Simulation of Biomathematical Models to support Fatigue Risk Management Systems (FRMS)

This article originally appeared in the ATC Network Special Bulletin
'Training and Simulation - September 2011. To read the complete publication go to:

S. D. Satyamurti, Ph D., P.E.

Sleeping is common for all mammals. Throughout the world, people go to sleep after the sun sets on the western sky. They follow the circadian rhythm and the sleep-wake cycle is tied to rising and setting of the sun. According medical professionals, an individual needs at least 8.5 hrs of sleep to stay in shape to perform his/her work and duties in an efficient manner. Telltale signs of sleep deprivation are fatigue and weariness; individuals are also known to lose alertness, frequent yawning, rubbing eyes and inability to function diligently. At the same time various body functions gets disturbed if one misses his/her sleep-wake cycle. Several medical studies have been conducted on group of people and on individuals to ascertain the effect of sound sleep and lack of it. The psychological and physiological impact is profound and requires medication and treatment. Rest and relaxation will aid in overcoming fatigue. Sleep deprivation also known to cause heart/digestive disorders as well as reduction in family and social interaction capabilities. It has also been found that the human circadian rhythm gets automatically adjusted to the new location when an individual moves from one time zone to another time zone because the sleep-wake cycle synchronizes with the movement of sun (exposure to day light)

Our work pattern has changed from the typical day time activities to around the clock shift work that requires adjusting to work during sleep time affecting the circadian rhythm. Especially in Aviation due to increased traffic and long distance travel across various time zones the aircraft crew had to adjust their life style and sleeping patterns in different parts of the world. New location, lack of rest, unfamiliar surroundings food, and discomfort with sleeping places influence them to get disoriented and to function below expectation and even provoke judgmental errors affecting safety.

It is of interest to compare the definition for fatigue from ICAO, FAA and others and finding ways and methods to overcome the stress to due to lack of necessary sleep time on personnel in various fields of aviation.

ICAO definition of fatigue is A physiological state of reduced mental or physical performance capability resulting from sleep loss or extended wakefulness, circadian phase, or workload (mental and/or physical activity) that can impair a crew members alertness and ability to safely operate an aircraft or perform safety related duties (1)

FAA definition Fatigue is a condition characterized by increased discomfort with lessened capacity for work, reduced efficiency of accomplishment, loss of power or capacity to respond to stimulation, and is usually accompanied by a feeling of weariness and tiredness. (2)

Professor Ann Williamson et al (University of South Australia) gave a definition of fatigue as a biological drive for a recuperative rest. In this perspective, fatigue covers a range of manifestations (physical and cognitive) that results from the absence of rest

The ICAO and FAA have introduced the Fatigue Risk Management System (FRMS) (6) which is currently under the umbrella of the Safety Management System. To facilitate the scheduling of operators in the ATC tower and in the cockpit of aircraft there is a push towards application of the results from simulation of biomathematical models that have been developed in the academics to study and forecast the behavior of individuals for the purpose of evaluation of fatigue in Flight Operations and Air Traffic Control operations (3). Feedback from operating personnel is used in the model to predict the behavior and the sleep-wake times by adding rest and sleep cycles within the normal eight hour shift. It has been observed that individual who work in the night shift have more reasons (looking at the dark sky or computer screens with blinking dots) to be ineffective and inattentive while in controls. Therefore the operators are forced to take a nap by administering medications followed by reduced lighting and comfortable environment for sleeping. The study found that the sleep inertia or waking from the short sleep, twenty minutes or less causes a person to lose orientation, alertness and to have power over a good mental judgment.(4)

Many biomathematical models recently developed in the academics are tested, calibrated and validated to support the implementation of FRMS, specifically for ATC staff scheduling and flight crew scheduling. These models tend to simulate the behavior of group of people or individuals and recommend when the subject may need rest or fatigue requires managing to stay alert at the controls and safely direct the air traffic or fly an aircraft.

List of six biomathematical fatigue models currently in testing state in the aviation industry (6) (7):-

  • Circadian Alertness Simulator (CAS)-USA:- This model incorporates sleep history (homeostatic) and circadian components, and an estimator of sleep timing.
  • Fatigue Audit InterDyne (FAID):- Australia This model originated from research at the Centre for Sleep Research, University of South Australia and was designed to predict worker fatigue directly from shift schedules.
  • Interactive Neurobehavioral Model (INN)-USA: - This model has been developed based on laboratory studies examining both fatigue factors and adaptation of circadian phase to light exposure.
  • Sleep, Activity, Fatigue and Task Effectiveness (SAFTE)-USA:- This model includes a sleep reservoir, circadian rhythm and sleep inertia component and has an auto sleep function that calculates likely sleep times based on work schedules and sleep physiology.
  • Sleep/Wake Predictor (SWP)-Sweden. This model is an improvement over the two-process model, but also accounts for sleep-inertia effects, predicts likelihood of sleep onset and sleeps termination based on physiological parameters and considers constant sleep restriction conditions.
  • System for Aircrew Fatigue Evaluation (SAFE)-UK:- Sponsored by Civil Aviation Authority (CAA) this model has the objective of supporting assessment of permissible Flight Time Limitations for Operators.

