Simulating flow induced migration in vascular remodelling

Abstract

Shear stress induces directed endothelial cell (EC) migration in blood vessels leading to vessel diameter increase and induction of vascular maturation. Other factors, such as EC elongation and interaction between ECs and non-vascular areas are also important. Computational models have previously been used to study collective cell migration. These models can be used to predict EC migration and its effect on vascular remodelling during embryogenesis. We combined live time-lapse imaging of the remodelling vasculature of the quail embryo yolk sac with flow quantification using a combination of micro-Particle Image Velocimetry and computational fluid dynamics. We then used the flow and remodelling data to inform a model of EC migration during remodelling. To obtain the relation between shear stress and velocity in vitro for EC cells, we developed a flow chamber to assess how confluent sheets of ECs migrate in response to shear stress. Using these data as an input, we developed a multiphase, self-propelled particles (SPP) model where individual agents are driven to migrate based on the level of shear stress while maintaining appropriate spatial relationship to nearby agents. These agents elongate, interact with each other, and with avascular agents at each time-step of the model. We compared predicted vascular shape to real vascular shape after 4 hours from our time-lapse movies and performed sensitivity analysis on the various model parameters. Our model shows that shear stress has the largest effect on the remodelling process. Importantly, however, elongation played an especially important part in remodelling. This model provides a powerful tool to study the input of different biological processes on remodelling.

Traffic Patterns of the Migrating Endothelium: How Force Transmission Regulates Vascular Malformation and Functional Shunting During Angiogenic Remodelling

“…The concept of “set point theory” in vascular remodelling proposes that ECs seek an optimal amount of shear stress, and deviations away from this optimal level promote a change from quiescence to the remodelling phenotype ( Baeyens and Schwartz, 2016 ). Further, there is evidence that EC migration speed follows a “band pass-like” behaviour as a function of shear stress in which EC migration slows down and stops all together for shear stress values that are too high or low flow ( Tabibian et al, 2020 ). This complicated relationship between migration speeds and shear stress could result in the “locking in” of ECs within vessels with exceptionally high or low shear stress (the latter of which may be relevant inside of large diameter AVMs) and result in a gradient of migration speeds across the vascular plexus (from venous to arterial) during remodelling.…”

“…This behaviour could be implemented in our model in future studies by describing the migration force parameter as a function of stress. We chose an elliptical representation of ECs as Tabibian et al demonstrated that EC elongation was a critical aspect of angiogenic remodelling ( Tabibian et al, 2020 ). However, in this current study we kept the extend of elongation constant; in future studies it might be interesting to vary the extent of EC elongation as a function of shear stress and other singalling regulators.…”

Vessel Enlargement in Development and Pathophysiology

“…It relates both to the speed of the blood flow and vessel geometry. In the migration paradigm of vessel enlargement, endothelial cells migrate against flow when shear stress levels are decreased compared to physiological normal levels (which are 15 dyn/cm 2 in humans or 30 dyn/cm 2 in mouse) and stop migrating in the presence of physiological levels ( Franco et al, 2015 ; Tabibian et al, 2020 ). Therefore, vessels with the lowest flow rates regress increasing the pool of available endothelial cells.…”

“…Our group has recently used the migration-induced mechanism of vessel enlargement to develop computational models of remodeling and vessel enlargement ( Tabibian et al, 2020 ). In vitro , we found that there is indeed a bell-shaped pattern of migration with respect to shear stress.…”

“…Endothelial cells exposed to shear stress levels between 0.5 and 5 dyn/cm 2 show the highest level of migration, with a peak at 1 dyn/cm 2 . Higher shear stress levels return migration rates to static levels ( Tabibian et al, 2020 ). This information was then used to build the computational model where shear-stress levels defined the speed of migration, but the direction of migration was influenced both by the direction of the flow and a requirement for collective cell movement.…”