A nonlinear rotation-free shell formulation with prestressing for vascular biomechanics

Area of Science:

• Computational mechanics
• Biomedical engineering
• Vascular biology

Background:

• Accurate modeling of vascular mechanics is essential for understanding diseases and developing treatments.
• Existing models may not fully capture large deformations and complex material behaviors of blood vessels.

Purpose of the Study:

• To develop and validate a nonlinear, rotation-free shell formulation for simulating large deformations in vascular structures.
• To incorporate realistic material properties and external tissue interactions into the model.
• To adapt a prestress methodology for accurate representation of in vivo vessel geometry.

Main Methods:

• Implementation of a nonlinear, rotation-free triangular shell element for membrane and bending behavior.
• Static condensation of thickness stretch to enforce incompressibility and enable 3D constitutive models.
• Inclusion of external tissue support conditions.
• Adaptation and verification of a prestress methodology for identifying unloaded configurations.
• Application to mouse arterial mechanics with a four-fiber constitutive model.

Main Results:

• The formulation accurately handles large deformations and incorporates 3D constitutive models.
• The prestress methodology effectively identifies unloaded configurations, crucial for in vivo geometry.
• The model demonstrates robustness in simulating mouse arterial mechanics.

Conclusions:

• The developed shell formulation provides a robust tool for analyzing large deformations in vascular biomechanics.
• Accurate modeling of prestress and external tissue support is significant for realistic simulations.
• The formulation is suitable for applications in disease modeling and treatment development.