Immersed finite element method and its applications to biological systems.

Area of Science:

• Computational mechanics
• Biomedical engineering
• Multiphysics simulation

Background:

• Fluid-structure interaction (FSI) is crucial in biological systems.
• Existing methods for FSI modeling can be computationally intensive and complex.
• Professor T.J.R. Hughes' work inspired novel FSI approaches.

Purpose of the Study:

• To introduce and detail the immersed finite element method (IFEM) for biological modeling.
• To demonstrate IFEM's application in simulating human cardiovascular systems.
• To explore IFEM's potential in understanding cellular dynamics and assembly.

Main Methods:

• Developed an immersed finite element method (IFEM) with a Lagrangian solid mesh over an Eulerian fluid mesh.
• Simplified mesh generation by using a background Eulerian mesh.
• Enforced continuity between fluid and solid domains using velocity interpolation and force distribution via the reproducing Kernel particle method (RKPM) delta function.

Main Results:

• Successfully simulated angioplasty stent deployment.
• Presented preliminary results on monocyte and platelet deposition.
• Modeled blood rheology, including red blood cell (RBC) cluster de-aggregation and deformable cell transport.
• Combined IFEM with electrokinetics to study nano/bio filament assembly and cell motility.

Conclusions:

• IFEM offers a simplified and effective approach for complex biological FSI problems.
• The method shows promise for detailed cardiovascular system modeling and medical device simulation.
• IFEM coupled with other physics, like electrokinetics, can elucidate fundamental biological processes at the cellular and nanoscale.