Signal Processing Methods For Inverse Problems In Electrophysiology

Estimation of bioelectric source potentials using remote electric field measurements is known as the inverse problem in electrophysiology. Both numerical and analytic approaches to this problem have been developed, analytic solutions having the advantage of explicit parameterization in terms of measurable tissue properties. This paper describes an analytic Fourier Transform method for determining frog sciatic nerve activity from limb surface potential measurements. The thigh is modeled as a cylinder containing one bioelectric source (the sciatic nerve) and a major inhomogeneity (the bone). Idealized electrical properties are assigned to the limb tissues. A forward solution predicting surface potentials resulting from sciatic nerve activity is derived, and re-expressed as the action of a 2D filter, representing the thigh, on source potentials. Inversion of the forward filter provides an ideal inverse solution, which is modified in the spatial frequency domain to eliminate excessive sensitivity to noise. Predicted and measured sciatic nerve potentials are compared, and various modifications to the idea filter are examined.