Hill function of oxyhemoglobin saturation quantifies power law parameters of subjective mental workload

Abstract Based on the assumption of limited cognitive and energetic resources and a formal logistic resource limitation model (LRL) we had published recently initial evidence for a power law function of quasi real-time measured subjective mental workload (MWL) as dependent on normalized task load (TL), using human-in-the-loop (HITL) air-traffic-control simulation experiments (Fürstenau & Radüntz 2022). Cognitive processing and memory resources invested in task execution determine MWL that is quantified through objective physiological measures such as heart rate and variability, EEG, HbO2 concentration changes in oxygenated and deoxygenated blood measured by fNIRS, and subjective methods like periodic quasi-real-time “instantaneous self-assessment” (ISA) with multilevel MWL-scales. Here we provide additional evidence for the cognitive MWL(TL) power law based on an extended LRL model, and we show quantitative parametric equivalence with the classical two-parametric Hill function of oxyhemoglobin (HbO2) saturation . Moreover, we derive a relationship between MWL and HbO2-saturation by extending the simple physicochemical reaction kinetics of Hb-oxygenation by a normalized TL-variable. MWL(HbO2) is characterized by the same parameters as the Hill function and provides a possibility to validate via regression based parameter estimates the model function directly through simultaneously measured quasi real-time subjective MWL and HbO2-oxygenation. Here we provide indirect evidence for the model by comparing corresponding theoretical MWL(HbO2-saturation) characteristics parametrized through experimental estimates of cognitive and equivalent physicochemical Hill parameters. Parameter estimates via nonlinear regression are based on published data sets from three independent HITL-simulation experiments with highly trained domain experts.