The Electrode-Tissue Interface in Living Heart: Equivalent Circuit as a Function of Surface Area

Abstract

Broadband impedance spectroscopy was performed in a three-electrode potentiostatic configuration to determine the equivalent circuit of the noble metal (smooth Pt) electrode–tissue interface in perfused living rat heart. The equivalent circuit was studied as a function of surface area (A = 0.049–13 mm2). Impedance plane plots (Nyquist plots) were determined. The large surface area impedance plane plot is characterized by two constant phase angle elements (CPE1 and CPE2), one of which is the finite (spatially-confined) Warburg impedance, CPE2 ≡ ZD, confirmed by its linearity with respect to ω−1/2. As the working electrode goes to smaller surface area the ZD circuit element becomes at first predominant. At 0.13–5.8 mm2 a discontinuous transition is seen to semicircular behavior in the impedance plane plot, indicating a circuit element composed of a parallel resistance and capacitance. Bulk resistance was in series with these circuit elements. The capacitance in the high frequency limit was linearly related to surface area C = kA, k = constant =δC/δS. The conductance at high frequency (at constant interelectrode distance) lim G=1/(Ral +RB) was an increasing function of surface area with intercept 0, where Ra1 denotes an access resistance and RB the bulk resistance. The unit equivalent circuit of the living electrode tissue interface was determined to be RB Ra1 [(C)(Ra2 ΘZD)]. In this equation Ra2 is a second access resistance, and ZD is the finite (spatially confined) Warburg impedance. The surprising presence of ZD but not ZW∞ (the semi-infinite Warburg impedance) is diagnostic of thin film formation at the bioelectrode's surface, which was not predicted theoretically or reported experimentally. We present a model that accounts for this behavior based on the appropriate solution of the diffusion equation. This is the first observation of a Warburg impedance in such a living system outside the microelectrode or ultramicroelectrode size range.