Noninvasive reconstruction of three-dimensional ventricular activation sequence from the inverse solution of distributed equivalent current density

Zhongming Liu, Chenguang Liu, Bin He

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80 Scopus citations


We propose a new electrocardiographic (ECG) inverse approach for imaging the three-dimensional (3-D) ventricular activation sequence based on the modeling and estimation of the equivalent current density throughout the entire volume of the ventricular myocardium. The spatio-temporal coherence of the ventricular excitation process has been utilized to derive the activation time from the estimated time course of the equivalent current density. In the present study, we explored four different linear inverse algorithms (the minimum norm and weighted minimum norm estimates in combination with two regularization schemes: the instant-by-instant regularization and the isotropy method) to estimate the current density at each time instant during the ventricular depolarization. The activation time at any given -location within the ventricular myocardium was determined as the time point with the occurrence of the maximum local current density estimate. Computer simulations were performed to evaluate this approach using single- and dual-site pacing protocols in a physiologically realistic cellular automaton heart model. The performance and stability of the proposed approach was evaluated with respect to the various levels of measurement noise (0, 5, 10, 20, 40, and 60 μV), the various numbers of ECG electrodes and the modeling errors on the torso geometry and heart position. The simulation results demonstrate that: 1) the single-site paced 3-D activation sequence can be well reconstructed from 200-channel body surface potential maps with additive Gaussian white noise of 20 μV (correlation coefficient = 0.90, relative error = 0.19, and localization error = 5.49 mm); 2) a higher imaging accuracy can be obtained when the activation is initiated from the left/right ventricle (LV/RV) compared to from the septum; 3) the isotropy method gives rise to a better performance than the conventional instant-by-instant regularization; 4) a decreased imaging accuracy results from a larger noise level, a fewer number of electrodes, or the volume conductor modeling errors; however, a reasonable imaging accuracy can still be obtained with a 60 /μV noise level, 64 electrodes, or mild errors on both the torso geometry and heart position, respectively; 5) the dual-site paced 3-D activation sequence can be imaged when the two sites are paced either simultaneously or with a time delay of 20 ms; 6) two pacing sites can be resolved and localized in the imaged 3-D activation sequence when they are located at the contralateral sides of ventricles or at the ventricular lateral wall and the apex, respectively.

Original languageEnglish (US)
Pages (from-to)1307-1318
Number of pages12
JournalIEEE Transactions on Medical Imaging
Issue number10
StatePublished - Oct 2006

Bibliographical note

Funding Information:
Manuscript received May 18, 2006; revised June 29, 2006. This work was supported in part by the National Science Foundation under Grant BES-0411480, in part by the American Heart Association under Grant 0140132N, in part by the National Institutes of Health under Grant RO1 EB-00178, and in part by the Biomedical Engineering Institute at the University of Minnesota. The work of Z. Liu and C. Liu was also supported in part by Predoctoral Fellowships from the American Heart Association, Greater Midwest Affiliates. Asterisk indicates corresponding author.


  • Activation sequence
  • Bidomain
  • Cardiac imaging
  • Electrocardiography
  • Equivalent current density
  • Inverse problem
  • Ventricular activation


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