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Summary of the key features of seven biomathematical models of human fatigue and performance

BACKGROUND: Biomathematical models that quantify the effects of circadian and sleep/wake processes on the regulation of alertness and performance have been developed in an effort to predict the magnitude and timing of fatigue-related responses in a variety of contexts (e.g., transmeridian travel, sustained operations, shift work). This paper summarizes key features of seven biomathematical models reviewed as part of the Fatigue and Performance Modeling Workshop held in Seattle, WA, on June 13-14, 2002. The Workshop was jointly sponsored by the National Aeronautics and Space Administration, U.S. Department of Defense, U.S. Army Medical Research and Materiel Command, Office of Naval Research, Air Force Office of Scientific Research, and U.S. Department of Transportation. METHODS: An invitation was sent to developers of seven biomathematical models that were commonly cited in scientific literature and/or supported by government funding. On acceptance of the invitation to attend the Workshop, developers were asked to complete a survey of the goals, capabilities, inputs, and outputs of their biomathematical models of alertness and performance. Data from the completed surveys were summarized and juxtaposed to provide a framework for comparing features of the seven models. RESULTS: Survey responses revealed that models varied greatly relative to their reported goals and capabilities. While all modelers reported that circadian factors were key components of their capabilities, they differed markedly with regard to the roles of sleep and work times as input factors for prediction: four of the seven models had work time as their sole input variable(s), while the other three models relied on various aspects of sleep timing for model input. Models also differed relative to outputs: five sought to predict results from laboratory experiments, field, and operational data, while two models were developed without regard to predicting laboratory experimental results. All modelers provided published papers describing their models, with three of the models being proprietary. CONCLUSIONS: Although all models appear to have been fundamentally influenced by the two-process model of sleep regulation by Borbely, there is considerable diversity among them in the number and type of input and output variables, and their stated goals and capabilities.

Fatigue/physiopathology↗

Validating and Verifying Biomathematical Models of Human Fatigue

Airline pilots experience acute and chronic sleep deprivation, sleep inertia, and circadian desynchrony due to the need to schedule flight operations around the clock. This sleep loss and circadian desynchrony gives rise to cognitive impairments, reduced vigilance and inconsistent performance. Several biomathematical models, based principally on patterns observed in circadian rhythms and homeostatic drive, have been developed to predict a pilots levels of fatigue or alertness. These models allow for the Federal Aviation Administration (FAA) and commercial airlines to make decisions about pilot capabilities and flight schedules. Although these models have been validated in a laboratory setting, they have not been thoroughly tested in operational environments where uncontrolled factors, such as environmental sleep disrupters, caffeine use and napping, may impact actual pilot alertness and performance. We will compare the predictions of three prominent biomathematical fatigue models (McCauley Model, Harvard Model, and the privately-sold SAFTE-FAST Model) to actual measures of alertness and performance. We collected sleep logs, movement and light recordings, psychomotor vigilance task (PVT), and urinary melatonin (a marker of circadian phase) from 44 pilots in a short-haul commercial airline over one month. We will statistically compare with the model predictions to lapses on the PVT and circadian phase. We will calculate the sensitivity and specificity of each model prediction under different scheduling conditions. Our findings will aid operational decision-makers in determining the reliability of each model under real-world scheduling situations.

fatigue↗

A Biomathematical Model of Lymphopoiesis and Its Application to Acute and Chronic Irradiation Assessment

After the events of September 11, 2001, there is an increasing concern of the occurrence of radiological terrorism that may result in significant casualties in densely populated areas. Much effort has been made to establish various biomarkers to rapidly assess radiation dose in mass-casualty and population-monitoring scenarios, which are demanded for effective medical management and treatment of the exposed victims. Among these the count of lymphocytes in peripheral blood and their depletion kinetics are the most important early indicators of the severity of the radiation injury. In this study, we examine a biomathematical model of lymphopoiesis which has been successfully utilized to simulate and interpret experimental data of acute and chronic irradiations on rodents [1]. With revised parameters for humans, we find this model can reproduce several sets of clinical lymphocyte data of accident victims over a wide range of absorbed doses. In addition, the absolute lymphocyte counts and the depletion rate constants calculated by this model also show good correlation with the Guskova formula and the Goans model, the two empirical tools which have been widely recognized for early estimation of the exposed dose after radiation accidents [2]. We also use the model to analyze the hematological data of the Techa River residents which were exposed to chronic low-dose irradiation during 1950-1956 [3]. This model can serve as a computational tool in radiation accident management, military operations involving nuclear warfare, radiation therapy, and space radiation risk assessment.

Hu, Shaowen↗

Kinetic principles of interaction of components in complex biological systems

A biomathematical analysis of component interaction in biological systems is given. Two primary types of systems are discussed - open systems and closed systems. The applicability of these systems to life support equipment in spacecraft is analyzed and formulae are provided to demonstrate the effect (theoretical) of closed and open systems in life support systems.

