A study of different modeling choices for simulating platelets within the immersed boundary method.

Area of Science:

• Computational fluid dynamics
• Biomedical engineering
• Numerical analysis

Background:

• The Immersed Boundary (IB) method is crucial for simulating fluid-structure interactions.
• Traditional IB methods often use piecewise linear approximations and Hookean springs for structural modeling.
• Accurate modeling of complex biological structures like platelets is essential in hemodynamics.

Purpose of the Study:

• To evaluate alternative representations for structural modeling within the IB framework.
• To compare radial basis functions (RBFs) and Fourier-based methods against traditional piecewise linear approximations.
• To analyze geometric errors, force computation accuracy, and computational costs for different representations.

Main Methods:

• Implementation of RBF and Fourier-based representations in the IB method.
• Comparison with piecewise linear approximations in 2D and 3D simulations.
• Quantitative assessment of geometric errors (position, normals) and force errors.
• Analysis of computational performance and resource utilization.

Main Results:

• RBF and Fourier-based methods demonstrate reduced geometric modeling errors compared to piecewise linear approximations for certain shapes.
• Force computation accuracy varies, with Fourier-based methods showing promise for smooth surfaces.
• Computational costs are higher for alternative methods but can be justified by improved accuracy.

Conclusions:

• Alternative representations like RBFs and Fourier-based methods offer significant improvements in geometric accuracy for IB simulations.
• The choice of representation depends on the specific application, desired accuracy, and available computational resources.
• This work provides a framework for selecting optimal IB structural representations in fluid-structure interaction problems, particularly for biological applications like platelet modeling.