Fig 1.
A schematic of the scales involved in the model and the important events considered in each scale.
At the tissue scale, single sprouts extend toward the tumor. The sprouts may fuse together and form closed loops. Following anastomosis and formation of a closed loop, blood flow starts in the capillaries. When single sprouts extend, environmental conditions of ECs activate a signaling cascade inside ECs. When blood flow starts, a different signaling cascade is activated inside ECs and consequently, a different behavior is observed from ECs before and after blood flow.
Fig 2.
The solution procedure for the multiscale model.
The yellow zone represents the tissue scale, the blue zone is intracellular (molecular) scale, and the red zone is cellular scale. In intracellular scale, different signaling cascades are used for EC phenotype determination before and after anastomosis. In cellular scale, growth and migration of ECs are calculated with similar formulation before and after anastomosis; however, the constants in the formulations depend on the predicted phenotype.
Fig 3.
Signaling cascade of shear stress.
An arrow indicates an activation signal while a hammerhead indicates inhibition. The second line in each box is the combination of input(s) required for activation or inhibition of the molecules.
Table 1.
Nodes dependence relation and corresponding reference for shear stress signaling cascade.
Fig 4.
A schematic of the solution domain in Pott’s model at the cellular scale.
Fig 5.
A sample of the solution domain with assigned numbers.
2s and 3s are two ECs, 0s are representing interstitial fluid, and 1s are matrix fibers. Matrix fibers in ECM are distributed randomly.
Fig 6.
Schematic of the vessel segments assumed for flow calculations.
Fig 7.
Few segments of a vessel from the loop.
Table 2.
Parameters used in the model and corresponding references.
Fig 8.
Closed loop formation in the model.
The X and Y-axis show the domain size in μm.
Fig 9.
EC phenotype considering both flow and no flow conditions.
The outputs are determined by letters, P: Proliferation, M: Migration, PM: Proliferation and Migration.
Fig 10.
Loop collapses when effect of flow in the cell phenotype is neglected.
The complete collapse is obvious after 700 MCS. The X and Y-axis show the domain size in μm.
Fig 11.
The process of shear stress calculation in the loop.
The X and Y-axis show the domain size in μm. A) The configuration of the loop changes in each MCS. The loop configuration is the input to the flow calculation procedure. The color bar shows the EC identity in the solution. B) The current configuration of loop is approximated by vessel segments. Some geometrical simplifications may be required. The color bar is identity of ECs in the solution. Based on the portion of each EC in segments, each segment is assigned to specific EC. C) The pressure, flow, and shear stress are calculated in each segment. The color bar shows shear stress in dyne/cm2. In areas with lower segment diameter, shear stress is higher. D) The average shear stress on each EC is calculated and used for shear stress activation of ECs. The color bar shows the average shear stress in dyne/cm2.
Fig 12.
Survival of loop when both proliferation and migration signals are activated by flow in the loop.
EC color is representative of their identity in the solution. The X and Y-axis show the domain size in μm.
Fig 13.
Blood flow in a closed loop with 30 Pa pressure difference in inlet and outlet of the loop.
Blood viscosity is assumed constant 0.0035 Pa.s. The flow data is averaged over 10 independent simulations.
Fig 14.
Blood flow in a closed loop with 30 Pa pressure difference in inlet and outlet of the loop.
Blood viscosity depends on vessel diameter and hematocrit. The flow data is averaged over 10 independent simulations.
Fig 15.
Flow variations in different values of pressure difference during loop elongation.
The flow data is averaged over 10 independent simulations.
Fig 16.
Phenotype distribution in ECs of a survived loop.
Proliferation and migration is the dominant phenotype.
Fig 17.
Stacked area diagram for portion of each phenotype in the loop during the solution.
A) The case without flow which leads to loop collapse. B) The case with flow which leads to loop survival.
Fig 18.
Comparison of number of ECs between two sprouts extend in parallel and two sprouts in a closed loop.
The number of ECs is averaged over 10 independent simulations.
Fig 19.
Extension speed of sprouts, averaged in time intervals of 2 hr.
After 6hr, a loop is formed and a jump in extension speed occurs.
Table 3.
Average extension speeds of single sprouts and loops.