Quantitative Evaluation of Intracardiac Vortex Blood Flow Using Topological Flow Data Analysis

A research group led by Professor Takashi Sakajo of Division of Mathematics, Graduate School of Science, Kyoto University has developed a new way to "read" the blood flow inside the heart. By using a specialized field of mathematics called topology and dynamical systems theory, the group created a new method of data analysis: Topological Flow Data Analysis (TFDA). This method allows us to identify and measure the complex, whirlpool-like blood patterns (vortices) in the heart with much greater accuracy and consistency than ever before.

Using this technology, the researchers converted these complex flow patterns into simple strings of characters, much like a code. This revealed a clear difference between a healthy heart and one in the early stages of heart failure—something that was previously too subtle to define. This breakthrough offers a new way to assess heart health through blood flow, promising earlier diagnosis and a deeper understanding of heart disease.

The Challenge of Measuring Complex Blood Flow

The heart acts as a vital pump, circulating blood throughout the entire body. To do this efficiently, the blood inside the heart creates complex, rotating patterns known as "vortex flows." In recent years, advanced imaging technologies like echocardiography and cardiac MRI have allowed us to visualize these vortices, revealing that their patterns change in patients with conditions such as heart failure.

However, accurately analyzing these flows is incredibly difficult. The heart is a dynamic organ that constantly changes shape as it beats, with its walls and valves in perpetual motion. While current imaging can show us the blood moving, it is hard to objectively identify and measure each individual vortex without ambiguity. To truly understand heart disease and provide personalized care for every patient, we need a new way to capture and quantify these complex blood flow patterns.

Successful Quantitative Evaluation of Intracardiac Blood Flow and Detection of Early Signs of Heart Failure

Development of a Topological Flow Data Analysis Method Tailored to Intracardiac Blood Flow

Professor Sakajo's group has long been developing TFDA as a unique mathematical approach to analyzing fluid motion. However, the original theory could not be directly applied to three-dimensional flows, and it did not account for scenarios where the domain shape changes due to pulsation, making it unsuitable for intracardiac blood flow analysis.

To overcome this, the group introduced a special flow structure called a degenerate singularity^*1 to mathematically handle flows enclosed by moving boundaries, such as heart walls and valves. This allowed us to stably capture the universal motion of blood flow, even within the ever-changing environment of a beating heart. Furthermore, they solved the challenges of 3D flow by mathematically expanding the conventional analysis to cover 2D compressible flows.

*1 Degenerate singularity
A special type of stagnation point in a flow where an infinite number of streamlines converge on that single point.

Using Topology to Extract Universal Patterns from Real-World Data

Measured data from echocardiography and cardiac MRI are often compromised by measurement noise and poor image quality, making conventional image analysis methods highly vulnerable to noise interference. Here, Professor Sakajo's research group turned to topology, which identifies geometric features invariant under continuous deformations. This approach enables the extraction of universal patterns from real-world data without being affected by measurement errors or localized noise disturbances. Furthermore, the group successfully assigned unique symbolic strings to individual vortex blood flow structures (Fig. 1). Through this string-based representation, the structure and dynamics of each vortex can be precisely captured, allowing intracardiac vortex blood flow—previously analyzed only qualitatively—to be expressed quantitatively and without ambiguity.

Detecting Heart Flow Vortices that Signal Early Heart Failure

By using this string representation to compare blood flow patterns, the researchers revealed distinct structural differences between a healthy heart and one in the very earliest stages of heart failure (Fig. 2). This means that a decline in the heart’s pumping function can now be described not just as a change in the amount of blood pumped out, but as a fundamental shift in the blood flow pattern itself. Furthermore, a commercial analysis software based on this method has already been developed and is beginning to be used in clinical research within basic medicine.

Toward Practical Application as a New Standard for Cardiac Evaluation

Moving forward, the research group aims to establish a new classification system for cardiac function using this string representation of vortex flows. This system is expected to be a powerful tool for the early diagnosis of heart failure and for assessing the effectiveness of treatments. Furthermore, by tracking how these blood flow structures change over time, the method holds great potential for predicting disease progression and evaluating patient prognosis.

These research findings not only deepen our fundamental medical understanding of intracardiac blood flow but also provide a transformative new metric for the diagnosis and treatment of cardiovascular diseases. Research and development are currently underway to bring this innovative technology into full practical use.