This repository contains experimental compression data and logistic fit parameters derived from chemical potential analysis of poroelastic biopolymer networks. These datasets serve as the foundational inputs for the multiscale computational modeling of growth factor transport and tumor growth. All data files in this Dryad repository are released under the CC0 1.0 Universal (Public Domain Dedication) license. You may use, copy, modify, and distribute them freely without restriction.

For the full computational pipeline, including the Julia advection-diffusion PDE solver and PhysiCell agent-based modeling scripts, please refer to the accompanying GitHub repository: https://github.com/Sharvari303/Tumor-poroelasticity-growth-modeling/tree/main

Note: The agent-based modeling results were generated using PhysiCell v1.14.0, third-party software distributed under the BSD 3-Clause License. PhysiCell and its associated files are not included in this Dryad deposit.

1. Advection-Diffusion PDE Solutions (Figure 4 & Supp. Fig 8)

The script and input CSVs are provided at this GitHub link: https://github.com/Sharvari303/Tumor-poroelasticity-growth-modeling/tree/main

This section describes the usage of the Julia script (advection_diffusion_solver.jl) to replicate the spatiotemporal concentration profiles and heatmaps.

Simulation Logic

The script solves the 2D advection-diffusion equation: ∂C/∂t = D∇²C − v · ∇C

The velocity field v is derived from the poroelastic fluid efflux calculated in the Finite Element (FEM) simulations. The simulation uses a moving-parameter approach, where the velocity field parameters (L, k, xlog) are updated iteratively from logistic_fit_result.csv to match the time-dependent relaxation of the hydrogel.

To reproduce the specific panels in Figure 8, modify the following variables in the script:

• Péclet Number (Pe):
  • Set global Pe = 5.0 to reproduce the primary results shown in Figure 8.
  • Vary Pe between 0.22 and 220.8 to see the transition from diffusion-dominated to advection-dominated transport.
• Initial & Boundary Conditions:
  • IC: u(t_min, x, y) ~ 1 (The domain starts fully saturated with growth factor).
  • BC: u(t, x_min, y) ~ 0 (Dirichlet conditions at the boundaries represent the external sink/washout).

Generated Outputs

Running the script generates the following visualization files:

• For Figure 8B (Heatmaps):
  • The script produces PNG files named Scenario1_surfaceplots__t[TIME]_Pe5_0.png.
  • These surface plots represent the 2D spatial distribution of growth factor concentration (C/C₀) across the 8x8 mm lattice at discrete time points.
• For Figure 8C (Radial Profiles):
  • The script calculates the mean concentration at each radial distance from the center.
  • Output File: Scenario1_radialconcprofiles_[DATE]_Pe5_0.csv.
  • Plot: Scenario2_radial_concentration_profiles_[DATE]_Pe5_0.png shows C/C₀ vs. Radius (mm) for multiple time points (e.g., t=0 to t=360 min).

Software Requirements

• Language: Julia (1.9+)
• Key Libraries: MethodOfLines.jl, ModelingToolkit.jl, and OrdinaryDiffEq.jl.
• Input Dependency: Requires logistic_fit_result.csv the same directory to provide the time-varying velocity parameters.

2. Supplementary Data Files

These files contain the underlying mechanical driving forces calculated via Finite Element Method (FEM) and the subsequent mathematical fitting used for the advection-diffusion modeling.

File 1: supplementary_fig4-chemicalpotentialdata.csv

• Description: Raw chemical potential (μ) distribution within the alginate gel across various radial distances and time points during the 30% compression relaxation.
• Columns:
  • time(min): The elapsed time of the simulation (Units: min).
  • distance(m): Radial distance from the center of the 8mm diameter gel disc (Units: m).
  • μ(Pa): Chemical potential value (Units: Pa).

File 2: supplementary_fig4-logisticfit.csv

• Description: Parameters for the logistic functions fitted to the spatial gradients of the chemical potential. These parameters are used as inputs for the velocity field in the Julia transport script.
• Columns:
  • time(min): Time point for the fit (Units: min).
  • L, k, xlog: Raw fitting parameters for the gradient profile.
  • R², MSE: Goodness-of-fit metrics.
  • L_s, k_s, xlog_s: Scaled parameters utilized directly in the Julia PDE solver to account for the mobility coefficient (M=k/η).
  • adv_time_scaled: Non-dimensionalized time used for the advection-diffusion simulation steps.

File 3: supplementary_fig5.csv

• Description: Temporal evolution of the solid volume fraction (ϕ) and the resulting hydraulic permeability (K).
• Columns:
  • Time(s): Simulation time (Units: seconds).
  • Phi_s: Solid volume fraction of the alginate network (Dimensionless).
  • K(m^2): Hydraulic permeability (Units: m²).

3. Agent-Based Modeling (Using PhysiCell software)

> License notice: PhysiCell v1.14.0 is third-party software under the BSD 3-Clause License and is not included in this Dryad deposit. A reference working directory (including configuration files) is available at: https://github.com/Sharvari303/Tumor-poroelasticity-growth-modeling/tree/main

We implemented agent-based modeling in PhysiCell to simulate tumor growth in response to growth factor gradients. The ABM utilizes the spatiotemporal results from the advection-diffusion PDE simulations (Julia) as its biochemical input.

Folder Structure

• config/: Contains the primary simulation configuration files, including PhysiCell_settings.xml (where domain, substrate, and global parameters are set) and cell_rules.csv (custom behavioral rules for the agents).
• custom_modules/: Contains custom.cpp and custom.h. These scripts house the specific C++ logic governing how cells sample their local environment and adjust their proliferation rates based on local growth factor availability.
• output/: The default destination directory where all generated simulation data, logs, images, and state files will be saved during a run.

Key Variables & Parameters

The simulation uses the following biological parameters and variables. This can be set up directly on PhysiCell by the users. For a working ABM directory, please refer to the GitHub link.

• Simulation Domain: 400 µm x 400 µm (Representing smaller Regions A and B within the larger PDE grid).
• Grid Resolution (dx, dy): 20 µm.
• Initial Cell Population: 200 cells.
• Simulation Time: 10,080 minutes (7 days).
• Growth Factor Diffusion Coefficient: 100 µm²/s.
• Cellular Apoptosis Rate: 5.3 x 10⁻⁵ min⁻¹.
• Cell Proliferation Function: Cell growth is governed by a sigmoidal (Hill) relationship to local growth factor concentration:
  • Max Proliferation Rate: 2 x 10⁻⁴ min⁻¹.
  • Half-max Concentration: 10⁻⁹ M.
  • Hill Coefficient: 2.0.