## The influence of bioreactor geometry and the mechanical environment on engineered tissues

Osborne, J.M. and O'Dea, Reuben D. and Whiteley, J.P. and Byrne, H.M. and Waters, S.L. (2010) The influence of bioreactor geometry and the mechanical environment on engineered tissues. Journal of Biomechanical Engineering, 132 (5). 051006/1-051006/12. ISSN 0148-0731

The governing equations are derived in O'Dea \emph{et al.} (A multiphase model for tissue construct growth in a perfusion bioreactor, \emph{Math. Med. Biol.}, In press), in which the long-wavelength limit was exploited to aid analysis; here, finite element methods are used to construct two-dimensional solutions to the governing equations and to investigate thoroughly their behaviour. Comparison of the total tissue yield and averaged pressures, velocities and shear stress demonstrates that quantitative agreement between the two-dimensional and long-wavelength approximation solutions is obtained for channel aspect ratios of order $10^{-2}$ and that much of the qualitative behaviour of the model is captured in the long-wavelength limit, even for relatively large channel aspect ratios. However, we demonstrate that in order to capture accurately the effect of mechanotransduction mechanisms on tissue construct growth, spatial effects in at least two-dimensions must be included due to the inherent spatial variation of mechanical stimuli relevant to perfusion bioreactors, most notably, fluid shear stress, a feature not captured in the long-wavelength limit.