Fractional-Order Bioimpedance Modelling for Early Detection of Tissue Freezing in Cryogenic and Thermal Medical Applications

Cryotherapy and radiofrequency (RF) treatments modulate tissue temperature to induce therapeutic effects; however, improper application can result in thermal injury. Traditional temperature-based monitoring methods rely on multiple thermal sensors whose accuracy strongly depends on their number and spatial positioning, often failing to detect early tissue crystallization. This study introduces a fractional order bioimpedance modelling framework for the early detection of tissue freezing during cryogenic and thermal medical treatments, with the feasibility and effectiveness of this approach having been reported in our prior publications. While bioimpedance spectroscopy itself is a well-est. The corresponablished technique in biomedical engineering, its novel application to predict and identify premature freezing events provides a new pathway for safe and efficient energy-based therapies. Fractional-order models derived from the Cole family accurately reproduce the complex electrical behavior of biological tissues using fewer parameters than classical integer-order models, thus reducing both hardware requirements and computational cost. Experimental impedance data from human abdominal, gluteal, and femoral regions were modelled to extract fractional parameters that serve as sensitive indicators of phase-transition onset. The results demonstrate that the proposed approach enables real-time identification of freezing-induced electrical transitions, offering a physiologically grounded alternative to conventional temperature-based monitoring. Furthermore, the fractional order bioimpedance method exhibits high reproducibility and selectivity, and its analytical figures of merit, including the limits of detection and quantification, support its use for reliable real-time tissue monitoring and early injury detection. Overall, the proposed fractional order bioimpedance framework enhances both safety and control precision in cryogenic and thermal medical applications.