Figure 1. Equivalent circuit models to simulate electrochemical impedance spectrum measured between the concentric bipolar electrodes.

(a) Equivalent Circuit 1 (EC1) encompassed electric circuit parameters for working and counter electrodes interface as well as arterial wall impedance. The electrode-endoluminal interface was modeled by a constant phase element (CPE) having an impedance $Z_{\text{CPE}}(Z_{\text{CPE}}=\frac{1}{\mathrm{Y}{(\mathrm{j}\mathrm{\omega })}^{\mathrm{a}}})$ in parallel with a charge transfer resistance (R_CT). The vessel wall harbors both resistive (R_B) and capacitive properties (C_B). Hence, a total of 8 electric circuit parameters were included. CE: Counter electrode; WE: working electrode. (b) Equivalent Circuit 2 (EC2) was a simplified version of EC1. By assuming a very large charge transfer resistance at the counter electrode interface, R_CT1 was removed. CPE in the working electrode was replaced with a double layer capacitor (C_DL2). The total number of electric circuit components was reduced to 6. (c) Equivalent Circuit 3 (EC3) was a further simplified version of EC2. By assuming that CPE in the counter electrode also acted as an ideal double layer capacitor (C_DL1), the total number of parameters was reduced to 5. (d) Both EC1 and EC2 simulated experimental EIS measurements accompanied by approximately 2.5% error, whereas EC3 was accompanied by 14.8% error and a deviated phase (θ) values from the endoluminal EIS signals. (e) Selected circuit parameter values for endoluminal EIS data shown in Fig. 1d. The values were derived from simulations using EC1, EC2 and EC3, respectively. Y₁, a₁, R_B and C_B values derived from EC1 and EC2 were almost identical. The best fit EC1 and EC2 models had comparable Goodness of Fit (6.34E-4 and 6.8E-4, respectively), whereas the best fit EC3 model had significantly higher Goodness of Fit (2.2E-2), indicating larger deviation from experimental data.