Hierarchical Multiple-Model Bayesian Approach to Transmural Electrophysiological Imaging

  • Azar Rahimi
  • Jingjia Xu
  • Linwei Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8674)


Noninvasive electrophysiological (EP) imaging of the heart aims to mathematically reconstruct the spatiotemporal dynamics of cardiac current sources from body-surface electrocardiographic (ECG) data. This ill-posed problem is often regularized by a fixed constraining model. However, this approach enforces the source distribution to follow a pre-assumed spatial structure that does not always match the varying spatiotemporal distribution of current sources. We propose a hierarchical Bayesian approach to transmural EP imaging that employs a continuous combination of multiple models, each reflecting a specific spatial property for current sources. Multiple models are incorporated as an Lp-norm prior for current sources, where p is an unknown hyperparameter with a prior probabilistic distribution. The current source estimation is obtained as an optimally weighted combination of solutions across all models, the weight being determined from the posterior distribution of p inferred from ECG data. The accuracy of our approach is assessed in a set of synthetic and real-data experiments on human heart-torso models. While the use of fixed models (L1- and L2-norm) only properly recovers sources with specific structures, our method delivers consistent performance in reconstructing sources with various extents and structures.


Transmural electrophysiological imaging Lp-norm regularization multiple-model estimation Bayesian inference 


  1. 1.
    Ghosh, S., Rudy, Y.: Application of l1-norm regularization to epicardial potential solutions of the inverse electrocardiography problem. Annals of Biomedical Engineering 37(5), 692–699 (2009)CrossRefGoogle Scholar
  2. 2.
    Plonsey, R.: Bioelectric phenonmena. McGraw Hill, New York (1969)Google Scholar
  3. 3.
    Pullan, A.J., Cheng, L.K., Nash, M.P., Bradley, C.P., Paterson, D.J.: Noninvasive electrical imaging of the heart: Theory and model development. Annals of Biomedical Engineering 29, 817–836 (2001)CrossRefGoogle Scholar
  4. 4.
    Huiskamp, G., Greensite, F.: A new method for myocardial activation imaging. IEEE Transactions on Biomedical Engineering 44(6), 433–446 (1997)CrossRefGoogle Scholar
  5. 5.
    Wang, L., Zhang, H., Wong, K., Liu, H., Shi, P.: Physiological-model-constrained noninvasive reconstruction of volumetric myocardial transmembrane potentials. IEEE Transactions on Biomedical Engineering 57(2), 296–315 (2010)CrossRefGoogle Scholar
  6. 6.
    He, B., Wu, D.: Imaging and visualization of 3-d cardiac electric activity. IEEE Transactions on Information Technology in Biomedicine 5(3), 181–186 (2001)CrossRefGoogle Scholar
  7. 7.
    Xu, J., Dehaghani, A.R., Gao, F., Wang, L.: Localization of sparse transmural excitation stimuli from surface mapping. In: Ayache, N., Delingette, H., Golland, P., Mori, K. (eds.) MICCAI 2012, Part I. LNCS, vol. 7510, pp. 675–682. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Shou, G., Xia, L., Liu, F., Jiang, M., Crozier, S.: On epicardial potential reconstruction using regularization schemes with the l1-norm data term. Physics in Medicine and Biology 56(1), 57–72 (2011)CrossRefGoogle Scholar
  9. 9.
    Wang, L., Qin, J., Wong, T.T., Heng, P.A.: Application of l1-norm regularization to epicardial potential reconstruction based on gradient projection. Physics in Medicine and Biology 56(19), 6291–6310 (2011)CrossRefGoogle Scholar
  10. 10.
    Rahimi, A., Xu, J., Wang, L.: Lp-norm regularization in volumetric imaging of cardiac current sources. Computational and Mathematical Methods in Medicine (2013)Google Scholar
  11. 11.
    Nash, M.: Mechanics and Material Properties of the Heart using an Anatomically Accurate Mathematical Model. PhD thesis, Univ. of Auckland, New Zealand (1998)Google Scholar
  12. 12.
    Neal, R.M.: Slice sampling. The Annals of Statistics 31, 705–767 (2003)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Goldberger, A.L., et al.: Physiobank, physiotoolkit, and physionet components of a new research resource for complex physiological signals. Circulation 101, 215–220 (2000)CrossRefGoogle Scholar
  14. 14.
    Title, L.M., Iles, S.E., Gardner, M.J., Penney, C.J., Clements, J.C., Horacek, B.M.: Quantitative assessment of myocardial ischemia by electrocardiographic and scintigraphic imaging. Journal of Electrocardiology 36(suppl.), 17–26 (2003)CrossRefGoogle Scholar
  15. 15.
    Cerqueira, M.D., Weissman, N.J., Dilsizian, V., et al.: Standardized myocardial segmentation and nomenclature for tomographic imaging of the heart. Circulation 105, 539–542 (2002)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Azar Rahimi
    • 1
  • Jingjia Xu
    • 1
  • Linwei Wang
    • 1
  1. 1.Rochester Institute of TechnologyRochesterUSA

Personalised recommendations