Branching Exponents of Synthetic Vascular Trees under Different Optimality Principles

authored by: Etienne Jessen, Marc C. Steinbach, Charlotte Debbaut, Dominik Schillinger
Abstract: <italic>Objective:</italic> 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. <italic>Methods:</italic> Our synthetic tree model does not incorporate Murray's law explicitly. Instead, we show that its validity depends on properties of the optimization model and investigate the effects of different physical constraints and optimization goals on the branching exponent that is now allowed to vary locally. In particular, we include variable blood viscosity due to the Fåhræs–Lindqvist effect and enforce an equal pressure drop between inflow and the micro-circulation. Using our global optimization framework, we generate vascular trees with over one million terminal vessels and compare them against a detailed corrosion cast of the portal venous tree of a human liver. <italic>Results:</italic> Murray's law is fulfilled when no additional constraints are enforced, indicating its validity in this setting. Variable blood viscosity or equal pressure drop lead to different optima but with the branching exponent inside the experimentally predicted range between 2.0 and 3.0. The validation against the corrosion cast shows good agreement from the portal vein down to the venules. <italic>Conclusion:</italic> Not enforcing Murray's law increases the predictive capabilities of synthetic vascular trees, and in addition reduces the computational cost. <italic>Significance:</italic> The ability to study optimal branching exponents across different scales can improve the functional assessment of organs.
Organisation(s): Institute of Applied Mathematics
External Organisation(s): Technische Universität Darmstadt
Ghent University
Type: Article
Journal: IEEE Transactions on Biomedical Engineering
Volume: 71
Pages: 1345-1354
No. of pages: 10
ISSN: 0018-9294
Publication date: 24.04.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Biomedical Engineering
Electronic version(s): https://doi.org/10.1109/TBME.2023.3334758 (Access: Open)

BibTeX

@article{be5439b95d2a4b4fbceaa8d19aa0c207,
title = "Branching Exponents of Synthetic Vascular Trees under Different Optimality Principles",
abstract = "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. Instead, we show that its validity depends on properties of the optimization model and investigate the effects of different physical constraints and optimization goals on the branching exponent that is now allowed to vary locally. In particular, we include variable blood viscosity due to the F{\aa}hr{\ae}s–Lindqvist effect and enforce an equal pressure drop between inflow and the micro-circulation. Using our global optimization framework, we generate vascular trees with over one million terminal vessels and compare them against a detailed corrosion cast of the portal venous tree of a human liver. Results: Murray's law is fulfilled when no additional constraints are enforced, indicating its validity in this setting. Variable blood viscosity or equal pressure drop lead to different optima but with the branching exponent inside the experimentally predicted range between 2.0 and 3.0. The validation against the corrosion cast shows good agreement from the portal vein down to the venules. Conclusion: Not enforcing Murray's law increases the predictive capabilities of synthetic vascular trees, and in addition reduces the computational cost. Significance: The ability to study optimal branching exponents across different scales can improve the functional assessment of organs.",
keywords = "Blood, branching exponents, Electron tubes, F{\aa}hr{\ae}s–Lindqvist effect, human liver, Liver, Minimization, Murray's law, Optimization, synthetic vascular trees, vascular corrosion cast, Vegetation, Viscosity, Branching exponents, F{\aa}hr{\ae}s-Lindqvist effect",
author = "Etienne Jessen and Steinbach, {Marc C.} and Charlotte Debbaut and Dominik Schillinger",
year = "2024",
month = apr,
day = "24",
doi = "10.1109/TBME.2023.3334758",
language = "English",
volume = "71",
pages = "1345--1354",
journal = "IEEE Transactions on Biomedical Engineering",
issn = "0018-9294",
publisher = "IEEE Computer Society",
number = "4",
}