Patient-Specific Hemodynamic Modeling of Cerebral Blood Flow: 1-D Mathematical Model
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Patient-Specific Hemodynamic Modeling of Cerebral Blood Flow: 1-D Mathematical Model

Abstract

Ischemic stroke is one of the leading causes of death in the US. It is estimated that intracranial stenosis, which refers to the narrowing of the blood vessels within the brain, accounts for 30% - 50% of ischemic strokes. Typical intracranial stenosis includes narrowing of arteries such as the middle cerebral artery (MCA) and the internal carotid artery (ICA). Among alltypes of intracranial stenosis, middle cerebral artery (MCA) stenosis poses a higher risk for ischemic stroke. Collateral circulation occurs when occlusion happens and plays a vital role in sustaining cerebral blood flow during ischemic strokes. However, the factors leading to the formation of collateral circulation remain unclear and are difficult to observe through image data alone. The imaging data provides only a snapshot, thereby limiting our understanding of stenosis development and the formation of collateral circulation. This work developed a computational tool that integrates patient-specific image data with fluid dynamics to investigate the development of MCA stenosis and explore possible causes of collateral circulation between MCA and PComm.

The hemodynamic data of arterial segments is extracted from individual computed tomography angiography (CTA) scan. The extracted network includes parent arterial segment ICA and daughter arterial segments MCA, ACA and PComm. The inlet blood flow profile is calibrated using color-coded duplex ultrasound from young, healthy volunteers, while a three-element Windkessel outlet boundary condition is attached to the end of each daughter arterial segment to simulate artificial wave reflection from the downstream vascular network. Our findings demonstrate that increases in area reduction increase the pressure of the unobstructed pathway and decrease the pressure of the obstructed pathway, which becomes significant after 90% of the MCA area is occluded, aligning with clinical observations. Wave Intensity Analysis (WIA) results reveal that the forward expansion wave (FEW) accelerates the pressure and blood flow from the downstream vascular network, particularly when MCA is highly occluded (90% cross-sectional area is occluded). The pressure/blood flow and WIA results show that the formation of collateral circulation is closely related to the high resistance of the upstream large artery, which aligns with the clinical hypothesis.

Furthermore, this work compares the two types of outlet boundary conditions: the three-element Windkessel 0-D outlet boundary condition and the 1-D binary tree outlet boundary condition. To assess their impact on the pressure and blood flow waveform of the upstream large artery, both types of outlet boundary conditions are connected to the upstream large artery. The findings reveal that the two types of outlet boundary conditions exhibit minimal differences in affecting the pressure/blood flow of upstream large artery. However, it should be noted that the utilization of the 1-D outlet boundary conditions is limited in the presented model due to the long-wave approximation.This work introduces a novel model that includes one parent arterial segment connected to three daughter arterial segments. It is the first time that the collateral circulation between MCA and PComm through the downstream vascular network is investigated. Additionally, the WIA method is employed for the first time to study the relationship between MCA stenosis and the formation of collateral circulation.

In summary, a computational tool is developed to understand the evolution of hemodynamic changes in cerebral blood flow and to reveal pathology of collateral circulation and MCA stenosis.

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