Using a quadratic parameter sinusoid model to characterize the structure of EEG sleep spindles

Sleep spindles are essentially non-stationary signals that display time and frequency-varying characteristics within their envelope, which makes it difficult to accurately identify its instantaneous frequency and amplitude. To allow a better parameterization of the structure of spindle, we propose modeling spindles using a Quadratic Parameter Sinusoid (QPS). The QPS is well suited to model spindle activity as it utilizes a quadratic representation to capture the inherent duration and frequency variations within spindles. The effectiveness of our proposed model and estimation technique was quantitatively evaluated in parameter determination experiments using simulated spindle-like signals and real spindles in the presence of background EEG. We used the QPS parameters to predict the energy and frequency of spindles with a mean accuracy of 92.34 and 97.73% respectively. We also show that the QPS parameters provide a quantification of the amplitude and frequency variations occurring within sleep spindles that can be observed visually and related to their characteristic "waxing and waning" shape. We analyze the variations in the parameters values to present how they can be used to understand the inter- and intra-participant variations in spindle structure. Finally, we present a comparison of the QPS parameters of spindles and non-spindles, which shows a substantial difference in parameter values between the two classes.