Accuracy of electrocardiographic imaging using the method of fundamental solutions

Solving the inverse problem of electrocardiology via the Method of Fundamental Solutions has been proposed previously. The advantage of this approach is that it is a meshless method, so it is far easier to implement numerically than many other approaches. However, determining the heart surface potential distribution is still an ill-posed problem and thus requires some form of Tikhonov regularisation to obtain the required distributions. In this study, several methods for determining an "optimal" regularisation parameter are compared in the context of solving the inverse problem of electrocardiology via the Method of Fundamental Solutions. It is found that the Robust Generalised Cross-Validation method most often yields epicardial potential distributions with the least relative error when compared to the input distribution. The study also compares the inverse solutions obtained with the Method of Fundamental Solutions with those obtained in a previous study using the boundary element method. It is found that choosing the best solution methodology and regularisation parameter determination method depends on the particular scenario being considered.

[1]  Alireza Mazloumi Gavgani,et al.  Use of genetic algorithm for selection of regularization parameters in multiple constraint inverse ECG problem , 2011, 2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[2]  Robert Michael Kirby,et al.  Inverse electrocardiographic source localization of ischemia: An optimization framework and finite element solution , 2013, J. Comput. Phys..

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

[4]  Rob S. MacLeod,et al.  Inverse electrocardiography by simultaneous imposition of multiple constraints , 1999, IEEE Transactions on Biomedical Engineering.

[5]  F. J. Claydon,et al.  A volume conductor model of the thorax for the study of defibrillation fields , 1988, IEEE Transactions on Biomedical Engineering.

[6]  Yves Coudière,et al.  Improving the Spatial Solution of Electrocardiographic Imaging: A New Regularization Parameter Choice Technique for the Tikhonov Method , 2017, FIMH.

[7]  R. Gulrajani.  Bioelectricity and biomagnetism , 1998 .

[8]  B. M. Horacek,et al.  Numerical Model of an Inhomogeneous Human Torso1 , 1974 .

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

[10]  R. Macleod,et al.  The Forward Problem of Electrocardiography , 2010 .

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

[12]  D. Lesnic,et al.  A survey of applications of the MFS to inverse problems , 2011 .

[13]  Quan Ni,et al.  Three-Dimensional Activation Mapping in Ventricular Muscle: Interpolation and Approximation of Activation Times , 1999, Annals of Biomedical Engineering.

[14]  Alireza Mazloumi Gavgani,et al.  Genetic algorithm-based regularization parameter estimation for the inverse electrocardiography problem using multiple constraints , 2012, Medical & Biological Engineering & Computing.

[15]  Alireza Mazloumi Gavgani,et al.  Noise reduction using anisotropic diffusion filter in inverse electrocardiology , 2012, 2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[16]  G. Wahba.  Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy , 1977 .

[17]  Per Christian Hansen,et al.  Rank-Deficient and Discrete Ill-Posed Problems , 1996 .

[18]  R M Gulrajani,et al.  A computer heart model incorporating anisotropic propagation. I. Model construction and simulation of normal activation. , 1993, Journal of electrocardiology.

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

[20]  Y. Rudy,et al.  Application of the Method of Fundamental Solutions to Potential-based Inverse Electrocardiography , 2006, Annals of Biomedical Engineering.

[21]  M. A. Lukas.  Robust generalized cross-validation for choosing the regularization parameter , 2006 .

[22]  Y. Rudy,et al.  The use of temporal information in the regularization of the inverse problem of electrocardiography , 1992 .

[23]  Cesare Corrado,et al.  Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography , 2015, J. Comput. Phys..

[24]  Clifford H. Thurber,et al.  Parameter estimation and inverse problems , 2005 .

[25]  Y. Hon,et al.  Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators , 2007 .

[26]  Leo K. Cheng,et al.  The inverse problem of electrocardiography , 2011 .

[27]  Mark A. Lukas,et al.  Comparing parameter choice methods for regularization of ill-posed problems , 2011, Math. Comput. Simul..

[28]  Olaf Dössel,et al.  Use of a Tolerance Operator in Wavefront-Based ECG Imaging of Transmembrane Voltages , 2013 .

[29]  Robert Michael Kirby,et al.  Resolution Strategies for the Finite-Element-Based Solution of the ECG Inverse Problem , 2010, IEEE Transactions on Biomedical Engineering.

[30]  Peter R Johnston,et al.  Application of robust Generalised Cross-Validation to the inverse problem of electrocardiology , 2016, Comput. Biol. Medicine.

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

[32]  R. Mathon,et al.  The Approximate Solution of Elliptic Boundary-Value Problems by Fundamental Solutions , 1977 .