After a tendon/ligament injury or surgical repair, tensile tolerance 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* tolerance 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 disorganized, joint stiffens.
- Optimal load (r ≈ r0) — controlled micro-strain triggers fibroblasts to lay down aligned type-I collagen, the "progressive loading" principle behind Phase 2 resistance training.
- Overload (r > r_max) — applied load exceeds what the current tissue can bear, a genuine re-injury event fires (flash + counter) and tolerance is knocked back.
- The chart plots two real curves against simulated weeks: the tolerance curve S(t) (green) climbing as it heals, and the applied load curve L(t) (orange) you control — every point where the orange line pokes above the green one past the safe margin is a real overload, marked with a red tick.
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. This 2D chart engine integrates the identical differential equations as the 3D fiber-bundle version of this sim, just rendered as time-series curves instead of a 3D scene.