TY - JOUR

T1 - Branching Exponents of Synthetic Vascular Trees under Different Optimality Principles

AU - Jessen, Etienne

AU - Steinbach, Marc C.

AU - Debbaut, Charlotte

AU - Schillinger, Dominik

PY - 2024/4/24

Y1 - 2024/4/24

N2 - 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 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. 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.

AB - 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 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. 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.

KW - Blood

KW - branching exponents

KW - Electron tubes

KW - Fåhræs–Lindqvist effect

KW - human liver

KW - Liver

KW - Minimization

KW - Murray's law

KW - Optimization

KW - synthetic vascular trees

KW - vascular corrosion cast

KW - Vegetation

KW - Viscosity

KW - Branching exponents

KW - Fåhræs-Lindqvist effect

UR - http://www.scopus.com/inward/record.url?scp=85178069346&partnerID=8YFLogxK

U2 - 10.1109/TBME.2023.3334758

DO - 10.1109/TBME.2023.3334758

M3 - Article

C2 - 37983147

VL - 71

SP - 1345

EP - 1354

JO - IEEE Transactions on Biomedical Engineering

JF - IEEE Transactions on Biomedical Engineering

SN - 0018-9294

IS - 4

ER -