT, Scher AM (1979) Influence of cardiac fiber orientation on wavefront voltage, conduction velocity and tissue resistivity in the dog. Circ Res 44:701–712

    CAS  PubMed  Google Scholar 

  87. Roberts DE, Scher AM (1982) Effects of tissue anisotropy on extracellular potential fields in canine myocardium in situ. Circ Res 50:342–351

    CAS  PubMed  Google Scholar 

  88. Roth BJ (1988) The electrical potential produced by a strand of cardiac muscle: a bidomain analysis. Ann Biomed Eng 16:609–637

    CAS  PubMed  Google Scholar 

  89. Roth BJ (1997) Electrical conductivity values used with the bidomain model of cardiac tissue. IEEE Trans Biomed Eng 44(4):326–328

    CAS  PubMed  Google Scholar 

  90. Roth BJ (1997) Nonsustained reentry following successive stimulation of cardiac tissue through a unipolar electrode. J Cardiovasc Electrophysiol 8:768–778

    CAS  PubMed  Google Scholar 

  91. Rush S, Abildskov JA, McFee R (1963) Resistivity of body tissues at low frequencies. Circ Res 12:40–50

    CAS  PubMed  Google Scholar 

  92. Sachse FB, Moreno A, Seemann G, Abildskov J (2009) A model of electrical conduction in cardiac tissue including fibroblasts. Ann Biomed Eng 37:874–889

    PubMed  Google Scholar 

  93. Sadleir R, Henriquez C (2006) Estimation of cardiac bidomain parameters from extracellular measurement: Two dimensional study. Ann Biomed Eng 34(8):1289–1303

    CAS  PubMed  Google Scholar 

  94. Sanchez C, D’Ambrosio G, Maffessanti F, Caiani EG, Prinzen FW, Krause R, A A, Potse M (2018) Sensitivity analysis of ventricular activation and eletrocardiogram in tailored models of heart-failure patients. Med Biol Eng Comput 56:491–504

    CAS  PubMed  Google Scholar 

  95. Schmitt OH (1969) Biological information processing using the concept of interpenetrating domains. In: Leibovic KN (ed) Information processing in the nervous system. chap. 18. Springer–Verlag, New York, pp 325–331

  96. Schwab BC, Seemann G, Lasher R, Torres N, Wulfers E, Arp M, Carruth E, Bridge J, Sachse F (2013) Quantitative analysis of cardiac tissue including fibroblasts using three-dimensional confocal microscopy and image reconstruction: towards a basis for electrophysiological modeling. IEEE Trans Med Imaging 32(5):862–872

    PubMed  PubMed Central  Google Scholar 

  97. Shome S, Stinstra JG, Hopenfeld B, Punske BB, MacLeod RS (2004) A study of the dynamics of cardiac ischaemia using experimental and modeling approaches. In: Proceedings of the IEEE engineering in medicine and biology 26th annual international conference. 3585-3588, IEEE EMBS, IEEE Press

  98. Shor NZ (1985) Minimization methods for Non-Differentiable Functions, Springer Series in Computational Mathematics, vol. 3 Springer–Verlag

  99. Smith W, Fleet W, Johnson F, Engle T, Cascio C (1995) The ib phase of ventricular arrhythmias in ischemic in situ porcine heart is related to changes in cell-to-cell electrical coupling. Circulation 92:3051–3060

    PubMed  Google Scholar 

  100. Steendijk P, Mur G, van der Velde ET, Baan J (1993) The four-electrode resistivity technique in anisotropic media: Theoretical analysis and application on myocardial tissue in Vivo. IEEE Trans Biomed Eng 40(11):1138–1147

    CAS  PubMed  Google Scholar 

  101. Stinstra J, Hopenfeld B, MacLeod R (2005) On the passive cardiac conductivity. Ann Biomed Eng 33(12):1743–1751

    PubMed  Google Scholar 

  102. Stinstra JG, Hopenfeld B, MacLeod R (2003) A model for the passive cardiac conductivity. Int J Biolectromagnetism 5(1):185–186

    Google Scholar 

  103. Streeter D Jr, Spotnitz H, Patel D, Ross J Jr, Sonnenblick E (1969) Fiber orientation in the canine left ventricle during diastole and systole. Circ Res 24:339–347

    PubMed  Google Scholar 

  104. Tikhonov AN, Arsenin VY (1977) Solutions of ill-posed problems. V.H. Winston and Sons Washington

  105. Trayanova N, Eason J, Aguel F (2002) Computer simulations of cardiac defibrillation: a look inside the heart. Comput Vis Sci 4:259–270

    Google Scholar 

  106. Trew ML, Caldwell BJ, Gamage TPB, Sands GB, Smaill BH (2008) Experiment-specific models of ventricular electrical activation: construction and application. In: 30Th annual international IEEE EMBS conference, pp 137–140

  107. Tung L (1978) A bi–domain model for describing ischaemic myocardial D-C potentials. Ph.D. thesis, Massachusetts Institute of Technology

  108. Varro A, Lathrop DA, Hester SB, Nanasi PP, Papp JGY (1193) Ionic currents and action potential in rabbit, rat and guinea pig ventricular myocytes. Basic Res Cardiol 88(2):93–102

    Google Scholar 

  109. Waits CMK, Barr RC, Pollard AE (2014) Sensor spacing affects the tissue impedance spectra of rabbit ventricular epicardium. Am J Physiol Heart Circ Physiol 306(12):H1660–H1668

    CAS  PubMed  PubMed Central  Google Scholar 

  110. Weidmann S (1970) Electrical constants of trabecular muscle from mammalian heart. J Physiol 210:1041–1054

    CAS  PubMed  PubMed Central  Google Scholar 

  111. Yang H, Veneziani A (2015) Estimation of cardiac conductivities in ventricular tissue by a variational approach. Inverse Probl 31(115):001

    Google Scholar 

  112. Yang H, Veneziani A (2017) Efficient estimation of cardiac conductvities via POD-DIEM model order reduction. Appl Numer Math 115:180–199

    Google Scholar 

Download references

Funding

We acknowledge funding from the National Institute of Health, Bethesda, USA (R03EB029625).

Author information

Authors and Affiliations

  1. School of Environment and Science, and Queensland Micro– and Nanotechnology Centre, Griffith University, Nathan, QLD, 4111, Australia

    Barbara M. Johnston & Peter R. Johnston

Authors
  1. Barbara M. Johnston
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter R. Johnston
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Barbara M. Johnston.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Johnston, B.M., Johnston, P.R. Approaches for determining cardiac bidomain conductivity values: progress and challenges. Med Biol Eng Comput 58, 2919–2935 (2020). https://doi.org/10.1007/s11517-020-02272-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-020-02272-z

Keywords

Search

Navigation