An asymptotic estimate for the effective radius of a concentric bipolar electrode

A concentric bipolar electrode (CBE) (consisting of a central disc and an outer annulus) has been proposed as an approximate method of measuring the surface Laplacian of the body surface electrical potential distribution. The derivation of the surface Laplacian approximation, in terms of the potential difference measured with the bipolar electrode, contained an unspecified parameter which has been dubbed the 'effective radius' of the concentric bipolar electrode. This paper presents an asymptotic analysis to derive an expression for the effective radius in terms of the physical dimensions of the electrode (the radius of the central disc and inner and outer radii of the annulus). Also studied is the way in which the value of the effective radius affects the behaviour of the relative error in the surface Laplacian measurement at various dipole source locations within a conducting medium.