Noninvasive monitoring of tissue temperature using differential Cole model parameters from bioimpedance spectroscopy

Bioelectrical impedance spectroscopy (BIS) provides a non-invasive approach for characterizing biological tissues; however, its application to temperature monitoring remains limited due to the lack of models incorporating temperature dependence. This study proposes an empirical method for estimating tissue temperature based on temperature-induced variations in Cole model parameters. Bioimpedance measurements were performed on six ex vivo biological tissues over a frequency range of 1 kHz–1 MHz and a temperature range of 20–50 °C. The Cole model was fitted to the measured impedance spectra to extract key parameters (R 0 , R ∞ , τ, and α). Results demonstrate that R 0 , R ∞ , and τ decrease with increasing temperature, whereas α exhibits comparatively weak temperature dependence. Derivative analysis reveals that the sensitivities of these parameters are temperature-dependent, indicating that a single linear model is insufficient to describe the full temperature range. To address this, a differential formulation combined with a piecewise linear model was developed. The proposed method estimates temperature using normalized changes in Cole parameters relative to a reference temperature. Experimental validation shows that the piecewise linear model significantly improves estimation accuracy compared to conventional linear approaches, reducing root mean square error (RMSE) from 0.58–4.98 °C to 0.50–2.48 °C across different tissue types, with percentage errors below 2% for most tissues. These findings demonstrate that differential analysis of Cole parameters enables accurate and non-invasive temperature estimation within the investigated frequency and temperature ranges. The proposed bioimpedance-based thermometry framework has potential applications in real-time monitoring of thermal therapies and biomedical sensing, with future work focused on in vivo validation and model generalization.