This present thesis comprise two major parts both experimental and numerical study which have been conducted in four distinct steps as following: (1) Design, construction, and evaluation of control and hydrodynamic of a bioreactor system. (2) Visualization of fluid flow perfusion in the hollow fibre membrane bioreactor (HFMB) using a biomedical noninvasive imaging technique, i.e. positron emission tomography (PET). (3) Development of a mathematical model for analyzing a hybrid hollow fibre membrane bioreactor (hHFMB) and (4) Development of a dynamic and two-porous media model for analyzing the HFMB with the aid of computational fluid dynamics (CFD), specifically for bone tissue engineering application. The experimental part includes the steps 1 and 2. In the step 1, the flow perfusion bioreactor system has been designed and constructed. The experimental evaluations of hydrodynamic, and control were performed. In this system, mean pressure, mean flow rate, frequency and waveform of the pulsatile pressure and flow rate can be modulated and controlled over the time to simulate both physiological and non-physiological conditions. The temperature, dissolved oxygen, and pH can be controlled.This bioreactor system can be applied to a variety of scaffold configurations, geometries, and sizes as the cell/tissue culture chamber is adjustable in length.This system is autoclavable, and compatible with noninvasive medical imaging techniques. Designing of the inlet and outlet manifold of the bioreactor were performed according to data obtained from CFD simulation of the flow distribution to achieve high efficiencies in the uniformity of flow perfusion. In the second step, PET was proposed for the very first time and a small animal PET system was used to obtain new information about steady and pulsatile flow patterns in the HFMB for tissue engineering applications. The non-homogeneous tracer distribution, as found with PET imaging, implies the occurrence of non-efficient regions with respect to mass transfer. In steady inlet flow condition, a non-uniform distribution of radioactive tracer was obtained. In contrast, the pulsatile inlet flow generated more uniform perfusion than that of steady flow. Further, it was found that in the case of pulsatile flow, the accumulation of the tracer within the bioreactor was efficiently less than that of steady inlet flow at the same condition. Therefore, in one hand these findings have the potential to improve bioreactor design and in the other hand can explore a very important rout to employ PET in developing bioreactors for tissue engineering applications. The numerical part includes the step 3 and 4 in which the numerical study has been performed for 3-D bone tissue growth in HFMB as a case study for large-scale tissue culture. In the step 3, the feasibility of utilizing newly proposed hHFMB for the growth of mesenchymal stem cells (MSCs) to form bone tissue was investigated using numerical simulations. To this aim, a mathematical model using a CFD code was developed to optimize the design and operation parameters of hHFMB for the growth of MSCs. The volume averaging method was used to formulate mass balance for the nutrients and the cells in the porous extracapillary space (ECS) of the hHFMB. The cell-scaffold construct in the ECS of the hollow fibres and membrane wall were treated as porous medium. Cell volume fraction dependent porosity, permeability, and diffusivity of mass were used in the model. The simulations allowed the simultaneous prediction of nutrient distribution and nutrient-dependent cell volume fraction. In addition, this model was used to study the effects of the operating and design parameters on the nutrient distribution and cell growth within the bioreactor. The modeling results demonstrated that the fluid dynamics within the ECS and transport properties and uptake rates in hHFMB were sufficient to support MSCs required for clinical-scale bone tissue growth in vitro and enabled to solve nutrition difficulties because of high cell density and scaffold size. In the step 4, the new dynamic and two-porous media model has been used for analyzing the nutrient-dependent MSCs growth in order to form the bone tissue in the HFMB. In the present model, hollow fibre scaffold within the bioreactor was treated as a porous domain. The domain consists of the porous lumen region available for fluid flow and the porous ECS region, filled with collagen gel containing cells, for growing tissue mass. Furthermore, the contributions of several design and process parameters, which enhance the performance of the bioreactor, were studied. In addition, the dynamic evaluation of cell growth, oxygen and glucose distributions were quantitatively analyzed. The obtained information can be used for better designing of the bioreactor, determining of suitable operational conditions and scale up of the bioreactor for engineering of clinical-scale bone tissue.--Résumé abrégé par UMI.