Objective.Electrical measurement of the activity of individual neurons is a primary goal for many invasive neural electrodes. Making these 'single unit' measurements requires that we fabricate electrodes small enough so that only a few neurons contribute to the signal, but not so small that the impedance of the electrode creates overwhelming noise or signal attenuation. Thus, neuroelectrode design often must strike a balance between electrode size and electrode impedance, where the impedance is often assumed to scale linearly with electrode area.Approach and main results. Here we study how impedance scales with neural electrode area and find that the 1 kHz impedance of Pt electrodes (but not Au electrodes) transitions from scaling with area (r-2) to scaling with perimeter (r-1) when the electrode radius falls below 10µm. This effect can be explained by the transition from planar to spherical diffusion behavior previously reported for electrochemical microelectrodes.Significance.These results provide important intuition for designing small, single unit recording electrodes. Specifically, for materials where the impedance is dominated by a pseudo-capacitance that is associated with a diffusion limited process, the total impedance will scale with perimeter rather than area when the electrode size becomes comparable with the diffusion layer thickness. For Pt electrodes this transition occurs around 10µm radius electrodes. At even lower frequencies (1 Hz) impedance approaches a constant. This transition tor-1scaling implies that electrodes with a pseudo-capacitance can be made smaller than one might expect before thermal noise or voltage division limits the ability to acquire high-quality single-unit recordings.
Keywords: diffusion; electrodes; impedances; pseudocapacitance; scaling.
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