Dynamic electrocardiography IV the “imaginary cardiac vector” hypothesis the evolution of the vectorcardiographic inverse solution

Abstract

This paper reviews the theory of electrocardiography and vectorcardiography and shows how this theory has attempted to circumvent the basic theoretical flaws of vectorcardiography arising from the fact that voltage is not a vector entity. First we describe the nature of the “forward” and “inverse” problems, the dependence of the inverse solution on a correct forward solution, and the concept of the transfer function. The “cardiac vector” approach is then seen to be a solution of the inverse problem based on a specific forward solution which defines the cardiac generator as a fixed-rotating dipole in a homogeneous volume conductor. The “simplistic” vectorcardiographers utilized voltage as a vector component until Burger emphasized that voltage is a scalar quantity. Burger attempted to circumvent this problem by proposing the “heart vector” ( H ) and “lead vector” ( L ) concepts. He defined the voltage in a lead as the scalar (dot) product of the “heart vector” and “lead vector”, of dimensions volt/cm 2. These dimensions do not apply to any known physical entity, and thus could well refer to an “imaginary” quantity. The current availability of 19 different vectorcardiographic lead systems indicates that no single attempt has adequately circumvented the problem arising from the basic theoretical flaws. The “imaginary cardiac vector” hypothesis suggests that these problems are likely to persist as no technique will be able to specify this “heart vector” if it does not exist as a real physical entity.