Visualizing Fluid Flows via Regularized Optimal Mass Transport with Applications to Neuroscience

Area of Science:

• Computational fluid dynamics
• Mathematical modeling
• Biomedical engineering

Background:

• The optimal mass transport (OMT) problem, formulated by Benamou and Brenier, provides a dynamic approach to mass distribution problems.
• The glymphatic system is crucial for waste clearance in the brain, and understanding its fluid dynamics is vital for neuroscience and medicine.
• Visualizing fluid flow in biological systems like the glymphatic system presents significant computational challenges.

Purpose of the Study:

• To demonstrate the utility of the regularized optimal mass transport (rOMT) model for visualizing fluid flows within the glymphatic system.
• To present modifications to existing numerical methods for efficient implementation of the rOMT model.
• To reduce the computational runtime associated with simulating fluid dynamics in the glymphatic system.

Main Methods:

• Incorporation of a diffusion term into the continuity equation of the original OMT formulation to create the rOMT model.
• Development and description of modified numerical algorithms for efficient rOMT computation.
• Application and validation of the enhanced numerical method using both synthetic and real-world glymphatic system data.

Main Results:

• The rOMT model effectively visualizes fluid flow patterns in the glymphatic system.
• The modified numerical method achieves a significant reduction in computational runtime compared to previous approaches.
• Successful application of the method to both simulated and experimentally derived datasets.

Conclusions:

• The regularized optimal mass transport (rOMT) model is a powerful tool for computational fluid dynamics, particularly for visualizing glymphatic system flows.
• The optimized numerical implementation makes the rOMT model more computationally feasible for complex biological fluid dynamics.
• This approach offers a valuable method for analyzing and understanding fluid transport in the brain and potentially other biological systems.