Relating the multipole moments of the heart to activated parts of the epicardium and endocardium

The electrical properties of the heart as the generator of the surface electrocardiogram are often described by its multipole moments. While it is possible to ascribe physiological meaning to the dipole moment, the physiological meaning of the higher moments (like quadrupole, octopole, etc.) is not clear. In the following, the multipole moments of the heart at any instant of its depolarization are related to the depolarized portions of the epicardium and endocardium at that time. The surfaces of the heart are divided into elements. Transfer coefficients between the known multipoles and these elements are defined. The transfer coefficients relate the multipoles and the fraction of depolarized area in each element. For the cases reported here, 3 to 8 surface elements are utilized, and the dipole, quadrupole, and octopole moments are studied. The general physiological characteristics of the activation process are formulated as a set of linear constraints. The whole problem is formulated as a quadratic programming problem and it is solved by standard techniques. The first three moments of an idealized human heart, the dipole, the quadrupole, and the octopole (the latter has not yet been measured), are calculated utilizing known experimental data of the activation of the heart. These moments and the activation data are used for testing the proposed procedures of interpreting multipolar data. It is found that from known dipole moments the depolarized fractions of 3 or 4 elements representing the left ventricular endocardium could be calculated. When the quadrupole moments are known, it might be possible to get some information about the activation of the right ventricle as well. These results are not improved by using octopole moments. The constraints used are valid only for the phase of activation of the ventricles. Supported in part by Program Research Grant HL-14388 from the National Heart and Lung Institute.