The human heart functions as a highly efficient fluid pump, maintaining circulation through organized blood-flow patterns. Characteristic vortex-like structures arise within the left ventricle—the main pumping chamber of the heart—facilitating smooth blood filling and ejection. In patients with cardiovascular diseases, the vortex-like structures are disturbed, reflecting impaired cardiac function. However, conventional diagnostic tools, such as echocardiography or magnetic resonance imaging, have mainly focused on structural and morphological abnormalities of the heart wall or valves, providing only limited access to the essential dynamics of blood flow. Methods for identifying and analyzing vortex flow structures remain insufficient, partly because of limitations in visualization and analysis techniques. To address the existing limitations, we developed a new computational algorithm, known as topological flow data analysis, that applies a topological approach to flow data analysis to extract vortex structures with unprecedented robustness. Rather than treating clinical data as a simple collection of velocity vectors, the proposed algorithm decomposes the measured vector field into fixed points, such as sources, sinks, and saddles, where flow velocity is zero, and separatrices—flow trajectories connecting these points. Since the topology focuses on the global connectivity of the flow trajectories, the analysis is robust to both numerical fluctuations and measurement errors inherent in clinical data. Even when the measured velocity field contains noise or missing data points, the underlying topological structure remains unchanged. This allows for a clear extraction of the “structural framework” of blood flow, successfully representing complex cardiac flows as unambiguous graphs—networks of nodes and edges representing the topological flow structures.

The main strength of the proposed method lies in its ability to generate a graph representing topological blood-flow patterns that can be interpreted immediately. Previously, understanding complex vortex behaviors relied heavily on the subjective experience and intuition of medical doctors. Even under the dynamic boundary conditions of a vigorously beating heart, the algorithm reliably identifies the essential blood-flow patterns. By representing blood-flow as graphs, the number, positions, and interrelationships of vortex-like structures can be quantitatively compared. The proposed method provides clinicians with a quantitative mathematical metric that eliminates subjectivity. This study is expected to enable precise cardiovascular diagnostics, including early disease detection and long-term outcome assessment (prognosis).

(Written by Takashi Sakajo on behalf of all authors)

Share this topic

Fields

Related Articles