Physiological framework for non-invasive detection and objective nociception activity in communicative patients: a pilot case study

Pain assessment in both communicative and non-communicative patients remains a major clinical challenge due to the inherently subjective nature of conventional tools such as the Numeric Rating Scale (NRS). In this study, we introduce a physiologically grounded and objective index, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Δ</mml:mi> <mml:mi>T</mml:mi> <mml:mo>=</mml:mo> <mml:mi>T</mml:mi> <mml:mi>S</mml:mi> <mml:mo>-</mml:mo> <mml:mi>T</mml:mi> <mml:mi>D</mml:mi></mml:mrow> </mml:math> , derived from fractional-order impedance modeling of nociceptive dynamics. Here, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>T</mml:mi> <mml:mi>D</mml:mi></mml:mrow> </mml:math> represents the transduction, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>T</mml:mi> <mml:mi>S</mml:mi></mml:mrow> </mml:math> reflects the transmission. These components are extracted non-invasively using the Anspec-Pro device, which records skin bioimpedance in real-time. A positive <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Δ</mml:mi> <mml:mi>T</mml:mi></mml:mrow> </mml:math> indicates enhanced central excitability, while a negative value suggests dominant inhibition. In a case study of postoperative patients, we show that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Δ</mml:mi> <mml:mi>T</mml:mi></mml:mrow> </mml:math> closely follows and often precedes subjective NRS scores, with correlation coefficients reaching up to 0.86 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.002</mml:mn></mml:mrow> </mml:math> ). We also introduce a refined index, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Δ</mml:mi> <mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow> <mml:mrow><mml:mtext>dyn</mml:mtext></mml:mrow> </mml:msub> </mml:mrow> </mml:math> , which incorporates the trend and local variability of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Δ</mml:mi> <mml:mi>T</mml:mi></mml:mrow> </mml:math> for improved temporal alignment with reported pain. To address the very limited dataset (three patients, nineteen intervals each), we implemented a data augmentation strategy based on autoregressive modeling of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Δ</mml:mi> <mml:mi>T</mml:mi></mml:mrow> </mml:math> and transfer-function mapping to NRS. This approach enabled the generation of synthetic trajectories per patient, thereby enriching the dataset while maintaining physiological plausibility. Analyses of the augmented data revealed consistent lead-lag patterns, correlations, and Granger causality relationships between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Δ</mml:mi> <mml:mi>T</mml:mi></mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Δ</mml:mi> <mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow> <mml:mrow><mml:mtext>dyn</mml:mtext></mml:mrow> </mml:msub> </mml:mrow> </mml:math> , and NRS, suggesting that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Δ</mml:mi> <mml:mi>T</mml:mi></mml:mrow> </mml:math> may serve both as an anticipatory biomarker of nociceptive activity and as a real-time index aligned with subjective pain reporting. Overall, these results provide proof-of-concept that the Anspec-Pro device can support objective, non-invasive nociceptive tracking in clinical environments.