In vitro activation of retinal cells: estimating location of stimulated cell by using a mathematical model

Activation of neurons at different depths within the retina and at various eccentricities from the stimulating electrode will presumably influence the visual percepts created by a retinal prosthesis. With an electrical prosthesis, neurons will be activated in relation to the stimulating charge that impacts their cell membranes. The common model used to predict charge density is Coulomb's law, also known as the square law. We propose a modified model that can be used to predict neuronal depth that takes into account: (1) finite dimensions related to the position and size of the stimulating and return electrodes and (2) two-dimensional displacements of neurons with respect to the electrodes, two factors that are not considered in the square law model. We tested our model by using in vitro physiological threshold data that we had obtained previously for eight OFF-center brisk-transient rabbit retinal ganglion cells. For our most spatially dense threshold data (25 microm increments up to 100 microm from the cell body), our model estimated the depth of one RGC to be 76 +/- 76 microm versus 87 +/- 62 microm (median: SD) for the square law model, respectively. This difference was not statistically significant. For the seven other RGCs for which we had obtained threshold data up to 800 microm from the cell body, the estimate of the RGC depth (using data obtained along the X axis) was 96 +/- 74 versus 20 +/- 20 microm for the square law and our modified model, respectively. Although this difference was not statistically significant (Student t-test: p = 0.12), our model provided median values much closer to the estimated depth of these RGCs (>>25 microm). This more realistic estimate of cell depth predicted by our model is not unexpected in this latter data set because of the more spatially distributed threshold data points that were evaluated. Our model has theoretical advantages over the traditional square law model under certain conditions, especially when considering neurons that are horizontally displaced from the stimulating electrode. Our model would have to be tested with a larger threshold data pool to permit more conclusive statements about the relative value of our model versus the traditional square law model under special circumstances.