Distraction osteogenesis exploits Ilizarov's law of tension-stress: when living bone is cut (a corticotomy) and the two fragments are then pulled apart gradually and steadily, the tissue bridging the gap does not scar over — it responds to the mechanical tension by forming new bone through intramembranous ossification, without a cartilage intermediate.
Clinical gold standard (rate & rhythm):
daily rate ≈ 1 mm / day
rhythm ≈ 4 increments × 0.25 mm
Interfragmentary strain (Perren):
ε = Δl / l (strain per increment, gap width l)
Too fast (ε too high) → fibrous, non-mineralizing tissue
Too slow (ε too low) → premature bony bridging, distraction stalls
This simulator tracks every millimetre of regenerate as a thin slice, born at the moment of its own distraction increment and carrying the "quality" of the protocol at that instant. Each slice then mineralizes over time following
dM/dt = Q · k · (1 − M)
where M is that slice's mineral maturity (0→1), k a fixed consolidation-rate constant, and Q the protocol quality factor — peaked at 1 mm/day delivered as 4×0.25 mm increments, exactly the regimen Ilizarov's own clinical series established as optimal. Push the rate too high and the regenerate stays translucent and fibrous (risk of non-union); drop it too low and the same tissue mineralizes and bridges before you reach your target length (premature consolidation) — both are real failure modes in limb-lengthening surgery, alongside pin-tract infection and joint contracture, which is why rate and rhythm are titrated weekly against X-rays in practice.
- Distraction rate — total daily lengthening in mm; sets how fast the fixator is turned.
- Increments per day — how that daily amount is split; more, smaller turns (the classic 4×/day) reduce the strain spike per increment and improve regenerate quality for the same total rate.
- Latency period — days after the corticotomy before distraction begins, giving early callus time to form so it can be pulled apart rather than re-fractured.