Year of Award


Document Type


Degree Type

Doctor of Philosophy (PhD)

Degree Name

Interdisciplinary Studies

Other Degree Name/Area of Focus

Fatigue Risk Management

Department or School/College

Interdisciplinary Studies Program

Committee Chair

Leonid V. Kalachev

Committee Co-chair

Hans P. A. Van Dongen

Commitee Members

Alden Wright, Eijiro Uchimoto, Gregory Belenky


Adenosine receptors, Cognitive performance, Coupled non-homogeneous first-order ordinary diffe, Fatigue and performance models, Two-process model of sleep regulation


University of Montana


Several biomathematical models have been developed to predict cognitive performance impairment due to sleep loss and/or circadian misalignment. In essence, these models are all based on the Two-Process Model (TPM) which contains a homeostatic process for the build-up and decline of sleep pressure across days, and a circadian process to keep track of time of day. The TPM has been used successfully to predict performance under conditions of total sleep deprivation. However, for conditions of chronic sleep restriction, the TPM predicts a rapid stabilization of performance impairment (within a day or two)---which is not in agreement with experimental observations. This discrepancy has led to the development of TPM variations with an additional process modulating the homeostatic process across days of sleep restriction. Yet, these models predict adaptation to chronic sleep restriction in the long run as well, regardless of how substantial the daily sleep reduction actually is.

We show in this thesis that the TPM, and the various models based on it and expanding it with a modulating process, can be written as a system of nonhomogeneous first-order ordinary differential equations with a much richer repertoire of predictions. We examine the dynamical properties of the model for states of equilibrium and stability, in the context of wake/sleep schedules with consolidated sleep episodes and schedules that repeat across days. We also extend the model framework to include multiple wake/sleep segments per day and explore the model behavior with scenarios that include napping.

We discovered that the model produces a bifurcation whereby daily wake durations extending up to a critical value lead to adaptation, whereas daily wake durations that extend beyond the critical value lead to escalating performance impairment over days. We found that the underlying model characteristics were unchanged for repeating schedules and scenarios with napping---the bifurcation was defined by the average duration of total daily wakefulness. Finally, we used our new modeling framework to develop a model formulation that exhibits realignment characteristics between the environment and the biological clock, which can be used to create a comprehensive dynamic model of the homeostatic and circadian regulation of cognitive performance.



© Copyright 2009 Peter J. McCauley