Forward problem of electrocardiography based on cardiac source vector orientations.

To localize the unusual cardiac activities non-invasively, one has to build a prior forward model that relates the heart, torso, and detectors. This model has to be constructed to mathematically relate the geometrical and functional activities of the heart. Several methods are available to model the prior sources in the forward problem, which results in the lead field matrix generation. In the conventional technique, the lead field assumed the fixed prior sources, and the source vector orientations were presumed to be parallel to the detector plane with the unit strength in all directions. However, the anomalies cannot always be expected to occur in the same location and orientation, leading to misinterpretation and misdiagnosis. To overcome this, the work proposes a new forward model constructed using the VCG signals of the same subject. Furthermore, three transformation methods were used to extract VCG in constructing the time-varying lead fields to steer to the orientation of the source rather than just reconstructing its activities in the inverse problem. In addition, the unit VCG loop of the acute ischemia patient was extracted to observe the changes compared to the normal subject. The abnormality condition was achieved by delaying the depolarization time by 15ms. The results involving the unit vectors of VCG demonstrated the anisotropic nature of cardiac source orientations, providing information about the heart's electrical activity.

Localization of magnetocardiographic sources for myocardial infarction cases using deterministic and Bayesian approaches.

In this paper, the inverse problems of cardiac sources using analytical and probabilistic methods are solved and discussed. The standard Tikhonov regularization technique is solved initially to estimate the under-determined heart surface potentials from Magnetocardiographic (MCG) signals. The results of the deterministic method subjected to noise in the measurements are discussed and compared with the probabilistic models. Hierarchical Bayesian modeling with fixed Gaussian prior is employed to quantify the uncertainties in source reconstructions. A novel application of Variational Bayesian inference approach has been presented to estimate the heart sources. The reconstruction results of Variational Bayesian model with non-stationary priors are compared with solutions of simplistic Bayesian approach; and the performances are evaluated using Root Mean Square Error (RMSE) and correlation co-efficient metrics. The Bayesian solutions in the study are also extended to localize the MCG sources for two types of Myocardial infarction cases.

Computational imaging of the cardiac activities using magnetocardiography.

The electrical impulses of the heart will generate a tiny magnetic field outside the thorax that is measured as Magnetocardiographic signals. The challenging study is to estimate the cardiac activities in terms of depolarisation and repolarization maps from the measured signals called as inverse problem. This is computed only if one has solved generic or subject- specific prior models using the anatomical structures of the myocardium, the torso and the detectors called as forward problem. In this study, the Discretised heart is priorily assumed as the dipolar sources forming a double layer. The thorax structure modelled with finite element meshes is considered in the forward study. The magnetocardiographic data are simulated using uniform double layer model representing transmembrane distribution on the epicardium and endocardium. Using this data, the activation maps are non-invasively imaged on the heart surface using Tikhonov's regularisation technique. The inverse study is extended to reconstruct the depolarisation sequences of the abnormal cases.