Branching Exponents of Synthetic Vascular Trees Under Different Optimality Principles.

Objective: The branching behavior of vascular trees is often characterized using Murray's law. We investigate its validity using synthetic vascular trees generated under global optimization criteria.

Methods: Our synthetic tree model does not incorporate Murray's law explicitly.

Rigorous mathematical optimization of synthetic hepatic vascular trees.

In this paper, we introduce a new framework for generating synthetic vascular trees, based on rigorous model-based mathematical optimization. Our main contribution is the reformulation of finding the optimal global tree geometry into a nonlinear optimization problem (NLP). This rigorous mathematical formulation accommodates efficient solution algorithms such as the interior point method and allows us to easily change boundary conditions and constraints applied to the tree.