A bilinear stress-strain relationship for arteries

Area of Science:

• Biomedical Engineering
• Vascular Physiology
• Materials Science

Background:

• Understanding blood vessel mechanical properties is crucial for vascular physiology, pathophysiology, and tissue engineering.
• Current methods using nonlinear stress-strain relations (e.g., Fung's model) present challenges in fitting experimental data to derive material parameters.
• The inherent nonlinearity of blood vessel tissue complicates accurate constitutive modeling.

Purpose of the Study:

• To develop a novel, linearized constitutive model for blood vessel mechanics.
• To simplify the determination of material constants by addressing elastic nonlinearity.
• To provide a clearer physical interpretation of model parameters in vascular tissue.

Main Methods:

• Generalizing the strain definition to incorporate elastic nonlinearity.
• Proposing a two-dimensional bilinear stress-strain relation using second Piola-Kirchhoff stress and the new strain measure.
• Comparing the proposed model's performance against established models like Fung's exponential model.

Main Results:

• The proposed model effectively linearizes the stress-strain relationship for blood vessels.
• The novel constitutive relation demonstrates excellent agreement with Fung's exponential model.
• The simplified model facilitates easier determination of material constants and offers improved parameter interpretability.

Conclusions:

• The developed linearized constitutive model offers a significant advancement in analyzing vascular mechanics.
• This approach simplifies the complex stress-strain behavior of blood vessels, aiding in material parameter derivation.
• The model has implications for improved vascular tissue engineering and understanding of vascular diseases.