Every pluripotency-derived cell product (iPSC- or ESC-derived) can carry a tiny fraction of cells that never finished differentiating. Left behind in the graft, they can still form a teratoma — a benign but disruptive tumor of mixed tissue types (its name literally means "monster tumor"). Their fate is a race between local proliferation and immune clearance, modeled here as logistic growth with a linear clearance term:
dN/dt = r·N·(1 − N/K) − c·N
N = residual undifferentiated cell count
r = 0.22 / week (intrinsic doubling ≈ 3.1 weeks)
K = niche carrying capacity (≈ 5×10⁷ cells)
c = immune clearance rate, 0 – 0.30 / week
Net growth only happens while r > c. A stronger host immune response (higher c, e.g. an autologous, non-immunosuppressed recipient) can clear the population outright; a weaker one (immunosuppressed or heavily allogeneic graft) lets it escape toward K. The clinical detection threshold is set at N ≈ 1×10⁷ cells — roughly a sub-centimeter nodule visible on imaging — shown as the amber ring around the growing mass in the dish view, and as a dashed amber line on the growth-curve chart.
- Residual pluripotent fraction — parts-per-million of the dose that never differentiated; sets the starting population N₀ = dose × ppm × 10⁻⁶. Regulatory guidance for cell therapy products typically demands this stay in the low single-digit ppm range.
- Transplanted cell dose — total cells delivered in the graft (log scale, 10⁶–10⁹); scales N₀ directly.
- Immune surveillance strength — sets the clearance rate c; higher values represent a more vigilant, less-suppressed host immune system actively killing undifferentiated cells (which display distinct surface markers). Watch the green immune-cell ring orbit faster as you raise it.
- The red cluster in the dish view is the growing undifferentiated population; its drawn radius scales with the cube root of N (a volume/area proxy, not a raw count) inside the graft bed of already-differentiated cells (blue). The chart below plots N(t) on a log scale against the K and detection lines.
- Drag the dish view to pan and use the scroll wheel (or pinch) to zoom — the simulation keeps running underneath.
Real-world relevance: teratoma-formation risk is the single biggest safety gate for any pluripotent-stem-cell-derived therapy reaching clinical trials — manufacturers must show residual pluripotent-marker-positive cells fall below validated release-testing limits before a batch can be dosed.