Preprocessing of general stenotic vascular flow data for topological data analysis

Abstract

A new analysis and classification method of vascular disease based on topological data analysis (TDA) has been proposed in [1]. The proposed method utilizes the application of persistent homology to hemodynamic variables. Particularly, 2D homology is obtained from the velocity field of the flow projected onto the unit sphere, known as so-called the S2 projection. It was shown that such homology is closely related to the degree of vascular disease. The original method was developed based on the computational fluid dynamic (CFD) solutions of the straight stenotic vessels. In this paper, we develop a preprocessing method that enables the proposed TDA method to be applied to general stenotic vessels of irregular geometry. The velocity field is subject to a coordinate transformation correcting for orientation and curved geometry. The preprocessed data is projected onto S2 and the corresponding homology is calculated. We show that this preprocessing is necessary for the proposed TDA method to be successfully applied to general types of stenotic vessels. Validation was performed on a set of clinical data including reconstructed vascular geometry with corresponding diagnostic indices.