Method for cycle detection in sparse, irregularly sampled, long-term neuro-behavioral timeseries: Basis pursuit denoising with polynomial detrending of long-term, inter-ictal epileptiform activity

Numerous physiological processes are cyclical, but sampling these processes densely enough to perform frequency decomposition and subsequent analyses can be challenging. Mathematical approaches for decomposition and reconstruction of sparsely and irregularly sampled signals are well established but have been under-utilized in physiological applications. We developed a basis pursuit denoising with polynomial detrending (BPWP) model that recovers oscillations and trends from sparse and irregularly sampled timeseries. We validated this model on a unique dataset of long-term inter-ictal epileptiform discharge (IED) rates from human hippocampus recorded with a novel investigational device with continuous local field potential sensing. IED rates have well established circadian and multiday cycles related to sleep, wakefulness, and seizure clusters. Given sparse and irregular samples of IED rates from multi-month intracranial EEG recordings from ambulatory humans, we used BPWP to compute narrowband spectral power and polynomial trend coefficients and identify IED rate cycles in three subjects. In select cases, we propose that random and irregular sampling may be leveraged for frequency decomposition of physiological signals. Author Summary Circadian and multiday cycles are an important part of many long-term neuro-behavioral phenomena such as pathological inter-ictal epileptiform discharges (IEDs) in epilepsy. Long-term, ambulatory, neuro-behavioral monitoring in human patients involves complex recording systems that can be subject to intermittent, irregular data loss and storage limitations, resulting in sparse, irregularly sampled data. Cycle identification in sparse data or irregular data using traditional frequency decomposition techniques typically requires interpolation to create a regular timeseries. Using unique, long-term recordings of pathological brain activity in patients with epilepsy implanted with an investigational device, we developed a method to identify cycles in sparse, irregular neuro-behavioral data without interpolation. We anticipate this approach will enable retrospective cycle identification in sparse neuro-behavioral timeseries and support prospective sparse sampling in monitoring systems to enable long-term monitoring of patients and to extend storage capacity in a variety of ambulatory monitoring applications.