Tissue-engineered tendon and ligament constructs are seeded with fibroblasts on a collagen scaffold and matured in a perfusion bioreactor. Cyclic uniaxial mechanical strain — mimicking physiological loading — drives the cells to remodel the surrounding collagen fibers so they progressively reorient along the strain axis, a process called strain-induced fiber realignment.
Each fiber's tilt angle θ (measured from the vertical loading axis, in this longitudinal-section view) relaxes under a torque proportional to the instantaneous strain, following a nematic-alignment model plus a small stochastic remodeling term:
dθ/dt = −k · ε(t) · sin(2θ) + η(t)
ε(t) = ε₀ · |sin(2πft)| (cyclic strain magnitude)
S = ⟨cos(2θ)⟩ (nematic order parameter, −1..1)
E∥ / E⊥ ≈ 1 + 4·max(0, S) (anisotropic modulus ratio)
Numerically verified: θ = 0 (aligned with the axis) is the stable fixed point of −k sin(2θ) and θ = ±90° is unstable, so any cyclic strain slowly drags every fiber toward alignment while noise alone (static culture) leaves the population isotropic, S ≈ 0.
- Strain amplitude — larger cyclic deformation applies more realignment torque per cycle.
- Cycling frequency — how fast the load oscillates; more cycles per unit time accelerates convergence.
- Conditioning rate — a time-lapse control so multi-day bioreactor protocols play out in seconds.
- Remodeling noise — scales the stochastic remodeling term η(t); higher noise fights the aligning torque and caps how ordered the construct can get.
- Static Culture — sets strain to zero, showing that without mechanical cues fibers stay randomly oriented (S ≈ 0) and the construct remains mechanically isotropic.
Real-world relevance: this is the working principle behind mechanical conditioning bioreactors used to grow engineered tendons, ligaments and heart-valve leaflets — aligned collagen gives the construct the directional tensile strength native tendon has, which unconditioned (static) constructs never develop.