After a tendon/ligament injury or surgical repair, tensile strength S (0–100% of pre-injury capacity) rebuilds through collagen synthesis. Mechanotransduction research (Cook & Purdam's tendon continuum model, Wolff's Law of bone/soft-tissue remodeling) shows healing rate depends on load L relative to *current* strength S — not a fixed number, because a healing tissue gets stronger over time:
r = L / S (relative load ratio)
stimulus(r) = exp(-((r - r0)/w)²) optimal loading bell curve, r0≈0.45, w≈0.35
dS/dt = k_heal · stimulus(r) · (1 - S/100) — mechanotransduction-driven synthesis
− k_damage · max(0, r - r_max)² — micro-tears above safe ratio
dROM/dt = k_rom · stimulus(r) · (1 - ROM/ROM_max) − k_stiff · [r < r_min]
- Too little load (r ≪ r0) — minimal mechanical stimulus, collagen stays thin and randomly oriented (disorganized "Phase 1" scar tissue), joint stiffens.
- Optimal load (r ≈ r0) — controlled micro-strain triggers fibroblasts to lay down aligned type-I collagen, exactly the "progressive loading" principle behind Phase 2 resistance training.
- Overload (r > r_max) — mechanical stress exceeds what the current tissue can bear, causing micro-damage that can outpace repair — the biomechanical basis of a rehab re-injury.
- The 3D scene shows the healing ligament as a fiber bundle: instanced cylinders that multiply and straighten (align to the joint axis) as strength and alignment increase, colored red→amber→green by tensile strength.
Real orthopedic rehab (per the site's Orthopedic Rehabilitation article) follows exactly these three phases — acute protection (RICE), progressive loading, and functional return — because loading too early or too aggressively risks re-injury, while loading too little leaves the tissue weak and stiff.