2D companion to the 3D scene: identical biophysics, rendered as a side-on cross-section instead of a rendered cell. A macrophage engulfs a particle by extending its membrane into a "phagocytic cup" that zippers closed around the target's entire contour. For a rigid fiber longer than the cell's spreading reach, the two rims of the cup can never meet — this is frustrated phagocytosis: the respiratory burst that would normally fire briefly inside a sealed phagosome instead stays switched on for hours at the open interface, dumping ROS and cytokines into the tissue.
This is the fiber pathogenicity paradigm (Stanton hypothesis, refined into the WHO fiber criteria) explaining why long, rigid, durable fibers (amphibole asbestos, some multi-walled CNTs) behave like miniature asbestos, while short or curly ones do not:
Engulfable if L_eff ≤ D_reach
L_eff = L · (1 − curl), curl = (1 − rigidity) · 0.6
D_reach ≈ 18 µm · (1 − 0.25 · d/5µm) (macrophage max spreading reach)
dL/dt = −k_diss · (1 − biopersistence) (dissolution shortens the fiber)
- Length — longer fibers exceed the macrophage's spreading reach.
- Diameter — thicker fibers are harder to wrap and, above ~3 µm, are no longer respirable into the deep lung at all (WHO criterion, live flag).
- Rigidity — flexible, curly fibers (chrysotile "serpentine" asbestos) fold up and can still be enclosed even when long; straight, rigid fibers (amphiboles, some CNTs) cannot.
- Biopersistence — fibers that dissolve quickly shorten below the closure threshold before doing lasting damage; biopersistent fibers stay at full length and keep the cup open indefinitely.
Real-world relevance: this length–diameter–biopersistence framework is what regulators (ECHA, US EPA, ISO/OECD nanomaterial test guidelines) use to flag engineered nanofibers and nanotubes for asbestos-like hazard scrutiny.