Computational Modeling of the Kidney Hemodynamics With a Coupled Unsteady Stokes-Darcy Model

Area of Science:

• Computational fluid dynamics
• Biomedical engineering
• Mathematical modeling

Background:

• Accurate simulation of blood flow in kidneys is crucial for understanding renal diseases.
• Existing models often struggle with the complex interplay between vascular and tissue regions.
• Patient-specific modeling requires robust and efficient computational techniques.

Purpose of the Study:

• To develop and validate a numerical method for simulating blood flow in patient-specific kidneys.
• To couple Stokes equations for vascular flow and Darcy equations for tissue flow.
• To ensure stability and convergence of the proposed numerical scheme.

Main Methods:

• Utilized a coupled system of unsteady Stokes-Darcy equations.
• Employed a stabilized P1-P1-P1 finite element method for spatial discretization.
• Implemented an implicit backward Euler method for temporal discretization.
• Developed a Krylov subspace method with a two-scale additive Schwarz preconditioner for efficient solution of algebraic systems.

Main Results:

• Established mathematical theory guaranteeing stability and convergence of the discretization method.
• Demonstrated the accuracy, robustness, and effectiveness of the proposed method through numerical experiments.
• Validated the approach on a benchmark problem and a patient-specific kidney model.

Conclusions:

• The proposed numerical method accurately and efficiently simulates blood flow in patient-specific kidneys.
• The developed method provides a valuable tool for clinical applications and further research in renal hemodynamics.
• The robust preconditioner is key to handling the complex, ill-conditioned systems arising in kidney flow simulations.