Integral characteristics of the cardiac electrical generator.
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Biomedical subjects
Publications and source records attributed to L I Titomir.
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Integral characteristics (dipole moment, localization of the electrical centre and complexity parameter) of cardiac electrical generator for the normal dog heart during the fast repolarization period (corresponding to the T wave of electrocardiogram) are considered. The characteristics are calculated using electrical field potentials measured on a spherical surface around the heart. It is found that during the repolarization period these characteristics change with time much less and provide more accurate description of the heart electrical state than during the depolarization period (corresponding to the QRS complex of electrocardiogram). It is shown that over all the cardiac cycle the equivalent generator having form of a single dipole localized at the moving electrical centre of the heart provides average error of potential approximation that does not exceed average random error of present electrocardiographic recording technique. In addition this model includes comparatively small number of variables and has explicit physical and physiological interpretation. Thus application of such a model for describing cardiac electrical generator is more reasonable than application of the classical multipole models of high orders.
On the basis of the bidomain model that takes into account the electric anisotropy of body tissues, analytical relationships were developed for calculating the characteristics of electric and magnetic fields produced by an elementary (dipole) bioelectric generator that arises in the electrogenic excitable tissue of the myocardium. The errors in the identification of intensity and location of the bioelectric generator in the myocardium were estimated from the measurements of its external fields (noninvasive identification of the excited region) using approximate methods based on isotropic models of the physical medium.
On the basis of the bidomain model of anisotropic myocardium, mathematical relationships for calculating the characteristics of the extracellular electric and magnetic fields outside a closed or open depolarization front were derived on the assumption that the generator and fields are axially symmetric with respect to the longitudinal direction of the fibres making up the excitable tissue. The spatial configuration of the fields was determined and quantitative estimates were obtained for the electric potential and magnetic induction caused solely by the macroscopic anisotropy of the myocardium tissue as a volume conductor.
The paper describes a technique and some results of experimental measurements of electrical potentials generated by an isolated dog heart in homogeneous conductor, drawing equipotential maps of the field, and calculating the characteristics of the dipole equivalent generator of the heart. The form of potential distribution on a spherical surface around the heart and its ideal orthogonal vectorcardiograms are discussed.
Using the equations of electrodynamics of stationary currents, relationships were derived for calculating the characteristics of electric and magnetic fields of an elementary (dipole) bioelectric generator in a heterogeneous medium consisting of two regions namely, an anisotropic conducting region corresponding to the excitable myocardium tissue and an isotropic conducting or dielectric region corresponding to the space outside the myocardium where the measurement is made. The shape of distributions of the electric potential and magnetic induction at the myocardium surface was determined, and the effect of anisotropy on these distributions was estimate. Formulas for the identification of the local excited zone within the myocardium from electric and magnetic measurements outside the excitable tissue or on its surface were obtained.
A method for determination of the cardiac electric center on the basis of noninvasive multichannel measurements and multipole description of the cardioelectric potential is proposed. The method provides a more accurate and stable spatial location of the cardioelectric generator as compared to other methods (in particular, those based on minimization of the quadrupole potential). The position of the electric center is a useful characteristic for topical diagnosis of the electrophysiological state and function of the heart. Using mathematical models, the dependence of the position of the electric center, determined by the method presented, on the configuration and spatial position of the cardiogenerator is illustrated.
A set of characterisitics of the cardiac electrical generator is described which expresses in an integral form some important properties of the electrical excitation wave, in particular its summary intensity, average spatial localization and distinction from a uniform double layer with planar rim. Relation of the proposed model to the multipole equivalent generator is discussed, and procedures for computing its characteristics are given. Calculation results for these characteristics on the basis of experimentally measured electrical field potentials of isolated dog hearts are presented.
Using mathematical models of the bioelectric generators of the heart with surface distributed configurations, it was shown that the coordinates of the moving electric center of the heart can facilitate the recognition of the global spatial position of electrogenic zones in the myocardium. These coordinates were determined by the previously proposed method from the cardioelectric potential measured noninvasively with a multichannel lead system in the framework of electrocardiographic mapping.
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