Effects of experimental and modeling errors on electrocardiographic inverse formulations

The inverse problem of electrocardiology aims to reconstruct the electrical activity occurring within the heart using information obtained noninvasively on the body surface. Potentials obtained on the torso surface can be used as input for the inverse problem and an electrical image of the heart obtained. There are a number of different inverse algorithms currently used to produce electrical images of the heart. By performing a detailed simulation study, we compare the performances of epicardial potential (Tikhonov, truncated singular value decomposition (TSVD), and Greensite) and myocardial activation-based (critical point) inverse simulations along with different methods of choosing the appropriate level of regularization (optimal, L-curve, composite residual and smoothing operator, zero-crossing) to apply to each of these inverse methods. We also examine the effects of a variety of signal error, material property error, geometric error and a combination of these errors on each of the electrocardiographic inverse algorithms. Results from the simulation study show that the activation-based method is able to produce solutions which are more accurate and stable than potential-based methods especially in the presence of correlated errors such as geometric uncertainty. In general, the Greensite-Tikhonov method produced the most realistic potential-based solutions while the zero-crossing and L-curve were the preferred method for determining the regularization parameter. The presence of signal or material property error has little effect on the inverse solutions when compared with the large errors which resulted from the presence of any geometric error. In the presence of combined Gaussian and correlated errors representing conditions which may be encountered in an experimental or clinical environment, there was less variability between potential-based solutions produced by each of the inverse algorithms.

[1]  R. Holland,et al.  The QRS complex during myocardial ischemia. An experimental analysis in the porcine heart. , 1976, The Journal of clinical investigation.

[2]  M. P. Nash,et al.  Noninvasive Electrical Imaging of the Heart: Theory and Model Development , 2004, Annals of Biomedical Engineering.

[3]  R. Gulrajani The forward and inverse problems of electrocardiography. , 1998, IEEE engineering in medicine and biology magazine : the quarterly magazine of the Engineering in Medicine & Biology Society.

[4]  B. Taccardi,et al.  Finite element approximation of regularized solutions of the inverse potential problem of electrocardiography and applications to experimental data , 1985 .

[5]  Andrew J. Pullan,et al.  Comparison of potential- and activation-based formulations for the inverse problem of electrocardiology , 2003, IEEE Transactions on Biomedical Engineering.

[6]  Y. Rudy,et al.  Electrocardiographic imaging: Noninvasive characterization of intramural myocardial activation from inverse-reconstructed epicardial potentials and electrograms. , 1998, Circulation.

[7]  Andrew J. Pullan,et al.  Modelling myocardial excitation wavefront propagation in ventricles by finite element solution of an eikonal equation , 1999, Proceedings of the First Joint BMES/EMBS Conference. 1999 IEEE Engineering in Medicine and Biology 21st Annual Conference and the 1999 Annual Fall Meeting of the Biomedical Engineering Society (Cat. N.

[8]  Y. Rudy,et al.  The Inverse Problem in Electrocardiography: A Model Study of the Effects of Geometry and Conductivity Parameters on the Reconstruction of Epicardial Potentials , 1986, IEEE Transactions on Biomedical Engineering.

[9]  Fred Greensite,et al.  Second-Order Approximation of the Pseudoinverse for Operator Deconvolutions and Families of Ill-Posed Problems , 1998, SIAM J. Appl. Math..

[10]  A. Rosenthal,et al.  Influence of Acute Variations in Hematocrit on the QRS Complex of the Frank Electrocardiogram , 1971, Circulation.

[11]  M. Mlynash,et al.  Closed-chest validation of source imaging from human ECG and MCG mapping data , 1999, Proceedings of the First Joint BMES/EMBS Conference. 1999 IEEE Engineering in Medicine and Biology 21st Annual Conference and the 1999 Annual Fall Meeting of the Biomedical Engineering Society (Cat. N.

[12]  J. Hadamard,et al.  Lectures on Cauchy's Problem in Linear Partial Differential Equations , 1924 .

[13]  R. Gulrajani,et al.  A new method for regularization parameter determination in the inverse problem of electrocardiography , 1997, IEEE Transactions on Biomedical Engineering.

[14]  D Kilpatrick,et al.  The inverse problem of electrocardiology: the performance of inversion techniques as a function of patient anatomy. , 1995, Mathematical biosciences.

[15]  G. Huiskamp,et al.  An improved method for estimating epicardial potentials from the body surface , 1998, IEEE Transactions on Biomedical Engineering.

[16]  G. Huiskamp,et al.  Tailored versus realistic geometry in the inverse problem of electrocardiography , 1989, IEEE Transactions on Biomedical Engineering.

[17]  Per Christian Hansen,et al.  Analysis of Discrete Ill-Posed Problems by Means of the L-Curve , 1992, SIAM Rev..

[18]  Per Christian Hansen,et al.  Truncated Singular Value Decomposition Solutions to Discrete Ill-Posed Problems with Ill-Determined Numerical Rank , 1990, SIAM J. Sci. Comput..

[19]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[20]  G. Huiskamp,et al.  A new method for myocardial activation imaging , 1997, IEEE Transactions on Biomedical Engineering.

[21]  Dana H. Brooks,et al.  Electrical imaging of the heart , 1997, IEEE Signal Process. Mag..