Lymphoma growth inside a lymph node is modeled with Gompertzian kinetics, the standard tumor-growth law: growth slows as the tumor approaches a carrying capacity set by blood supply and available space.
dV/dt = a·V·ln(K/V)
V(t) = tumor volume (cm³)
a = intrinsic growth rate (/day)
K = carrying capacity (≈1000 cm³ here)
Each R-CHOP chemotherapy cycle applies the log-kill hypothesis (Skipper's law): a fixed fraction of clonogenic cells dies per cycle, not a fixed number — so shrinking tumors need fewer cells killed in absolute terms to keep shrinking, but a small residual clone can regrow between cycles.
V → V·(1 − f) at each cycle, f = kill fraction
Between cycles, Gompertzian regrowth resumes immediately.
Immune surveillance raises the effective log-kill fraction slightly and caps regrowth, modeling cytotoxic T-cell and NK-cell activity against residual disease — the same mechanism exploited by maintenance immunotherapy after induction chemo.
- Growth rate a — how aggressive the clone is; higher-grade lymphomas (e.g. Burkitt) sit far right, indolent ones (e.g. follicular) sit far left.
- Immune surveillance — background clearance rate; scales down effective carrying capacity and adds a small continuous kill term.
- Cycle interval / kill fraction — the two levers real oncologists tune: dose-dense regimens shorten the interval, dose-intense regimens raise the kill fraction per cycle.
- Remission is declared once volume drops below a detectable threshold (0.1 cm³, ≈10⁸ cells) and held there; if regrowth outpaces surveillance between cycles, the status flips to Relapse.
The node view (top) packs malignant cells (red) into a Vogel/sunflower disc whose visible count tracks tumor volume on a log scale, with immune cells (green) orbiting the rim; drag to pan, scroll/pinch to zoom. The strip chart (bottom) plots volume on a log axis over time with vertical markers at each chemo cycle — the same Gompertz–log-kill framework (Norton–Simon) used to design real chemotherapy dosing schedules.