Ellipsoidal needle source

This geometry is important as a model for invasive electrodes, often used in neurophysiology with insulated shaft and an open half-elhpsoid-like end as the active electrode. The conductance of a half-ellipsoid of revolution in a half-infinite homogeneous medium is  

Equation (6.20) is for a noninsulated half-ellipsoid inserted from the surfaee. When the needle shaft is insulated so that when the needle is inserted from the surfaee and penetrates deeper into the tissue, the model may he regarded as a gradual ehange towards a full-length ellipsoid in an infinite medium. The eonductance given hy Eq. (6.20) would then be doubled. A slightly different model is to eonsider the half-ellipsoid positioned at the end of an insulating rod. 

A cylinder of length L and limited by two insulating plates perpendicular to the cylinder axis has the same electrical properties as the infinitely long cylinder per length L. 

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