Relation between branching patterns and perfusion in stochastic generated coronary arterial trees

Abstract

Biological variation in branching patterns is likely to affect perfusion of tissue. To assess the fundamental consequences of branching characteristics, 50 stochastic asymmetrical coronary trees and one nonstochastic symmetrical branching tree were generated. In the stochastic trees, area growth, A, at branching points was varied: A = random; 1.00; 1.10; 1.13 and 1.15 and symmetry, S, was varied: S = random; 1.00; 0.70; 0.58; 0.50 and 0.48. With random S and A values, a large variation in flow and volume was found, linearly related to the number of vessels in the trees. Large A values resulted in high number of vessels and high flow and volume values, indicating vessels connected in parallel. Lowering symmetry values increased the number of vessels, however, without changing flow, indicating a dominant connection of vessels in series. Both large A and small S values gave more realistic gradual pressure drops compared to the symmetrical non-stochastic branching tree. This study showed large variations in tree realizations, which may reflect real biological variations in tree anatomies. Furthermore, perfusion of tissue clearly depends on the branching rules applied.

Fluid-dynamic optimality in the generation-averaged length-to-diameter ratio of the human bronchial tree

“…Furthermore, absolute values of l/d for diameters of 15-100 lm lie in the range 2.8-4.7, which is in a fair coincidence with the predictions, considering that the branching angles of small arterioles can be quite large. Then the data of Dankelman et al [1] for coronary arterial tree can be said to be in good agreement with the prediction of the present study.…”

“…As is well documented in Dankelman et al [1] for the coronary arteries and arterioles of a pig, the area ratio, the ratio of total cross sectional areas of the daughters to the mother, consistently increases toward small diameter tubes, and l/d follows the same trend. Since the increased area ratio implies the increased diameter ratio in general, the increasing l/d for smaller branches can be thought to come from the increased area ratio.…”

Small Artery Remodeling: Current Concepts and Questions

“…Interaction schemes such as this can be refined and extended to networks and metabolic variables. Yet the presence of multiple regulated variables, acute and structural effects, and the complexity of network architecture [166,167,168] obscures a straightforward insight into the integrated behavior of the resistance vasculature. Several authors built simulation models of vascular regulation in order to obtain a better understanding or to derive new concepts for vascular regulation.…”

Dynamics of pulsatile flow in fractal models of vascular branching networks

“…Flow in a branching vascular network is affected by the network geometry which is defined by the branching pattern [5]. Distributions of pressure and flow rate in a tree-like network can easily be defined if the branch deformation (compliance) is ignored (see [19]).…”