This project is hosted by the CFisUC at the University of Coimbra and consists in a phase-field model for tumor angiogenesis. The model is based on the paper published by Travasso et al. (2011) with some physical and computational improvements.
- Coupled the blood flow and the hypoxic cell deactivation;
- The hypoxic cells have volume;
- The system is modeled in three dimensions;
- tools: Routines to measure the number of branches, anastomoses and the vessels diameter;
- Build the image:
docker build --platform linux/x86_64 -t angio docker/(the--platformflag is necessary for the image to run on Apple Silicon) - Run the container:
docker run -it -v $(pwd):/code angio /bin/bash run.sh <run_id>. Please make sure that an input file namedinp<run_id>is present in the root directory of the project.
We provide typical parameters for simulations in input_file.
See the description of each paramter in the table bellow and the mapping with experimental data in Supplementary material.
| Reference value | Variable | Description |
|---|---|---|
| 4.00 | cell_radius | Radius of individual cells |
| 100.0 | diffusion_const | Diffusion constant for VEGF |
| 1.00 | interface_width | Width of the phase-field interface |
| 0.30 | vegf_p | VEGF concentration for maximum proliferation |
| 0.09 | vegf_c | VEGF concentration for branching |
| 20.0 | diff_oxy_length | Diffusion length for oxygen |
| 6.25 | vegf_rate | Rate of VEGF uptake by cells |
| 1.00 | vegf_source_conc | Concentration of VEGF at source |
| 1.00 | prolif_rate | Rate of proliferation of endothelial cells |
| 5.00 | vessel_radius | Initial radius of blood vessels |
| 150000 | total_time_step | Total time steps for simulation |
| 0.0010 | dt | Time step size |
| 800.00 | chi_chemiotactic_resp | Chemotactic response of endothelial cells |
| 100, 100, 50, 1, 1, 1 | Lx_Ly_Lz_dx_dy_dz | Simulation domain size and grid spacing |
| -754333222 | random_seed | Seed for random number generation - must be negative |
| 20 | number_of_boundary_points | Number of boundary points to keep track |
| 10000 | source_max | Maximum number of VEGF source points |
| 0.01 | vegf_grad_min | Threshold for VEGF gradient |
| 0.03 | vegf_max | Maximum VEGF concentration |
| 2.00 | depletion_weight | Energy cost to avoid overlap between vessels and hypoxic cells |
| 2000 | output_period | Time period between outputting results |
| 40000 | extra_steps | Additional time steps for simulation |
| 4000 | max_number_of_tip_cells | Maximum number of tip cells allowed |
| T | thinning_FT | Flag for using thinning algorithm |
| F | periodic_FT | Flag for using periodic boundary conditions |
| F | flow_FT | Flag for computing the blood flow |
Beware that the input file inp001 is solely used to run the docker image with Github actions. The parameters were changed to produce a short simulation with small grid, few iterations, and no sources of VEGF. Please do not base future studies on this file.
In the folder tools we have scripts to postprocess the data generated with the simulations. The documentation for each script is found here.
M. Moreira-Soares, R. Coimbra, L. Rebelo, J. Carvalho & R. D. M. Travasso. Angiogenic Factors produced by Hypoxic Cells are a leading driver of Anastomoses in Sprouting Angiogenesis–a computational study. Scientific Reports 8, 8726 (2018)
Special thanks to João Simões for supporting the long term reproducibility of this code by dockerizing the repository.
This project was funded by the National Council of Technological and Scientific Development (CNPq - Brazil) under the grant 235101/2014-1.