Applicability of the single equivalent point dipole model to represent a spatially distributed bio-electrical source

Although the single equivalent point dipole model has been used to represen t well-localised bio-electrical sources, in realistic situations the source is distributed. Consequently, position estimates of point dipoles determin ed by inverse algorithms suffer from systematic error due to the non-exact applicability of the inverse model. In realistic situations, this systemati c error cannot be avoided, a limitation that is independent of the complexi ty of the torso model used. This study quantitatively investigates the intr insic limitations in the assignment of a location to the equivalent dipole due to distributed electrical source. To simulate arrhythmic activity in th e heart, a model of a wave of depolarisation spreading from a focal source over the surface of a spherical shell is used. The activity is represented by a sequence of concentric belt sources (obtained by slicing the shell wit h a sequence of parallel plane pairs), with constant dipole moment per unit length (circumferentially) directed parallel to the propagation direction. The distributed source is represented by N dipoles at equal arc lengths al ong the belt. The sum of the dipole potentials is calculated at predefined electrode locations. The inverse problem involves finding a single equivale nt point dipole that best reproduces the electrode potentials due to the di stributed source. The inverse problem is implemented by minimising the chi (2) per degree of freedom. It is found that the trajectory traced by the eq uivalent dipole is sensitive to the location of the spherical shell relativ e to the fixed electrodes. It is shown that this trajectory does not coinci de with the sequence of geometrical centres of the consecutive belt sources . For distributed sources within a bounded spherical medium, displaced from the sphere's centre by 40% of the sphere's radius, it is found that the er ror in the equivalent dipole location varies from 3 to 20% for sources with size between 5 and 50% of the sphere's radius. Finally, a method is devise d to obtain the size of the distributed source during the cardiac cycle.