Optimizing Non-Intersecting Synthetic Vascular Trees in Nonconvex Organs.

Area of Science:

• Biomedical Engineering
• Computational Biology
• Medical Imaging

Background:

• Understanding vascular development mechanisms remains a challenge.
• Existing synthetic vascular tree generation methods are limited to single trees and convex volumes.
• A need exists for algorithms capable of generating complex vascular networks in non-convex geometries.

Purpose of the Study:

• To introduce a novel framework for generating multiple vascular trees within general non-convex perfusion volumes.
• To overcome limitations of existing methods by enabling synthetic vascular generation in complex anatomical spaces.

Main Methods:

• The framework integrates topology and global geometry optimization.
• It utilizes a nonlinear optimization problem (NLP) based on Murray's formulation for efficient solutions.
• The NLP is extended to constrain multiple trees within non-convex boundaries, preventing intersections.

Main Results:

• The framework significantly improves total tree energy compared to local optimization approaches.
• Tests on brain tissue and human liver vasculature benchmarks demonstrate framework efficacy.

Conclusions:

• The developed method successfully generates non-intersecting vascular trees in non-convex volumes.
• This capability allows for the reproduction of physiological vascular features like parallel and tortuous vessels.
• The framework enhances functional assessment of organs through improved vascular modeling.