Generative Modeling and Inverse Imaging of Cardiac Transmembrane Potential

  • Sandesh GhimireEmail author
  • Jwala Dhamala
  • Prashnna Kumar Gyawali
  • John L. Sapp
  • Milan Horacek
  • Linwei Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11071)


Noninvasive reconstruction of cardiac transmembrane potential (TMP) from surface electrocardiograms (ECG) involves an ill-posed inverse problem. Model-constrained regularization is powerful for incorporating rich physiological knowledge about spatiotemporal TMP dynamics. These models are controlled by high-dimensional physical parameters which, if fixed, can introduce model errors and reduce the accuracy of TMP reconstruction. Simultaneous adaptation of these parameters during TMP reconstruction, however, is difficult due to their high dimensionality. We introduce a novel model-constrained inference framework that replaces conventional physiological models with a deep generative model trained to generate TMP sequences from low-dimensional generative factors. Using a variational auto-encoder (VAE) with long short-term memory (LSTM) networks, we train the VAE decoder to learn the conditional likelihood of TMP, while the encoder learns the prior distribution of generative factors. These two components allow us to develop an efficient algorithm to simultaneously infer the generative factors and TMP signals from ECG data. Synthetic and real-data experiments demonstrate that the presented method significantly improve the accuracy of TMP reconstruction compared with methods constrained by conventional physiological models or without physiological constraints.


Inverse problem ECG imaging Sequential variational auto-encoder Bayesian inference 



This work is supported by the National Science Foundation under CAREER Award ACI-1350374.


  1. 1.
    Aliev, R.R., Panfilov, A.V.: A simple two-variable model of cardiac excitation. Chaos Solitons Fractals 7(3), 293–301 (1996)CrossRefGoogle Scholar
  2. 2.
    Bowman, S.R., Vilnis, L., Vinyals, O., Dai, A.M., Jozefowicz, R., Bengio, S.: Generating sentences from a continuous space. arXiv preprint arXiv:1511.06349 (2015)
  3. 3.
    Ghimire, Sandesh, Sapp, John L., Horacek, Milan, Wang, Linwei: A variational approach to sparse model error estimation in cardiac electrophysiological imaging. In: Descoteaux, Maxime, Maier-Hein, Lena, Franz, Alfred, Jannin, Pierre, Collins, D.Louis, Duchesne, Simon (eds.) MICCAI 2017. LNCS, vol. 10434, pp. 745–753. Springer, Cham (2017). Scholar
  4. 4.
    Ghodrati, A., Brooks, D.H., Tadmor, G., MacLeod, R.S.: Wavefront-based models for inverse electrocardiography. IEEE TBME 53(9), 1821–1831 (2006)Google Scholar
  5. 5.
    Greensite, F., Huiskamp, G.: An improved method for estimating epicardial potentials from the body surface. IEEE TBME 45(1), 98–104 (1998)Google Scholar
  6. 6.
    Gulrajani, R.M.: The forward and inverse problems of electrocardiography. IEEE Eng. Med. Biol. Mag. 17(5), 84–101 (1998)CrossRefGoogle Scholar
  7. 7.
    He, B., Li, G., Zhang, X.: Noninvasive imaging of cardiac transmembrane potentials within three-dimensional myocardium by means of a realistic geometry anisotropic heart model. IEEE TBME 50(10), 1190–1202 (2003)Google Scholar
  8. 8.
    Kingma, D.P., Welling, M.: Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114 (2013)
  9. 9.
    Plonsey, R., Barr, R.C.: Bioelectricity: A Quantitative Approach. Springer, New York (2007). Scholar
  10. 10.
    Pullan, A., Cheng, L., Nash, M., Bradley, C., Paterson, D.: Noninvasive electrical imaging of the heart: theory and model development. Ann. Biomed. Eng. 29(10), 817–836 (2001)CrossRefGoogle Scholar
  11. 11.
    Van Dam, P.M., Oostendorp, T.F., Linnenbank, A.C., Van Oosterom, A.: Non-invasive imaging of cardiac activation and recovery. Ann. Biomed. Eng. 37(9), 1739–1756 (2009)CrossRefGoogle Scholar
  12. 12.
    Wang, L., Zhang, H., Wong, K.C., Liu, H., Shi, P.: Physiological-model-constrained noninvasive reconstruction of volumetric myocardial transmembrane potentials. IEEE Trans. Biomed. Eng. 57(2), 296–315 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Sandesh Ghimire
    • 1
    Email author
  • Jwala Dhamala
    • 1
  • Prashnna Kumar Gyawali
    • 1
  • John L. Sapp
    • 2
  • Milan Horacek
    • 2
  • Linwei Wang
    • 1
  1. 1.Rochester Institute of TechnologyRochesterUSA
  2. 2.Dalhouse UniversityHalifaxCanada

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