Pierre J, Oddou C
Laboratoire B2OA, UMR CNRS 7052, Faculté des Sciences et Technologie, Université Paris 12, Créteil Cedex, France.
Comput Methods Biomech Biomed Engin. 2007 Dec;10(6):429-38. doi: 10.1080/10255840701494635. Epub 2007 Aug 22.
Successful bone cell culture in large implants still is a challenge to biologists and requires a strict control of the physicochemical and mechanical environments. This study analyses from the transport phenomena viewpoint the limiting factors of a perfusion bioreactor for bone cell culture within fibrous and porous large implants (2.5 cm in length, a few cubic centimetres in volume, 250 microm in fibre diameter with approximately 60% porosity). A two-dimensional mathematical model, based upon stationary mass and momentum transport in these implants is proposed and numerically solved. Cell oxygen consumption, in accordance theoretically with the Michaelis-Menten law, generates non linearity in the boundary conditions of the convection diffusion equation. Numerical solutions are obtained with a commercial code (Femlab 3.1; Comsol AB, Stockholm, Sweden). Moreover, based on the simplification of transport equations, a simple formula is given for estimating the length of the oxygen penetration within the implant. Results show that within a few hours of culture process and for a perfusion velocity of the order of 10(-4) m s(-1), the local oxygen concentration is everywhere sufficiently high to ensure a suitable cell metabolism. But shear stresses induced by the fluid flow with such a perfusion velocity are found to be locally too large (higher than 10(-3) Pa). Suitable shear stresses are obtained by decreasing the velocity at the inlet to around 2 x 10(-5) m s(-1). But consequently hypoxic regions (low oxygen concentrations) appear at the downstream part of the implant. Thus, it is suggested here that in the determination of the perfusion flow rate within a large implant, a compromise between oxygen supply and shear stress effects must be found in order to obtain a successful cell culture.
在大型植入物中成功进行骨细胞培养对生物学家来说仍是一项挑战，需要严格控制物理化学和机械环境。本研究从传输现象的角度分析了用于在纤维状和多孔大型植入物（长度为2.5厘米，体积为几立方厘米，纤维直径为250微米，孔隙率约为60%）中进行骨细胞培养的灌注生物反应器的限制因素。提出了一个基于这些植入物中稳态质量和动量传输的二维数学模型，并进行了数值求解。细胞耗氧量理论上符合米氏定律，在对流扩散方程的边界条件中产生非线性。使用商业代码（Femlab 3.1；Comsol AB，瑞典斯德哥尔摩）获得了数值解。此外，基于传输方程的简化，给出了一个用于估计植入物内氧气渗透长度的简单公式。结果表明，在培养过程的几个小时内，对于约为10^(-4) m s^(-1)的灌注速度，局部氧气浓度在各处都足够高，以确保合适的细胞代谢。但发现以这样的灌注速度由流体流动引起的剪切应力在局部过大（高于10^(-3) Pa）。通过将入口处的速度降低到约2×10^(-5) m s^(-1)可获得合适的剪切应力。但结果是在植入物的下游部分出现了低氧区域（低氧浓度）。因此，这里建议在确定大型植入物内的灌注流速时，必须在氧气供应和剪切应力效应之间找到折衷方案，以获得成功的细胞培养。
