Evidence for Hill-function of Oxyhemoglobin Saturation to quantify Stevens Law of Subjective Cognitive Load

Fürstenau, Norbert · 2026 · Crossref

DOI: 10.21203/rs.3.rs-8895239/v1

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Summary

This paper investigates the biophysical energetic foundation of subjective mental workload (MWL) by establishing a quantitative link between cognitive load and oxyhemoglobin (HbO2) saturation. The research addresses the need for objective, non-intrusive methods to quantify cognitive demand in safety-critical industries, specifically Remote Tower Operations in air traffic control. The author hypothesizes that subjectively reported MWL serves as a direct measure of the approach to cortical energy resource limits, represented physiologically by HbO2 saturation. The study utilizes data from a 2011 human-in-the-loop air traffic control simulation involving twelve professional controllers. Participants performed tasks under two work conditions: standard single-airport control and a novel dual-airport remote control setup. Subjective MWL was assessed quasi-real-time using instantaneous self-assessment (ISA) on a 5-point Likert scale, while objective task load (TL) was measured via radio communication frequency. The author derives a theoretical model based on logistic resource limitation (LRL), demonstrating that the relationship between ISA-MWL and TL can be formalized as a cognitive Hill function. This function is shown to be formally equivalent to the classical Hill function describing HbO2 saturation as a function of oxygen partial pressure, and transformable into a psychophysical Stevens power law. Nonlinear regression analysis of the experimental data yielded parameter estimates for the cognitive Hill function. The derived power law exponent ($\gamma$) for both work conditions was approximately 1.3–1.4, which aligns closely with the physiological Hill coefficient ($m = 1.4$) for oxygen-hemoglobin binding. Furthermore, the dimensionless scaling product of the cognitive model ($K'_c$) was found to be within the same order of magnitude as the physiological counterpart ($K' \approx 9.46$). The results indicate that the cognitive Stevens law and the physiological Hill function share structural and parametric similarities, suggesting a generalized linear relationship between subjective MWL and HbO2 saturation. The significance of these findings lies in providing indirect evidence for the hypothesis that subjective cognitive load reflects underlying cortical energy consumption. By bridging cognitive and physiological variables, the study supports the use of functional near-infrared spectroscopy (fNIRS) as a direct, objective measure of mental workload. This theoretical framework offers a robust method for evaluating human performance and cognitive resource limits in complex operational environments, moving beyond subjective self-reports to biophysically grounded metrics.

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Topics

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• workload measurement
• mental demand
• neuro workload indices