A Lagrangian level set-like method for modelling and simulation in bioengineering.

Area of Science:

• Computational Solid Mechanics
• Numerical Analysis
• Geometric Modeling

Background:

• The level set method is a powerful tool for tracking moving interfaces in various physical applications, offering an alternative to explicit geometric descriptions.
• Existing methods often require complex geometric representations, limiting their efficiency and applicability in dynamic scenarios.

Purpose of the Study:

• To develop and validate an innovative update method for the level set function in solid mechanics.
• To accurately track sub-domain boundaries and assign material properties based on level set function values.
• To demonstrate the method's versatility across different physical applications.

Main Methods:

• A novel update method for the level set function is proposed, based on computing a displacement field derived from level set function values.
• A criterion for assigning material properties is developed, utilizing the values of the level set function.
• The method is validated through 2D simulations, including a through-thickness hole plate, brain tumor expansion, and grasping scenarios.

Main Results:

• The proposed method accurately predicts the evolution of sub-domain boundaries.
• The approach demonstrates efficient tracking of moving interfaces without explicit geometric descriptions.
• Successful application in diverse cases highlights the method's robustness and broad applicability.

Conclusions:

• The developed level set method offers an accurate and efficient approach for tracking moving interfaces in solid mechanics.
• The innovative update and material property assignment strategies enhance the prediction of sub-domain boundary evolution.
• The method's successful validation across multiple applications underscores its potential for wide-ranging physical simulations.