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Topology and hemodynamics of the cortical cerebrovascular system.

Hirsch S, Reichold J, Schneider M, Székely G, Weber B - J. Cereb. Blood Flow Metab. (2012)

Bottom Line: In the first part, we present the current knowledge of the vascular anatomy.This is followed by a theory of topology and its application to vascular biology.We then discuss possible interactions between cerebral blood flow and vascular topology, before summarizing the existing body of the literature on quantitative cerebrovascular topology.

View Article: PubMed Central - PubMed

Affiliation: Computer Vision Laboratory, Federal Institute of Technology ETH, Zurich, Switzerland.

ABSTRACT
The cerebrovascular system continuously delivers oxygen and energy substrates to the brain, which is one of the organs with the highest basal energy requirement in mammals. Discontinuities in the delivery lead to fatal consequences for the brain tissue. A detailed understanding of the structure of the cerebrovascular system is important for a multitude of (patho-)physiological cerebral processes and many noninvasive functional imaging methods rely on a signal that originates from the vasculature. Furthermore, neurodegenerative diseases often involve the cerebrovascular system and could contribute to neuronal loss. In this review, we focus on the cortical vascular system. In the first part, we present the current knowledge of the vascular anatomy. This is followed by a theory of topology and its application to vascular biology. We then discuss possible interactions between cerebral blood flow and vascular topology, before summarizing the existing body of the literature on quantitative cerebrovascular topology.

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Related in: MedlinePlus

Two graphs. (A) Network graph featuring loops. (B) Graph of a binary tree.
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fig6: Two graphs. (A) Network graph featuring loops. (B) Graph of a binary tree.

Mentions: The vessel network is represented simply by bifurcation points and the geometrical properties of the vessel segment in-between. This abstraction resembles the discrete geometrical concept of graphs (e.g., Diestel, 2010). A graph consists of vertices (i.e., bifurcation points) and interconnecting edges (i.e., vessel segments). A graph G=(V,E) is a pair of disjoint sets with a set of nodes V (as well called vertices, or points) and a set of edges E (as well called lines). Each edge is a 2-element subset of V. A graph has no metric in a geometrical sense (e.g., Euclidean). The distance between two nodes is given by the number of edges that the shortest connecting path comprises. Graphically, nodes are represented as dots and edges as interconnecting lines. A graph may generally contain loops (Figure 6A). A tree (Figure 6B) is a graph without loops, where any two vertices are connected by exactly one path. The degree of a node is the number of edges connected to the node. Nodes with only one edge are called leaves. In a binary tree, each node contains at most two children (Figure 6B).


Topology and hemodynamics of the cortical cerebrovascular system.

Hirsch S, Reichold J, Schneider M, Székely G, Weber B - J. Cereb. Blood Flow Metab. (2012)

Two graphs. (A) Network graph featuring loops. (B) Graph of a binary tree.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3367227&req=5

fig6: Two graphs. (A) Network graph featuring loops. (B) Graph of a binary tree.
Mentions: The vessel network is represented simply by bifurcation points and the geometrical properties of the vessel segment in-between. This abstraction resembles the discrete geometrical concept of graphs (e.g., Diestel, 2010). A graph consists of vertices (i.e., bifurcation points) and interconnecting edges (i.e., vessel segments). A graph G=(V,E) is a pair of disjoint sets with a set of nodes V (as well called vertices, or points) and a set of edges E (as well called lines). Each edge is a 2-element subset of V. A graph has no metric in a geometrical sense (e.g., Euclidean). The distance between two nodes is given by the number of edges that the shortest connecting path comprises. Graphically, nodes are represented as dots and edges as interconnecting lines. A graph may generally contain loops (Figure 6A). A tree (Figure 6B) is a graph without loops, where any two vertices are connected by exactly one path. The degree of a node is the number of edges connected to the node. Nodes with only one edge are called leaves. In a binary tree, each node contains at most two children (Figure 6B).

Bottom Line: In the first part, we present the current knowledge of the vascular anatomy.This is followed by a theory of topology and its application to vascular biology.We then discuss possible interactions between cerebral blood flow and vascular topology, before summarizing the existing body of the literature on quantitative cerebrovascular topology.

View Article: PubMed Central - PubMed

Affiliation: Computer Vision Laboratory, Federal Institute of Technology ETH, Zurich, Switzerland.

ABSTRACT
The cerebrovascular system continuously delivers oxygen and energy substrates to the brain, which is one of the organs with the highest basal energy requirement in mammals. Discontinuities in the delivery lead to fatal consequences for the brain tissue. A detailed understanding of the structure of the cerebrovascular system is important for a multitude of (patho-)physiological cerebral processes and many noninvasive functional imaging methods rely on a signal that originates from the vasculature. Furthermore, neurodegenerative diseases often involve the cerebrovascular system and could contribute to neuronal loss. In this review, we focus on the cortical vascular system. In the first part, we present the current knowledge of the vascular anatomy. This is followed by a theory of topology and its application to vascular biology. We then discuss possible interactions between cerebral blood flow and vascular topology, before summarizing the existing body of the literature on quantitative cerebrovascular topology.

Show MeSH
Related in: MedlinePlus