A Memristive Model of Trans-Epithelial Electrical Resistance in a Breathing Lung-on-Chip: Mathematical Framework, Simulation, Advanced Analysis Extensions, and Experimental Validation Strategy

We present the first memristive model of trans-epithelial electrical resistance (TEER) for a cyclic-strain Lung-on-Chip device. Classical circuit models treat TEER as a memoryless resistor, failing to capture tight-junction fatigue, mechanical pre-conditioning, and breathing-rate-dependent barrier remodelling. A scalar state variable w(t) ∈ [0,1] governs TEER through algebraic memristance M(w) = TEER₀(1 − αw), satisfying all three Chua fingerprints: pinched hysteresis loop, frequency-dependent loop-area shrinkage, and single-valued monotone state map. An adaptive RK45 solver over 200 breathing cycles reveals steady-state TEER depression of 3.9% within two cycles, spectral doubling at 2f_b as a falsifiable on-chip diagnostic signature, a stable toroidal limit cycle (Lyapunov λ ≈ 0), and 107 Ω·cm² cumulative fatigue depression modelling ventilator-induced lung injury. Damköhler classification confirms recovery-dominant dynamics across all five canonical organ barriers, validating multi-organ framework universality. Global Sobol analysis identifies α as the dominant parameter for barrier integrity (S_T = 0.43) and τ_rec for fatigue dynamics (S_T = 0.81); only two new parameters are required, both identifiable from standard TEER time-series protocols. A protective ventilation target (ε_max = 7%, f_b = 0.25 Hz) achieving 31% VILI reduction below eupnoea is identified. This framework establishes the alveolar epithelium as a genuine biological memristive system, providing a quantitative foundation for real-time impedance monitoring, VILI risk assessment, and lung-protective ventilation design in organ-on-chip platforms.