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Atrial cell action potential parameter fitting using genetic algorithms

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Abstract

Understanding of the considerable variation in action potential (AP) shape throughout the heart is necessary to explain normal and pathological cardiac function. Existing mathematical models reproduce typical APs, but not all measured APs, as fitting the sets of non-linear equations is a tedious process. The study describes the integration of a pre-existing mathematical model of an atrial cell AP with a genetic algorithm to provide an automated tool to generate APs for arbitrary cells by fitting ionic channel conductances. Using the Nygren model as the base, the technique was first verified by starting with random values and fitting the Nygren model to itself with an error of only 0.03%. The Courtemanche model, which has a different morphology from that of the Nygren model, was successfully fitted. The AP duration restitution curve generated by the fit matched that of the target model very well. Finally, experimentally recorded APs were reproduced. To match AP duration restitution behaviour properly, it was necessary simultaneously to fit over several stimulation frequencies. Also, fitting of the upstroke was better if the stimulating current pulse replicated that foundin situ as opposed to a rectangular pulse. In conclusion, the modelled parameters were successfully able to reproduce any given atrial AP. This tool can be useful for determining parameters in new AP models, reproducing specific APs, as well as determining the locus of drug action by examining changes in conductance values.

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References

  • Ayyub, B. M., andMcCuen, R. H. (1996): ‘Numerical methods for engineers’ (Prentice Hall, Upper Saddle River, New Jersey, 1996), pp. 61–77

    Google Scholar 

  • Cantú-Paz, E. (2000): ‘Efficient and accurate parallel genetic algorithms’ (Kluwer Academic Publishers, Norwell, Massachusetts, 2000)

    Google Scholar 

  • Chen, Q., andGuan, S.-U. (2004): ‘Incremental multiple objective genetic algorithms’,IEEE Trans. Syst. Man Cybern. B, Cybon.,34, pp. 1325–1334

    Google Scholar 

  • Cherry, E. M., andFenton, F. H. (2004): ‘Suppression of alternans and conduction blocks despite steep APD restitution: electrotonic, memory, and conduction velocity restitution effects’,Am. J. Physiol. Heart Circ. Physiol.,286, pp. H2332-H2341

    Article  Google Scholar 

  • Courtemanche, M., Rafael, J. R., andNattel, S. (1998): ‘Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model’,Am. J. Physiol., Heart Circ. Physiol.,44, pp. H301-H321

    Google Scholar 

  • Durant, E. A., Wakefield, G. H., Tasell, D. J. V., andRickert, M. E. (2004): ‘Efficient perceptual tuning of hearing aids with genetic algorithms’,IEEE Trans. Speech Audio Process.,12, pp. 144–155

    Article  Google Scholar 

  • Feng, J., Yue, L., Wang, Z., andNattel, S. (1998): ‘Ionic mechanisms of regional action potential heterogeneity in the canine right atrium’,Circ Res.,83, pp. 541–551

    Google Scholar 

  • Herrera, F., andLozano, M. (2000): ‘Gradual distributed real-coded genetic algorithms’,IEEE Trans. Evol. Comput.,4, pp. 43–63

    Google Scholar 

  • Hodgkin, A. L., andHuxley, A. F. (1952): ‘A quantitative description of membrane current and its application to conduction and excitation in nerve’,J. Physiol.,117, pp. 500–544

    Google Scholar 

  • Hussein, Y. A., andEl-Ghazaly, S. M. (2004): ‘Modelling and optimization of microwave devices and circuits using genetic algorithms’,IEEE Trans. Microw. Theory Tech.,52, pp. 329–336

    Article  Google Scholar 

  • Kneller, J., Zou, R., Vigmond, E. J., Wang, Z., Leon, L. J., andNattel, S. (2002): ‘Cholinergic atrial fibrillation in a computer model of a two-dimensional sheet of canine atrial cells with realistic ionic properties’,Circ Res.,90, pp. E73–87

    Article  Google Scholar 

  • Leung, F. H. F., Lam, H. K., Ling, S. H., andTam, P. K. S. (2004): ‘Optimal and stable fuzzy controllers for nonlinear systems based on an improved genetic algorithm’,IEEE Trans. Indust. Electron.,51, pp. 172–182

    Google Scholar 

  • Liu, X. K., Jahangir, A., Terzic, A., Gersh, B. J., Hammill, S. C., andShen, W. K. (2004): ‘Age- and sex-related atrial electrophysiologic and structural changes’,Am. J. Cardiol.,94, pp. 373–375

    Article  Google Scholar 

  • Michalewicz, Z. (1996): ‘Genetic algorithms+data structures= evolution programs’ (Springer-Verlag, Berlin, Heidelberg, New York, 1996), pp. 1–177

    Google Scholar 

  • Nygren, A., Fiset, L., Clark, J. W., Lindbald D. S., Clark, R. B., andGiles, W. R. (1998): ‘Mathematical model of an adult human atrial cell-the role of K+currents in repolarization’,Circ. Res.,82, pp. 63–81

    Google Scholar 

  • Nygren, A., Leon, L. J., andGiles, W. R. (2001): ‘Simulations of the human atrial action potential’,Phil. Trans. R. Soc. Lond. A,359, pp. 1111–1125

    Google Scholar 

  • Pacheco, P. S. (1997): ‘Parallel programming with MPI’ (Morgan Kaufmann Publishers Inc., San Francisco, California 1997)

    Google Scholar 

  • Pastore, J. M., Girouard, S. D., Laurita, K. R., Akar, F. G., andRosenbaum, D. S. (1999): ‘Mechanism linking T-wave alternans to the genesis of cardiac fibrillation’,Circulation, pp. 1385–1394

  • Ramirez, R.J., Nattel, S., andCourtemanche, M. (2000): ‘Mathematical analysis of canine atrial action potentials: rate, regional factors, and electrical remodelling’,Am. J. Physiol., Heart Circ. Physiol.,279, pp. H1767-H1785

    Google Scholar 

  • Schram, G., Pourrier, M., Melnyk, P., andNattel, S. (2002): ‘Differential distribution of cardiac ion channel expression as a basis for regional specialization in electrical function’,Circ. Res.,90, pp. 939–950

    Article  Google Scholar 

  • Shaw, R. M., andRudy, Y. (1997): ‘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.,81, pp. 727–741

    Google Scholar 

  • Vieira, D. A. G., Adriano, R. L. S., Vasconcelos, J. A., andKrahenbuhl, L. (2004): ‘Treating constraints as objectives in multiobjective optimization problems using niched Pareto genetic algorithm’,IEEE Trans. Magnetics,40, pp. 1188–1191

    Google Scholar 

  • Vigmond, E. J., andLeon, L. J. (2002): ‘The effect of ionic current modulation on restitution curves and the onset of fibrillation in a simulated block of cardiactissue’,Comput. Visual. Sci.,4, pp. 237–247

    Article  Google Scholar 

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Correspondence to L. J. Leon.

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Syed, Z., Vigmond, E., Nattel, S. et al. Atrial cell action potential parameter fitting using genetic algorithms. Med. Biol. Eng. Comput. 43, 561–571 (2005). https://doi.org/10.1007/BF02351029

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  • DOI: https://doi.org/10.1007/BF02351029

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