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Volume ordering for analysis and modeling of vascular systems
M Marxen1, J G Sled, R M Henkelman
1Rotman Research Institute, Baycrest Centre for Geriatric Care, 3560 Bathurst St., Toronto, ON M6A 2E1, Canada. mmarxen@rotman-baycrest.on.ca
Annals of Biomedical Engineering
|December 25, 2008
Summary
A new volume ordering scheme offers a more precise way to analyze vascular systems than the traditional Strahler order. This method accounts for asymmetry, improving insights into vascular design and blood flow modeling.
Area of Science:
- Vascular biology
- Biophysics
- Mathematical modeling
Background:
- Vascular systems are often characterized by Strahler order, which relates vessel properties to branching levels.
- Strahler order's integer limitations restrict precise geometric and physiological interpretation.
- Asymmetries in vascular trees complicate Strahler order analysis.
Purpose of the Study:
- Introduce and validate a novel volume ordering scheme for vascular analysis.
- Compare the volume ordering scheme with the traditional Strahler order.
- Demonstrate the benefits of volume ordering for understanding vascular design and function.
Main Methods:
- Defined volume order number based on the logarithm of estimated perfused tissue volume per segment.
- Compared Strahler and volume order numbers in both symmetrical and asymmetrical branching models.
- Analyzed arterial kidney data using both ordering schemes.
Main Results:
- Volume and Strahler orders are equivalent in perfectly symmetrical trees but diverge with asymmetry.
- Both ordering schemes show linear relationships between logarithmic vessel diameter/conductance and order number.
- Proportionality constants differ between Strahler and volume orders, influenced by organ-specific branching.
Conclusions:
- The volume ordering scheme overcomes Strahler order's limitations by using a physiology-based continuous measure.
- Volume ordering provides enhanced insights into vascular design, fractal properties, and blood flow.
- This method offers a more accurate and interpretable approach to analyzing complex vascular networks.
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