Viscous traveling waves: a reaction-diffusion approach to atherosclerosis dynamics

Atherosclerosis, a progressive vascular disease characterized by plaque formation in arterial walls, is influenced by complex biochemical and cellular interactions. In this study, we employ a reaction-diffusion framework to analyze the spatiotemporal evolution of atherosclerotic plaques through viscous traveling waves. We capture key aspects of plaque development and progression by modeling lipid accumulation, inflammatory response, and immune cell migration using reaction-diffusion equations. Introducing viscosity-like terms accounts for resistance in cellular movement, refining the wave dynamics that govern disease propagation. Our findings demonstrate that the velocity and stability of traveling waves depend on critical parameters such as lipid influx rates, diffusion coefficients, and immune response intensity. Numerical simulations reveal distinct wave behaviors, including steady progression, stagnation, or oscillatory patterns, offering insight into the mechanisms regulating atherosclerotic growth. The model is interpreted as a theoretical framework rather than a clinically validated predictor: its parameters can be linked conceptually to measurable processes such as lipid burden, inflammatory activity, and tissue resistance, while clinical calibration would require imaging and longitudinal biomarker data. The results therefore provide testable hypotheses for how lipid-lowering and anti-inflammatory modulation could alter plaque-progression dynamics, rather than claiming direct therapeutic efficacy. This study presents a mathematical perspective that connects reaction-diffusion traveling waves with biomedical mechanisms and identifies pathways for future translational validation.