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Showing content from https://link.springer.com/article/10.1007/s10439-010-0100-9 below:

Stiffness Analysis of Cardiac Electrophysiological Models

References

  1. http://bioeng.washington.edu/jsim/.

  2. Aliev, R. R., and A. V. Panfilov. A simple two-variable model of cardiac excitation. Chaos, Solitions and Fractals 7(3):293–301, 1996.

    Article  Google Scholar 

  3. Artebrant, R., J. Sundnes, O. Skavhaug, and A. Tveito. A second order method of Rush–Larsen type. Technical Report, Simula Research Laboratory, 2008.

  4. Ascher, U. M., and L. R. Petzold. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), 1998.

  5. Atkinson, K., and W. Han. Elementary Numerical Analysis, 3rd ed. Hoboken, NJ: John Wiley & Sons Ltd, 2005.

    Google Scholar 

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

    PubMed  CAS  Google Scholar 

  7. Bischof, C. H., H. M. Bücker, and A. Vehreschild. A macro language for derivative definition in ADiMat. In: Automatic Differentiation: Applications, Theory, and Implementations, vol. 50, Lecture Notes in Computer Science Engineering. Berlin: Springer, 2006, pp. 181–188.

  8. Bondarenko, V. E., G. P. Szigeti, G. C. L. Bett, S. J. Kim, and R. L. Rasmusson. Computer model of action potential of mouse ventricular myocytes. Am. J. Physiol. Heart Circ. Physiol. 287(3):H1378–H1403, 2004.

    Article  PubMed  CAS  Google Scholar 

  9. Burkardt, J. http://orion.math.iastate.edu/burkardt/math2071/be_newton.m.

  10. Butcher, J. C. Order, stepsize and stiffness switching. Computing 44(3):209–220, 1990.

    Article  Google Scholar 

  11. Courtemanche, M., R. J. Ramirez, and S. Nattel. Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model. Am. J. Physiol. 275(1):H301–H321, 1998.

    PubMed  CAS  Google Scholar 

  12. Demir, S. S., J. W. Clark, W. R. Giles. Parasympathetic modulation of sinoatrial node pacemaker activity in rabbit heart: a unifying model. Am. J. Physiol. 276(6 Pt 2):H2221–H2244, 1999.

    PubMed  CAS  Google Scholar 

  13. Demir, S. S., J. W. Clark, C. R. Murphey, and W. R. Giles. A mathematical model of a rabbit sinoatrial node cell. Am. J. Physiol. 266(3 Pt 1):C832–C852, 1994.

    PubMed  CAS  Google Scholar 

  14. DiFrancesco, D., and D. Noble. A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philos. Trans. R. Soc. Lond. B Biol. Sci. 307(1133):353–398, 1985.

    Article  PubMed  CAS  Google Scholar 

  15. Dokos, S., B. Celler, and N. Lovell. Ion currents underlying sinoatrial node pacemaker activity: a new single cell mathematical model. J. Theor. Biol. 181(3):245–272, 1996.

    Article  PubMed  CAS  Google Scholar 

  16. Faber, G. M., and Y. Rudy. Action potential and contractility changes in [Na(+)](i) overloaded cardiac myocytes: a simulation study. Biophys. J. 78(5):2392–2404, 2000.

    Article  PubMed  CAS  Google Scholar 

  17. FitzHugh, R. Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1(6):445–466, 1961.

    Article  PubMed  CAS  Google Scholar 

  18. Fox, J. J., J. L. McHarg, and R. F. Gilmour. Ionic mechanism of electrical alternans. Am. J. Physiol. Heart Circ. Physiol. 282(2):H516–H530, 2002.

    PubMed  CAS  Google Scholar 

  19. Hairer, E., and G. Wanner. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, 2nd ed. Berlin: Springer-Verlag, 1996.

    Google Scholar 

  20. Hilgemann, D. W., and D. Noble. Excitation-contraction coupling and extracellular calcium transients in rabbit atrium: reconstruction of basic cellular mechanisms. Proc. R. Soc. Lond. B Biol. Sci. 230(1259):163–205, 1987.

    Article  PubMed  CAS  Google Scholar 

  21. Hodgkin, A., and A. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (Lond) 117(4):500–544, 1952.

    CAS  Google Scholar 

  22. Hund, T.J., and Y. Rudy. Rate dependence and regulation of action potential and calcium transient in a canine cardiac ventricular cell model. Circulation 110(20):3168–3174, 2004.

    Article  PubMed  CAS  Google Scholar 

  23. Jafri, M. S., J. J.Rice, and R. L. Winslow. Cardiac Ca2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys. J. 74(3):1149–1168, 1998.

