A new approach to calculating fiber fields in 2D vessel cross sections using conformal maps

Area of Science:

• Biomedical Engineering
• Computational Mechanics
• Cardiovascular Science

Background:

• Arterial vessels possess three layers (intima, media, adventitia) with strain-stiffening collagen fibers crucial for mechanical response.
• Accurate modeling of arterial mechanics is vital for cardiovascular applications like stenosis prediction and hemodynamic simulations.
• Understanding fiber configurations in the unloaded state is essential for analyzing vessel wall mechanics under load.

Purpose of the Study:

• To introduce a new numerical technique for calculating the fiber field in general arterial cross-sections.
• To utilize conformal maps for precise determination of collagen fiber orientations in arterial tissue.

Main Methods:

• A novel technique employing conformal maps to numerically calculate the fiber field in arterial cross-sections.
• Rational approximation of conformal maps to transform points from the physical cross-section to a reference annulus.
• Mapping angular unit vectors back to the physical cross-section using the inverse conformal map.

Main Results:

• Successful application of conformal mapping for calculating fiber configurations in arterial cross-sections.
• Demonstration of a robust numerical method for determining the unloaded fiber field.
• MATLAB software packages were utilized to implement and achieve the computational goals.

Conclusions:

• The proposed conformal mapping technique provides an effective method for calculating arterial fiber fields.
• This approach enhances the accuracy of mathematical models for arterial expansion and mechanics.
• The findings contribute to improved cardiovascular simulations and a deeper understanding of vascular disease.