Application of Fractional Polynomial Model Based on Bayesian Criterion in Cerebrovascular Diseases: A Robust Framework for Occlusion Simulation and Topology Reconstruction

arXiv:2606.06507v1 Announce Type: new Abstract: The internal carotid artery (ICA), especially its cervical segment (ICA-C1), holds significant importance in the diagnosis of cerebrovascular diseases. Traditional polynomial fitting methods often encounter problems such as order selection, overfitting, and oscillation. To address these issues, this paper proposes a fractional polynomial fitting model based on the effective order and Bayesian Information Criterion (BIC). Through statistical analysis, the high-frequency effective orders $\{1.1, 1.5, 2.0, 2.7, 3.4\}$ are determined to improve computational efficiency. The experimental results of 379 clinical cases show that the proposed method outperforms the traditional methods in terms of fitting accuracy, noise resistance and computational efficiency. It can achieve low-error fitting and accurately depict the complex spatial morphology of the ICA-C1 segment. Moreover, by optimizing the solution strategy and sequence selection mechanism, the running time of the algorithm has been reduced from 153.145 seconds to 23.054 seconds. Furthermore, the proposed model shows good application potential in predicting missing vascular segments in imaging tasks. The prediction results are overall stable, and in most cases, the error is small. The normalized mean square error (NMSE) is below 1.68\% in 90\% of the cases. This study presents a stable, efficient and clinically interpretable model approach for analyzing the morphology of cerebral vessels, opening up a new technological frontier for intelligent diagnosis of cerebral vascular diseases.