Focused multipolar weights were constructed using methods adapted from van den Honert and Kelsall
43 for the cochlear implant. A transimpedance matrix was constructed by stimulating each electrode in turn while recording voltages on every other electrode. To measure these voltages, the electrode array was connected to a 512 cross-point switch matrix (PXI 2523; National Instruments). Channels of the switch matrix also were connected to an isolated constant current stimulator and a digital multimeter (PXI 4072; National Instruments), allowing stimulation and voltage recording at any electrode site. Voltage waveforms were collected from every electrode in response to MP stimulation of every other electrode. Each trial was repeated 5 times and the waveforms were averaged. Transimpedance was calculated by dividing the voltage at the end of the first phase by the current, and arranged in a matrix where the columns corresponded to stimulating electrodes, and the rows to recording electrodes as follows:
where
Zx,y is the transimpedance between stimulating electrode
x and recording electrode
y. Transimpedance measurements where the stimulating and recording electrodes are the same (on the diagonal of the matrix) could not be measured accurately due to the effects of polarization on the electrode carrying the current pulse. Therefore, these values were estimated using a linear extrapolation method adapted from van den Honert and Kelsall.
43 For a linear electrode array, such as the one used in a cochlear implant, values are estimated by taking the maximum among four values extrapolated from adjacent electrode pairs.
43 As the retinal array is two-dimensional, this was repeated in up to six directions, yielding, depending on electrode positioning, up to 12 extrapolated values. The maximum extrapolated value was chosen as the transimpedance of each stimulating electrode on the diagonal. The transimpedance matrix was averaged with its own transpose (
Z =
Zm +
ZTm) to decrease measurement noise and then inverted (
Y =
Z −1), yielding a matrix of transadmittance values. Each column (
j ) of transadmittances then were normalized to the admittance value of the PSE (
Yj,j on the diagonal of the matrix), to give the current weights to nullify the voltage at every electrode on the array except the PSE. These weights have been referred to as the phased array.
42 Focused multipolar weights typically presented as concentric circles of alternating positive and negative weights progressively approaching zero with greater distance from the PSE (see
Fig. 1).