When a tumor's blood-supply network is disrupted below its percolation threshold, large-scale connectivity collapses and nutrient delivery fails — the same phase transition that physicists use to model connectivity in random graphs and porous media. Adaptive therapy (cycling drug doses to exploit competitive suppression) may be deliberately tuned to keep the network near — but just below — the percolation threshold, maximising tumor fragmentation while avoiding full drug-resistance selection. Neither oncologists nor physicists have yet jointly designed dosing schedules using percolation-threshold mathematics as the objective function.
This bridge connects Oncology and Statistical Physics through shared mathematical structure. Status: Proposed connection.
| Domain A Term | Domain B Term | Note |
|---|---|---|
| bond percolation probability | vessel patency under treatment pressure | Fraction of edges (vessel segments) still functional |
| giant connected component | viable tumour vascular core | The dominant connected region supplying nutrients |
| percolation threshold p_c | minimum viable vascular density | Critical fraction below which nutrient supply collapses |
| cluster size distribution | isolated tumour micro-regions | Disconnected fragments starved of blood supply |
| renormalisation group | adaptive dosing schedule optimisation | Multi-scale description of how local drug actions aggregate to global effects |
Oncology journals rarely cite statistical-physics literature, and vice versa. Clinical trials measure tumour volume or survival endpoints, not topological graph metrics. The toolchains (MATLAB/Python network libraries vs. medical imaging suites) are largely siloed, and grant bodies do not routinely fund physics-oncology hybrids.
Runnable experiment protocols promoted from this bridge. USDR maps what connects; Crosscheck proves it.
On an L=32 square site-percolation lattice, mean giant-component fraction S(p) (largest cluster / L^2) and top-bottom spanning fraction are measurable at occupancies p in {0.40, 0.50, 0.59, 0.70} with 8 trials per p. ...
Crosscheck manifesto
· Generate more drafts: python scripts/generate_crosscheck.py --bridge b-percolation-oncology --write
u-tumor-containment-percolationh-adaptive-therapy-percolation-threshold