Perren's interfragmentary strain theory (1979) — tissue at a fracture gap can only differentiate into a tissue type that can mechanically tolerate the local strain it experiences. Strain is the fractional deformation of the gap under load:
ε = ΔL / L₀ (interfragmentary strain)
ΔL = F / k_total (gap displacement under axial load F)
k_total = k_fix + k_callus(t)
where k_fix is the stiffness contributed by the fixation hardware and k_callus(t) grows over time as callus bridges the gap, modeled here with cross-sectional scaling k_callus ∝ r(t)². As the callus radius r(t) grows, k_total rises, ΔL falls, and ε falls — softer tissue becomes possible to harden into stiffer tissue.
Tissue-tolerance thresholds (approximate, from Perren and Claes & Heitemeyer):
- ε ≤ 2% — lamellar/woven bone can form directly (primary/intramembranous healing)
- 2–10% — cartilage forms, later replaced by bone (endochondral ossification)
- 10–30% — fibrocartilage only
- 30–100% — fibrous granulation tissue, healing stalls
- >100% — tissue disruption at every cell division; nonunion risk
Callus growth rate here follows a Gaussian "mechanobiological window" centred near ε ≈ 15%: rigid fixation (low strain) produces fast bridging via direct bone but only a thin callus, moderate micromotion (external fixator/cast) stimulates a larger periosteal callus, and excessive strain (very flexible fixation, large gap, or heavy load) can stall bridging entirely — a simplified but literature-consistent picture of why rigid plates heal with little visible callus while external fixation produces a large bridging callus.
Controls: pick a fixation method (sets k_fix), then adjust axial load and gap size to see how strain — and therefore the tissue pathway — changes; simulation speed advances days post-fracture.