Abstract
Vascular disease is a leading cause of death world wide and therefore the treatment thereof is critical. Understanding and classifying the types and levels of stenosis can lead to more accurate and better treatment of vascular disease. In this paper, we propose a new methodology using topological data analysis, which can serve as a supplementary way of diagnosis to currently existing methods. We show that we may use persistent homology as a tool to measure stenosis levels for many different types of stenotic vessels. We first propose the critical failure value, which is an application of the $1$-dimensional homology to stenotic vessels as a generalization of the percent stenosis. We then propose the spherical projection method, which is meant to allow for future classification of different types and levels of stenosis. We use the $2$-dimensional homology of the spherical projection and showed that it can be used as a new index of vascular characterization. The main interest of this paper is to focus on the theoretical development of the framework for the proposed method using a simple set of vascular data.
Highlights
Vascular disease is the primary cause of human mortality in the United States and worldwide1,2
To construct a meaningful topological space, we found that the projection of the raw data onto the n-unit sphere, which we call an n-spherical projection, is the key element of topological data analysis (TDA) of vascular disease [22]
We proposed to use TDA of vascular flows
Summary
Vascular disease is the primary cause of human mortality in the United States and worldwide. Accurate diagnosis for the prediction and treatment of vascular disease is crucial. Increasing the diagnosis success rate even by a few percent would result in saving a significant number of human lives. For this reason, a great deal of manpower and funding are used up for vascular research each year worldwide. Developing high precision diagnosis methodology is crucial for proper medial treatment and saving human lives. We propose a new method of diagnosis using topological data analysis (TDA). In this paper we explored how TDA could be used to understand the complexity of vascular flows, and proposed a theoretical framework of the new method that could characterize and classify the vascular flow conditions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
