A neural field model of the brain is used to represent brain states using physiologically based parameters rather than arbitrary, discrete sleep stages. Each brain state is represented as a point in a physiologically parametrized space. Over time, changes in brain state cause these points to trace continuous trajectories, unlike the artificial discrete jumps in sleep stage that occur with traditional sleep staging. The discrete Rechtschaffen and Kales sleep stages are associated with regions in the physiological parameter space based on their electroencephalographic features, which enables interpretation of traditional sleep stages in terms of physiological trajectories. Wake states are found to be associated with strong positive corticothalamic feedback compared to sleep. The existence of physiologically valid trajectories between brain states in the model is demonstrated. Actual trajectories for an individual can be determined by fitting the model using EEG alone, and enable analysis of the physiological differences between subjects.