A Pluripotent Progression of the Gate Control System Theory of Pain–Modeling Ascending & Descending Pain Pathways as a Lotka-Volterra Coupled Control & Feedback Loop

Introduction: Pain is a subjective experience, the perception of stimulus input transmitted by neurons that respond to real or perceived tissue injury and propagate the information to the brain. Under normal conditions, the perception is a reliable indicator of the magnitude and duration of the sensory input (viz. threat), so that appropriate action can be taken (eg, fight-or-flight). Two pathways have been recognized: “ascending pathways” mediating sensory input→perception and “descending pathways” mediating perception→response. Interactions between the two are increasingly appreciated, ie, ascending signals often modulated by descending ones. Our thesis is that there is an interactive feedback loop that allows pain to be modeled as a control system (with a postulated thermostat-analogous “nocistat”) and that such an undertaking could lead to better understanding of pain dynamics, and ultimately to recommendations for better pain treatment. Methods: We here introduce a system-theoretical approach, based on the well-known Lotka-Volterra dynamics, to describe ascending and descending pain pathways as a coupled control and feedback loop. The resulting model is mathematically represented by a system of coupled differential equations with a non-linear interaction term, and poses a pluripotent progression of the Gate Control System Theory to a macroscopic, clinically applicable view of pain and its mitigation through modulation. Results: We present preliminary, qualitative simulation results for a variety of sensory inputs (ie, pain stimuli) that are inspired by clinical pain conditions. These comprise, but are not limited to, sudden onset of (1) constant pain stimulus; (2) exponentially decaying pain stimulus; (3) linearly decaying pain stimulus; (4) exponentially increasing pain stimulus; and (5) linearly increasing pain stimulus. Discussion: The introduced coupled control and feedback loop model is accessible and readily extensible, while mathematically rigorous, to approximate clinical findings more realistically, both qualitatively and quantitatively, the latter taking advantage of the fitting parameters in the model.