The fluid dynamics of an aneurysm
Original story from the Institute of Science Tokyo (Japan).
To simulate blood flow inside brain aneurysms, a computational method that combines 4D flow MRI, computational fluid dynamics and data assimilation has been developed.
Brain aneurysms, also known as cerebral aneurysms, are pathological dilations of blood vessel walls that form bulges in blood vessels of the brain. These bulges form due to weakening of the blood vessels and can arise from different conditions like high blood pressure, genetics, unhealthy lifestyle or underlying heart conditions. Rupture of brain aneurysms is a serious event that can lead to stroke or even death. Therefore, to assess the risk of rupture, it is important to understand how blood flows inside a brain aneurysm.
Many blood flow simulation methods exist to date, including those using phase-contrast magnetic resonance imaging (MRI), also known as four-dimensional (4D) flow MRI, and computational fluid dynamics (CFD) – a computational simulation for the flow of fluids. But these methods often require higher spatiotemporal resolution or lack patient-specific data.
Another approach is optimizing the methods with variational data assimilation (DA) – a technique that combines observational data with a numerical model. However, the models developed with this technique often require high computational costs arising from analyzing the entire vascular system, in addition to the aneurysms, limiting their practical use in clinical settings.
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To overcome the limitations of previous approaches, a research team led by Professor Satoshi Ii from the Department of Mechanical Engineering at the Institute of Science Tokyo (Science Tokyo; Japan) has developed a practical and efficient strategy to estimate blood flow within brain aneurysms using a smarter combination of 4D flow MRI and CFD with DA.
Unlike previous models that require full vessel data, this new approach focuses only on the aneurysm region, significantly reducing the computational costs. Moreover, it uses limited MRI data to specifically analyze the flow velocities near the aneurysm neck, which is required for input in CFD, and it uses the variational DA method to estimate the full velocity profile inside the aneurysm.
“Our method avoids modeling the entire vascular system,” explained Ii, “Even with minimal data, we could achieve simulations that match patient-specific blood flow patterns with remarkable accuracy.”
The researchers validated their method using both synthetic data and real patient datasets. When tested with simulated data, the velocity mismatch between the developed model and ground truth was only 4–7%. Whereas in tests with MRI data from three patients, the method reduced its velocity errors by 37–44% in comparison to traditional 4D flow MRI and CFD models and was therefore more efficient. In effect, it captured more realistic flow patterns using limited data and minimum computing power.
The key innovation of the method was the use of ‘Fourier series-based model order reduction,’ a mathematical optimization technique that simplified how the time-varying flow of blood was represented. This significantly reduced computational complexity and avoided errors in fluid dynamics. Additionally, not only did the new model simulate flow with better accuracy, but it also offered clearer insights into critical hemodynamic factors such as wall shear stress and pressure of the flow.
By harnessing the data assimilation to focus on the aneurysm zone, the method bypasses the challenges of extracting clean boundary conditions from noisy MRI scans of full vessel branches, making the method more efficient and robust for clinical applications.
“This approach could become a valuable tool for neurosurgeons and radiologists,” concluded Ii, “The quantitative evaluation of patient-specific blood flow using this method may aid future predictions of aneurysm growth and rupture, supporting early medical decisions and better management.”
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