Towards Robust Control of PNS for Chronic Pain: Modeling Spinal Cord Wide-Dynamic Range Neurons with Structured Uncertainty

Pain is a protective physiological system essential for survival. However, it can malfunction and create a debilitating disease known as chronic pain (CP), which is primarily treated with drugs that can produce negative side effects (e.g., opioid addiction). Peripheral nerve stimulation (PNS) is a promising alternative therapy; it has fewer negative side effects but has been associated with suboptimal efficacy since its mechanisms are unclear, and the current therapies are primarily open-loop (i.e. manual adjustment). To adapt to the needs of the user, the next step in advancing PNS therapies is to "close the loop" by using feedback to adjust the stimulation in real-time. A critical step in developing closed-loop PNS treatment is a deeper understanding of pain processing in the dorsal horn (DH) of the spinal cord, which is the first central relay station on the pain pathway. Mechanistic models of the DH have been developed to investigate modulation mechanisms but are non-linear, high-dimensional, and thus difficult to analyze. In this paper, we propose a novel application of structured uncertainty to model and analyze the nonlinear dynamical nature of the DH, and provide the foundation for developing robust PNS controllers using mu-synthesis. Using electrophysiological DH recordings from both naive and nerve-injured rats during windup stimulation, we build two separate models, which contains a linear time-invariant nominal (average) model, and structured uncertainty to quantify the nonlinear deviations in response from the nominal model. Using the structured uncertainty, we analyze the naive and injured models to discover underlying DH dynamics not identifiable using traditional methods, such as spike counting.