The branching angles in computer-generated optimized models of arterial trees.

Schreiner, Wolfgang; Neumann, Martin; Neumann, Friederike; Roedler, Suzanne; End, Adelheid; P, Buxbaum; Müller, Michael; Spieckermann, P. G.

doi:10.1085/jgp.103.6.975

Cited by 47 publications

(44 citation statements)

References 14 publications

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“…The large-scale geometry of arterial networks has been little studied in the light of these optimality principles, with the exception of Kamiya and Togawa (1972) who found the locally optimal tree for one mesenteric tree in a dog and Schreiner and Buxbaum (1993) and Schreiner et al (1994Schreiner et al ( , 1996 who built model vascular trees by iteratively adding locally optimal 'Y' junctions. The research presented here is the first to employ algorithms capable of predicting the arterial tree given only the coordinates of the source and leaf segments.…”

Section: Introductionmentioning

confidence: 99%

Modeling the large-scale geometry of human coronary arteries

Changizi¹,

Cherniak²

2000

Rev. can. physiol. pharmacol.

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Abstract:Two principles suffice to model the large-scale geometry of normal human coronary arterial networks. The first principle states that artery diameters are set to minimize the power required to distribute blood through the network. The second principle states that arterial tree geometries are set to globally minimize the lumen volume. Given only the coordinates of an arterial tree's source and "leaves", the model predicts the nature of the network connecting the source to the leaves. Measurements were made of the actual geometries of arterial trees from postmortem healthy human coronary arteriograms. The tree geometries predicted by the model look qualitatively similar to the actual tree geometries and have volumes that are within a few percent of those of the actual tree geometries. Human coronary arteries are therefore within a few percent of perfect global volume optimality. A possible mechanism for this nearperfect global volume optimality is suggested. Also, the model performs best under the assumption that the flow is not entirely steady and laminar.Key words: arteries, optimization, volume, power, geometry.Résumé : On peut modéliser la géométrie d'un réseau d'artères coronaires humaines normales en faisant appel à deux principes. Le premier veut que les diamètres artériels soient tels qu'ils minimisent le travail nécessaire pour distribuer le sang à travers le réseau. Le second veut que la géométrie de l'arbre artériel soit telle qu'elle minimise globalement le volume de la lumière. S'appuyant uniquement sur les coordonnées de source et de terminaisons d'un arbre, le modèle peut alors prédire le réseau. Les géométries réelles d'arbres artériels sains, obtenus par coronarographie postmortem chez des humains, ont été mesurées. Les géométries prédites par le modèle sont qualitativement similaires aux géométries réelles et ont des volumes correspondant à un pourcentage près à ceux des géométries réelles. Ainsi, les artères coronaires humaines ont une optimalité de volume global presque parfaite. On suggère un mécanisme possible pour cette optimalité presque parfaite. Le modèle est meilleur sous l'hypothèse que l'écoulement n'est pas entièrement stationnaire et laminaire.

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Section: Introductionmentioning

confidence: 99%

Modeling the large-scale geometry of human coronary arteries

Changizi¹,

Cherniak²

2000

Rev. can. physiol. pharmacol.

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“…Without the input of anatomical information or morphometric data, the growth process of CCO trees is based on principles of optimization. The resulting structures, obtained by successive adding of new segments and optimization of the growing tree at each step of development, are geometrically and topologically optimized branching networks which resemble real vascular trees with regard to visual appearance and morphometric parameters [4, 5, 6, 7]. However, the algorithm could only be used for vessel trees in a two-dimensional perfusion area, representing an infinitesimally thin layer of tissue.…”

Section: Introductionmentioning

confidence: 99%

Functional Characteristics of Optimized Arterial Tree Models Perfusing Volumes of Different Thickness and Shape

Karch¹,

Neumann²,

Neumann

et al. 2000

J Vasc Res

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The relationship between the ‘shape of an organ’ and the ‘cost of blood transport’ to perfuse its tissue was evaluated on the basis of optimized arterial model trees simulated to perfuse square-based 100-cm³ volumes of different shape (‘flat’ versus ‘thick’ as defined by the ratio of thickness to side-length h/s ≤1). Specifically, the effects of ‘shape’ on tree structure, blood transport, and on hemodynamic characteristics were investigated. Branching models of arterial trees were generated by constrained constructive optimization (CCO), based on an identical set of model parameters. All model trees were geometrically and topologically optimized for intravascular volume. Tree structures achieved tremendous savings of blood (transport medium) in comparison to a system of separate tubes. Thickening the perfusion volume (increasing h/s) resulted in a significant decrease of mean transport length, deposition time, and intravascular total volume in the tree. ‘Thick’ perfusion volumes induced CCO trees to branch more symmetrically into a number of equivalent subtrees repetitiously splitting into smaller ones; ‘flat’ structures were dominated throughout by a few asymmetrically branching major vessels. In summary, we conclude from systematic variation of shape that thicker perfusion volumes (h/s >0.1) facilitate efficient delivery of blood in comparison to large amounts of ‘dead volume’ to be carried over long distances in very thin pieces of tissue.

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“…From capillaries (the root segments), the vascular tree successively bifurcates down to the larger diameter level, where the vascular tree is truncated in the form of terminal segment [28] .…”

Section: The Basic Assumptions For Establishment Of a Vascular Treementioning

confidence: 99%

Creation of a vascular system for organ manufacturing

Liu¹,

Wang²

2024

IJB

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Abstract:The creation of a vascular system is considered to be the main object for complex organ manufacturing. In this short review, we demonstrate two approaches to generate a branched vascular system which can be printed using rapid prototyping or bioprinting techniques. One approach is constructing mathematical tree models on the basis of human physiological characteristics and calculating the model using constrained constructive optimization to obtain three-dimensional (3D) geometrical structures. The rules of the branching of the vessel tree were extracted from the literature. Another approach is using computer-aided design models to build a multi-scale vascular network including arteries, veins, and capillaries. A 3D vascular template with both synthetic scaffold polymer and cell/hydrogel was created in our group, using a double-nozzle, low-temperature deposition technique. Each of the approaches holds promise in producing a vascular system.

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The branching angles in computer-generated optimized models of arterial trees.

Cited by 47 publications

References 14 publications

Modeling the large-scale geometry of human coronary arteries

Modeling the large-scale geometry of human coronary arteries

Functional Characteristics of Optimized Arterial Tree Models Perfusing Volumes of Different Thickness and Shape

Creation of a vascular system for organ manufacturing

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