Fractal analysis of vascular networks: insights from morphogenesis

Journal of Theoretical Biology
Sylvie Lorthois, Francis Cassot

Abstract

Considering their extremely complicated and hierarchical structure, a long standing question in vascular physio-pathology is how to characterize blood vessels patterns, including which parameters to use. Another question is how to define a pertinent taxonomy, with applications to normal development and to diagnosis and/or staging of diseases. To address these issues, fractal analysis has been applied by previous investigators to a large variety of healthy or pathologic vascular networks whose fractal dimensions have been sought. A review of the results obtained on healthy vascular networks first shows that no consensus has emerged about whether normal networks must be considered as fractals or not. Based on a review of previous theoretical work on vascular morphogenesis, we argue that these divergences are the signature of a two-step morphogenesis process, where vascular networks form via progressive penetration of arterial and venous quasi-fractal arborescences into a pre-existing homogeneous capillary mesh. Adopting this perspective, we study the multi-scale behavior of generic patterns (model structures constructed as the superposition of homogeneous meshes and quasi-fractal trees) and of healthy intracortical networks in or...Continue Reading

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