The cyclical and progressively decreasing dynamics of electroencephalogram (EEG) based slow-wave activity (SWA) during sleep reflects the homeostatic component of sleep-wake regulation. The dynamic changes of heart rate (HR) and heart rate variability (HRV) indices during sleep also exhibit quasi-cyclic trends that appear to correlate with SWA. This article proposes a model to characterize the relationship between SWA, HR and HRV in the polar-coordinate (r-theta) domain. Polar coordinates are particularly well-suited to model cyclic shapes with simple (linear) equations in the r-theta plane. Group-level analyses and individual-level ones of the correlations between the polar-coordinate transformations of SWA and HR reveal R(2) values of 0.99 and 0.95 respectively. Given that, HR and HRV can be estimated in less obtrusive ways compared to EEG. This research offers relevant options to conveniently monitor sleep SWA.Clinical Relevance- Slow wave activity is a marker of sleep restoration that most prominently manifests in the EEG. This research suggests that an electrocardiography (ECG)-based non-linear model can approximate a polar-coordinate version of SWA. Since ECG correlates can be unobtrusively acquired during sleep, these results suggest that practical SWA monitoring can be achieved through cardiac activity measurements.