    Article  PubMed  CAS  Google Scholar 

  24. Kogan, B. Y., W. J. Karplus, B. S. Billett, A. Pang, H. S. Karagueuzian, and S. S. Kahn. The simplified FitzHugh–Nagumo model with action potential duration restitution: effects on 2-D wave propagation. Physica D 50:327–340, 1991.

    Article  Google Scholar 

  25. Lambert, J. D. Numerical Methods for Ordinary Differential Systems: The Initial Value Problem. Chichester: John Wiley & Sons Ltd., 1991.

  26. Lloyd, C. M., J. R. Lawson, P. J. Hunter, and P. F. Nielsen. The CellML model repository. Bioinformatics 24(18):2122–2123, 2008.

    Article  PubMed  CAS  Google Scholar 

  27. Luo, C., and Y. Rudy. A model of ventricular cardiac action potential. Circ. Res. 68(6):1501–1526, 1991.

    Article  PubMed  CAS  Google Scholar 

  28. Maclachlan, M. C., J. Sundnes, and R. J. Spiteri. A comparison of non-standard solvers for ODEs describing cellular reactions in the heart. Comput. Methods Biomech. Biomed. Eng. 10(5):317–326, 2007.

    Article  PubMed  Google Scholar 

  29. Maleckar, M. M., J. L. Greenstein, N. A. Trayanova, and W. R. Giles. Mathematical simulations of ligand-gated and cell-type specific effects on the action potential of human atrium. Prog. Biophys. Mol. Biol. 98(2–3):161–170, 2008.

    Article  PubMed  CAS  Google Scholar 

  30. MathWorks Inc., The: Matlab R2008b. http://www.mathworks.com/, 2008.

  31. McAllister, R. E., D. Noble, and R. W. Tsien. Reconstruction of the electrical activity of cardiac Purkinje fibres. J. Physiol. 251(1):1–59, 1975.

    PubMed  CAS  Google Scholar 

  32. Nagumo, J., S. Arimoto, and S. Yoshizawa. An active pulse transmission line simulating nerve axon. Proc. IRE 50(10):2061–2070, 1962.

    Article  Google Scholar 

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

    PubMed  CAS  Google Scholar 

  34. Noble, D., and S. J. Noble. 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(1228):295–304, 1984.

    Article  PubMed  CAS  Google Scholar 

  35. Noble, D., S. J. Noble, G. C. Bett, Y. E. Earm, W. K. Ho, and I. K. So. The role of sodium-calcium exchange during the cardiac action potential. Ann. N. Y. Acad. Sci. 639(NIL):334–353, 1991.

    Article  PubMed  CAS  Google Scholar 

  36. Noble, D., A. Varghese, P. Kohl, and P. Noble. Improved guinea-pig ventricular cell model incorporating a diadic space, IKr and IKs, and length- and tension-dependent processes. Can. J. Cardiol. 14(1):123–134, 1998.

    PubMed  CAS  Google Scholar 

  37. Nygren, A., C. Fiset, L. Firek, J. W. Clark, D. S. Lindblad, R. B. Clark, and W. R. Giles. Mathematical model of an adult human atrial cell: the role of K+ currents in repolarization. Circ. Res. 82(1):63–81, 1998.

    Article  PubMed  CAS  Google Scholar 

  38. Pandit, S. V., R. B. Clark, W. R. Giles, and S. S. Demir. A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes. Biophys. J. 81(6):3029–3051, 2001.

    Article  PubMed  CAS  Google Scholar 

  39. Pandit, S. V., W. R. Giles, and S. S. Demir. A mathematical model of the electrophysiological alterations in rat ventricular myocytes in type-I diabetes. Biophys. J. 84(2 Pt 1):832–841, 2003.

    Article  PubMed  CAS  Google Scholar 

  40. Petzold, L. Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations. SIAM J. Sci. Stat. Comput. 4(1):137–148, 1983.

    Google Scholar 

  41. Puglisi, J. L., and D. M. Bers. Labheart: an interactive computer model of rabbit ventricular myocyte ion channels and ca transport. Am. J. Physiol. Cell Physiol. 281(6):C2049–C2060, 2001.

    PubMed  CAS  Google Scholar 

  42. Pullan, A. J., M. J. Buist, and L. K. Cheng. Mathematically Modelling the Electrical Activity of the Heart: From Cell to Body Surface and Back Again. New Jersey: World Scientific, 2005.

    Google Scholar 

  43. Rogers, J., and A. McCulloch. A collocation–galerkin finite element model of cardiac action potential propagation. IEEE Trans. Biomed. Eng. 41(8):743–757, 1994.

