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Estimation of Activation Times in Cardiac Tissue Using Graph Based Methods

  • Conference paper
Functional Imaging and Modeling of the Heart (FIMH 2011)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6666))

Abstract

The bidomain and monodomain equations are well established as the standard set of equations for the simulation of cardiac electrophysiological behaviour. However, the computational cost of detailed bidomain/monodomain simulations limits their applicability to scenarios in which results are needed in real time (e.g. clinical scenarios). In this study, we present a graph based method which relies on point to point path finding to estimate activation times in cardiac tissue with minimal computational costs. Activation times are compared to bidomain simulation results for heterogeneous tissue slabs and an anatomically-based rabbit ventricular model. Differences in activation times between our proposed graph based method and bidomain results are less than 10% of the total activation time and computational performance is orders of magnitude faster with the graph based method. These results suggest that the graph based method could provide a viable alternative to the bidomain formalism for the fast estimation of activation times when the need for fast performance justifies limited loss of accuracy.

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References

  1. Keener, J., Sneyd, J.: Mathematical Physiology, 2nd edn. Springer, New York (1998)

    MATH  Google Scholar 

  2. Plonsey, R., Barr, R.C.: Mathematical modeling of electrical activity of the heart. Journal of electrocardiology 20(3), 219–226 (1987)

    Article  Google Scholar 

  3. Ye, P., Entcheva, E., Grosu, R., Smolka, S.A.: Efficient modeling of excitable cells using hybrid automata. In: Proc. of CMSB, pp. 216–227 (2005)

    Google Scholar 

  4. Tomlinson, K.A., Hunter, P.J., Pullan, A.J.: A finite element method for an eikonal equation model of myocardial excitation wavefront propagation. SIAM J. Appl. Math. 63(1), 324–350 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Pashaei, A., Sebastian, R., Zimmerman, V., Bijnens, B.H., Frangi, A.F.: A mesh-less approach for fast estimation of electrical activation time in the ventricular wall. In: Computers in Cardiology 2009, pp. 209–212 (2010)

    Google Scholar 

  6. Hart, P., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems Science and Cybernetics 4(2), 100–107 (1968)

    Article  Google Scholar 

  7. van Dam, P.M., Oostendorp, T.F., Oosterom, A.: Application of the fastest route algorithm in the interactive simulation of the effect of local ischemia on the ECG. Medical & Biological Engineering & Computing 47(1), 11–20 (2008)

    Google Scholar 

  8. Pitt-Francis, J., Pathmanathan, P., Bernabeu, M.O., Bordas, R., Cooper, J., Fletcher, A.G., Mirams, G.R., Murray, P., Osborne, J.M., Walter, A., et al.: Chaste: a test-driven approach to software development for biological modelling. Computer Physics Communications 180(12), 2452–2471 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Streeter, D.D., Spotnitz, H.M., Patel, D.P., Ross, J., Sonnenblick, E.H.: Fiber orientation in the canine left ventricle during diastole and systole. Circulation Research 24(3), 339–347 (1969)

    Article  Google Scholar 

  10. Corrias, A., Jie, X., Romero, L., Bishop, M.J., Bernabeu, M., Pueyo, E., Rodriguez, B.: Arrhythmic risk biomarkers for the assessment of drug cardiotoxicity: from experiments to computer simulations. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368(192), 3001–3025 (1921)

    Google Scholar 

  11. Sethian, J.A., Vladimirsky, A.: Fast methods for the eikonal and related Hamilton Jacobi equations on unstructured meshes. Proceedings of the National Academy of Sciences of the United States of America 97(11), 5699–5703 (2000)

    Article  MathSciNet  MATH  Google Scholar 

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© 2011 Springer-Verlag Berlin Heidelberg

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Wallman, M., Smith, N., Rodriguez, B. (2011). Estimation of Activation Times in Cardiac Tissue Using Graph Based Methods. In: Metaxas, D.N., Axel, L. (eds) Functional Imaging and Modeling of the Heart. FIMH 2011. Lecture Notes in Computer Science, vol 6666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21028-0_9

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  • DOI: https://doi.org/10.1007/978-3-642-21028-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21027-3

  • Online ISBN: 978-3-642-21028-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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