Rubin, A. B.↗

A Cell Kinetic Model of Granulocytopoiesis Under Radiation Exposure: Extension from Murines to Canines and Humans

Space radiation poses significant challenges to space travel, and it is essential to understand the possible adverse effects from space radiation exposure to the radiosensitive organ systems that are important for immediate survival of human, e.g., the hematopoietic system. In this presentation a biomathematical model of granulocytopoiesis is described and used to analyze the blood granulocyte changes seen in the blood of mammalians under continuous and acute radiation exposure. This is one of a set of hematopoietic models that have been successfully utilized to simulate and interpret the experimental data of acute and chronic radiation on rodents. We discuss the underlying implicit regulation mechanism and the biological relevance of the kinetic parameters estimation method. Extension of the model to predictions in dogs and humans systems indicates that the modeling results are consistent with the cumulative experimental and empirical data from various sources. This implies the potential to integrate the models into one united system for monitoring the hematopoietic response of various species under irradiation. Based on the evidence of threshold responses of dogs to extended periods of low daily dose exposures, we discuss the potential health risks of the space traveler under chronic stress of low-dose irradiation and the possibly encountered Solar Particle Events.

Hu, Shaowen↗

HEMODOSE: A Set of Multi-parameter Biodosimetry Tools

After the events of September 11, 2001 and recent events at the Fukushima reactors in Japan, there is an increasing concern of the occurrence of nuclear and radiological terrorism or accidents that may result in large casualty in densely populated areas. To guide medical personnel in their clinical decisions for effective medical management and treatment of the exposed individuals, biological markers are usually applied to examine the radiation induced changes at different biological levels. Among these the peripheral blood cell counts are widely used to assess the extent of radiation induced injury. This is due to the fact that hematopoietic system is the most vulnerable part of the human body to radiation damage. Particularly, the lymphocyte, granulocyte, and platelet cells are the most radiosensitive of the blood elements, and monitoring their changes after exposure is regarded as the most practical and best laboratory test to estimate radiation dose. The HEMODOSE web tools are built upon solid physiological and pathophysiological understanding of mammalian hematopoietic systems, and rigorous coarse-grained biomathematical modeling and validation. Using single or serial granulocyte, lymphocyte, leukocyte, or platelet counts after exposure, these tools can estimate absorbed doses of adult victims very rapidly and accurately. Some patient data in historical accidents are utilized as examples to demonstrate the capabilities of these tools as a rapid point-of-care diagnostic or centralized high-throughput assay system in a large scale radiological disaster scenario. Unlike previous dose prediction algorithms, the HEMODOSE web tools establish robust correlations between the absorbed doses and victim's various types of blood cell counts not only in the early time window (1 or 2 days), but also in very late phase (up to 4 weeks) after exposure

Hu, Shaowen↗

HEMODOSE: A Set of Multi-parameter Biodosimetry Tools

There continues to be important concerns of the possibility of the occurrence of acute radiation syndromes following nuclear and radiological terrorism or accidents that may result in mass casualties in densely populated areas. To guide medical personnel in their clinical decisions for effective medical management and treatment of the exposed individuals, biological markers are usually applied to examine radiation induced biological changes to assess the severity of radiation injury to sensitive organ systems. Among these the peripheral blood cell counts are widely used to assess the extent of radiation induced bone marrow (BM) injury. This is due to the fact that hematopoietic system is a vulnerable part of the human body to radiation damage. Particularly, the lymphocyte, granulocyte, and platelet cells are the most radiosensitive of the blood elements, and monitoring their changes after exposure is regarded as a practical and recommended laboratory test to estimate radiation dose and injury. In this work we describe the HEMODOSE web tools, which are built upon solid physiological and pathophysiological understanding of mammalian hematopoietic systems, and rigorous coarse-grained biomathematical modeling and validation. Using single or serial granulocyte, lymphocyte, leukocyte, or platelet counts after exposure, these tools can estimate absorbed doses of adult victims very rapidly and accurately to assess the severity of BM radiation injury. Some patient data from historical accidents are utilized as examples to demonstrate the capabilities of these tools as a rapid point-of-care diagnostic or centralized high-throughput assay system in a large-scale radiological disaster scenario. HEMODOSE web tools establish robust correlations between the absorbed doses and victim's various types of blood cell counts not only in the early time window (1 or 2 days), but also in very late phase (up to 4 weeks) after exposure.

Hu, Shaowen↗

Why are cell populations maintained via multiple compartments?

