PDEOncology
A browser-based simulator for tumor drug penetration using reaction-diffusion partial differential equations (PDEs). No installation required — all computation runs client-side in JavaScript.
Where C is drug concentration, D is the spatially-varying diffusion coefficient, λ is the degradation rate, k is the cellular uptake rate, and ρ(x,y) is the local cell density field.
Numerical method
Explicit finite difference (FTCS scheme) on a 2D uniform grid. Stability enforced via CFL condition: dt ≤ dx² / (4D).
Grid size: 80×80 nodes representing a 1cm × 1cm tissue cross-section.
AI integration
Uses the Claude API to extract biophysically grounded PDE parameters from a natural-language drug + tumor description. Parameters are auto-loaded into the simulator.
Requires a valid Anthropic API key (set in AI Drug Input tab).
Tumor model
Circular tumor geometry with a radially-graded cell density field. Diffusion coefficient is attenuated in the tumor core to simulate interstitial fluid pressure (IFP) and extracellular matrix barriers.
How to use
1. Go to Simulation — pick a drug + tumor preset or set sliders manually.
2. Or go to AI Drug Input — type a description and let Claude set parameters.
3. Click Run Simulation.
4. View and export results in Results.
PDE parameters explained
| Parameter | Symbol | Meaning | Typical range |
|---|---|---|---|
| Diffusion coefficient | D | How fast the drug spreads through tissue | 0.005 – 0.25 (normalised) |
| Degradation rate | λ | Drug breakdown / metabolic clearance | 0.001 – 0.05 |
| Uptake rate | k | Rate at which cancer cells absorb the drug | 0.01 – 0.15 |
| Cell density | ρ(x,y) | Spatial distribution of tumor cells | 0.05 – 1.0 |
| Tumor radius | r | Radius of the tumor region in grid units | 10 – 38 px |
Parameters
Radial penetration curve
AI Drug Input
Describe a drug and tumor type in plain English. Claude will extract biophysically grounded PDE parameters and load them directly into the simulator.
API key
Your key is stored only in this browser session — never sent anywhere except directly to api.anthropic.com.
Describe your simulation
Results & Report
Run a simulation first, then return here to view analytics and export data.
No simulation data yet. Go to Simulation →
Drug Database
Built-in parameter library for common oncology drugs across tumor types. All values are normalised for the PDE model. Click a row to load into the simulator.
| Drug | Tumor | D | λ | k | Radius | Difficulty | Class |
|---|
About these parameters
Diffusion coefficients are scaled relative to free diffusion in water (~10⁻⁵ cm²/s). Uptake rates reflect receptor expression levels. Degradation rates account for metabolic clearance. Values are indicative — for research use only.
Sources: Jain RK (1987), Nugent & Jain (1984), Thurber et al. (2008), Chauhan et al. (2011).