Uncertainty quantification in cerebral circulation simulations focusing on the collateral flow: Surrogate model approach with machine learning

Abstract

Collateral circulation in the circle of Willis (CoW), closely associated with disease mechanisms and treatment outcomes, can be effectively investigated using one-dimensional–zero-dimensional hemodynamic simulations. As the entire cardiovascular system is considered in the simulation, it captures the systemic effects of local arterial changes, thus reproducing collateral circulation that reflects biological phenomena. The simulation facilitates rapid assessment of clinically relevant hemodynamic quantities under patient-specific conditions by incorporating clinical data. During patient-specific simulations, the impact of clinical data uncertainty on the simulated quantities should be quantified to obtain reliable results. However, as uncertainty quantification (UQ) is time-consuming and computationally expensive, its implementation in time-sensitive clinical applications is considered impractical. Therefore, we constructed a surrogate model based on machine learning using simulation data. The model accurately predicts the flow rate and pressure in the CoW in a few milliseconds. This reduced computation time enables the UQ execution with 100 000 predictions in a few minutes on a single CPU core and in less than a minute on a GPU. We performed UQ to predict the risk of cerebral hyperperfusion (CH), a life-threatening condition that can occur after carotid artery stenosis surgery if collateral circulation fails to function appropriately. We predicted the statistics of the postoperative flow rate increase in the CoW, which is a measure of CH, considering the uncertainties of arterial diameters, stenosis parameters, and flow rates measured using the patients’ clinical data. A sensitivity analysis was performed to clarify the impact of each uncertain parameter on the flow rate increase. Results indicated that CH occurred when two conditions were satisfied simultaneously: severe stenosis and when arteries of small diameter serve as the collateral pathway to the cerebral artery on the stenosis side. These findings elucidate the biological aspects of cerebral circulation in terms of the relationship between collateral flow and CH.

Computational modeling of multiscale collateral blood supply in a whole-brain-scale arterial network

“…Fifth, this study investigated the effects of Tier 2 and Tier 3 anastomoses while the relative effects of Tier 1 anastomoses (Circle of Willis) were not considered because the tier 1 anastomoses play a minor role in the case of acute ischemic stroke caused by large vessel occlusion at the post-Circle of Wills, which is the main target of this study. However, in cases where abnormalities occur at the pre-Circle of Wills, such as carotid artery stenosis, full-scale anastomoses including Tier 1 to 3 may help to ensure sustained blood supply, as noted in our previous study [ 11 ]. Further systematic analyses of the effects of multiscale anastomoses in various abnormal conditions would provide a comprehensive understanding of the sustainability of the cerebral blood supply.…”

“…Tier 1 refers to the anterior and posterior communicating arteries that constitute the circle of Willis, located at the base of the brain. Each anastomose connects the left–right anterior cerebral arteries (ACAs) and the middle cerebral artery (MCA)–posterior cerebral artery (PCA); this is widely accepted to provide system redundancies [ 11 ]. Tier 2 refers to the intermediate anastomoses between branches of the three main arteries (ACA, MCA, and PCA).…”

Aging and Sex Differences in Brain Volume and Cerebral Blood Flow

“…These findings suggest that blood supply varies more between individuals and between left and right than conventionally thought even in healthy young adults, not only through the circle of Willis, but also through the peripheral leptomeningeal anastomosis, and perfusion in the deep white matter and subcortical gray matter from the perforating arteries or superficial cortical arteries. Therefore, the CBF of the intracranial artery should be determined based on the area supplied by the artery rather than its diameter estimating the CBF is difficult with only the artery diameter, and direct measurement of CBF with 4D flow MRI or 2D PC MRI is necessary to further develop our computational simulation model of cerebral circulation [29][30][31]. Regarding aging and sex differences, total CBFs decreased with age in proportion to decreased cortical gray matter volume, whereas the cerebral white matter had the largest difference in the 40s and had a low correlation with total CBFs.…”

Development of a 3D Vascular Network Visualization Platform for One-Dimensional Hemodynamic Simulation

“…Furthermore, the capacity for these models to replicate the arterial remodeling in pathological states has been validated, as evidenced by the simulations of carotid artery stenosis [18] and abdominal artery stenosis [19]. Recent research has pivoted towards the quantification of uncertainty within these simulations [20], aiming to bolster the fidelity of 1D-0D models in mirroring the in vivo circulation and providing actionable insights to healthcare practitioners. Previous studies have demonstrated a good consistency between 3D and 1D arterial blood flow simulations [21][22][23].…”