Numerical study on the cerebral blood flow regulation in the circle of Willis with the vascular absence and internal carotid artery stenosis.

Objectives: This study explores how vascular stenosis and absence affect the regulation of cerebral blood flow in the Circle of Willis (CoW) and the hemodynamic changes downstream of the stenosis. Materials and Methods: Forty idealized CoW models were simulated to analyze the impact of vascular absence and internal carotid artery (ICA) stenosis on hemodynamics. Inlet conditions were set using a physiological pressure waveform, and outflow boundaries were modeled using three-element Windkessel models. Results: The absence of vessels such as RP1, LP1, RA1, or LA1 had a comparable effect on total blood flow to a 40% stenosis of the left internal carotid artery (LICA) across the entire CoW. Specifically, when LP1 and RA1 were absent with a 50% LICA stenosis, the total blood flow closely resembled that of a complete CoW with 75% LICA stenosis. In cases of proximal ICA stenosis, downstream regions showed elevated oscillatory shear index (OSI >0.2) and reduced time-averaged wall shear stress (TAWSS <1 Pa). With increasing stenosis severity, areas of high OSI shifted, and regions of low TAWSS expanded notably. At 75% stenosis, the area with TAWSS <1 Pa downstream significantly increased. Until complete occlusion, the area of low TAWSS and high OSI were maximized. Conclusion: This study underscores how anatomical variations in the CoW, combined with ICA stenosis, impact both total cerebral blood flow and its distribution among different outlets. Moreover, it highlights the potential for increased atherosclerosis development in affected areas. Particularly notable is the finding the absence of LP1 and RA1 vessels alongside 50% LICA stenosis results in blood flow patterns similar to those seen with 75% LICA stenosis in a complete CoW, emphasizing clinical implications for the patient. Hemodynamic changes, including TAWSS and OSI, are most pronounced downstream of the stenosis especially when the stenosis rate exceeds 75%.