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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

(A) Graph with two loops and one bridge. (B) Graph containing two generating loops. The choice of the generating loops is arbitrary. (C) The Strahler number is an interesting taxonomy to characterize the hierarchy of a binary tree. Leaf nodes are of order 1 and orders increase upstream (see text).
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fig8: (A) Graph with two loops and one bridge. (B) Graph containing two generating loops. The choice of the generating loops is arbitrary. (C) The Strahler number is an interesting taxonomy to characterize the hierarchy of a binary tree. Leaf nodes are of order 1 and orders increase upstream (see text).

Mentions: It is straightforward to reduce a graph by successively cutting single-ended nodes and eliminating transition nodes. In the general case, this will result in loop structures (containing only edges which are part of a loop) connected by single edges (bridges). Deleting a bridge splits the graph and consequently the bridge is not part of a loop. Figure 8A consists of two loops connected by a bridge. If all bridges are removed from the network, then only loop structures of higher connectivity remain (Tarjan, 1974). Loop structures are somewhat difficult to assess, as multiple paths between two nodes are possible, as well as multiple passes through the same loop. They can be quantitatively characterized by the edge connectivity of a graph, which is defined as the minimal number of cuts (i.e., elimination of an edge) that will split the graph. The number is characteristic, but the individual cuts are not.


Topology and hemodynamics of the cortical cerebrovascular system.

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

(A) Graph with two loops and one bridge. (B) Graph containing two generating loops. The choice of the generating loops is arbitrary. (C) The Strahler number is an interesting taxonomy to characterize the hierarchy of a binary tree. Leaf nodes are of order 1 and orders increase upstream (see text).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig8: (A) Graph with two loops and one bridge. (B) Graph containing two generating loops. The choice of the generating loops is arbitrary. (C) The Strahler number is an interesting taxonomy to characterize the hierarchy of a binary tree. Leaf nodes are of order 1 and orders increase upstream (see text).
Mentions: It is straightforward to reduce a graph by successively cutting single-ended nodes and eliminating transition nodes. In the general case, this will result in loop structures (containing only edges which are part of a loop) connected by single edges (bridges). Deleting a bridge splits the graph and consequently the bridge is not part of a loop. Figure 8A consists of two loops connected by a bridge. If all bridges are removed from the network, then only loop structures of higher connectivity remain (Tarjan, 1974). Loop structures are somewhat difficult to assess, as multiple paths between two nodes are possible, as well as multiple passes through the same loop. They can be quantitatively characterized by the edge connectivity of a graph, which is defined as the minimal number of cuts (i.e., elimination of an edge) that will split the graph. The number is characteristic, but the individual cuts are not.

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