Details
| Original language | English |
|---|---|
| Pages (from-to) | 1345-1354 |
| Number of pages | 10 |
| Journal | IEEE Transactions on Biomedical Engineering |
| Volume | 71 |
| Issue number | 4 |
| Early online date | 20 Nov 2023 |
| Publication status | Published - 24 Apr 2024 |
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.
Keywords
- Blood, branching exponents, Electron tubes, Fåhræs–Lindqvist effect, human liver, Liver, Minimization, Murray's law, Optimization, synthetic vascular trees, vascular corrosion cast, Vegetation, Viscosity, Branching exponents, Fåhræs-Lindqvist effect
ASJC Scopus subject areas
- Engineering(all)
- Biomedical Engineering
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In: IEEE Transactions on Biomedical Engineering, Vol. 71, No. 4, 24.04.2024, p. 1345-1354.
Research output: Contribution to journal › Article › Research › peer review
}
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 -