Each CAR-T cell performs a biased random walk through the tissue volume. Outside its sensing radius it drifts by Brownian motion; once a tumor cell's antigen signal enters range, its velocity steers toward the nearest live target (chemotaxis):
v(t+dt) = normalize(v + k·(target − pos)·dt + noise)
On contact, binding is a per-second Poisson process converted to a frame probability so the outcome is frame-rate independent:
P(bind this frame) = 1 − exp(−affinity · exhaustion · dt)
Each successful kill raises that T-cell's activation count, and repeated activation drives real CAR-T exhaustion — a documented drop in cytotoxic efficiency after sustained antigen exposure:
exhaustion(kills) = max(0.15, 1 − 0.12·kills)
- CAR-T cell dose — how many engineered T-cells patrol the tissue at once.
- CAR binding affinity — the base per-second kill rate on contact; a stronger CAR construct binds tumor antigen faster.
- Tumor regrowth rate — the probability per second that surviving tumor tissue seeds a new malignant cell, modeling ongoing proliferation the therapy must outpace.
- Spawn Wave — injects a fresh cluster of tumor cells, simulating relapse or a larger initial burden.
This is the same population-dynamics logic behind real CAR-T therapy planning: dose and affinity must clear tumor burden faster than it regrows, while exhaustion caps how long a single T-cell dose stays effective — which is why durable remission often depends on re-dosing or exhaustion-resistant CAR designs.