Hill function of oxyhemoglobin saturation quantifies power law parameters of subjective mental workload
DOI: 10.21203/rs.3.rs-5128944/v1
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Summary
This paper addresses the formal relationship between subjective mental workload (MWL) and objective task load (TL) in cognitive tasks, specifically within air traffic control (ATC) simulations. The author, Norbert Fürstenau, investigates whether the previously established power law function describing MWL as a function of normalized task load exhibits quantitative parametric equivalence with the classical two-parametric Hill function of oxyhemoglobin (HbO2) saturation. The motivation stems from the assumption of limited cognitive and energetic resources, linking psychophysical models of mental load to biophysical constraints on cerebral energy supply. The study employs a theoretical derivation combined with regression analysis of data from three independent human-in-the-loop (HITL) ATC simulation experiments involving highly trained domain experts. The methodology involves extending a "logistic resource limitation" (LRL) model, which describes MWL as a sigmoid function of traffic load, by coupling it with a logistic characteristic for objective task load (specifically the rate of radio calls). By transforming the task load variable into a normalized stimulus function, the author derives a cognitive power law for MWL. This derived function is then compared to the physicochemical Hill function of HbO2 saturation. Parameter estimates for the cognitive power law (exponent and logistic shift factor) were obtained via nonlinear regression using published datasets from the three experiments, which included quasi-real-time subjective MWL reports and objective traffic variables. The results demonstrate that the cognitive power law exhibits formal and quantitative parametric correspondence to the Hill function of HbO2 saturation. The regression-based estimates of the cognitive power law parameters from the experimental data are of the same order of magnitude as the physicochemical Hill function parameters. Furthermore, the paper derives a relationship between MWL and HbO2 saturation by extending the reaction kinetics of hemoglobin oxygenation with a normalized task load variable. The theoretical MWL(HbO2-saturation) curves, parametrized by experimental estimates, align with the empirical Hill function characteristics. This confirms the early findings of Gopher and Braune regarding the psychophysical foundation of cognitive load and links it to excitable network-based power law functions. The significance of this work lies in providing a formal link between subjective cognitive load and biophysical energy limits. By establishing that the parameters governing subjective mental workload mirror those of hemoglobin oxygen saturation, the study suggests that subjective reporting of cognitive load may be driven by interoceptive monitoring of cortical energy resource supply chains. This offers a new avenue for validating cognitive workload models through simultaneous measurement of subjective reports and physiological oxygenation data, bridging psychophysics and neuroenergetics.
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| Stage | Outcome | Tool | Model | Prompt | Attempts | Completed |
|---|---|---|---|---|---|---|
| discover | success | Crossref | — | — | 1 | 2026-08-09 |
| archive | success | canonical_url | — | — | 1 | 2026-08-09 |
| extract | success | cached | — | — | 4 | 2026-08-23 |
| clean | success | clean | — | — | 1 | 2026-08-09 |
| chunk | success | chunk | — | — | 1 | 2026-08-09 |
| embed | success | embed | Qwen/Qwen3-Embedding-8B | — | 1 | 2026-08-09 |
| promote | success | — | — | — | 1 | 2026-08-09 |
| summarize | success | llm | qwen3.8-27b-gittensor | summ-v5 | 3 | 2026-08-23 |
| tag | success | vector_similarity | — | — | 11 | 2026-08-11 |
| verify | success | — | — | — | 2 | 2026-08-09 |
Summary generated by qwen3.8-27b-gittensor on 2026-08-23; verification: pending re-verification.
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