Peng C A, Palsson B Ø
Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136, USA.
Biotechnol Bioeng. 1996 Jun 5;50(5):479-92. doi: 10.1002/(SICI)1097-0290(19960605)50:5<479::AID-BIT2>3.0.CO;2-C.
Tissue function is comprised of a complex interplay between biological and physicochemical rate processes. The design of bioreactors for tissue engineering must account for these processes simultaneously in order to obtain a bioreactor that provides a uniform environment for tissue growth and development. In the present study we consider the effects of fluid flow and mass transfer on the growth of a tissue in a parallel-plate bioreactor configuration. The parenchymal cells grow on a preformed stromal (feeder) layer that secretes a growth factor that stimulates parenchymal stem cell replication and differentiation. The biological dynamics are described by a unilineage model that describes the replication and differentiation of the tissue stem cell. The physicochemical rates are described by the Navier-Stokes and convective-diffusion equations. The model equations are solved by a finite element method. Two dimensionless groups govern the behavior of the solution. One is the Graetz number (Gz) that describes the relative rates of convection and diffusion, and the other a new dimensionless ratio (designated by P) that describes the interplay of the growth factor production, diffusion, and stimulation. Four geometries (slab, gondola, diamond, and radial shapes) for the parallel-plate bioreactor are analyzed. The uniformity of cell growth is measured by a two-dimensional coefficient of variance. The concentration distribution of the stroma-derived growth factor was computed first based on fluid flow and bioreactor geometry. Then the concomitant cell density distribution was obtained by integrating the calculated growth factor concentration with the parenchymal cell growth and unilineage differentiation process. The spatiotemporal cell growth patterns in four different bioreactor configurations were investigated under a variety of combinations of Gz (10(-1), 10(0), and 10(1)) and P(10(-2), 10(-1), 10(0), 10(1), and 10(2)). The results indicate high cell density and uniformity can be achieved for parameter values of P = 0.01, ..., 0.1 and Gz = 0.1, ..., 1.0. Among the four geometries investigated the radial-flow-type bioreactor provides the most uniform environment in which parenchymal cells can grow and differentiate ex vivo due to the absence of walls that are parallel to the flow paths creating slow flowing regions.
组织功能由生物和物理化学速率过程之间复杂的相互作用组成。用于组织工程的生物反应器的设计必须同时考虑这些过程，以便获得一个为组织生长和发育提供均匀环境的生物反应器。在本研究中，我们考虑了流体流动和传质对平行板生物反应器中组织生长的影响。实质细胞生长在预先形成的基质（饲养层）上，该基质分泌一种刺激实质干细胞复制和分化的生长因子。生物动力学由描述组织干细胞复制和分化的单系模型描述。物理化学速率由纳维 - 斯托克斯方程和对流扩散方程描述。模型方程通过有限元方法求解。两个无量纲组控制解的行为。一个是描述对流和扩散相对速率 的格雷茨数（Gz），另一个是描述生长因子产生、扩散和刺激相互作用的新的无量纲比（用P表示）。分析了平行板生物反应器的四种几何形状（平板、吊篮、菱形和径向形状）。细胞生长的均匀性通过二维方差系数来衡量。首先根据流体流动和生物反应器几何形状计算基质衍生生长因子的浓度分布。然后通过将计算出的生长因子浓度与实质细胞生长和单系分化过程相结合，获得伴随的细胞密度分布。在Gz（10^(-1)、10^(0)和10^(1)）和P（10^(-2)、10^(-1)、10^(0)、10^(1)和10^(2)）的各种组合下，研究了四种不同生物反应器配置中的时空细胞生长模式。结果表明，对于P = 0.01，...，0.1和Gz = 0.1，...，1.0的参数值，可以实现高细胞密度和均匀性。在所研究的四种几何形状中，径向流型生物反应器提供了最均匀的环境，在这种环境中，实质细胞可以在体外生长和分化，因为不存在与流动路径平行从而产生缓慢流动区域的壁。
