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Angiogenesis Project

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.

What is new on v6.0.s

  • 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;

Running with Docker

  1. Build the image: docker build --platform linux/x86_64 -t angio docker/ (the --platform flag is necessary for the image to run on Apple Silicon)
  2. Run the container: docker run -it -v $(pwd):/code angio /bin/bash run.sh <run_id>. Please make sure that an input file named inp<run_id> is present in the root directory of the project.

Parameters

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.

Postprocessing tools

In the folder tools we have scripts to postprocess the data generated with the simulations. The documentation for each script is found here.

Publications

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)

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Acknowledgements

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.

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