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Sleep and Performance Research Center

Mathematical Models and Computational Tools in Sleep Research


Areas of Interest

Neurobiology of sleep, mathematical and computational modeling, astrocytic and neuronal sleep regulatory networks, fatigue risk management, sleep and circadian data processing

Research Scope

Computational tools for data wrangling

The study of sleep generates large amounts of data. In some experiments these data arise from several different sources: EEG, EMG, imaging, visual stimuli, etc. These diverse data streams need to be merged and synchronized before they can be analyzed. In other studies, there are only a few streams of data (like EEG and EMG for instance), but researchers use multiple tools to analyze the data. Sometimes when used in conjunction with one another, each tool requires the data to be formatted in a different way. In either case (merging or using multiple tools), it is better to use computational tools to carry out these tasks rather than doing them manually in a spreadsheet or similar program. I develop, maintain and run these computational tools.

Mathematical modeling

Sleep involves several different brain regions that interact with each other on a diverse set of time scales. To understand the mechanisms underlying sleep, we develop and analyze mathematical models: quantitative representations of how key elements (variables) of a system are thought to be related. In this sense a mathmatical model is a concrete representation of a hypothesis. The process of developing, running and analyzing a mathematical model of sleep serves several purposes: it helps us identify key elements in a system and organize our understanding of it. It can also help generate new hypotheses. Since running a mathematical model is faster and cheaper than carrying out an experiment, it can be used to quickly predict the outcome of several different experimental conditions. Mathematical modeling of sleep has given researchers insight that could not have been gained with traditional experiments alone.

Data analysis (visualization and quantification)

In studies involving sleep and shift work, it can be difficult to tease apart the various factors affecting the timing of sleep. After collecting data on the sleep patterns of shift workers, we develop hypotheses about which factors are most important for determining the timing of sleep. Rather than proceeding directly to statistical tests to determine how well each factor predicts the timing of sleep, it can be very helpful to first visualize the sleep data in several different ways. Since these visualizations require substantial restructuring of the data, this cannot be done with simple tools, but instead requires the writing of code. Effective visualizations can provide tremendous insight into patterns underlying the data, even before one proceeds with a formal statistical analysis.

Research Focus

Managing sleep data streams for automated scoring

Commercially available software packages exist for manually classifying (also called “scoring”) sleep data. The use of these tools is the industry standard, but the tools require the visual inspection of each epoch of data. Several research groups have developed automated scoring tools, but the most effective versions are not built into the software packages. One of my data wrangling projects consists of reformatting polysomnography datasets so they can be uploaded to an automatic scoring platform and then reformatting the output of the algorithm so the data can be easily visualized. The visualization is important because it allows researchers to correct mistakes made by the automatic scoring.

Mathematical models of sleep in rodents and humans

I developed a mathematical model of sleep in rats that I used to gain new insight into experimental data. I am currently improving this modeling framework and applying it to other experiments in rodents. I am also developing a new version of the modeling framework that can be used for human sleep rather than rodent sleep.

Airline pilot sleep patterns during flights and layovers

As part of a fatigue risk management strategy, we collect and analyze sleep and performance data from airline pilots. We are interested in how pilots sleep during layovers of long international trips. I developed a method of visualizing the sleep data of all participants over the entire course of the trip: pre-trip, outbound flight, layover, inbound flight, post-trip. This has given us insight into the patterns of sleep during layover on several different routes. Currently we are untangling the factors that most reliably predict both the amount and timing of pilot sleep during layovers.

Approaches Used

  • Mathematical modeling of sleep (differential equation based) in humans and rodents
  • Stochastic models of sleep
  • Data analysis and visualization using MATLAB, R and Python
  • Statistical approaches to analyzing sleep and performance data
  • Data wrangling (managing diverse data streams, communication between data collection systems, etc.)