Quantitative evaluation of the effect of circle of willis structures on cerebral hyperperfusion: A multi-scale model analysis

Cerebral hyperperfusion occurs in some patients after superficial temporal artery–middle cerebral artery bypass surgery. However, there is uncertainty about cerebral hyperperfusion after bypass for patients with different Circle of Willis (CoW) structures.

This study established a lumped parameter model coupled with one–dimensional model (0–1D), whilst a deep learning model for predicting pressure drop (DLM–PD) caused by stenosis and a cerebral autoregulation model (CAM) were introduced into the model. Based on this model, 9 CoW structural models before and after bypass was constructed, to investigate the effects of different CoW structures on cerebral hyperperfusion after bypass. The model and the results were further verified by clinical data.

The MSE of mean flow rates from 0–1D model calculation and from clinically measurement was 1.4%. The patients exhibited hyperperfusion in three CoW structures after bypass: missing right anterior segment of anterior cerebral artery (mRACA1) (13.96% hyperperfusion), mRACA1 and foetal-type right anterior segment of posterior cerebral artery (12.81%), and missing anterior communicating artery and missing left posterior communicating artery (112.41%). The error between the average flow ratio from the model calculations and fromclinical measurement was less than 5%.

This study demonstrated that the CoW structure had a significant impact on hyperperfusion after bypass. The general 0–1D model coupled with DLM–PD and CAM proposed in this study, could accurately simulate the hemodynamic environment of different CoW structures before and after bypass, which might help physicians identify high–risk patients with hyperperfusion before surgery, and promote the development of non-invasive diagnosis and treatment of cerebrovascular diseases.