We consider the maintenance of ‘product’ cell populations from ‘progenitor’ cells via a sequence of one or more cell types, or compartments, where each cell’s fate is chosen stochastically. If there is only one compartment then large amplification, that is, a large ratio of product cells to progenitors comes with disadvantages. The product cell population is dominated by large families (cells descended from the same progenitor) and many generations separate, on average, product cells from progenitors. These disadvantages are avoided using suitably constructed sequences of compartments: the amplification factor of a sequence is the product of the amplification factors of each compartment, while the average number of generations is a sum over contributions from each compartment. Passing through multiple compartments is, in fact, an efficient way to maintain a product cell population from a small flux of progenitors, avoiding excessive clonality and minimizing the number of rounds of division en route. We use division, exit and death rates, estimated from measurements of single-positive thymocytes, to choose illustrative parameter values in the single-compartment case. We also consider a five-compartment model of thymocyte differentiation, from double-negative precursors to single-positive product cells.

59 BASIC BIOLOGICAL SCIENCES↗

Seeing through noise in power laws

Despite widespread claims of power laws across the natural and social sciences, evidence in data is often equivocal. Modern data and statistical methods reject even classic power laws such as Pareto’s law of wealth and the Gutenberg–Richter law for earthquake magnitudes. We show that the maximum-likelihood estimators and Kolmogorov–Smirnov (K-S) statistics in widespread use are unexpectedly sensitive to ubiquitous errors in data such as measurement noise, quantization noise, heaping and censorship of small values. This sensitivity causes spurious rejection of power laws and biases parameter estimates even in arbitrarily large samples, which explains inconsistencies between theory and data. We show that logarithmic binning by powers of λ > 1 attenuates these errors in a manner analogous to noise averaging in normal statistics and that λ thereby tunes a trade-off between accuracy and precision in estimation. Binning also removes potentially misleading within-scale information while preserving information about the shape of a distribution over powers of λ, and we show that some amount of binning can improve sensitivity and specificity of K-S tests without any cost, while more extreme binning tunes a trade-off between sensitivity and specificity. We therefore advocate logarithmic binning as a simple essential step in power-law inference.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

The reproduction number and its probability distribution for stochastic viral dynamics

We consider stochastic models of individual infected cells. The reproduction number, R, is understood as a random variable representing the number of new cells infected by one initial infected cell in an otherwise susceptible (target cell) population. Variability in R results partly from heterogeneity in the viral burst size (the number of viral progeny generated from an infected cell during its lifetime), which depends on the distribution of cellular lifetimes and on the mechanism of virion release. We analyse viral dynamics models with an eclipse phase: the period of time after a cell is infected but before it is capable of releasing virions. The duration of the eclipse, or the subsequent infectious, phase is non-exponential, but composed of stages. We derive the probability distribution of the reproduction number for these viral dynamics models, and show it is a negative binomial distribution in the case of constant viral release from infectious cells, and under the assumption of an excess of target cells. In a deterministic model, the ultimate in-host establishment or extinction of the viral infection depends entirely on whether the mean reproduction number is greater than, or less than, one, respectively. Here, the probability of extinction is determined by the probability distribution of R, not simply its mean value. In particular, we show that in some cases the probability of infection is not an increasing function of the mean reproduction number.

59 BASIC BIOLOGICAL SCIENCES↗

Quantifying the basic reproduction number and underestimated fraction of Mpox cases worldwide at the onset of the outbreak

In 2022, there was a global resurgence of mpox, with different clinical-epidemiological features compared with previous outbreaks. Sexual contact was hypothesized as the primary transmission route, and the community of men having sex with men (MSM) was disproportionately affected. Because of the stigma associated with sexually transmitted infections, the real burden of mpox could be masked. We quantified the basic reproduction number (R 0 ) and the underestimated fraction of mpox cases in 16 countries, from the onset of the outbreak until early September 2022, using Bayesian inference and a compartmentalized, risk-structured (high-/low-risk populations) and two-route (sexual/non-sexual transmission) mathematical model. Machine learning (ML) was harnessed to identify underestimation determinants. Estimated R 0 ranged between 1.37 (Canada) and 3.68 (Germany). The underestimation rates for the high- and low-risk populations varied between 25–93% and 65–85%, respectively. The estimated total number of mpox cases, relative to the reported cases, is highest in Colombia (3.60) and lowest in Canada (1.08). In the ML analysis, two clusters of countries could be identified, differing in terms of attitudes towards the 2SLGBTQIAP+ community and the importance of religion. Given the substantial mpox underestimation, surveillance should be enhanced, and country-specific campaigns against the stigmatization of MSM should be organized, leveraging community-based interventions.

60 APPLIED LIFE SCIENCES↗

Validation of Fatigue Modeling Predictions in Aviation Operations

Bio-mathematical fatigue models that predict levels of alertness and performance are one potential tool for use within integrated fatigue risk management approaches. A number of models have been developed that provide predictions based on acute and chronic sleep loss, circadian desynchronization, and sleep inertia. Some are publicly available and gaining traction in settings such as commercial aviation as a means of evaluating flight crew schedules for potential fatigue-related risks. Yet, most models have not been rigorously evaluated and independently validated for the operations to which they are being applied and many users are not fully aware of the limitations in which model results should be interpreted and applied.

operational safety↗