Mathematical modeling demonstrates that when arterial stenosis progressively occupies 80% of the lumen over 12 years, blood flow velocity decreases by 75.6% and volumetric flow rate decreases by 94.0%.
A mathematical model of progressive arterial stenosis demonstrates that increasing stenosis thickness over time decreases velocity and volumetric flow rate while increasing pressure drop, providing a framework to estimate time to complete occlusion.
The deposition of fatty particles leading to atherosclerosis may occur in arteries, which alters hemodynamics. This effect becomes more pronounced when a stenosis thickness increases continuously over time. Since atherosclerotic plaque formation is a major cause of cardiovascular disease, understanding its influence on blood flow characteristics is of significant clinical importance. In this study, hemodynamic behaviors due to increasing stenosis is analyzed. A proper increasing rate can estimate the time for complete occlusion and the cardiovascular disease can be cured previously without reaching to the alarming situation. A new mathematical model is developed by incorporating a non-dimensional temporal term in the geometry of the symmetric shaped stenosis and used it in the Navier–Stokes equations in cylindrical coordinates system. The equation is then solved for analytical solution under certain boundary conditions. Analytical expressions for velocity distribution, volumetric flow rate, pressure drop, pressure drop ratio, shear stress and shear stress ratio are derived and evaluated using computational tools. The results indicate that velocity and volumetric flow rate decrease with increasing time and stenotic thickness, while pressure drop and pressure drop ratio increase. The study further demonstrates that the shear stress ratio decreases as stenosis thickness progresses over time. By comparing these theoretical predictions with clinical measurements of plaque growth rates, the approximate time to complete arterial occlusion can be estimated. This modeling framework overcomes limitations associated with symmetric stenosis assumptions and provides a more realistic description of progressive arterial narrowing. The findings offer valuable insights for early diagnosis, prediction of disease progression, and timely clinical intervention in cardiovascular disorders.
Gautam et al. (2026) studied Arterial stenosis. Progressive symmetric shaped stenosis model vs. Normal artery (baseline) was evaluated on Hemodynamic parameters (velocity, volumetric flow rate, pressure drop, shear stress). Mathematical modeling demonstrates that when arterial stenosis progressively occupies 80% of the lumen over 12 years, blood flow velocity decreases by 75.6% and volumetric flow rate decreases by 94.0%.