Fig 1.
Initial vessel outline and μPIV results were used as inputs for the CFD module which gives the shear stress levels and velocity field for each point within the vasculature. Vascular and avascular agents were defined based on the vessel shape. Shear stress levels together with in vitro data for the relation between shear stress and EC migration rate were used to determine the velocity of migration of each vascular agent in each time-step. The velocity field was used to determine the direction of migration for ECs, such that the ECs migrated in the opposite direction of flow. These were used as the inputs for the computational model which predicts the final vessel shape based on the vascular agents’ final coordinates. Finally, the model prediction was compared with the real outline of the vessel after the period of prediction using rigid registration.
Fig 2.
In vitro model of shear mediated migration.
A) The custom designed flow chamber. ROI = Region of Interest. B) CFD results of shear stress throughout the flow chamber. C) Tracking of the migration of ECs using Imaris. Confluent monolayer of ECs is present but only 15% of the cells have been labelled with CellTracker to facilitate cell tracking. D) ECs have the highest migration rate when exposed to 0.1 Pa shear stress. n = 3-4 per shear stress level. Values are mean ± SEM. Significance is calculated by one-way ANOVA with Tukey’s test. * P<0.01, and ** <0.001. Scale bar = 50 μm.
Fig 3.
Role of avascular growth in vascular remodelling.
A) Fluorescent microscopy images of quail embryo indicating avascular area change (coloured) over time. Blood vessels are labelled by injection of fluorescently labelled acetylated low-density lipoprotein (AcLDL) and unlabled areas are avascular regions. B) Quantitative analysis of the mean change in avascular area (n = 9 embryos). Values are mean ± SEM. Significance is calculated by one-way ANOVA with Tukey’s test. * P<0.05, ** <0.01, and *** <0.001. Scale bar = 100 μm.
Fig 4.
Change in cell shape and density during early stages of development.
A) VE-Cadherin staining of ECs in the yolk sac vasculature of a mouse embryo between 6 and 20 somite stage. Solid yellow line shows the vessel diameter and the dotted yellow line shows the vessel centreline. B) Length and width of the selected ECs shown by yellow arrowed lines whereas green shows an individual EC outline. C) EC length increases between somites 10 and 14. D) No significant change in EC width occurs. E) No difference in the extent of elongation between ECs in vessels with different diameters is present (only data from 20 somites is shown). Each data point represents the average for an embryo (n = 3-4 embryos per stage), with between two and 19 cells per embryo analysed. Values are mean ± SEM. Significance is calculated by one-way ANOVA with Tukey’s test. *P<0.05, and ** <0.01. Scale bar = 50 μm.
Fig 5.
To include agent elongation in the computational model, the circular agent at t = 0 is transformed to an ellipse with an increasing major axis in time. A) Definition of agents’ dimensions and their rotations. B) For two agents to be in equilibrium, sum of the forces from the centre and two foci of an agent on the other agent’s centre should be zero.
Fig 6.
Model prediction for a simple vessel shape.
First row shows the shape of vessels, with white as vascular and black as avascular regions, from a time-lapse of an embryonic vasculature undergoing remodelling at time zero (used as an input for the model) and after two and four hours. The second row shows how vascular (red) and avascular agents (blue) migrate and how vascular agents elongate and avascular agents expand, leading to the final position of these agents. The third row compares the real outlines with the model prediction of the vascular regions using rigid registration. To make the binary image of the model prediction, the elliptical agents were assigned a flexibility of 25%. The blue arrows show the avascular expansion. The parameters used for this model: α = 100, β = 40, ζ = 0, ω = 20, η = 0.1, κ = 20, βav = 100, ωav = 10, and κav = 10. Scale bar = 100 μm.
Fig 7.
Visual representation and four lowest scores for variations in Vmax and τmax.
Four best predictions from the grid search and their Hausdorff distance are shown for three different experiments. The variable which provides the smallest dH for all cases was selected (bold).
Table 1.
Two best predictions for variations in α and ζ.
The grid search results for the two best fits for three different experiments. The variable which provides the smallest dH for all cases was selected (bold).
Table 2.
Best six values for β, κ, and ω from analysis of Time-lapse 1.
Results of the six best predictions represented by smaller dH for three different experiments. The variable which provides the smallest dH for all cases was selected (bold).
Fig 8.
A) Change in geometry due to remodelling when overlaying the real initial and the real final shapes (after four hours) of the vessels without computational simulation. B) Error in the final shape with a model based on random migration. C) Overlay of the final predicted shape based on the Grégorie’s model. D) Overlay of the final predicted shape using our model. Similarity of the images can be compared by their dH (with smaller dH representing a better prediction). The parameters used for this model: α = 100, β = 40, ζ = 0, ω = 20, η = 0.1, κ = 20, βav = 100, ωav = 10, and κav = 10. Scale bar = 100 μm.
Fig 9.
Model cannot accurately predict sprouting angiogenesis.
First column shows the shape of vessel at time zero. Second column shows the vessel shape after four hours. Third column shows the vascular and avascular agents at 4h. Fourth column shows the results of rigid registration of the model output on the real final shape. A) Model output for a simple shape. B) Model output for a larger region. C) Model output for a region with sprouting angiogenesis (blue arrows). The parameters used for this model: α = 100, β = 40, ζ = 0, ω = 20, η = 0.1, κ = 20, βav = 100, ωav = 10, and κav = 10. Scale bar = 100 μm.
Fig 10.
Vascular agent elongation and avascular growth impact the remodelling.
A) Error in the final shape with a model without vascular agents’ ellongation. B) Overlay of the final predicted shape without avascular growth. C) Overlay of the final predicted shape with the complete model. Scale bar = 100 μm.