Strain distribution in an elastic substrate vibrated in a bioreactor for vocal fold tissue engineering

A bioreactor previously described was used to quantify the shear strain along a bioengineered tissue scaffold driven at low audio frequencies (20–200 Hz). Standing wave patterns were calculated analytically by solving a classical boundary value problem for a vibrating string under tension and bending stiffness. Boundary conditions were non-traditional in that small pivot arms at the endpoints allowed neither the displacement nor the velocity to go to zero. The calculations were corroborated with stroboscopic measurement of the motion of the material in the bioreactor. Results indicate that shear strains up to 0.2 can be obtained at low frequencies (20 Hz), with a gradual decrease at higher frequencies due to the decaying amplitude response of the mechanical driver. The bioreactor may be useful for approximating the Young's modulus of the material in situ by probing for resonance frequencies in the standing wave pattern. A yet unsolved problem is a variable drag coefficient along the length of the material due to fluid turbulence in the culture medium.