Jacobian-Based Optimal Frequency Selection for Bioimpedance Spectroscopy With a Reduced Number of Frequencies

Bioimpedance spectroscopy has emerged as a fundamental non-invasive technique for characterizing biological tissues and monitoring physiological parameters in clinical diagnostics and wearable health systems. Current frequency selection approaches rely on empirical methods, logarithmic distributions, or heuristic optimization rather than systematic mathematical frameworks, leading to inefficient measurement protocols requiring extensive frequency sweeps. This paper presents the first analytically-driven frequency selection method for bioimpedance spectroscopy based on Jacobian sensitivity analysis of the simplified Cole-Cole equivalent circuit model. The proposed method systematically determines both the minimum number and optimal positioning of measurement frequencies by computing normalized sensitivity functions for circuit parameters and identifying frequency regions where parameter variations exhibit maximum sensitivity. The approach exploits the mathematical structure of the R-R//C circuit impedance function to quantify parameter identifiability through combined sensitivity metrics, enabling strategic frequency selection that maximizes information content while minimizing measurement requirements. Validation through Monte Carlo simulations with four different frequency sets demonstrates consistent sub-percentage accuracy levels, achieving mean relative errors of 0.64% for series resistance, 0.84% for charge transfer resistance, and 0.62% for capacitance under 1% Gaussian noise conditions. This mathematically rigorous framework provides theoretical foundations for frequency-optimized bioimpedance measurements with direct applications in clinical diagnostics, tissue characterization, and wearable health monitoring systems where measurement efficiency and accuracy are critical.