Robust Differential Spiral EIS Co-Design for Bladder Cancer Urine Sensing with Measured-Data Validation

Abstract

This paper presents a robust co-design framework for differential spiral electrical impedance spectroscopy (EIS) biosensors, developed as an in silico methodological study for urine-sensing applications in bladder cancer surveillance. The objective is to improve parameter identifiability in label-free differential urine sensing when nuisance effects, fabrication tolerances, and reference mismatch reduce estimation reliability. The framework combines differential sensing to suppress shared common-mode nuisance with joint optimization of sensor geometry and frequency selection. The design is formulated as a minimax Fisher-information problem to improve worst-case identifiability. The primary co-design evaluation uses an application-motivated synthetic protocol with matched budgets and multiple baselines. The proposed method improves worst-case identifiability and Cramér–Rao lowerbound proxy metrics at the same frequency budget, with consistent gains under budget variation, uncertainty amplification, and reference mismatch. To examine transfer beyond the synthetic model family at component level, we additionally analyzed an independent measured EIS dataset using grouped hold-out validation and training-only empirical minimax frequency selection. At a four-frequency budget, the measured-data analysis achieved a balanced accuracy of 79.6% ± 11.6%, compared with 70.4% ± 14.0% for log-uniform selection and 74.1% ± 8.5% for the full 101-frequency spectrum. This independent analysis supports the differential sparsefrequency design principle outside the synthetic generator, but it does not validate the optimized spiral geometry, urine sensing, bladder-cancer diagnosis, or clinical readiness.