Multiscale modeling of vascularized tissues via nonmatching immersed methods

Area of Science:

• Computational mechanics
• Biomaterials science
• Tissue engineering

Background:

• Modeling complex biological tissues with integrated vascular networks presents significant computational challenges.
• Existing methods often struggle to efficiently capture the mechanical interplay between the tissue matrix and intricate vascular structures.

Purpose of the Study:

• To develop an efficient multiscale computational approach for modeling vascularized tissues.
• To reduce the complexity of computational models by treating vascular structures as lower-dimensional manifolds.

Main Methods:

• Utilized an immersed method approach for computational modeling of tissues with elastic matrices and vascular structures.
• Derived variational formulations incorporating singular or hypersingular forcing terms to represent vasculature effects.
• Reduced model complexity by using information solely from co-dimension two manifolds (e.g., vessel center lines, cross-sectional areas).

Main Results:

• Demonstrated the efficiency of the immersed method through numerical tests, including cases with known solutions.
• Successfully modeled materials with random vessel distributions.
• Performed in silico characterization of effective biphasic material properties using statistical simulations.

Conclusions:

• The proposed immersed method offers an efficient and accurate approach for computational modeling of vascularized tissues.
• This technique significantly simplifies the modeling of complex vascular networks, enabling detailed mechanical analysis.
• The method facilitates in silico characterization of tissue mechanical properties, advancing biomaterials research.