Rigorous mathematical optimization of synthetic hepatic vascular trees.

Area of Science:

• Biomedical Engineering
• Computational Biology
• Mathematical Modeling

Background:

• Generating realistic synthetic vascular trees is crucial for various biomedical applications.
• Existing methods often struggle with accurately replicating complex vascular geometries and topologies.

Purpose of the Study:

• To introduce a new model-based mathematical optimization framework for generating synthetic vascular trees.
• To improve the accuracy and realism of synthetic vascular structures.

Main Methods:

• Reformulated vascular tree generation as a nonlinear optimization problem (NLP).
• Integrated topology optimization using constrained constructive optimization (CCO) and heuristic search.
• Combined NLP and topology optimization into a single algorithmic approach.
• Validated the framework using a human liver corrosion cast.

Main Results:

• The new framework successfully generates asymmetric synthetic vascular trees.
• The generated trees quantitatively match experimental data from human liver corrosion casts.
• The model-based optimization approach outperforms the standard CCO method in accuracy.

Conclusions:

• The proposed framework offers a rigorous and flexible approach to synthetic vascular tree generation.
• This method provides a significant improvement in accurately replicating in vivo vascular structures.
• The framework's ability to handle complex constraints and generate trifurcations enhances its applicability.