Dynamic adaptive moving mesh finite-volume method for the blood flow and coagulation modeling

Area of Science:

• Computational fluid dynamics
• Biomedical engineering
• Numerical analysis

Background:

• Accurate simulation of blood flow and coagulation is crucial for understanding cardiovascular diseases and developing treatments.
• Existing numerical methods often struggle with the complex, dynamic geometries of biological systems and the coupled physics of fluid flow and biochemical reactions.

Purpose of the Study:

• To develop and validate advanced numerical methods for simulating blood flow and coagulation on dynamic adaptive moving meshes.
• To apply these methods to complex biological scenarios, including the human right ventricle and microfluidic capillaries.

Main Methods:

• Development of moving mesh collocated finite-volume methods for incompressible Newtonian fluid flow (Navier-Stokes equations).
• Incorporation of blood coagulation via a Darcy term with a reaction-dependent permeability coefficient.
• Implementation of a monolithic nonlinear solver for time advancement and a robust method for stiff reaction cascades.
• Verification using analytical problems and application to patient-specific computed tomography data and microfluidic experiments.

Main Results:

• The developed finite volume method is conservative and inf-sup stable for the Navier-Stokes equations, even with collocated variables.
• Successful application to blood flow simulation in a deforming right ventricle model.
• Demonstration of the capability to model coagulation processes in deforming microfluidic capillaries.

Conclusions:

• The proposed numerical framework effectively handles blood flow and coagulation on dynamic adaptive meshes.
• This approach provides a powerful tool for in silico studies of cardiovascular physiology and pathology.
• The methods are validated and show promise for clinical and research applications in hemorheology and thrombosis.