Shear stress is not sufficient to control growth of vascular networks: a model study

Abstract

Local vessel wall shear stress is considered to be important for vessel growth. This study is a theoretical investigation of how this mechanism contributes to the structure of a vascular network. The analyses and simulations were performed on vascular networks of increasing complexity, ranging from single-vessel resistance to large hexagonal networks. These networks were perfused by constant-flow sources, constant-pressure sources, or pressure sources with internal resistances. The mathematical foundation of the local endothelial shear stress and vessel wall adaptation was as follows: delta d/delta t = K*(tau-tau desired)*d, where d is vessel diameter, tau desired is desired shear stress, and K is a growth factor. Single vessels and networks with vessels in series developed stable optimal diameters when perfused at constant flow or with a constant-pressure source with internal resistance. However, when constant-pressure perfusion was applied, these vessels developed ever-increasing diameters or completely regressed. In networks with two vessels in parallel, only one; vessel attained an optimal diameter and the other regressed, irrespective of the nature of the perfusion source. Finally, large hexagonal networks regressed to a single vessel when perfused with a pressure source with internal resistance. The behavior was independent of variation in parameters, although the adaptation rate and the diameter of the final vessel were altered. Similar conclusions hold for models of vascular trees. We conclude that the effect of shear stress on vascular diameter alone does not lead to stable network structures, and additional factor(s) must be present.

Computational hemodynamic optimization predicts dominant aortic arch selection is driven by embryonic outflow tract orientation in the chick embryo

“…The change in resistance caused more flow to the larger vessel and less flow to the smaller, creating positive feedback loop, which eventually led to a single vessel. This dynamic vessel competition has also been demonstrated in the adaptation of larger microvascular networks, where τ w maintenance led to rarefaction to a single vessel (Hacking et al 1996;Hudetz and Kiani 1992). Our methodology for the power -only optimization follows these previous models, as the number of aortic arches reduces to one.…”

Shear Stress Biology of the Endothelium

“…7 Furthermore, wall shear stress has been implicated in the development and adaptation of vascular beds, 30,38 and in the chronic physiological remodeling of large arteries 20 where the presence of the endothelium determines the outcome. 35 Although theoretical and experimental studies 1,43 implicate shear as only one of the determinants of vascular adaptation, 23,44 the endothelium clearly plays a central role, and its relationship to shear stress needs to be understood.…”

From cardiac output to blood flow auto-regulation in shock

“…These adaptations are triggered by biological signals related to cell metabolism, working as a negative feedback regulation. [40] This negative feedback counteracts the positive signals responsible for vessel diameter changes to haemodynamic signals that produce a maldistribution of microvascular blood flow, increasing flow in vessels with a greater wall shear stress and predisposing one to arterial-venous shunt [41,42].…”