Osborne J M, O'Dea R D, Whiteley J P, Byrne H M, Waters S L
Oxford University Computing Laboratory, Oxford, UK.
J Biomech Eng. 2010 May;132(5):051006. doi: 10.1115/1.4001160.
A three phase model for the growth of a tissue construct within a perfusion bioreactor is examined. The cell population (and attendant extracellular matrix), culture medium, and porous scaffold are treated as distinct phases. The bioreactor system is represented by a two-dimensional channel containing a cell-seeded rigid porous scaffold (tissue construct), which is perfused with a culture medium. Through the prescription of appropriate functional forms for cell proliferation and extracellular matrix deposition rates, the model is used to compare the influence of cell density-, pressure-, and culture medium shear stress-regulated growth on the composition of the engineered tissue. The governing equations are derived in O'Dea et al. "A Three Phase Model for Tissue Construct Growth in a Perfusion Bioreactor," Math. Med. Biol., 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 behavior. 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 behavior 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.
研究了灌注生物反应器内组织构建体生长的三相模型。细胞群体（以及随之产生的细胞外基质）、培养基和多孔支架被视为不同的相。生物反应器系统由一个二维通道表示，该通道包含一个接种细胞的刚性多孔支架（组织构建体），并灌注有培养基。通过规定细胞增殖和细胞外基质沉积速率的适当函数形式，该模型用于比较细胞密度、压力和培养基剪切应力调节生长对工程组织组成的影响。控制方程在奥戴等人的《灌注生物反应器中组织构建体生长的三相模型》中推导得出，其中利用了长波长极限来辅助分析；在此，使用有限元方法来构建控制方程的二维解，并深入研究其行为。对总组织产量以及平均压力、速度和剪切应力的比较表明，对于数量级为10^(-2)的通道纵横比，二维解和长波长近似解之间获得了定量一致性，并且即使对于相对较大的通道纵横比，模型的许多定性行为在长波长极限中也能体现。然而，我们证明，为了准确捕捉机械转导机制对组织构建体生长的影响，由于与灌注生物反应器相关的机械刺激存在固有的空间变化，最显著的是流体剪切应力，这是长波长极限中未捕捉到的特征，因此必须至少在两个维度上考虑空间效应。
