Derivation of aimed electrocardiographic leads from the multiple expansion.

Summary The electrical sources which give rise to the surface electrocardiogram can be represented by a multipole expansion. An electrocardiographic lead can be looked upon as a weighted vectorial sum of the cardiac current source moments. An aimed lead is defined as one which responds predominantly to activity in a local region of the heart. The heart is here represented as a spherical shell of mean radius R. The aimed lead is developed by taking the weighting function to be an impulse function on the sphere of radius R. Expansion of the impulse function in spherical harmonics leads to the following expression for the voltage in the aimed lead: V=1.5a 10 +1.25a 20 /R+1.17a 30 /R 2 +… where a no are multipole coefficients at the center of the sphere for a particular, but arbitrary, orientation of the Z axis. In practice, these coefficients would be calculated from body surface potentials.

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