A Principle for Solving a Class of Anisotropic Current Flow Problems and Applications to Electrocardiography

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Abstract
In studies of electrocardiographic lead performance, theoretical analyses of the influence of the anisotropic heart and skeletal muscle are particularly difficult. In this paper, the basic differential equations of static fields and steady current flow are arranged to emphasize the field and conductivity dependent charge distributions which arise in anisotropic media. The equations are applied to two types of problems of immediate interest. Firstly, the equations are used to explain how anisotropic media may be included in current digital computer studies of the heart-lead relation and to conclude that the techniques which made the computer studies possible tend to lose their advantage when applied to arbitrary anisotropic configurations. Secondly, the equations are used to develop a principle which permits exact solutions for the fields of numerous simple anisotropic configurations. Three such configurations useful for heart-lead studies are analyzed with the following results: the anisotropic skeletal muscle can be treated in special cases such as a head-foot heart-vector lead approximately as isotropic with resistivity of 280 ohm cm; the closed dipolar layer in an anisotropic, inhomogeneous heart produces the same null electric field as it does in homogeneous isotropic media; bounds on the influence of the heart's anisotropy on a heart-vector lead field are estimated at plus or minus 12 percent of the average lead field intensity.