IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 56, NO. 4, APRIL 2009 923 Effect of Cardiac Motion on Solution of the Electrocardiography Inverse Problem Mingfeng Jiang, Ling Xia ∗ , Member, IEEE, Guofa Shou, Qing Wei, Feng Liu, and Stuart Crozier, Member, IEEE Abstract—Previous studies of the ECG inverse problem often assumed that the heart was static during the cardiac cycle; con- sequently, a time-dependent geometrical error was thought to be unavoidably introduced. In this paper, cardiac motion is included in solutions to the electrocardiographic inverse problem. Cardiac dynamics are simulated based on a previously developed biventric- ular model that coupled the electrical and mechanical properties of the heart, and simulated the ventricular wall motion and de- formation. In the forward computation, the heart surface source model method is employed to calculate the epicardial potentials from the action potentials, and then, the simulated epicardial po- tentials are used to calculate body surface potentials. With the inclusion of cardiac motion, the calculated body surface potentials are more reasonable than those in the case of static assumption. In the epicardial potential-based inverse studies, the Tikhonov regu- larization method is used to handle ill-posedness of the ECG inverse problem. The simulation results demonstrate that the solutions ob- tained from both the static ECG inverse problem and the dynamic ECG inverse problem approaches are approximately the same dur- ing the QRS complex period, due to the minimal deformation of the heart in this period. However, with the most obvious deforma- tion occurring during the ST-T segment, the static assumption of heart always generates something akin to geometry noise in the ECG inverse problem causing the inverse solutions to have large errors. This study suggests that the inclusion of cardiac motion in solving the ECG inverse problem can lead to more accurate and acceptable inverse solutions. Index Terms—Cardiac motion, ECG inverse problem, heart sur- face source method, static heart model. I. INTRODUCTION N ONINVASIVE electrical imaging of the heart aims to quantitatively reconstruct epicardial, endocardial, and my- ocardial potentials, electrograms, and isochrones of the heart Manuscript received February 14, 2008; revised July 14, 2008. First published October 3, 2008; current version published May 6, 2009. This work was supported in part by the 973 National Key Basic Research and Development Program under Grant 2003CB716106, by the 863 High-Tech Research and Development Program under Grant 2006AA02Z307, by the National Natural Science Foundation of China under Grant 30570484, by the Program for New Century Excellent Talents in University under Grant NCET-04-0550, and by the Australian Research Council. Asterisk indicates corresponding author. M. Jiang is with the Department of Biomedical Engineering, Zhejiang Uni- versity, Hangzhou 310027, China, and also with the College of Electronics and Informatics, Zhejiang Sci-Tech University, Hangzhou 310018, China (e-mail: peterjiang0517@163.com). ∗ L. Xia is with the Department of Biomedical Engineering, Zhejiang Univer- sity, Hangzhou 310027, China (e-mail: xialing@zju.edu.cn). G. Shou is with the Department of Biomedical Engineering, Zhejiang Uni- versity, Hangzhou, 310027, China (e-mail: shouguofa@hotmail.com). Q. Wei, F. Liu, and S. Crozier are with the School of Information Tech- nology and Electrical Engineering, University of Queensland, Brisbane, Qld. 4072, Australia (e-mail: tracy@itee.uq.edu.au; feng@itee.uq.edu.au; stuart@ itee.uq.edu.au). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TBME.2008.2005967 from torso surface potentials. In recent years, several stud- ies [1]–[7] have demonstrated that this technique can be used to image normal and abnormal cardiac electrophysiological activ- ity with accuracy for both simulation and experimental studies. In general, the major challenge of this imaging method is that it involves a noninvasive computing procedure for the predic- tion of epicardial surface potentials (or other types of cardiac sources) from torso surface potentials, which constitutes one form of the inverse problem of ECG [1], [8]–[10]. Body surface potentials (BSPs) (ϕ B ) are related to epicardial potentials (EPs) (ϕ H ) through a linear system of equations T BH ϕ H = ϕ B (1) where T BH is the transfer matrix associated with volume con- ductor (torso) properties including geometry, conductivity, and distance between the epicardial surface and the torso surface. The transfer matrix T BH can be obtained by a numerical method, such as a boundary-element method (BEM) [11]–[13]. However, the system function (1) is ill-conditioned. Small measurement errors in the surface potentials (vector ϕ B ), or any geometrical error in the constructed volume conductor model (matrix T BH ), can lead to large unbound errors when trying to solve the associ- ated inverse problem [14]–[16]. Certainly, a direct inverse does not exist, given the fact that practice (1) may be over- or under- determined. To find a practical solution, the previous problem can be reformatted to be a minimization problem f = arg min ϕ H ‖T BH ϕ H − ϕ B ‖ 2 . (2) This treatment can help us to find a solution; however, the ill-posedness of the problem is not handled by doing so, and should be overcome later by regularization techniques. To solve the system function (1) or (2), some work considered differ- ent geometric noises. For example, in [17] and [18], the effect of geometry errors are mainly addressed under the valid static assumption during diastole. Some other researchers [19], [20] have attempted to introduce geometric noise by a 1-cm offset of the heart position relative to the torso center: moving inward to the torso center or moving outward to the anterior torso surface. Clearly, however, the heart sources move due to mechanical deformations during the cardiac cycle, and this change should lead to a different heart displacement that produces a different volume conductor model (matrix T BH ). It is therefore important to investigate the error introduced by the static assumption in terms of the inverse epicardial solutions (ϕ H ). Quantitative and accurate estimates of heart motion and deformation are of im- portance for determining the transfer matrix (T BH ) and seeking the inverse solutions (ϕ H ). 0018-9294/$25.00 © 2009 IEEE