Physics-constrained coupled neural differential equations for one dimensional blood flow modeling

Area of Science:

• Computational fluid dynamics
• Biomedical engineering
• Machine learning applications

Background:

• Computational cardiovascular flow modeling is vital for understanding blood dynamics.
• 3D models offer detail but are computationally expensive, especially with fluid-structure interaction (FSI).
• 1D models are efficient but often lack accuracy compared to 3D solutions.

Purpose of the Study:

• To introduce a novel physics-constrained machine learning technique to enhance 1D cardiovascular flow model accuracy and efficiency.
• To compare the performance of this new method against conventional finite element method (FEM)-based 1D models.
• To address limitations in traditional 1D modeling approaches.

Main Methods:

• Utilized a physics-constrained coupled neural differential equation (PCNDE) framework.
• Developed a spatial formulation for the momentum conservation equation, switching space and time.
• Applied the model across various inlet boundary condition waveforms and stenosis blockage ratios.

Main Results:

• The PCNDE model demonstrated superior performance over 1D FEM models.
• Achieved 3-5 times smaller error than 1D FEM and less than 1.2% relative error compared to 3D averaged training data.
• Accurately captured flow rate, area, and pressure variations for unseen data, overcoming coupling stability and smoothness issues.

Conclusions:

• The advanced 1D modeling technique offers a promising approach for rapid cardiovascular simulations.
• Combines physics-based and data-driven modeling for enhanced computational efficiency and accuracy.
• Enables fast and accurate cardiovascular simulations, crucial for clinical applications.