Topological Flow Data Analysis for Blood Flows Inside a Heart

Complex vortex patterns of blood flow in the heart play an important role in an efficient blood flow supply from the heart to the organs. Recent progress in medical imaging and computer technology such as echocardiography and cardiac MRI yields blood flow visualization tools recently. On the other hand, however, there are still few mathematical theories to clearly define the vortex flow structures such as size and location, or change over time in the main chamber in the heart. Although the function of the vortex blood flow inside the left ventricle is highly unstable and complex, we propose a new mathematical theory to extract topological features of the flows in the heart in terms of discrete graphs, called partially cyclically ordered rooted tree (COT) representations, thereby identifying well-organized vortex flow structures as topological vortex structures and characterizing healthy blood flows as well as inefficient flow patterns in the diseased heart. Developing an image processing software based on mathematical theory, we have conducted the topological classification of 2D blood flow patterns obtained by visualization tools. This realizes a new image processing characterizing healthy blood flow patterns as well as inefficient patterns in diseased hearts.