Semi-Analytical Dual-Substrate Modeling of Glucose Oxidase Biosensors: Butler-Volmer Boundary Conditions, Impedance Spectroscopy, and Oxygen Co-Limitation Diagnostics

A dual-substrate reaction-diffusion framework is developed, validated, and extended to electrochemical analysis for glucose oxidase biosensors, incorporating oxygen co-substrate dependence through the dimensionless oxygen-to-glucose ratio γ. Two independent semi-analytical methods — the Rajendran-Joy Method (RJM) and the Akbari-Ganji Method (AGM) — are applied to the coupled nonlinear Michaelis–Menten governing system. Inter-method validation across 500 parameter combinations yields a mean relative difference of 3.88% (maximum 6.93%), with 94% of cases below 7%. Validation against 17 glucose oxidase K _m values from the BRENDA database (EC 1.1.3.4) yields mean R² = 0.9981 across Low, Mid, and High kinetic categories. Three kinetic regimes are identified: oxygen-limited (γ < 0.2), transition (0.2 ≤ γ ≤ 1.0), and glucose-limited (γ > 1.0); implanted CGM sensors operate firmly in the oxygen-limited regime (γ ≈ 0.003–0.01). A revised Butler–Volmer electrode boundary condition replaces the passive zero-flux assumption, introducing the electrode kinetic parameter Λ. An analytical electrochemical impedance spectroscopy model predicts Nyquist spectra with a Warburg slope deviation |Δθ| = 5°-12° under physiological conditions, providing a direct experimental diagnostic for oxygen co-limitation. Charge transfer resistance R _ct = 36–90 Ω across BRENDA categories is consistent with published GOx electrode data. Quantitative membrane engineering guidelines for oxygen-independent CGM operation are derived.