Localization of an Equivalent Central Cardiac Electric Dipole for Electrocardiography Applications

In the dipole approach the activity of the heart is represented by one or two moving-rotating current dipoles. The basic underlying principle is to select the amplitudes and coordinates of these dipoles within an appropriate model of the torso such that calculated torsosurface potential distribution closely matches the measured body-surface-potential distribution. This source model was used by Gulrajani et al, [2, 3], in some earlier investigations and Guard et al, [4]. Also Armoundas et al. [5], and Abstract— An efficient and robust method for the solution of the non-linear and ill-posed inverse problem of electrocardiography is presented. The hearts activity is modeled by a central cardiac electric dipole, which within the present work is allowed only to rotate about a fixed origin. For this purpose a three-dimensional volume conductor model of the human body is constructed based on a classical anatomic atlas. This is excited by an assumed (initial guess) dipole located at the center of the heart. In turn a Least squares optimization scheme is employed, aiming at the matching of the potential distribution calculated on the torso surface to the corresponding distribution measured with the aid of multiple electrodes. The efficiency of the method stems from the employment of arbitrary shaped hexahedral elements within the finite element method for the minimization of the required computational resources while the model realistically reflects the body internal structure. Finally, the algorithm is successfully tested using measured data available online H Bruder et al, [6] used the single moving dipole to simulate the electrical activity of the heart. There are many other research groups, [7,8] in the inverse electrocardiography field which aim at the definition of epicardial potential distribution either by using realistic geometry anisotropic heart models or trying to exploit a priory information. The research status up to 1998 is given in the review paper [1]. A common characteristic of these inverse problems is their ill-posed nature, where this difficulty becomes worst when the number of unknown parameters is increased. Namely, the problem is best conditioned when a single cardiac equivalent electric dipole is considered, which in turn involves a compromise in modeling accuracy. The solution of this inverse problem is generally based on a “volume conductor model” representing the whole body, which enables the solution of the forward problem. Preferably this model should retain high spatial resolution around the heart. The assumed equivalent electric source for heart activity is modeled and the generalized Laplace or Poisson equation (forward problem) is solved to obtain a “calculated data set” for the body surface potentials. At this point a multiple lead (e.g. 24 electrodes or more) electrocardiographer is required to facilitate the “measured data set” on the actual human subject to be diagnosed. In turn an inverse problem solution algorithm like Newton’s, Newton-Raphson e.t.c can be employed for the minimization of a cost function, usually in the least squares means. Moreover, like most inverse problems this is a non-linear one. So, the initially assumed equivalent electric dipole parameters (e.g. 3 dipole moment components and 3 dipole coordinates) are iteratively updated until the differences between the measured and calculated data sets become comparable to an accepted error tolerance. The latter may be defined by the measurements errors and their noise as well as the computer modeling inaccuracies.