Model data input

Sleep input

  • Actual Sleep time-The quantity and timing of actual sleep acquired is the primary determining factor in predicting fatigue related to sleep deficit.
  • Actigraphy Measuring the physical activity of an individual over a twenty-four hour period, typically using a wrist-worn accelerometer, provides a motion signal which manual or computerized analysis can estimate wake and sleep periods.
  • Scheduled sleep When a person takes a nap or sleep time based on a predetermined sleep period
  • Work schedule Sleep periods that are likely to occur between on-duty shifts

Circadian Input

  • Light exposure, directly influences the shifts in the timing of an individuals circadian biological clock cycle. Adaptation to a new time zone, for instance, occurs due to exposure to the shifted hours of daylight and the resulting gradual synchronization of the circadian biological clock.

Aviation Specific input

  • Crew type, sleep locations, number of sectors, and departure/destination points

Model components

The internal components of fatigue models are the characteristics of human neurobehavioral psychology that are described by the biomathematical model equations in the model. Some of the following characteristics are included in the models.

  • Homeostatic sleep drive. The deficit in sleep duration between the actual awake period and sleep period
  • Circadian process. The biological clock simulation
  • Chronic sleep restriction. Inability to sleep due to long hours of work beyond the normal hours of sleep time
  • Circadian phase adaptation. Natural adjustment to day and night in the new location
  • Sleep Inertia. Inability to perform in a normal manner when the sleep duration is not sufficient to reduce fatigue
  • Individualization Predict the alertness of a normal person
  • Caffeine. In the form of a medication provides a temporary alerting effect that decreases the desire to sleep
  • Time-on-task. Greater time spent on task reduces the period available for sleep.

Model Output

  • Objective measures of neurobehavioral performance
  • Subjective assessments of fatigue
  • Fatigue related task errors
  • Fatigue related risk of operational accidents
  • Estimated sleep/wake times
  • Confidence intervals
  • Sleeping is a natural phenomenon for humans


Present day 24/7 work schedule has forced humans to work side by side with computers and machines diligently, unwavering and persistent like machines in their work place. Technological advances in modeling and simulation of biological clock coupled with human behavior and medicines to control sleep-wake cycle are helping to reduce the risk of fatigues impact at work places. Sleep inertia and forced sleep patterns require in depth study. Sleep patterns and human behavior after forced nap (20 minutes or less) necessitates further study as the sleep inertia is not the same with all people around the world, and should differ with other nationals and women as there are rapid changes in demography. Disturbing sleep-wake cycle may also have a long term impact on peoples life and health. It is suggested that an extensive research should be undertaken to study the health and sleep behavior of retirees who had worked long hours exhibited high degree of professionalism, team work and work ethics have since left their work place in the ATC towers and aircraft cockpits. Many of the mathematical models postulated require thorough scientific validation, testing, reliability and calibration.


1. Fatigue Risk Management System (FRMS) Implementation Guide for Operators, ICAO, Montreal, Quebec, Canada, July 2011,

2. Fatigue Risk Management in Aviation Maintenance: Current Best Practices and Potential Future Countermeasures, FAA, Washington, DC 20591, June 2011

3. Sleep/Wake Cycles and Performance of ATC Operators, David Schroeder, Ph.D. Retired FAA, Federal Aviation Administration, Washington, DC 20591

4. Aviation Fatigue Management Symposium: Partnerships for solutions, June 17 19, 2008 Sheraton Premiere at Tysons Corner 8661 Leesburg Pike, Vienna, Virginia

5. Fatigue Risk Management Systems (FRMS) AC: 120-103, 8-3-2010, Federal Aviation Administration, Washington, DC 20591

6. Summary of the Key Features of Seven Biomathematical Models of Human Fatigue and Performance by Melissa M. Mallis, Sig Mejdal, Tammy T. Nguyen*, and David F. Dinges

7. Biomathematical Fatigue Modelling in Civil Aviation Fatigue Risk Management-Application Guidance, Civil Aviation Safety Authority (CASA) Human Factors Section, Australia, March 2010

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