van Bavel, E. | Search bioRxiv

bioRxiv2024

Arterial arcades and collaterals regress under hemodynamics-based diameteradaptation: a computational and mathematical analysis

Segments in the arterial network have a >1000-fold span of radii. This is believed to result from adaptation of each segment to the wall shear stress (WSS), with outward respectively inward remodeling if WSS is higher or lower than some reference value. While this seems a straightforward mechanism for arterial tree design, the arterial network is not a tree but contains numerous arcades, collaterals and other looping structures. In this theoretical study, we analyzed stability of looping structures in arterial networks under WSS control. Simulation models were based on very simple network topologies as well as on published human coronary and mouse cerebral arterial networks. Adaptation was implemented as a rate of change of structural radius of each segment that is proportional to the deviation from its reference WSS. A more generalized model was based on adaptation to a large range of other local hemodynamic stimuli, including velocity, flow and power dissipation. For over 12,000 tested parameter sets, the simulations invariably predicted loss of loops due to regression of one or more of the segments. In the small networks, this was the case for both the WSS and the generalized model, and for a large range of initial conditions and model parameters. Loss of loopiness also was predicted by models that included direction-dependent adaptation rates, heterogeneous reference WSS or adaptation rates among the adapting segments, and adaptation under dynamic conditions. Loss of loops was also found in the coronary and cerebral artery networks subjected to adaptation to WSS. In a mathematical analysis we proved that loss of loops is a direct consequence of Kirchhoffs circuit law, which for each loop leads to a positive eigenvalue in the Jacobian matrix of partial derivatives in the adaptation model, and therefore to unstable equilibria in the presence of loops. Loss of loops is an inherent property of arterial networks that adapt to local hemodynamics. Additional mechanisms are therefore needed to explain their presence, including direct communication between connected segments.

physiology↗

bioRxiv2022

Quantification of hypoxic regions distant from occlusions in cerebral penetrating arteriole trees

The microvasculature plays a key role in oxygen transport in the mammalian brain. Despite the close coupling between cerebral vascular geometry and local oxygen demand, recent experiments have reported that microvascular occlusions can lead to unexpected distant tissue hypoxia and infarction. To better understand the spatial correlation between the hypoxic regions and the occlusion sites, we used both in vivo experiments and in silico simulations to investigate the effects of occlusions in cerebral penetrating arteriole trees on tissue hypoxia. In a rat model of microembolisation, 25 {micro}m microspheres were injected through the carotid artery to occlude penetrating arterioles. In representative models of human cortical columns, the penetrating arterioles were occluded by simulating the transport of microspheres of the same size and the oxygen transport was simulated using a Greens function method. The locations of microspheres and hypoxic regions were segmented, and two novel distance analyses were implemented to study their spatial correlation. The distant hypoxic regions were found to be present in both experiments and simulations, and mainly due to the hypoperfusion in the region downstream of the occlusion site. Furthermore, a reasonable agreement for the spatial correlation between hypoxic regions and occlusion sites is shown between experiments and simulations, which indicates the good applicability of in silico models in understanding the response of cerebral blood flow and oxygen transport to microemboli. Author summaryThe brain function depends on the continuous oxygen supply through the bloodstream inside the microvasculature. Occlusions in the microvascular network will disturb the oxygen delivery in the brain and result in hypoxic tissues that can lead to infarction and cognitive dysfunction. To aid in understanding the formation of hypoxic tissues caused by micro-occlusions in the penetrating arteriole trees, we use rodent experiments and simulations of human vascular networks to study the spatial correlations between the hypoxic regions and the occlusion locations. Our results suggest that hypoxic regions can form distally from the occlusion site, which agrees with the previous observations in the rat brain. These distant hypoxic regions are primarily due to the lack of blood flow in the brain tissues downstream of the occlusion. Moreover, a reasonable agreement of the spatial relationship is found between the experiments and the simulations, which indicates the applicability of in silico models to study the effects of microemboli on the brain tissue.

bioengineering↗