Uncertainty quantification in cerebral circulation simulations focusing on the collateral flow: Surrogate model approach with machine learning
Authors: Yuhn Changyoung , Oshima Marie , Chen Yan , Hayakawa Motoharu , Yamada Shigeki 
Published: March 2022

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.

Author summary

Cerebral arteries generate a ring-like network that provides alternative routes for blood supply in the case of carotid artery stenosis. This collateral circulation is closely associated with the potential risk of stroke and treatment outcomes in patients with stenosis. In this study, we propose a method to elucidate the cerebral circulation of individual patients using a blood flow simulation that incorporates the patient’s clinical data. A key feature of our approach is its capability to obtain the probability of the different outputs using simulation, considering the uncertainty of patient conditions. Although this capability is essential for obtaining reliable results, the process is time-consuming and requires numerous computer resources. We solved this problem by combining the blood flow simulation with machine learning to perform predictions 43 000 times faster than conventional simulations. We applied the proposed method to predict cerebral circulation following surgery in three patients with stenosis and verified that the method can assess the surgical risk almost in real-time, even on a desktop computer. Additionally, extensive prediction results (100 000 cases for each patient) obtained using this method clarify the relationship between collateral circulation and life-threatening surgical outcomes.