    Article  PubMed  CAS  Google Scholar 

  44. Rush, S., and H. Larsen. A practical algorithm for solving dynamic membrane equations. IEEE Trans. Biomed. Eng. BME-25(4):389–392, 1978.

    Article  Google Scholar 

  45. Sakmann, B. F., A. J. Spindler, S. M. Bryant, K. W. Linz, and D. Noble. Distribution of a persistent sodium current across the ventricular wall in guinea pigs. Circ. Res. 87(10):910–914, 2000.

    Article  PubMed  CAS  Google Scholar 

  46. Shampine, L. F. Type-insensitive ODE codes based on extrapolation methods. SIAM J. Sci. Stat. Comput. 4(4):635–644, 1983.

    Article  Google Scholar 

  47. Shampine, L. F. Stiffness and the automatic selection of ode codes. J. Comput. Phys. 54:74–86, 1984.

    Article  Google Scholar 

  48. Spiteri, R. J., and R. C. Dean. On the performance of an implicit-explicit Runge–Kutta method in models of cardiac electrical activity. IEEE Trans. Biomed. Eng. 55(5):1488–1495, 2008.

    Article  PubMed  Google Scholar 

  49. Spiteri, R. J., and R. C. Dean. Stiffness analysis of cardiac electrophysiological models. Technical Report, Department of Computer Science, University of Saskatchewan, 2009.

  50. Spiteri, R. J., and M. C. MacLachlan. An efficient non-standard finite difference scheme for an ionic model of cardiac action potentials. J. Differ. Equ. Appl. 9(12):1069–1081, 2003.

    Article  Google Scholar 

  51. Stewart, P., O. V. Aslanidi, D. Noble, P. J. Noble, M. R. Boyett, and H. Zhang. Mathematical models of the electrical action potential of Purkinje fibre cells. Philos. Transact. A Math. Phys. Eng. Sci. 367(1896):2225–2255, 2009.

    Article  PubMed  CAS  Google Scholar 

  52. Sundnes, J., R. Artebrant, O. Skavhaug, and A. Tveito. A second-order algorithm for solving dynamic cell membrane equations. IEEE Trans. Biomed. Eng. 56(10):2546–2548, 2009.

    Article  PubMed  Google Scholar 

  53. Sundnes, J., G. T. Lines, X. Cai, B. F. Nielsen, K. A. Mardal, and A. Tveito. Computing the Electrical Activity in the Heart. Berlin: Springer-Verlag, 2006.

    Google Scholar 

  54. Ten Tusscher, K. H. W. J., D. Noble, P. J. Noble, and A. V. Panfilov. A model for human ventricular tissue. Am. J. Physiol. Heart Circ. Physiol. 286(4):H1573–H189, 2004.

    Article  PubMed  CAS  Google Scholar 

  55. Ten Tusscher, K. H. W. J., and A. V. Panfilov. Cell model for efficient simulation of wave propagation in human ventricular tissue under normal and pathological conditions. Phys. Med. Biol. 51(23):6141–6156, 2006.

    Article  PubMed  CAS  Google Scholar 

  56. Van Capelle, F. J. L., and D. Durrer. Computer simulation of arrhythmias in a network of coupled excitable elements. Circ. Res. 47:454–466, 1980.

    Article  PubMed  CAS  Google Scholar 

  57. Vigmond, E. J., R. W. dos Santos, A. J. Prassl, M. Deo, and G. Plank. Solvers for the cardiac bidomain equations. Prog. Biophys. Mol. Biol. 96(1–3):3–18, 2008.

    Article  PubMed  CAS  Google Scholar 

  58. Wang, L. J., and E. A. Sobie. Mathematical model of the neonatal mouse ventricular action potential. Am. J. Physiol. Heart Circ. Physiol. 294(6):H2565–H2575, 2008.

    Article  PubMed  CAS  Google Scholar 

  59. Winslow, R. L., J. Rice, S. Jafri, E. Marbán, and B. O’Rourke. Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, II model studies. Circ. Res. 84(5):571–586, 1999.

    Article  PubMed  CAS  Google Scholar 

  60. Ying, W., D. J. Rose, and C. S. Henriquez. Efficient fully implicit time integration methods for modeling cardiac dynamics. IEEE Trans. Biomed. Eng. 55(12):2701–2711, 2008.

    Article  PubMed  Google Scholar 

  61. Zhang, H., A. V. Holden, I. Kodama, H. Honjo, M. Lei, T. Varghese, and M. R. Boyett. Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node. Am. J. Physiol. Heart Circ. Physiol. 279(1):H397–H421, 2000.

    PubMed  CAS  Google Scholar 

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