Determination of transmembrane currents from external potential measurements by the method of regularization

A novel non-invasive technique for measuring the transmembrane currents during action potential depolarizations of stalk segments of the giant unicellular alga Acetabularia mediterranea is described. This involves measurement of spatial samples of the time-dependent potential in the external medium (sea water) and an inverse transformation to give the current distribution at the cell surface. A detailed description of the method of regularization needed to handle this ill-conditioned inversion problem is presented in this paper, along with the results of test experiments to demonstrate its validity. An example of its application to the data recorded from an actual cell is also given.