Reconstructing Mammalian Sleep Dynamics with Data Assimilation

Data assimilation is a valuable tool in the study of any complex system, where measurements are incomplete, uncertain, or both. It enables the user to take advantage of all available information including experimental measurements and short-term model forecasts of a system. Although data assimilation has been used to study other biological systems, the study of the sleep-wake regulatory network has yet to benefit from this toolset. We present a data assimilation framework based on the unscented Kalman filter (UKF) for combining sparse measurements together with a relatively high-dimensional nonlinear computational model to estimate the state of a model of the sleep-wake regulatory system. We demonstrate with simulation studies that a few noisy variables can be used to accurately reconstruct the remaining hidden variables. We introduce a metric for ranking relative partial observability of computational models, within the UKF framework, that allows us to choose the optimal variables for measurement and also provides a methodology for optimizing framework parameters such as UKF covariance inflation. In addition, we demonstrate a parameter estimation method that allows us to track non-stationary model parameters and accommodate slow dynamics not included in the UKF filter model. Finally, we show that we can even use observed discretized sleep-state, which is not one of the model variables, to reconstruct model state and estimate unknown parameters. Sleep is implicated in many neurological disorders from epilepsy to schizophrenia, but simultaneous observation of the many brain components that regulate this behavior is difficult. We anticipate that this data assimilation framework will enable better understanding of the detailed interactions governing sleep and wake behavior and provide for better, more targeted, therapies. Author Summary: Mathematical models are developed to better understand interactions between components of a system that together govern the overall behavior. Mathematical models of sleep have helped to elucidate the neuronal cell groups that are involved in promoting sleep and wake behavior and the transitions between them. However, to be able to take full advantage of these models one must be able to estimate the value of all included variables accurately. Data assimilation refers to methods that allow the user to combine noisy measurements of just a few system variables with the mathematical model of that system to estimate all variables, including those originally inaccessible for measurement. Using these techniques we show that we can reconstruct the unmeasured variables and parameters of a mathematical model of the sleep-wake network. These reconstructed estimates can then be used to better understand the underlying neuronal behavior that results in sleep and wake activity. Because sleep is implicated in a wide array of neurological disorders from epilepsy to schizophrenia, we anticipate that this framework will enable better understanding of the link between sleep and the rest of the brain and provide for better, more targeted, therapies.