Figure 1.
Schematic of different scales of simulated solid tumor growth.
Figure 2.
The results of discrete sprouting angiogenesis.
Five initial sprouts move toward the tumor on the right of the domain.
Figure 3.
The results of discrete sprouting angiogenesis.
Ten initial sprouts move toward the tumor on the right of the domain.
Figure 4.
Schematic representation of blood flux at each vascular node.
Figure 5.
Schematic representation of blood flux through capillary or transformation from capillary and related parameters.
Figure 6.
A schematic of calculated domain for fluid flow simulation.
Table 1.
Material properties used in numerical simulations, as taken from [2].
Figure 7.
Schematic of different patterns of blood flow in networks a) Blood flow from one (two) node(s) into one (two) node(s).
b) Blood flow from three nodes into one node. c) Blood flow from one node into three nodes.
Figure 8.
Shear stress induced by intravascular pressure in a range of intravascular pressure flows in circulatory system.
Equation is derived by Pries et al. [33] with curve fitting from experimental results obtained on rat mesentery vessels.
Figure 9.
Algorithm for calculating interstitial pressure in tissue without considering capillary network.
Figure 10.
Algorithm for calculating interstitial pressure in tissue and blood flow through capillary network with rigid vessels.
Figure 11.
Algorithm for calculating interstitial pressure in tissue and blood flow through capillary network with adaptable vessels and non-continuous behavior of blood.
Table 2.
Parameter values used in the adaptation.
Figure 12.
A 3D graph (a) and the contour (b) of interstitial pressure in the computational domain for both normal and tumor tissues in which uniform distribution and constant values for intravascular pressure are assumed.
The maximum pressure is around 500Pa in the tumor region.
Figure 13.
The vascular network after pruning for a network with five (a) and ten (b) endothelial cells in parent vessel.
The green lines show the pruned network. The blue lines are killed segments that do not make a loop.
Figure 14.
The 3D graph (a) and the contour (b) of interstitial pressure in the computational domain for both normal and tumor tissues for a network with 5 endothelial cells in the parent vessel.
The figure is obtained by simulating blood flow through a vascular network found by the discrete sprouting angiogenesis method, with rigid capillaries and continuum properties of blood and coupling by fluid flow in tissue. The maximum pressure is around 700Pa in the tumor region.
Figure 15.
The 3D graph (a) and the contour (b) of interstitial pressure in the computational domain for both normal and tumor tissues for a network with 10 endothelial cells in the parent vessel.
The figure is obtained by simulating blood flow through a vascular network found by the discrete sprouting angiogenesis method, with rigid capillaries and continuum properties of blood and coupling by fluid flow in tissue. The maximum pressure is around 800Pa in the tumor region.
Figure 16.
Fluid flow in simulated rigid network and adapted network for network with 5 endothelial cells.
In adapted network, some segments eliminated because their diameter is small and they pass very low flow. In both cases, when a segment’s flow rate is less than 0.01 of the maximum flow rate in the network, this segment is pruned.
Figure 17.
Fluid flow in simulated rigid network and adapted network for network with 10 endothelial cells.
In adapted network, some segments eliminated because their diameter is small and they pass very low flow. In both cases, when a segment’s flow rate is less than 0.01 of the maximum flow rate in the network, this segment is pruned.
Figure 18.
Intravascular pressure in two cases: rigid network and adaptive network for network with 5 endothelial cells.
Adaptive network shows higher pressure near the solid tumor. This pressure can affect interstitial flow in this region.
Figure 19.
Intravascular pressure in two cases: rigid network and adaptive network for network with 10 endothelial cells.
Adaptive network shows higher pressure near the solid tumor. This pressure can affect interstitial flow in this region.
Figure 20.
The 3D graph (a) and the contour (b) of interstitial pressure in the computational domain for both normal and tumor tissues for a network with 5 endothelial cells in the parent vessel.
Figure is obtained by simulating blood flow through a vascular network found by the discrete sprouting angiogenesis method, with adaptable capillaries and non-Newtonian and non-continuous properties of blood and coupling by fluid flow in tissue. The maximum pressure is above 1100Pa in the tumor region.
Figure 21.
The 3D graph (a) and the contour (b) of interstitial pressure in the computational domain for both normal and tumor tissues for a network with 10 endothelial cells in the parent vessel.
Figure is obtained by simulating blood flow through a vascular network found by the discrete sprouting angiogenesis method, with adaptable capillaries and non-Newtonian and non-continuous properties of blood and coupling by fluid flow in tissue. The maximum pressure is above 1200Pa in the tumor region.