Fig 1.
A diagram identifying important events in angiogenesis at the cellular level.
Tumor cells secrete VEGF that drives the activation of Endothelial cells by binding to VEGF-receptors on the ECs’ surface. VEGF meditated ECs undertake two distinct phenotypes: tip and stalk cell. Tip cells migrate towards the tumor to reach the VEGF source and highly proliferative stalk cells form the new sprouts body.
Fig 2.
Signaling networks considered in the model that are involved in tumor growth; the implemented network focuses on Ras- PI3K-Akt and Wnt/ß-catenin signaling that control the cancer cell state.
Highlighting the relationship between external stimuli, Wnt, RTK, cadherin and integrin, the cell can be growing, proliferating, migrating or undergoing apoptosis. A pointed head arrow indicates activation whereas a blunt head refers to inhibition.
Table 1.
Boolean dependence relations between molecules of the signaling cascades presented in Fig 2, and the corresponding references.
Fig 3.
Boolean model prediction of cell phenotype (state) for various input configurations.
Colors correspond to the color of the nodes in Fig 2, indicating activity of the receptors’ signal (i.e. integrin, RTK, Wnt) and inactivation of receptor is shown in grey. Tumor suppressors are deactivated. For instance, if the cell receives a signal from integrin and RTK, and no signal from Wnt (110), considering cadherin activation, the model predicts that the cell starts to grow and proliferate (1100). The binary code on the first row specify the integrin, RTK and Wnt states, respectively.
Table 2.
Parameters used in the model and corresponding references.
Table 3.
Quantitative comparison of simulated average sprout velocity with various experimental observations.
Fig 4.
The average sprout extension velocity calculated from 5 independent simulations with and without including the intracellular signal transduction pathways, in comparison with experimental measurements extracted from Bauer et al. [26]. (Model validation; the error bars are the standard deviation on the mean of n = 5 simulation runs).
Table 4.
Parameters used in the models and corresponding references.
Fig 5.
Tumor radius changes over time.
A comparison between numerical results from the Taghibakhshi et al. [119] model, based on Michaelis-Menten reaction of oxygen consumption, and the current study. Initial radius of the tumor is 24.3 μm. Error bars represent standard deviations of the mean of 5 simulations.
Fig 6.
First steps of tumor avascular development in the presence of a vascular network: (A) Initial tumor with proliferating and migrating cells and a diameter of 51 μm on day 1. (B) The growing tumor reaches a diameter of 100 μm on day 2. (C) The tumor continues to grow up to a diameter of about 142μm on day 3. (D) Cells in the core of the tumor with a diameter of about 200 μm suffer from hypoxia and change their phenotype to quiescent (hypoxic cells are in purple). (E) As the tumor grows, lack of oxygen increases leading to expansion of the hypoxic core. (F) Shortage of oxygen and nutrients in the hypoxic region leads to necrosis after 20 hours on day 5 (necrotic cells are in blue).
Fig 7.
(A) Concentration of VEGF production rate per unit time (in pg/cell/s) from the tumor hypoxic core inducing the ECs’ activation. (B) Activated ECs (in green) move through chemotaxis up the gradients of VEGF.
Fig 8.
(A) Concentration of VEGF (in pg/cell/s) released from the tumor hypoxic core inducing the activation of ECs on day 12. (B) Activated ECs (in green) move through chemotaxis up the gradients of VEGF.
Fig 9.
Tumor area growth rate with and without angiogenesis.
Fig 10.
Number of viable tumor cells (non-necrotic) with time.
There is an increase in the growth rate of proliferating cancer cells on day 12, when vessels surround the tumor.
Fig 11.
Comparison of the number of cancer cells in two different scenarios of tumor avascular growth.
Bars indicate difference between maximum and minimum number of viable cells during a day. Results are the mean values extracted from four independent runs.
Fig 12.
Tumor vascular growth in presence of normal healthy tissue: (A) Tumor on day 5, (B) Tumor on day 7, (C) Tumor on day 8.
Fig 13.
Number of tumor cells in two different conditions, with and without normal cells, of tumor vascular growth.
Fig 14.
Tumor with a dense capillary network.
(A) Simulation results of a high vascularized tumor, with a similar vasculature profile as the experimental image of the network in a tumor [128], (B) Left: Ultrasound Microvessel Imaging; center: fluorescent histology of vessel area around viable tumor cells (scale bar is 1mm); right: enlargement of square area from previous image [128].
Fig 15.
Intratumoral vascularization density in the tumor area.
Comparison between simulation results from the present work with the experimental data reported in [128].
Fig 16.
Structure of vascular network for low values of JEC-EC, on day 7, which leads to an accumulation of active and inactive ECs during angiogenesis and to vessel rupture.
Fig 17.
Intratumoral vascularization density as a function of the tumor area, resulting from interventions in signals activation.
Comparison between simulation results from present work with experimental data reported in [128].
Fig 18.
Tumor area evolution with therapy for various treatment initiation days.
In all three cases there is a significant initial area decrease on the first day of therapy.
Fig 19.
Tumor area percent reduction during 10 days of treatment in comparison with the 25000 μm2 baseline area.
Blocking the pathways kills cancer cells and prevents tumor growth.